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Lecture notes, cheat sheets
Medical physics. Cheat sheet: briefly, the most important
Directory / Lecture notes, cheat sheets Table of contents
1. Medical physics. Short story Medical physics is the science of a system that consists of physical devices and radiation, medical and diagnostic devices and technologies. The purpose of medical physics is to study these systems for the prevention and diagnosis of diseases, as well as the treatment of patients using the methods and means of physics, mathematics and technology. The nature of diseases and the mechanism of recovery in many cases have a biophysical explanation. Medical physicists are directly involved in the treatment and diagnostic process, combining physical and medical knowledge, sharing responsibility for the patient with the doctor. The development of medicine and physics have always been closely intertwined. Even in ancient times, medicine used physical factors for medicinal purposes, such as heat, cold, sound, light, various mechanical effects (Hippocrates, Avicenna, etc.). The first medical physicist was Leonardo da Vinci (five centuries ago), who conducted research on the mechanics of movement of the human body. Medicine and physics began to interact most fruitfully from the end of the XNUMXth - beginning of the XNUMXth centuries, when electricity and electromagnetic waves were discovered, that is, with the advent of the era of electricity. Let's name a few names of great scientists who made the most important discoveries in different eras. Late XNUMXth - mid XNUMXth centuries associated with the discovery of x-rays, radioactivity, theories of the structure of the atom, electromagnetic radiation. These discoveries are associated with the names of V.K. Roentgen, A. Becquerel, M. Skladovskoy-Curie, D. Thomson, M. Planck, N. Bohr, A. Einstein, E. Rutherford. Medical physics really began to establish itself as an independent science and profession only in the second half of the XNUMXth century. with the advent of the atomic age. In medicine, radiodiagnostic gamma devices, electronic and proton accelerators, radiodiagnostic gamma cameras, X-ray computed tomographs and others, hyperthermia and magnetotherapy, laser, ultrasound and other medical-physical technologies and devices have become widely used. Medical physics has many sections and names: medical radiation physics, clinical physics, oncological physics, therapeutic and diagnostic physics. The most important event in the field of medical examination can be considered the creation of computed tomographs, which expanded the study of almost all organs and systems of the human body. OCT has been installed in clinics all over the world, and a large number of physicists, engineers and doctors have worked to improve the technique and methods to bring it almost to the limits of what is possible. The development of radionuclide diagnostics is a combination of radiopharmaceutical methods and physical methods for recording ionizing radiation. Positron emission tomography imaging was invented in 1951 and published in the work of L. Renn. 2. Main problems and concepts of metrology Metrology is the science of measurements, methods and means of ensuring their unity, ways to achieve the required accuracy. Measurement is called finding the value of a physical quantity empirically using technical means. Measurements allow you to establish the laws of nature and are an element of knowledge of the world around us. There are direct measurements, in which the result is obtained directly from the measurement of the quantity itself (for example, measuring body temperature with a medical thermometer, measuring the length of an object with a ruler), and indirect, in which the desired value of the quantity is found from a known relationship between it and directly measured quantities (for example, determining body mass when weighed, taking into account the buoyancy force determined by the viscosity of the liquid according to the speed of the ball falling in it). Technical means for making measurements can be of different types. The most famous are devices in which measurement information is presented in a form accessible to direct perception (for example, temperature is represented in a thermometer by the length of a column of mercury, current strength by the indication of an ammeter needle or a digital value). A unit of a physical quantity is a physical quantity accepted by agreement as the basis for quantifying the corresponding physical quantity. To express the sound pressure level, the sound intensity level, the amplification of the electrical signal, the expression of the frequency interval, and otherwise, it is more convenient to use the logarithm of the relative value (the decimal logarithm is more common and more common): lg = a2/a1 where a1 and a2 are physical quantities of the same name. The unit of the logarithmic value is bel (B): 1B \uXNUMXd lg \uXNUMXd a2/ai, at a2 = 10a, if a is an energy quantity (power, intensity, energy, etc.), or  if a is a power quantity (force, mechanical stress, pressure, electric field strength, etc.). A fairly common submultiple unit is the decibel (dB): 1 dB = 0,1B. 1 dB corresponds to the ratio of energy quantities a2 = 1,26a:  3. Medical metrology and its specifics Technical devices used in medicine are called the generalized term "medical equipment". Most of the medical equipment refers to medical equipment, which in turn is divided into medical devices and medical devices. A medical device is considered to be a technical device intended for diagnostic or therapeutic measurements (medical thermometer, sphygmomanometer, electrocardiograph, etc.). Medical device - a technical device that allows you to create an energy impact of therapeutic, surgical or bactericidal properties, as well as to provide a certain composition of various substances for medical purposes (UHF therapy, electrosurgery, artificial kidney, ear prosthesis, etc.). Metrological requirements for medical devices are quite obvious. Many medical devices are designed to have a dosing energy effect on the body, which is why they deserve the attention of the metrological service. Measurements in medicine are quite specific, therefore, a separate area has been singled out in metrology - medical metrology. Considering some problems specific to medical metrology and partly to medical instrumentation, it should be noted that at present, medical measurements in most cases are carried out by medical personnel (doctor, nurse), who are not technically trained. Therefore, it is advisable to create medical devices graduated in units of physical quantities, the values of which are the final medical measurement information (direct measurements). It is desirable that the measurement time up to obtaining a useful result be spent as little as possible, and the information be as complete as possible. These requirements are met by computers. In the metrological standardization of a medical device, it is important to take into account medical indications. The clinician must determine with what accuracy it is sufficient to present the results so that a diagnostic conclusion can be made. Many medical devices provide information on a recording device (for example, an electrocardiograph), so the errors inherent in this form of recording should be taken into account. One of the problems is thermological. According to the requirements of metrology, the name of the measuring instrument must contain a physical quantity or unit (ammeter, voltmeter, frequency meter, etc.). The names for medical devices do not correspond to this principle (electrocardiograph, phonocardiograph, rheograph, etc.). So, an electrocardiograph should be called a millivoltmeter with recording readings. In a number of medical measurements, there may be insufficient information about the relationship between the directly measured physical quantity and the corresponding biomedical parameters. So, for example, in the clinical (bloodless) method of measuring blood pressure, it is assumed that the air pressure inside the cuff is approximately equal to the blood pressure in the brachial artery. 4. Random value. distribution law Definition of a random variable. Many random events can be quantified as random variables. Random is a quantity that takes on values depending on a combination of random circumstances. There are discrete and continuous random variables. Distribution of a discrete random variable. A discrete value is considered given if its possible values and their corresponding probabilities are indicated. Denote a discrete random variable x, its values x1, x2…, in probability: P (x1) =p2, P (x2) = p2 etc. The set of x and P is called the distribution of a discrete random variable. Since all possible values of a discrete random variable represent a complete system, the sum of the probabilities is equal to one:  Here it is assumed that the discrete random variable has n values. The expression is called the normalization condition. In many cases, along with the distribution of a random variable or instead of it, information about these quantities can be given by numerical parameters, which are called the numerical characteristics of a random variable. The most common of them are: 1) the mathematical expectation (average value) of a random variable is the sum of the products of all its possible values and the probabilities of these values; 2) the variance of a random variable is the mathematical expectation of the squared deviation of a random variable from its mathematical expectation. For a continuous random variable, the mathematical expectation and variance are written as:  where f(x) is the probability density or probability distribution function. It shows how the probability of assigning a random variable to the interval dx depends on the value of this variable itself. Normal distribution law. In theories of probability and mathematical statistics, in various applications, the normal distribution law (Gaussian law) plays an important role. A random variable is distributed according to this law if its probability density has the form:  where a = M(x) - mathematical expectation of a random variable; σ - standard deviation; Consequently; σ2is the variance of the random variable. The curve of the normal distribution law has a bell-shaped shape, symmetrical with respect to the straight line x \uXNUMXd a (scattering center). 5. Maxwell distribution (velocity distribution of gas molecules) and Boltzmann The Maxwell distribution - in the equilibrium state, the gas parameters (pressure, volume and temperature) remain unchanged, but the microstates - the mutual arrangement of molecules, their speeds - are constantly changing. Due to the huge number of molecules, it is practically impossible to determine the values of their velocities at any moment, but it is possible, considering the speed of molecules as a continuous random variable, to indicate the distribution of molecules over velocities. The velocity distribution of molecules has been confirmed by various experiments. The Maxwell distribution can be considered as the distribution of molecules not only in terms of velocities, but also in terms of kinetic energies (since these concepts are interrelated). Let's isolate a single molecule. The randomness of motion allows, for example, for the projection of the velocity Vx of a molecule, to accept the normal distribution law. In this case, as shown by J.K. Maxwell, the probability density that the molecule has a velocity component Ux is written as follows:  You can get the Maxwellian probability distribution function of the absolute values of the speed (Maxwell's velocity distribution):  Boltzmann distribution. If the molecules are in some external force field (for example, in the gravitational field of the Earth), then it is possible to find the distribution of their potential energies, i.e., to establish the concentration of particles that have some specific value of potential energy. The distribution of particles over potential energies in force fields - gravitational, electric, etc. - is called the Boltzmann distribution. As applied to the gravitational field, this distribution can be written as the dependence of the concentration of n molecules on the height h above ground level, or the potential energy mgh:  Such a distribution of molecules in the Earth's gravitational field can be qualitatively, within the framework of molecular kinetic concepts, explained by the fact that molecules are influenced by two opposite factors: the gravitational field, under the influence of which all molecules are attracted to the Earth, and molecular-chaotic motion , tending to evenly scatter molecules over the entire possible object. 6. Mathematical statistics and correlation dependence Mathematical statistics is the science of mathematical methods of systematization and use of statistical data for solving scientific and practical problems. Mathematical statistics closely adjoins the theory of probability and is based on its concepts. However, the main thing in mathematical statistics is not the distribution of random variables, but the analysis of statistical data and finding out which distribution they correspond to. A large statistical population from which a part of the objects for research is selected is called the general population, and the set of objects collected from it is called the sampling population, or sample. A statistical distribution is a collection of variants and their corresponding frequencies (or relative frequencies). For clarity, statistical distributions are depicted graphically in the form of a polygon and a histogram. The polygon of frequencies is a broken line, the segments of which connect points with coordinates (x1; P1), (X2; P2)…. or for the polygon of relative frequencies - with coordinates (x1;R1),(X2;R2). Frequency histogram - a set of adjacent rectangles built on one straight line, the bases of the rectangles are the same and equal to a, and the heights are equal to the ratio of the frequency (or relative frequency) to a:  The most common characteristics of a statistical distribution are means: mode, median, and arithmetic mean (or sample mean). Mode (Mo) is equal to the variant that corresponds to the highest frequency. The median (Me) is equal to the variant that is located in the middle of the statistical distribution. It divides the statistical (variational) series into two equal parts. The sample mean (XV) is defined as the arithmetic mean of a variant of a statistical series. correlation dependence. Functional dependencies can be expressed analytically. So, for example, the area of a circle depends on the radius (S = pr2), acceleration F of the body - from force and mass (a = F/m0). However, there are dependencies that are not too obvious and are not expressed in simple and unambiguous formulas. For example, there is a connection between the height of people and their body weight, changes in weather conditions affect the number of colds in the population, etc. Such a more complex than functional, probabilistic dependence is a correlation (or simply a correlation). In this case, a change in one of their values affects the average value of the other. Suppose that we are studying the relationship between a random variable X and a random variable Y. Each specific value of X will correspond to several values of Y: y1Have2 etc. Conditional mean Yх let's call the arithmetic mean value Y corresponding to the value X = x. Correlation dependence, or correlation of Y from X, is the function Y x = f(x). The equality is called the Y-on-X regression equation, and the graph of the function is called the Y-on-X regression line. 7. Cybernetic systems A cybernetic system is an ordered set of objects (system elements), interacting and interconnected, which are able to perceive, remember and process information, as well as exchange it. Examples of cybernetic systems are groups of people, brains, computers, automata. Accordingly, the elements of a cybernetic system can be objects of different physical nature: a person, brain cells, computer units, etc. The state of the elements of the system is described by a certain set of parameters, which are divided into continuous, taking any real values in a certain interval, and discrete, taking finite sets of values. So, for example, a person's body temperature is a continuous parameter, and his gender is a discrete parameter. The functioning of a cybernetic system is described by three properties: functions that take into account changes in the states of the system elements, functions that cause changes in the structure of the system (including due to external influences), and functions that determine the signals transmitted by the system outside of it. In addition, the initial state of the system is taken into account. Cybernetic systems vary in their complexity, degree of certainty, and level of organization. Cybernetic systems are divided into continuous and discrete. In continuous systems, all the signals circulating in the system and the states of the elements are set by continuous parameters, in discrete ones - by discrete ones. However, there are also mixed systems in which there are parameters of both types. The division of systems into continuous and discrete is conditional and is determined by the required degree of accuracy of the process under study, technical and mathematical conveniences. Some processes or quantities that are discrete in nature, such as electric current (the discreteness of the electric charge: it cannot be less than the charge of an electron), are conveniently described by continuous quantities. In other cases, on the contrary, it makes sense to describe a continuous process with discrete parameters. In cybernetics and technology, systems are usually divided into deterministic and probabilistic. A deterministic system, the elements of which interact in a certain way, its state and behavior are predicted unambiguously and are described by unambiguous functions. The behavior of probabilistic systems can be determined with some certainty. A system is called closed if its elements exchange signals only with each other. Open, or open, systems necessarily exchange signals with the external environment. To perceive signals from the external environment and transmit them into the system, any open system has receptors (sensors or transducers). In animals, as in a cybernetic system, the receptors are the sense organs - touch, sight, hearing, etc., in automata - sensors: strain gauge, photoelectric, induction, etc. 8. The concept of medical cybernetics Medical cybernetics is a scientific direction associated with the use of ideas, methods and technical means of cybernetics in medicine and healthcare. Conventionally, medical cybernetics can be represented by the following groups. Computational diagnosis of diseases. This part is mainly related to the use of computers for the preparation of the diagnosis. The structure of any diagnostic system consists of a medical memory (cumulative medical experience for a given group of diseases) and a logical device that allows you to compare the symptoms found in a patient by a survey and laboratory examination with the available medical experience. The diagnostic computer follows the same structure. First, methods are developed for a formal description of the patient's state of health, a thorough analysis of the clinical signs used in diagnosis is carried out. Select mainly those features that can be quantified. In addition to the quantitative expression of the physiological, biochemical and other characteristics of the patient, computational diagnostics requires information about the frequency of clinical syndromes and diagnostic signs, their classification, dependence, assessment of the diagnostic effectiveness of signs, etc. All these data are stored in the memory of the machine. She compares the symptoms of the patient with the data stored in her memory. The logic of computational diagnostics corresponds to the logic of the doctor making the diagnosis: the totality of symptoms is compared with the previous experience of medicine. The machine will not detect a new (unknown) disease. A doctor who encounters an unknown disease will be able to describe its symptoms. Details about such a disease can be established only by conducting special studies. Computers can play an auxiliary role in such investigations. Cybernetic approach to the healing process. After the doctor establishes the diagnosis, treatment is prescribed, which is not limited to a one-time exposure. This is a complex process during which the doctor constantly receives medical and biological information about the patient, analyzes it and, in accordance with it, refines, changes, stops or continues the therapeutic effect. At present, the cybernetic approach to the treatment process facilitates the work of a doctor, makes it possible to treat seriously ill patients more efficiently, take timely measures in case of complications during surgery, develop and control the process of drug treatment, create biocontrolled prostheses, diagnose diseases, and control devices that regulate vital functions. The tasks of operational medical control include monitoring the condition of seriously ill patients using tracking systems (monitor systems for monitoring the condition of healthy people in extreme conditions: stressful conditions, weightlessness, hyperbaric conditions, an environment with a low oxygen content, etc.). 9. Fundamentals of mechanics Mechanics is a branch of physics that studies the mechanical motion of material bodies. Under the mechanical movement understand the change in the position of the body or its parts in space over time. For physicians, this section is of interest for the following reasons: 1) understanding the mechanics of movement of the whole organism for the purposes of sports and space medicine, the mechanics of the human musculoskeletal system - for the purposes of anatomy and physiology; 2) knowledge of the mechanical properties of biological tissues and fluids; 3) understanding the physical foundations of some laboratory techniques used in the practice of biomedical research, such as centrifugation. Mechanics of rotational motion of an absolutely rigid body An absolutely rigid body is one whose distance between any two points is constant. When moving, the dimensions and shape of an absolutely rigid body do not change. The speed of rotation of the body is characterized by an angular velocity equal to the first derivative of the angle of rotation of the radius vector with respect to time: ω = dt/da Angular velocity is a vector that is directed along the axis of rotation and is related to the direction of rotation. The angular velocity vector, unlike the velocity and force vectors, is sliding. Thus, specifying the vector w specifies the position of the axis of rotation, the direction of rotation, and the modulus of the angular velocity. The rate of change of the angular velocity is characterized by an angular acceleration equal to the first derivative of the angular velocity with respect to time:  From this it can be seen that the angular acceleration vector coincides in direction with an elementary, sufficiently small change in the angular velocity vector dw: with accelerated rotation, the angular acceleration is directed in the same way as the angular velocity, with slow rotation, it is opposite to it. Here are the formulas for the kinematics of the rotational motion of a rigid body around a fixed axis: 1) the equation of uniform rotational motion: a = wt + a0 where a0 - initial value of the angle; 2) the dependence of the angular velocity on time in a uniform rotational motion: w = et + W0, where w0 - initial angular velocity; 3) equation of uniform rotational motion:  10. Basic concepts of mechanics Moment of power. The moment of force about the axis of rotation is the vector product of the radius vector and the force: Mi =ri ×Fi, where ri and Fi - vectors. Moment of inertia. Mass is the measure of inertia of bodies in translational motion. The inertia of bodies during rotational motion depends not only on the mass, but also on its distribution in space relative to the axis. The moment of inertia of the body about the axis is the sum of the moments of inertia of the material points that make up the body:  The moment of inertia of a solid body is usually determined by integration:  The angular momentum of the body relative to the axis is equal to the sum of the angular momentum of the points that make up this body:  Kinetic energy of a rotating body. As a body rotates, its kinetic energy is from the kinetic energies of its individual points. For a rigid body:  Let us equate the elementary work of all external forces during such a rotation to an elementary change in kinetic energy: Mda=Jwdw, whence  we reduce this equality by ω:  whence  Law of conservation of angular momentum. If the total momentum of all external forces acting on a body is zero, then the angular momentum of this body remains constant. This law is valid not only for an absolutely rigid body. So, for a system consisting of N bodies rotating around a common axis, the law of conservation of angular momentum can be written in the form:  11. Joints and levers in the human musculoskeletal system. Ergometry Moving parts of mechanisms are usually connected by parts. The movable connection of several links forms a kinematic connection. The human body is an example of a kinematic connection. The musculoskeletal system of a person, consisting of articulated bones of the skeleton and muscles, represents, from the point of view of physics, a set of levers held by a person in balance. In anatomy, there are levers of power, in which there is a gain in strength, but a loss in movement, and levers of speed, in which, losing in strength, they gain in speed of movement. A good example of a speed lever is the lower jaw. The acting force is carried out by the masticatory muscle. The opposing force - the resistance of crushed food - acts on the teeth. The shoulder of the acting force is much shorter than that of the reaction forces, so the chewing muscle is short and strong. When you need to gnaw something with your teeth, the shoulder of the resistance force decreases. If we consider the skeleton as a collection of separate links connected into one organism, then it turns out that all these links, with a normal stand, form a system that is in an extremely unstable balance. So, the support of the body is represented by the spherical surfaces of the hip joint. The center of mass of the body is located above the support, which creates an unstable balance with a ball support. The same applies to the knee joint, and to the ankle joint. All these links are in a state of unstable equilibrium. The center of mass of a human body in a normal stance is located just on the same vertical with the centers of the hip, knee and ankle joints of the leg, 2-2,5 cm below the cape of the sacrum and 4-5 cm above the hip axis. Thus, this is the most unstable state of the heaped links of the skeleton. And if the whole system is kept in balance, it is only due to the constant tension of the supporting muscles. The mechanical work that a person is able to do during the day depends on many factors, so it is difficult to indicate any limit value. This also applies to power. So, with short-term efforts, a person can develop a power of the order of several kilowatts. If an athlete weighing 70 kg jumps from a place so that his center of mass rises 1 m in relation to the normal stance, and the repulsion phase lasts 0,2 s, then he develops a power of about 3,5 kW. When walking, a person does work, since energy is expended on periodic small raising of the limbs, mainly the legs. Work goes to zero if there is no movement. Therefore, when the load is on a support or stand, or suspended from a pole, no work is done by gravity. However, if you hold a weight or dumbbell motionless on an outstretched arm, fatigue of the muscles of the arm and shoulder is noted. In the same way, the muscles of the back and lumbar region get tired if a load is placed on the back of a seated person. 12. Mechanical vibrations Repetitive movements (or changes in state) are called oscillations (alternating electric current, the phenomenon of a pendulum, the work of the heart, etc.). Distinguish: 1) free, or natural, oscillations - such oscillations that occur in the absence of variable external influences on an oscillatory system and arise as a result of any initial deviation of this system from its state of stable equilibrium; 2) forced oscillations - oscillations during which the oscillating system is exposed to an external periodically changing force; 3) harmonic oscillations are oscillations in which the displacement changes according to the law of sine or cosine depending on time. The speed and acceleration of a point along the X axis are equal, respectively:  where u0 = Aw - velocity amplitude; a0 =Aw2 =u0w is the acceleration amplitude; 4) damped oscillations - oscillations with values of the amplitude of oscillations decreasing in time, due to the loss of energy by the oscillatory system to overcome the resistance force. The period of damped oscillations depends on the coefficient of friction and is determined by the formula:  With very little friction (β2 <<ω02) the period of the damped oscillation is close to the period of the undamped free oscillation  In practice, the degree of damping is often characterized by the logarithmic damping decrement s:  where Nl is the number of oscillations during which the oscillation amplitude decreases by l times. The damping coefficient and the logarithmic damping decrement are related by a fairly simple relationship: l = bT; 5) forced oscillations - oscillations that occur in the system with the participation of an external force. The equation of motion of forced oscillations has the form:  where F is the driving force. The driving force changes according to the harmonic law F = F0 coswt. 13. Mechanical water Mechanical waves are disturbances that propagate in space and carry energy. There are two types of mechanical waves: elastic waves and waves on the surface of liquids. Elastic waves arise due to the bonds existing between the particles of the medium: the movement of one particle from the equilibrium position leads to the movement of neighboring particles. A transverse wave is a wave whose direction and propagation are perpendicular to the direction of oscillation of the points of the medium. A longitudinal wave is a wave whose direction and propagation coincide with the direction of oscillation of the points of the medium. The wave surface of a harmonic wave is a singly connected surface in a medium, which is geometrically or in phase (in one phase) a series of oscillating points of the medium with a harmonic traveling wave. The wave front is the farthest wave surface at the moment, where the wave has reached to this moment. A plane wave is a wave whose front is a plane perpendicular to the propagation of the wave. Spherical wave - a wave whose front is a spherical surface with a radius coinciding with the direction of wave propagation. Huygens principle. Each point of the medium, to which the perturbation has reached, itself becomes a source of secondary spherical waves. Wave propagation velocity (phase) - the propagation velocity of a surface of equal phase for a harmonic wave. The wave speed is equal to the product of the frequency of oscillations in the wave and the wavelength: n = lυ. A standing wave is a state of the medium in which the location of the maxima and minima of the movements of oscillating points does not change in time. Elastic waves - elastic perturbations propagating in solid, liquid and gaseous media (for example, waves that arise in the earth's crust during an earthquake, sound and ultrasonic waves in gaseous, liquid and solid bodies). Shock waves are one common example of a mechanical wave. Sound wave - oscillatory motion of particles of an elastic medium, propagating in the form of elastic waves (compressional deformations, shear, which are transferred by waves from one point of the medium to another) in a gaseous, liquid and solid medium. Sound waves, acting on the human hearing organs, are capable of causing sound sensations if the frequencies of the vibrations corresponding to them lie within 16 - 2 h 104 Hz (audible sounds). Elastic waves with frequencies less than 16 Hz are called infrasound, and those with frequencies greater than 16 Hz are called ultrasound. The speed of sound is the phase speed of sound waves in an elastic medium. The speed of sound is different in different environments. The speed of sound in air is 330-340 m/s (depending on the state of the air). The loudness of a sound is related to the energy of the oscillations in the source and in the wave and, therefore, depends on the amplitude of the oscillations. Sound pitch - the quality of sound, determined by a person subjectively by ear and depending mainly on the frequency of the sound. 14. Doppler effect The Doppler effect is a change in the frequency of the waves recorded by the receiver, which occurs due to the movement of the source of these waves and the receiver. For example, when a fast moving train approaches a stationary observer, the tone of the sound signal of the latter is higher, and when the train is moving away, it is lower than the tone of the signal given by the same train when it is standing at the station. Let us imagine that the observer is approaching with a speed v to a source of waves that is motionless with respect to the medium. At the same time, it encounters more waves in one and the same time interval than in the absence of movement. This means that the perceived frequency vy is greater than the frequency of the wave emitted by the source. But if the wavelength, frequency and wave propagation speed are related by:  The Doppler effect can be used to determine the speed of a body in a medium. For medicine, this is of particular importance. For example, consider this case. The ultrasound generator is combined with the receiver in the form of some technical system. The technical system is immobile relative to the environment. In a medium with speed u0 an object (body) is moving. The generator emits ultrasound with a frequency v1. The moving object perceives the frequency v1, which can be found by the formula:  where v is the propagation speed of a mechanical wave (ultrasound). In medical applications, the speed of ultrasound is much greater than the speed of the object (u > u0). For these cases we have:  The Doppler effect is used to determine the speed of blood flow, the speed of movement of the valves and walls of the heart (Doppler echocardiography) and other organs; wave energy flow. The wave process is associated with the propagation of energy. A quantitative characteristic of energy is the flow of energy. The wave energy flux is equal to the ratio of the energy carried by waves through a certain surface to the time during which this energy was transferred:  The unit of wave energy flux is the watt (W). The wave energy flux related to the area oriented perpendicular to the direction of wave propagation is called the wave energy flux density, or wave intensity. 15. Acoustics Acoustics is a field of physics that studies elastic vibrations and waves from the lowest frequencies to the highest (1012-1013 Hz). Modern acoustics covers a wide range of issues, there are a number of sections in it: physical acoustics, which studies the features of the propagation of elastic waves in various media, physiological acoustics, which studies the structure of sound-receiving and sound-forming organs in humans and animals, etc. Acoustics is understood as the doctrine of sound, i.e., elastic vibrations and waves in gases, liquids and solids, perceived by the human ear (frequencies from 16 to 20 Hz). Hearing is an object of auditory sensations, therefore it is evaluated by a person subjectively. Perceiving tones, a person distinguishes them by height. Pitch is a subjective characteristic, primarily determined by the frequency of the fundamental tone. To a much lesser extent, the pitch depends on the complexity of the tone and its intensity: a sound of greater intensity is perceived as a sound of a lower tone. The timbre of a sound is almost exclusively determined by its spectral composition. Different acoustic spectra correspond to different timbres, although the fundamental tone and hence the pitch are the same. Loudness characterizes the level of auditory sensation. Although subjective, loudness can be quantified by comparing the auditory sensation from two sources. The creation of the loudness level scale is based on the psychophysical law of Weber-Fechner. According to this law, if the stimulus is increased exponentially (i.e., by the same number of times), then the sensation of this stimulus increases in arithmetic progression (i.e., by the same amount). With regard to sound, this means that if the intensity of the sound takes on a series of successive values, for example, a10, a210, a310 (a is a certain coefficient, a > I), and so on, then the sensation of sound volume corresponding to them is equal to E0, 2E0, 3E0, etc. e. Mathematically, this means that the loudness of a sound is proportional to the logarithm of the intensity of the sound. If there are two sound stimuli with intensities I and I0, and I0 - the threshold of hearing, then on the basis of the Weber-Fechner law, the loudness relative to it is related to the intensities as follows:  where k is some proportionality factor depending on frequency and intensity. The method of measuring sound acuity is called audiometry. With audiometry on a special device (audiometer), the threshold of hearing sensation at different frequencies is determined; the resulting curve is called an audiogram. Comparison of an audiogram of a sick person with a normal hearing threshold curve helps to diagnose a disease of the hearing organs. 16. Physical basis of sound research methods in the clinic Sound, like light, is a source of information, and this is its main significance. The sounds of nature, the speech of people around us, the noise of working machines tell us a lot. To imagine the meaning of sound for a person, it is enough to temporarily deprive yourself of the ability to perceive sound - close your ears. Naturally, sound can also be a source of information about the state of human internal organs. A common sound method for diagnosing diseases is auscultation (listening). For au-scultation, a stethoscope or phonendoscope is used. The phonendoscope consists of a hollow capsule with a sound-transmitting membrane applied to the patient's body, rubber tubes go from it to the doctor's ear. In the hollow capsule, the resonance of the air column occurs, as a result of which the sound is amplified and auscultation improves. During auscultation of the lungs, breath sounds, various wheezing, characteristic of diseases, are heard. By changing the heart sounds and the appearance of noise, one can judge the state of cardiac activity. Using auscultation, you can establish the presence of peristalsis of the stomach and intestines, listen to the fetal heartbeat. For simultaneous listening to the patient by several researchers for educational purposes or during a consultation, a system is used that includes a microphone, amplifier and loudspeaker or several telephones. To diagnose the state of cardiac activity, a method similar to auscultation and called phonocardiography (FCG) is used. This method consists in graphic recording of heart sounds and murmurs and their diagnostic interpretation. A phonocardiogram is recorded using a phonocardiograph, which consists of a microphone, an amplifier, a system of frequency filters and a recording device. Fundamentally different from the two sound methods outlined above is percussion. With this method, the sound of individual parts of the body is heard when they are tapped. Schematically, the human body can be represented as a combination of gas-filled (lungs), liquid (internal organs) and solid (bone) volumes. When hitting the surface of the body, oscillations occur, the frequencies of which have a wide range. From this range, some oscillations will die out rather quickly, while others, coinciding with the natural oscillations of the voids, will intensify and, due to resonance, will be audible. An experienced doctor determines the state and location (tonography) of the internal organs by the tone of percussion sounds. 17. Physics of hearing The auditory system connects the direct receiver of the sound wave with the brain. Using the concepts of cybernetics, we can say that the auditory system receives, processes and transmits information. From the entire auditory system, for consideration of the physics of hearing, the outer, middle and inner ear are distinguished. The outer ear consists of the auricle and the external auditory meatus. The auricle in humans does not play a significant role in hearing. It helps to determine the localization of the sound source at its location - the sound from the source enters the auricle. Depending on the position of the source in the vertical plane, sound waves will diffract differently on the auricle due to its specific shape. This also leads to a different change in the spectral composition of the sound wave entering the ear canal. A person has learned to associate the change in the spectrum of a sound wave with the direction to the sound source. Different directions to the sound source in the horizontal plane will correspond to the phase difference. It is believed that a person with normal hearing can fix directions to the sound source with an accuracy of 3 °, this corresponds to a phase difference of - 6 °. Therefore, it can be assumed that a person is able to distinguish the change in the phase difference of sound waves entering his ears with an accuracy of 6 °. In addition to the phase difference, the binaural effect is facilitated by the difference in sound intensities in different ears, as well as the "acoustic shadow" from the head to one ear. The length of the human ear canal is approximately 2,3 cm; therefore, acoustic resonance occurs at a frequency:  The most essential parts of the middle ear are the tympanic membrane and the auditory ossicles: the malleus, anvil and stirrup with the corresponding muscles, tendons and ligaments. The system of bones at one end is connected with the tympanic membrane by a malleus, at the other - by a stirrup with an oval window of the inner ear. Sound pressure acts on the tympanic membrane, which causes a force F1 = P1 S1 (P1 - sound pressure, S1 - square). The ossicular system works like a lever, with a gain in strength from the inner ear in humans by 1,3 times. Another of the functions of the middle ear is the weakening of the transmission of vibrations in the case of a sound of great intensity. The human cochlea is a bony formation about 3,5 mm long and has the shape of a capsule-shaped spiral with 2-3/4 whorls. Three canals run along the cochlea. One of them, which starts from the oval window, is called the vestibular scala. Another channel comes from the round window, it is called the tympanic staircase. The vestibular and tympanic scala are connected in the region of the dome of the cochlea through a small opening - the helicotrema. Between the cochlear canal and the scala tympani, the main (basilar) membrane runs along the cochlea. On it is the organ of Corti, containing receptor (hair) cells, from the cochlea comes the auditory nerve. 18. Ultrasound and its application in medicine Ultrasound is a high-frequency mechanical vibration of particles of a solid, liquid or gaseous medium, inaudible to the human ear. The frequency of ultrasound oscillations is above 20 per second, i.e., above the threshold of hearing. For therapeutic purposes, ultrasound is used with a frequency of 800 to 000 vibrations per second. Devices called ultrasonic transducers are used to generate ultrasound. The most widely used electromechanical emitters. The use of ultrasound in medicine is associated with the peculiarities of its distribution and characteristic properties. By physical nature, ultrasound, like sound, is a mechanical (elastic) wave. However, the wavelength of ultrasound is much smaller than the wavelength of the sound wave. The greater the various acoustic impedances, the stronger the reflection and refraction of ultrasound at the boundary of dissimilar media. The reflection of ultrasonic waves depends on the angle of incidence on the affected area - the greater the angle of incidence, the greater the reflection coefficient. In the body, ultrasound with a frequency of 800-1000 kHz propagates to a depth of 8-10 cm, and at a frequency of 2500-3000 Hz - by 1,0-3,0 cm. Ultrasound is absorbed by tissues unevenly: the higher the acoustic density, the lower the absorption. Three factors act on the human body during ultrasound therapy: 1) mechanical - vibration micromassage of cells and tissues; 2) thermal - an increase in the temperature of tissues and the permeability of cell membranes; 3) physical and chemical - stimulation of tissue metabolism and regeneration processes. The biological effect of ultrasound depends on its dose, which can be stimulating, depressing or even destructive for tissues. The most adequate for therapeutic and prophylactic effects are small dosages of ultrasound (up to 1,2 W/cm2), especially in a pulsed mode. They are able to provide analgesic, antiseptic (antimicrobial), vasodilating, resolving, anti-inflammatory, desensitizing (antiallergic) action. In physiotherapy practice, mainly domestic devices of three series are used: UZT-1, UZT-2, UZT-3. Ultrasound is not applied to the area of the brain, cervical vertebrae, bony prominences, areas of growing bones, tissues with severe circulatory disorders, to the abdomen during pregnancy, the scrotum. With caution, ultrasound is used on the region of the heart, endocrine organs. Distinguish between continuous and pulsed ultrasound. Continuous ultrasound is called a continuous stream of ultrasonic waves. This type of radiation is mainly used to affect soft tissues and joints. Pulsed ultrasound is a discontinuous radiation, i.e. ultrasound is sent in separate pulses at regular intervals. 19. Hydrodynamics Hydrodynamics is a branch of physics that studies the issues of the movement of incompressible fluids and their interaction with surrounding solid bodies, the theory of deformations and the fluidity of a substance. The set of methods for measuring viscosity is called viscometry, and the instruments used for such purposes are called viscometers. The most common method of viscometry - capillary - is to measure the time of flow through the capillary of a liquid of known mass under the action of gravity at a certain pressure drop. A capillary viscometer is used to determine the viscosity of blood. Rotational viscometers are also used, in which the liquid is located in the gap between two coaxial bodies, such as cylinders. One of the cylinders (rotor) rotates, while the other is inactive. Viscosity is measured by the angular velocity of the rotor, which creates a certain moment of force on a stationary cylinder, or by the moment of force acting on a stationary cylinder, or by the moment of force acting on a stationary cylinder, at a given angular velocity of rotation of the rotor. With the help of rotational viscometers, the viscosity of liquids is determined - lubricating oils, molten silicates and metals, high-viscosity varnishes and adhesives, clay solutions. Currently, the clinic uses a Hess viscometer with two capillaries to determine blood viscosity. In the Hess viscometer, the volume of blood is always the same, and the volume of water is measured by divisions on the tube, so the value of the relative viscosity of the blood is directly obtained. The viscosity of human blood is normally 0,4-0,5 Pas, with pathology it ranges from 0,17 to 2,23 Pas, which affects the erythrocyte sedimentation rate (ESR). Venous blood has a slightly higher viscosity than arterial blood. Laminar and turbulent flows. Reynolds number. Fluid flow can be layered or laminar. An increase in the flow velocity of a viscous fluid due to the inhomogeneity of pressure across the cross section of the pipe creates a swirl, and the movement becomes vortex, or turbulent. In a turbulent flow, the speed of particles in each place changes randomly, the movement is unsteady. Kinematic viscosity more fully than dynamic, takes into account the influence of internal friction on the nature of the flow of a liquid or gas. Thus, the viscosity of water is approximately 100 times greater than that of air (at 0 °C), but the kinematic viscosity of water is 10 times less than that of air, and therefore the viscosity has a stronger effect on the nature of the flow of air than water. The nature of the flow of liquid or gas depends on the size of the pipe. The flow of blood in the arteries is normally laminar, with slight turbulence occurring near the valves. In pathology, when the viscosity is less than normal, the Reynolds number may be higher than the critical value, and the movement will become turbulent. 20. Mechanical properties of solids and biological tissues A characteristic feature of a solid body is the ability to retain its shape. Solids can be divided into crystalline and amorphous. A distinctive feature of the crystalline state is anisotropy - the dependence of physical properties (mechanical, thermal, electrical, optical) on the direction. The reason for the anisotropy of crystals lies in the ordered arrangement of atoms or molecules from which they are built, which is manifested in the correct external faceting of individual single crystals. However, as a rule, crystalline bodies are found in the form of polycrystals - a set of sets of intergrown, randomly oriented individual small crystals (crystallites). Depending on the nature of the particles in the nodes and the nature of the interaction forces, 4 types of crystal lattices are distinguished: ionic, atomic, metallic and molecular. Positive metal ions are located in all nodes of the metal lattice. Electrons move randomly between them. The main feature of the internal structure of bodies in the amorphous state is the strict repetition in the arrangement of atoms or groups of atoms in all directions along the entire body. Amorphous bodies under the same conditions have larger than crystals, specific volume, entropy and internal energy. The amorphous state is characteristic of substances of very different nature. At low pressure and high temperature, substances in this state are very mobile: low molecular weight are liquids, high molecular weight are in a highly elastic state. With a decrease in temperature and an increase in pressure, the mobility of amorphous substances decreases, and they all become solids. Polymers are substances whose molecules are long chains composed of a large number of atoms or atomic groups connected by chemical bonds. The peculiarity of the chemical structure of polymers also determines their special physical properties. Polymeric materials include almost all living and plant materials, such as wool, leather, horn, hair, silk, cotton, natural rubber and others, as well as all kinds of synthetic materials - synthetic rubber, plastics, fibers, etc. Of great interest to medicine are tissue adhesives (for example, alkyl-a-cyanoacrylates, p-butyl-a-zinocrylate), which quickly polymerize into a film, which are used to close wounds without suturing. Liquid crystals are substances that have the properties of both liquids and crystals. According to their mechanical properties, these substances are similar to liquids - they flow. According to the nature of molecular ordering, nematic and smectic liquid crystals are distinguished. In nematic liquid crystals, the molecules are oriented in parallel, but their centers are located randomly. Smectic crystals consist of parallel layers in which the molecules are ordered. A special class is made up of cholesteric type crystals (their structure is characteristic of compounds containing cholesterol). 21. Mechanical properties of biological tissues Under the mechanical properties of biological tissues understand their two varieties. One is related to the processes of biological mobility: muscle contraction of animals, cell growth, movement of chromosomes in cells during their division, etc. These processes are caused by chemical processes and are provided with energy by ATP, their nature is considered in the course of biochemistry. Conventionally, this group is called the active mechanical properties of biological systems. Bone. Bone is the main material of the musculoskeletal system. Two-thirds of the mass of compact bone tissue (0,5 volume) is made up of inorganic material, the mineral substance of the bone is hydroxylantite 3 Ca3 (PO) x Ca (OH) 2. This substance is presented in the form of microscopic crystals. The density of bone tissue is 2400 kg/m3, its mechanical properties depend on many factors, including age, individual growth conditions of the organism and, of course, on the site of the organism. The structure of the bone gives it the necessary mechanical properties: hardness, elasticity and strength. Leather. It consists of collagen and elastin fibers and the main tissue - the matrix. Collagen is about 75% dry weight, and elastin is about 4%. Elastin stretches very strongly (up to 200-300%), much like rubber. Collagen can stretch up to 10%, which corresponds to nylon fiber. Thus, the skin is a viscoelastic material with highly elastic properties, it is well stretched and elongated. Muscles. Muscles are made up of connective tissue made up of collagen and elastin fibers. Therefore, the mechanical properties of muscles are similar to the mechanical properties of polymers. The mechanical behavior of a skeletal muscle is as follows: when the muscles are quickly stretched by a certain amount, the tension increases sharply and then decreases. With greater deformation, an increase in interatomic distances in molecules occurs. Blood vessel tissue (vascular tissue). The mechanical properties of blood vessels are determined mainly by the properties of collagen, elastin and smooth muscle fibers. The content of these components of the vascular tissue changes along the course of the circulatory system: the ratio of elastin to collagen in the common carotid artery is 2: 1, and in the femoral artery - 1: 2. With distance from the heart, the proportion of smooth muscle fibers increases, in arterioles they are already the main component of the vascular fabrics. In a detailed study of the mechanical properties of the vascular tissue, it is distinguished how the sample is cut out of the vessel (along or across the vessel). It is possible to consider the deformation of the vessel as a whole as a result of the action of pressure from the inside on the elastic cylinder. Two halves of a cylindrical vessel interact with each other along the sections of the cylinder walls. The total area of this interaction cross section is 2hl. If there is a mechanical stress s in the vascular wall, then the force of interaction between the two halves of the vessel is equal to: F = sx2hl. 22. Physical issues of hemodynamics Hemodynamics is a field of biomechanics that studies the movement of blood through the vascular system. The physical basis of hemodynamics is hydrodynamics. There is a relationship between the stroke volume of blood (the volume of blood ejected by the ventricle of the heart in one systole), the hydraulic resistance of the peripheral part of the circulatory system X0 and the change in pressure in the arteries: since the blood is in an elastic reservoir, its volume at any time depends on the pressure p according to the following ratio: v=v0 +kp, where k - elasticity, elasticity of the reservoir; v0 - tank volume in the absence of pressure (p = 0). The elastic reservoir (arteries) receives blood from the heart, the volumetric blood flow rate is equal to Q. Blood flows from the elastic reservoir with a volumetric blood flow rate Q0 in the peripheral system (arterioles, capillaries). You can make a fairly obvious equation:  showing that the volumetric velocity of blood flow from the heart is equal to the rate of increase in the volume of the elastic reservoir. pulse wave. When the heart muscle contracts (systole), blood is ejected from the heart into the aorta and arteries extending from it. If the walls of these vessels were rigid, then the pressure arising in the blood at the outlet of the heart would be transmitted to the periphery at the speed of sound. Normal human systolic blood pressure is approximately 16 kPa. During the relaxation of the heart (diastole), the distended blood vessels subside, and the potential energy communicated to them by the heart through the blood is converted into the kinetic energy of the blood flow, while maintaining a diastolic pressure of approximately 11 kPa. The pulse wave propagates at a speed of 5-10 m/s and even more. The viscosity of the blood and the elastic-viscous properties of the walls of the vessel reduce the amplitude of the wave. You can write the following equation for a harmonic pulse wave:  where p0 - pressure amplitude in the pulse wave; x - distance to an arbitrary point from the source of vibrations (heart); t - time; w - circular frequency of oscillations; c is some constant that determines the attenuation of the wave. The pulse wave length can be found from the formula:  where E is the modulus of elasticity; p is the density of the substance of the vessel; h is the vessel wall thickness; d is the diameter of the vessel. 23. Work and power of the heart. Heart-lung machine The work done by the heart is expended on overcoming resistance and communicating kinetic energy to the blood. Calculate the work done with a single contraction of the left ventricle. Vу - stroke volume of blood in the form of a cylinder. We can assume that the heart supplies this volume through the aorta with a cross section S to a distance I at an average pressure p. The work done is equal to: A1=FI=pSI=pVy. The work expended on the communication of kinetic energy to this volume of blood is:  where p is the density of blood; υ - blood velocity in the aorta. Thus, the work of the left ventricle of the heart during contraction is:  Since the work of the right ventricle is taken equal to 0,2 of the work of the left, the work of the whole heart with a single contraction is equal to:  This formula is valid both for rest and for the active state of the body, but these states differ in different blood flow rates. Physical foundations of the chemical method for measuring blood pressure. The physical parameter - blood pressure - plays an important role in the diagnosis of many diseases. Systolic and diastolic pressure in any artery can be measured directly with a needle connected to a manometer. However, in medicine, the bloodless method proposed by N. S. Korotkov is widely used. The essence of the method: a cuff is placed around the arm between the shoulder and elbow. When pumping air through the hose into the cuff, the arm is compressed. Then, air is released through the same hose and the air pressure in the cuff is measured using a manometer. Releasing air, reduce the pressure in the cuff and in the soft tissues with which it comes into contact. When the pressure becomes equal to systolic, the blood will be able to break through the squeezed artery - a turbulent flow occurs. The characteristic tones and noises that accompany this process are listened to by the doctor when measuring pressure, placing the phonendoscope on the artery below the cuff (i.e., at a great distance from the heart). By continuing to reduce the pressure in the cuff, it is possible to restore the laminar flow of blood, which is noticeable by a sharp weakening of the audible tones. The cuff pressure corresponding to the restoration of laminar flow in the artery is recorded as diastolic. To measure blood pressure, devices are used - a sphygmomanometer with a mercury manometer, a sphygmotonometer with a metal membrane manometer. 24. Thermodynamics Thermodynamics is understood as a branch of physics that considers systems between which energy can be exchanged without taking into account the microscopic structure of the bodies that make up the system. A distinction is made between the thermodynamics of equilibrium systems (or systems passing to equilibrium) and the thermodynamics of non-equilibrium systems, which plays a special role in the consideration of biological systems. Basic concepts of thermodynamics. First law of thermodynamics. The state of a thermodynamic system is characterized by physical quantities called parameters (such as volume, pressure, temperature, density, etc.). If the parameters of the system during its interaction with the surrounding bodies do not change over time, then the state of the system is called stationary. In different parts of a system that is in a stationary state, the values of the parameters usually differ: temperature in different parts of the human body, concentration of diffusing molecules in different parts of the biological membrane, etc. The steady state is maintained due to energy and substance flows passing through the system. In a stationary state, there can be such systems that either exchange both energy and matter with surrounding systems (open systems), or exchange only energy (closed systems). A thermodynamic system that does not exchange either energy or matter with surrounding bodies is called isolated. An isolated system eventually comes to a state of thermodynamic equilibrium. In this state, as in the stationary state, the parameters of the system remain unchanged in time. However, it is essential that in the equilibrium state the parameters that do not depend on the mass or number of particles (pressure, temperature, etc.) are the same in different parts of this system. Any thermodynamic system will not be isolated, since it is impossible to surround it with a shell that does not conduct heat. An isolated system is considered as a convenient thermodynamic model. The law of conservation of energy for thermal processes is formulated as the first law of thermodynamics. The amount of heat transferred to the system goes to change the internal energy of the system and the performance of work by the system. The internal energy of a system is understood as the sum of the kinetic and potential energies of the particles that make up the system. The internal energy is a function of the state of the system and has a well-defined value for this state: DU is the difference between two values of the internal energy corresponding to the final and initial states of the system: DU=U2- OR1 The amount of heat, like work, is a function of the process, not the state. The first law of thermodynamics can be written as: dQ = dU + dA. The values of Q, A, DU and dQ, dA, dU can be either positive (heat is transferred to the system by external bodies, internal energy increases) or negative (heat is removed from the system, internal energy decreases). 25. The second law of thermodynamics. Entropy There are several formulations of the second law of thermodynamics: heat cannot by itself transfer from a body with a lower temperature to a body with a higher temperature (Clausius's formulation), or a perpetual motion machine of the second kind is impossible (Thomson's formulation). A process is called reversible if it is possible to complete the reverse process through all intermediate states so that after the system returns to its original state, no changes occur in the surrounding bodies. The efficiency of a heat engine, or direct cycle, is the ratio of the work done to the amount of heat received by the working substance from the heater:  Since the work of a heat engine is performed due to the amount of heat, and the internal energy of the working substance does not change per cycle (DU = 0), it follows from the first law of thermodynamics that the work in circular processes is equal to the algebraic sum of the amounts of heat: A = Q1 + Q2. Consequently:  Quantity of heat Q1, received by the working substance, is positive, the amount of heat Q2 given by the working substance to the refrigerator is negative. The sum of the reduced amounts of heat for a reversible process can be represented as the difference between two values of some system state function, which is called entropy:  where s2 and S1 - entropy, respectively, in the final second and initial first states. Entropy is a function of the state of the system, the difference between the values of which for two states is equal to the sum of the reduced amounts of heat during the reversible transition of the system from one state to another. The physical meaning of entropy:  If the system has passed from one state to another, then, regardless of the nature of the process, the change in entropy is calculated by the formula for any reversible process occurring between these states:  where Q is the total amount of heat received by the system during the transition from the first state to the second state at a constant temperature T. This formula is used to calculate the entropy change in processes such as melting, vaporization, etc. 26. Stationary state The principle of entropy production. The body as an open system The trend of thermodynamic processes in an isolated system has been described above. However, real processes and states in nature and technology are non-equilibrium, and many systems are open. These processes and systems are considered in nonequilibrium thermodynamics. Just as in equilibrium thermodynamics the state of equilibrium is a special state, so in nonequilibrium thermodynamics stationary states play a special role. Despite the fact that in the stationary state the necessary processes occurring in the system (diffusion, heat conduction, etc.) increase the entropy, the entropy of the system does not change. Let us represent the change in the entropy DS of the system as the sum of two terms: DS=DSi+DSl, where DSi - entropy change due to irreversible processes in the system; DSl is the change in entropy caused by the interaction of the system with external bodies (flows passing through the system). Irreversibility of processes leads to DSi > 0, stationarity of the state - to DSi = 0; hence: DSl = DS - DSi < 0. This means that the entropy in the products (matter and energy) entering the system is less than the entropy in the products leaving the system. The initial development of thermodynamics was stimulated by the needs of industrial production. At this stage (the XNUMXth century), the main achievements were the formulation of laws, the development of methods of cycles and thermodynamic potentials in relation to idealized processes. Biological objects are open thermodynamic systems. They exchange energy and matter with the environment. For an organism - a stationary system - one can write dS = 0, S = = const, dS i> 0, dSe < 0. This means that a large entropy should be in the excretory products, and not in the food. Under some pathological conditions, the entropy of a biological system can increase (dS > 0), this is due to the lack of stationarity, an increase in disorder. The formula can be represented:  or for steady state  This shows that in the normal state of the organism, the rate of change in entropy due to internal processes is equal to the rate of change in negative entropy due to the exchange of matter and energy with the environment. 27. Thermometry and calorimetry Accurate temperature measurements are an essential part of research and development, as well as medical diagnostics. Methods for obtaining and measuring temperatures in a wide range are very different. The field of physics in which the methods of measuring temperature and related issues are studied is called thermometry. Since temperature is determined by the value of any characteristic of a thermometric substance, its definition consists in measuring such physical parameters and properties as volume, pressure, electrical, mechanical, optical, magnetic effects, etc. A variety of temperature measurement methods is associated with a large the number of thermometric substances and the properties used in this. A thermometer - a device for measuring temperature - consists of a sensitive element in which a thermometric property is realized, and a measuring device (dilatometer, manometer, galvanometer, potentiometer, etc.). A necessary condition for measuring temperature is the thermal equilibrium of the sensitive element and the body, the temperature of which is determined. Depending on the measured temperature ranges, the most common liquid, gas thermometers, resistance thermometer, thermocouple as thermometers and pyrometers. In a liquid thermometer, the thermometric characteristic is the volume, the sensitive element is a reservoir of liquid (usually mercury or alcohol). Pyrometers use radiation intensity as a thermometric property. When measuring ultralow temperatures, paramagnets serve as thermometric substances, and the measured property is the dependence of their magnetization on temperature. The mercury thermometer used in medicine indicates the maximum temperature and is called the maximum thermometer. This feature is due to its design: the reservoir with mercury is separated from the graduated capillary by a narrowing, which does not allow mercury to return to the reservoir when the thermometer is cooled. There are also minimum thermometers that show the lowest temperature observed over a long period of time. For this purpose, thermostats are used - devices in which the temperature is maintained constant, which is carried out either by automatic regulators, or for this they use the property of one-time transitions to proceed at a constant temperature. To measure the amount of heat released or absorbed in various physical, chemical and biological processes, a number of methods are used, the totality of which constitutes calorimetry. Calorimetric methods measure the heat capacity of bodies, the heat of phase transitions, dissolution, wetting, adsorption, heat accompanying chemical reactions, radiation energy, radioactive decay, etc. Similar measurements are made using calorimeters. 28. Physical properties of hot and cold media used for treatment In medicine, hot or cold bodies are used for local heating or cooling. Usually, relatively accessible media are chosen for this, some of them may also have a useful mechanical or chemical effect. The physical properties of such media are determined by their purpose. First, it is necessary that the desired effect be produced over a relatively long time. Therefore, the media used must have a high specific heat capacity (water, dirt) or specific heat of phase transformation (paraffin, ice). Secondly, media applied directly to the skin should not cause pain. On the one hand, this limits the temperature of such media, and on the other hand, it encourages choosing media with a low heat capacity. So, for example, water used for treatment has a temperature of up to 45 ° C, and peat and mud - up to 50 ° C, since heat transfer (convection) in these environments is less than in water. Paraffin is heated to 60-70 °C, as it has a low thermal conductivity, and parts of the paraffin directly adjacent to the skin quickly cool down, crystallize and delay the influx of heat from the rest of its parts. Ice is used as a cooling medium used for treatment. In recent years, low temperatures have been widely used in medicine. At a low temperature, such preservation of individual organs and tissues is carried out in connection with transplantation, when the ability to live and function normally is preserved for a sufficiently long time. The cryogenic method of tissue destruction during freezing and thawing is used by physicians to remove tonsils, warts, etc. For this purpose, special cryogenic apparatuses and cryoprobes are created. With the help of cold, which has an anesthetic property, it is possible to destroy the nuclear cells in the brain responsible for certain nervous diseases, such as parkinsonism. Microsurgery uses the freezing of wet tissues to a cold metal instrument to capture and transfer these tissues. In connection with the medical use of low temperature, new terms have appeared: "cryogenic medicine", "cryotherapy", "cryosurgery", etc. 29. Physical processes in biological membranes Biological membranes are an important part of the cell. They delimit the cell from the environment, protect it from harmful external influences, control the metabolism between the cell and its environment, contribute to the generation of electrical potentials, participate in the synthesis of universal ATP energy accumulators in mitochondria, etc. The structure and models of membranes Membranes surround all cells (plasma and outer cell membranes). Without a membrane, the contents of the cell would simply spread out, diffusion would lead to thermodynamic equilibrium, which means the absence of life. We can say that the first cell appeared when it was fenced off from the environment by a membrane. Intracellular membranes subdivide the cell into a number of closed compartments, each of which performs a specific function. The basis of the structure of any membrane is a double lipid layer (largely - phospholipids). The lipid bilayer is formed from two monolayers of lipids so that the hydrophobic "tails" of both layers are directed inward. This ensures the least contact of the hydrophobic regions of the molecules with water. This idea of the structure of the membrane did not give answers to many questions. Subsequently, a model was proposed based on the same lipid biolayered membrane. This phospholipid base is like a two-dimensional solvent in which more or less immersed proteins float. Due to these proteins, the specific functions of membranes are fully or partially carried out - permeability, generation of electric potential, etc. Membranes are not immobile, calm structures. Lipids and proteins exchange membranes and move both along the plane of the membrane - lateral diffusion, and across it - the so-called flip flop. Refinement of the structure of the biomembrane and the study of its properties turned out to be possible using physicochemical models of the membrane (artificial membranes). Three of these models are the most widely used. The first model is monolayers of phospholipids at the water-air or water-oil interface. The second widespread model of a biomembrane is liposomes, which are like a biological membrane completely devoid of protein molecules. The third model, which made it possible to study some properties of biomembranes by direct methods, is the biolipid (biolayer lipid) membrane (BLM). Membranes perform two important functions: matrix (i.e., they are a matrix, the basis for holding proteins that perform different functions) and barrier (they protect the cell and individual compartments from the penetration of unwanted particles). 30. Physical properties and parameters of membranes Measuring the mobility of membrane molecules and the diffusion of particles through the membrane indicates that the bilipid layer behaves like a liquid. However, the membrane is an ordered structure. These two facts suggest that the phospholipids in the membrane during its natural functioning are in a liquid crystalline state. When the temperature changes in the membrane, phase transitions can be observed: melting of lipids when heated and crystallization when cooled. The liquid-crystalline state of the biolayer has a lower viscosity and greater solubility of various substances than the solid state. The thickness of the liquid crystal biolayer is less than that of the solid one. The structure of molecules in liquid and solid states is different. In the liquid phase, phospholipid molecules can form cavities (kinks) into which molecules of a differentiating substance can be introduced. The movement of the kink in this case will lead to diffusion of the molecule across the membrane. Transport of molecules (atoms) across membranes An important element in the functioning of membranes is their ability to pass or not pass molecules (atoms) and ions. The probability of such penetration of particles depends both on the direction of their movement (for example, into the cell or out of the cell), and on the type of molecules and ions. Transfer phenomena are irreversible processes, as a result of which a spatial movement (transfer) of the mass of an impulse, charge, or some other physical quantity occurs in a physical system. Transfer phenomena include diffusion (transfer of mass of a substance), viscosity (transfer of momentum), thermal conductivity (transfer of energy), electrical conductivity (transfer of electric charge). There is a potential difference across the membrane, therefore, there is an electric field in the membrane. It affects the diffusion of charged particles (ions and electrons). The transport of ions is determined by two factors: the unevenness of their distribution (i.e., the concentration gradient) and the effect of an electric field (the Nernst-Planck equation):  The equation relates the stationary ion flux density to three quantities: 1) membrane permeability for a given ion, which characterizes the interaction of membrane structures with an ion; 2) electric field; 3) the concentration of ions in the aqueous solution surrounding the membrane. Transfer phenomena are related to passive transport: the diffusion of molecules and ions occurs in the direction of their lower concentration, the movement of ions - in accordance with the direction of the force acting on them from the electric field. Passive transport is not associated with the consumption of chemical energy, it is carried out as a result of the movement of particles towards a lower electrochemical potential. 31. A kind of passive transfer of molecules and ions through biological membranes Simple diffusion through the lipid layer in a living cell ensures the passage of oxygen and carbon dioxide. A number of medicinal substances and poisons also penetrate the lipid layer. However, simple diffusion proceeds rather slowly and cannot supply the cell with the required amount of nutrients. Therefore, there are other mechanisms of passive transfer of matter in the membrane, these include diffusion and facilitated diffusion (in combination with the carrier). Sometimes, or a channel, is called a section of the membrane, including protein molecules and lipids, which forms a passage in the membrane. This passage allows not only small molecules, such as water molecules, but also larger ions to pass through the membrane. Channels can exhibit selectivity for different ions. Facilitates the diffusion of ion transport by special carrier molecules. Resting potential. The surface membrane of a cell is not equally permeable to different ions. In addition, the concentration of any specific ions is different on different sides of the membrane, the most favorable composition of ions is maintained inside the cell. These factors lead to the appearance in a normally functioning cell of a potential difference between the cytoplasm and the environment (resting potential). The main contribution to the creation and maintenance of the resting potential is made by Na+, K+, Cl- ions. Total the flux density of these electrons, taking into account their signs, is equal to: J=JNA +JK +JCI-. In the stationary state, the total flux density is zero, i.e., the number of different ions passing through the membrane into the cell per unit time is equal to the number leaving the cell through the membrane: j = 0. Goldman-Hodgkin-Katz equation (dimensionless potential returns to electric):  Various concentrations of ions inside and outside the cell are created by ion pumps - active transport systems. The main contribution to the resting potential is made only by the K+ and Cl- ions. Action potential and its propagation When excited, the potential difference between the cell and the environment changes, an action potential arises. An action potential propagates in nerve fibers. The propagation of the action potential along the nerve fiber occurs in the form of an autowave. Excitable cells are the active medium: the rate of propagation of excitation along smooth unmyelinated nerve fibers is approximately proportional to the square root of their radius (υ≈√r). 32. Electrodynamics Electric and magnetic phenomena are associated with a special form of the existence of matter - electric and magnetic fields and their impact. These fields are generally so interconnected that it is customary to speak of a single electric field. Electromagnetic phenomena have three areas of biomedical applications. The first of these is the understanding of the electrical processes occurring in the body, as well as knowledge of the electrical and magnetic properties of biological media. The second direction is connected with the understanding of the mechanism of the influence of electromagnetic fields on the body. The third direction is instrumentation, hardware. Electrodynamics is the theoretical basis of electronics and, in particular, medical electronics. The energy field is a kind of matter, through which a force is exerted on the electric charges that are in this field. The characteristics of the electric field generated by biological structures are a source of information about the state of the body. Tension and potential - characteristics of the electric field. The power characteristic of an electric field is a strength equal to the ratio of the force acting at a given point of the field on a point charge to this charge: E=F/q Tension is a vector whose direction coincides with the direction of the force acting at a given point of the field on a positive charge. The electric field strength is expressed by three equations: Ex = f1 (x, y, z); Ey = f2 (x, y, z); Ez = f3(x, y, z), where Eх, Eу and Ez - projections of the intensity vector on the corresponding coordinate axes introduced to describe the field. The energy characteristic of the electric field is the potential. The potential difference between two points of the field is the ratio of the work done by the forces of the field when moving a point positive charge from one point of the field to another, to this charge:  where f1 and F2 - potentials at points 1 and 2 of the electric field. The potential difference between two points depends on the strength of the electric field. Along with the potential difference, the concept of potential is used as a characteristic of the electric field. Potentials at different points can be represented as surfaces of the same potential (equipotential surfaces). Existing electrical measuring instruments are designed to measure the potential difference, not the intensity. 33. Electric dipole and multipole An electric dipole is a system consisting of two equal but opposite in sign point electric charges located at some distance from each other (dipole arm). The main characteristic of a dipole is its electric (or dipole) moment - a vector equal to the product of the charge and the arm of the dipole, directed from a negative charge to a positive one: p = dl. The unit of electric moment of a dipole is the coulomb meter. A dipole in a uniform electric field is subjected to a torque that depends on the electric moment, the orientation of the dipole in the field, and the field strength. A force acts on the dipole, depending on its electric moment and the degree of field inhomogeneity dE/dx If the dipole is oriented in an inhomogeneous electric field not along the line of force, then a torque also acts on it. A free dipole is almost always drawn into the region of high field strengths. A dipole is a special case of a system of electric charges with a certain symmetry. The general name for such charge distributions is electric multipoles (I = 0, 1, 2, etc.), the number of multipole charges is determined by the expression 21. So, a zero-order multipole (20 = 1) is a single point charge, a first-order multipole (21 = 2) is a dipole, a second-order multipole (22 = 4) is a quadrupole, a third-order multipole (23 = 8) is an octupole, etc. e. The potential of the multipole field decreases at significant distances from it (R > d, where d are the dimensions of the multipole) proportional to I/R1 + 1. If the charge is distributed in a certain region of space, then the potential of the electric field outside the system of charges can be represented as some approximate series:  Here R is the distance from the system of charges to point A with potential F; f1, F2, F3…. - some functions depending on the type of the multipole, its charge and direction to point A. The first term corresponds to a monopole, the second to a dipole, the third to a quadrupole, and so on. In the case of a neutral system of charges, the first term is equal to zero. Dipole electric generator (current dipole) In a vacuum or in an ideal insulator, an electric dipole can persist for an arbitrarily long time. However, in a real situation (an electrically conductive medium), under the action of the electric field of the dipole, the movement of free charges occurs, and the dipole is neutralized. The current strength in the external circuit will remain almost constant, it almost does not depend on the properties of the medium. Such a two-pole system, consisting of a current source and a current drain, is called a dipole electric generator, or a current dipole. 34. Physical basis of electrocardiography Living tissues are a source of electrical potentials (biopotentials). Registration of biopotentials of tissues and organs for diagnostic purposes is called electrography. Such a general term is used relatively rarely, specific names of the corresponding diagnostic methods are more common: electrocardiography (ECG) - registration of biopotentials that occur in the heart muscle when it is excited, electromyography (EMG) - a method for recording the bioelectrical activity of muscles, electroencephalography (EEG) - a method for recording bioelectrical brain activity, etc. In most cases, biopotentials are taken by electrodes not directly from the organ (heart, brain), but from other adjacent tissues, in which electric fields are created by this organ. In clinical terms, this greatly simplifies the registration procedure itself, making it safe and uncomplicated. The physical approach to electrography consists in creating (choosing) a model of an electric generator that corresponds to the picture of "removable" potentials. The whole heart is electrically represented as some kind of electrical generator in the form of a real device and as a set of electrical sources in a conductor shaped like a human body. On the surface of the conductor, during the operation of an equivalent electrical generator, there will be an electrical voltage that occurs on the surface of the human body during cardiac activity. It is quite possible to simulate the electrical activity of the heart if a dipole equivalent electrical generator is used. The dipole view of the heart underlies Einthoven's lead theory. According to her, the heart is such a dipole with a dipole moment that rotates, changes its position and point of application during the cardiac cycle. V. Einthoven proposed to measure the differences in the biopotentials of the heart between the vertices of an equilateral triangle, which are approximately located in the right and left arms and left leg. According to the terminology of physiologists, the difference in biopotentials recorded between two points of the body is called abduction. There are lead I (right hand - left hand), lead II (right hand - left leg) and lead III (left hand - left foot). According to V. Einthoven, the heart is located in the center of the triangle. Since the electric moment of the dipole - the heart - changes with time, temporary voltages will be obtained in the leads, which are called electrocardiograms. The electrocardiogram does not give an idea of the spatial orientation. However, for diagnostic purposes such information is important. In this regard, a method of spatial study of the electric field of the heart, called vector cardiography, is used. A vector-cardiogram is a locus of points corresponding to the end of a vector, the position of which changes during the cardiac cycle. 35. Electric current Electric current is usually understood as the directed movement of electric charges. Distinguish between conduction current and convection current. Conduction current is the directed movement of charges in conducting bodies: electrons - in metals, electrons and holes - in semiconductors, ions - in electrolytes, ions and electrons - in gases. Convection current is the movement of charged bodies and the flow of electrons or other charged particles in a vacuum. Current density is a vector characteristic of an electric current, numerically equal to the ratio of the strength of the current passing through a small surface element, normal to the direction of movement of charged particles that form the current, to the area of this element: j = dl/dS If this formula is multiplied by the charge q of the current carrier, then we get the current density: j = qj = qnv. In vector form: j = qnv. The vector j is directed tangentially to the streamlines. For the current strength, we write the following expression: j=dq/dt. The current strength is the time derivative of the charge passing through a certain section or surface. In order for direct current to flow through a conductor, it is necessary to maintain a potential difference at its ends. This is done by current sources. The electromotive force of the source is a value that is numerically equal to the work of external forces when moving a single positive charge throughout the circuit. In practice, the work of external forces is different from zero only inside the current source. The ratio of an external force to a unit positive charge is equal to the field strength of external forces: ECT = FCT/q The electromotive force corresponds to an abrupt change in the potential in the current source. Electrical conductivity of electrolytes. Biological fluids are electrolytes, the electrical conductivity of which is similar to the electrical conductivity of metals: in both media, unlike gases, current carriers exist independently of the electric field. The direction of movement of ions in an electric field can be approximately considered uniform, while the force qE acting on the ion from the electric field is equal to the friction force rv: qE = rv, from where we get: v = bE. The coefficient of proportionality b is called the ion mobility. 36. Electrical conductivity of biological tissues and liquids at direct current. Electric discharge in gases Biological tissues and organs are rather heterogeneous formations with different electrical resistances, which can change under the action of an electric current. This makes it difficult to measure the electrical resistance of living biological systems. The electrical conductivity of individual parts of the body located between electrodes applied directly to the surface of the body depends significantly on the resistance of the skin and subcutaneous layers. Inside the body, the current spreads mainly through the blood and lymphatic vessels, muscles, and sheaths of the nerve trunks. The resistance of the skin, in turn, is determined by its condition: thickness, age, humidity, etc. The electrical conductivity of tissues and organs depends on their functional state and, therefore, can be used as a diagnostic indicator. So, for example, during inflammation, when cells swell, the cross section of intercellular connections decreases and electrical resistance increases; physiological phenomena that cause sweating are accompanied by an increase in the electrical conductivity of the skin, etc. A gas consisting only of neutral particles is an insulator. If it is ionized, it becomes electrically conductive. Any device, phenomenon, factor that can cause the ionization of molecules and atoms of a gas is called an ionizer. They can be light, X-rays, flames, ionizing radiation, etc. An electric charge in air can also be formed when polar liquids are sprayed into it (balloelectric effect), i.e., liquids whose molecules have a constant electric dipole moment. So, for example, when crushed in air, water breaks up into charged droplets. The sign of the charge of large drops (positive for hard water) is opposite in sign to the charge of the smallest drops. Larger droplets settle relatively quickly, leaving negatively charged water particles in the air. This phenomenon is observed at the fountain. The electrical conductivity of the gas also depends on the secondary ionization. The ionized potential of internal electrons is much higher. Under terrestrial conditions, air almost always contains a certain amount of ions due to natural ionizers, mainly radioactive substances in soil and gases and cosmic radiation. Ions and electrons in the air can, by joining neutral molecules and suspended particles, form more complex ions. These ions in the atmosphere are called air ions. They differ not only in sign, but also in mass, they are conditionally divided into light (gas ions) and heavy (suspended charged particles - dust particles, smoke and moisture particles). Heavy ions have a harmful effect on the body, light and mostly negative air ions have a beneficial effect. They are used for treatment (aeroionotherapy). 37. Magnetic field A magnetic field is called all matter, through which a force is exerted on moving electric charges placed in a field, and other bodies that have a magnetic moment. For a magnetic field, as well as for an electrostatic one, there is a quantitative characteristic - a magnetic moment (vector quantity). The magnetic induction at a certain point in the field is equal to the ratio of the maximum torque acting on the loop with current in a uniform magnetic field to the magnetic moment of this loop. The unit of magnetic flux is weber (Wb): 1Wb = 1Tlm2. Tl is the unit of magnetic induction (Tesla). It can be seen from the formula that the flow can be both positive and negative. Ampere's law. The energy of a circuit with current in a magnetic field. One of the main manifestations of the magnetic field is its force effect on moving electric charges and currents. A. M. Ampere established the law that determines this force effect. In a conductor in a magnetic field, we select a fairly small section dI, which is considered as a vector directed towards the current. The product IdI is called the current element. The force acting from the magnetic field on the current element is equal to: dF = kIB sinb × dl, where k is the coefficient of proportionality; or in vector form dF = ldl × B. These ratios express Ampère's law. The force acting according to Ampère's law on a current-carrying conductor in a magnetic field is the result of its action on moving electric charges that create this current. The force acting on a separate moving charge is determined by the ratio of the force F applied to a current-carrying conductor to the total number N of current carriers in it: fЛ =F/N(I) The current strength is: I = jS, F = jSBL sinb, where j is the current density. We get: F = jSBL sinb = qnvSBL sinb2, where n =N/ SI is the concentration of particles. Substituting the last expression to the first, we obtain an expression for the force acting from the magnetic field on a separate moving electric charge and called the Lorentz force:  The direction of the Lorentz force can be determined from the vector notation of the equation fn = qvB. 38. Magnetic field strength and its other properties The strength of the magnetic field depends on the properties of the medium, and is determined only by the strength of the current flowing through the circuit. The strength of the magnetic field created by direct current is composed of the strength of the fields created by its individual elements (Biot-Savart-Laplace Law):  (dH - tension, k - coefficient of proportionality, di and r - vectors). Integrating, we find the strength of the magnetic field created by the circuit with current or part of this circuit:  Circular is the current flowing through the conductor in the form of a circle. This current also corresponds to a circularly rotating electric charge. Knowing the strength of the magnetic field and the relative magnetic permeability of the medium, one can find the magnetic induction: B = M + M0H = mNf(2r). Magnetic properties of matter There are no such substances, the state of which would not change when they are placed in a magnetic field. Moreover, being in a magnetic field, substances themselves become sources of such a field. In this sense, all substances are called magnets. Since the macroscopic differences of magnets are due to their structure, it is advisable to consider the magnetic characteristics of electrons, nuclei, atoms and molecules, as well as the behavior of these particles in a magnetic field. The ratio of the magnetic moment of a particle to the moment of its momentum is called magnetomechanical. The relations show that there is a well-defined "hard" connection between the magnetic and mechanical (moment of moment) moments; this connection manifests itself in magnetomechanical phenomena. Magneto-mechanical phenomena make it possible to determine magnetomechanical relationships and, on the basis of this, draw conclusions about the role of orbital or spin magnetic moments in magnetization processes. So, for example, Einstein's experiments showed that the spin magnetic moments of electrons are responsible for the magnetization of ferromagnetic (iron-magnetic) materials. Nuclei, atoms and molecules also have a magnetic moment. The magnetic moment of a molecule is the vector sum of the magnetic moments of the atoms that make it up. The magnetic field acts on the orientation of particles that have magnetic moments, as a result of which the substance is magnetized. The degree of magnetization of a substance is characterized by magnetization. The average value of the magnetization vector is equal to the ratio of the total magnetic moment Spmi of all particles located in the volume of the magnet to this volume:  Thus, magnetization is the average magnetic moment per unit volume of a magnet. The unit of magnetization is the ampere per meter (A/m). 39. Properties of magnets and magnetic properties of human tissues Paramagnetic molecules have nonzero magnetic moments. In the absence of a magnetic field, these moments are arranged randomly and their magnetization is zero. The degree of ordering of magnetic moments depends on two opposite factors - the magnetic field and molecular-chaotic motion, so the magnetization depends on both magnetic induction and temperature. In a non-uniform magnetic field in vacuum, particles of a paramagnetic substance move towards a higher value of magnetic induction, as they say, they are drawn into the field. Paramagnets include aluminum, oxygen, molybdenum, etc. Diamagnetism is inherent in all substances. In paramagnets, diamagnetism is overridden by stronger paramagnetism. If the magnetic moment of molecules is zero or so small that diamagnetism prevails over paramagnetism, then substances consisting of such molecules are referred to as diamagnets. The magnetization of diamagnets is directed opposite to the magnetic induction, its value increases with increasing induction. Diamagnet particles in a vacuum in a non-uniform magnetic field will be pushed out of the field. Ferromagnets, like paramagnets, create a magnetization aimed at inducing a field; their relative magnetic permeability is much greater than unity. Ferromagnetic properties are not inherent in individual atoms or molecules, but only in some substances that are in a crystalline state. Ferromagnets include crystalline iron, nickel, cobalt, many alloys of these elements with each other and with other non-ferromagnetic compounds, as well as alloys and compounds of chromium and manganese with non-ferromagnetic elements. The magnetization of ferromagnets depends not only on the magnetic induction, but also on their previous state, on the time the sample was in the magnetic field. Although there are not very many ferromagnets in nature, they are mainly used as magnetic materials in technology. Body tissues are largely diamagnetic, like water. However, in the body there are also paramagnetic substances, molecules and ions. There are no ferromagnetic particles in the body. Biocurrents arising in the body are a source of weak magnetic fields. In some cases, the induction of such fields can be measured. So, for example, based on the registration of the time dependence of the induction of the magnetic field of the heart (heart biocurrents), a diagnostic method was created - magnetocardiography. Since the magnetic induction is proportional to the current strength, and the current strength (biotok) according to Ohm's law is proportional to the voltage (biopotential), in general, the magnetocardiogram is similar to the electrocardiogram. However, magnetocardiography, unlike electrocardiography, is a non-contact method, because the magnetic field can also be recorded at some distance from the biological object - the source of the field. 40. Electromagnetic induction. Magnetic field energy The essence of electromagnetic induction is that an alternating magnetic field generates an electric field (discovered by M. Faraday in 1831). The basic law of electromagnetic induction With any change in the magnetic flux, electromotive forces of electromagnetic induction arise in it.  where e - electromotive forces; dt - time interval; dФ is the change in the magnetic flux. This is the basic law of electromagnetic induction, or Faraday's law. When the magnetic flux penetrating the circuit changes (the magnetic field changes with time, the magnet approaches or moves away, the current strength changes in the adjacent or distant circuit, etc.), an electromotive force of electromagnetic induction always appears in the circuit, proportional to the rate of change of the magnetic flux. A change in the magnetic field causes an electric field. Since the current is the derivative of the charge with respect to time, we can write:  It follows that the charge flowing in the conductor due to electromagnetic induction depends on the change in the magnetic flux penetrating the circuit and its resistance. This dependence is used to measure the magnetic flux by devices that record the electric charge induced in the circuit. One of the manifestations of electromagnetic induction is the occurrence of closed induction currents (eddy currents, or Foucault currents) in solid conductive bodies, such as metal parts, electrolyte solutions, biological organs, etc. Eddy currents are formed when a conducting body moves in a magnetic field, when change with time of the field induction, as well as under the combined action of both factors. The intensity of eddy currents depends on the electrical resistance of the body and, consequently, on the resistivity and dimensions, as well as on the rate of change of the magnetic flux. In physiotherapy, the heating of individual parts of the human body with eddy currents is prescribed as a medical procedure called inductothermy. Electromagnetic oscillations are called periodic interrelated changes in charges, currents, electric and magnetic field strengths. The propagation of electromagnetic oscillations in space occurs in the form of electromagnetic waves. Among various physical phenomena, electromagnetic oscillations and waves occupy a special place. Alternating current is any current that changes with time. However, more often the term "alternating current" is applied to quasi-stationary currents that depend on time according to a harmonic law. 41. Total resistance ((impedance) of body tissues. Physical basis of rheography Body tissues conduct not only direct but also alternating current. There are no such systems in the body that would be similar to inductance coils, so its inductance is close to zero. Biological membranes (and, consequently, the whole organism) have capacitive properties, in connection with this, the total resistance of body tissues is determined only by ohmic and capacitive resistances. The presence of capacitive elements in biological systems is confirmed by the fact that the current strength is ahead of the applied voltage in phase. The frequency dependence of the impedance makes it possible to assess the viability of body tissues; this is important to know for the transplantation (transplantation) of tissues and organs. The impedance of tissues and organs also depends on their physiological state. Thus, when blood vessels are filled with blood, the impedance changes depending on the state of cardiovascular activity. A diagnostic method based on registering the use of tissue impedance in the process of cardiac activity is called rheography (impedance plethysmography). Using this method, rheograms of the brain (rheoencephalograms), hearts (rheocardiograms), main vessels, lungs of the liver and extremities are obtained. Measurements are usually carried out at a frequency of 30 kHz. Electric impulse and impulse current An electric impulse is a short-term change in electric voltage or current strength. In technology, pulses are divided into two large groups: video and radio pulses. Video pulses are such electrical current or voltage pulses that have a constant component that is different from zero. Thus, the video pulse has predominantly one polarity. The shape of the video pulses are rectangular, sawtooth, trapezoidal, exponential, bell-shaped, etc. Radio pulses are modulated electromagnetic oscillations. In physiology, the term "electrical impulse" (or "electrical signal") refers specifically to video impulses. Repetitive impulses are called impulse current. It is characterized by a period (pulse repetition period) T - the average time between the beginnings of adjacent pulses and frequency (pulse repetition frequency): f=1/T. The duty cycle of the pulses is the ratio:  The reciprocal of the duty cycle is the fill factor:  42. The concept of Maxwell's theory. Bias current J. Maxwell created the theory of the electromagnetic field within the framework of classical physics. The theory of J. Maxwell is based on two provisions. 1. Any displaced electric field generates a vortex magnetic field. An alternating electric field was named by Maxwell because, like an ordinary current, it induces a magnetic field. A vortex magnetic field is generated both by conduction currents Ipr (moving electric charges) and displacement currents (displaced electric field E). Maxwell's first equation  2. Any displaced magnetic field generates a vortex electric field (the basic law of electromagnetic induction). Maxwell's second equation:  It relates the rate of change of the magnetic flux through any surface and the circulation of the vector of the electric field strength that arises in this case. The circulation is taken along the contour on which the surface rests. It follows from the provisions of Maxwell's theory that the appearance of any field (electric or magnetic) at some point in space entails a whole chain of mutual transformations: an alternating electric field generates a magnetic field, a change in a magnetic field generates an electric one. The mutual formation of electric and magnetic fields leads to an electromagnetic field - the propagation of a single electromagnetic field in space. The propagation speed of electromagnetic waves is equal to the speed of light. This was the basis for Maxwell's creation of the electromagnetic theory of light. This theory has become a very important stage in the further development of medical physics. 43. Classification of frequency intervals adopted in medicine It follows from Maxwell's theory that various electromagnetic waves, including light waves, have a common nature. In this regard, it is advisable to represent all kinds of electromagnetic waves in the form of a single scale. Each scale is conditionally divided into six ranges: radio waves (long, medium and short), infrared, visible, ultraviolet, x-ray and gamma radiation. This classification is determined either by the mechanism of wave formation, or by the possibility of their visual perception by a person. Radio waves are caused by alternating currents in conductors and electronic flows (macroradiators). Infrared, visible and ultraviolet radiations come from atoms, molecules and fast charged particles (microemitters). X-ray radiation occurs during intra-atomic processes. Gamma radiation is of nuclear origin. Some ranges overlap because waves of the same length can be produced by different processes. So, the most short-wave ultraviolet radiation is blocked by long-wave X-rays. In this regard, the boundary region of infrared waves and radio waves is very characteristic. Until 1922 there was a gap between these ranges. The shortest wavelength radiation of this unfilled gap was of molecular atomic origin (radiation of a heated body), while the longest wavelength was emitted by macroscopic Hertz vibrators. Even millimeter waves can be generated not only by radio engineering, but also by molecular transitions. The section "Radiospectroscopy" has appeared, which studies the absorption and emission of radio waves by various substances. In medicine, the following conditional division of electromagnetic oscillations into frequency ranges is accepted (Table 1). Table 1 Conditional division of electromagnetic oscillations into frequency ranges  Often physiotherapeutic electronic equipment of low and audio frequency is called low-frequency. Electronic equipment of all other frequencies is called a generalizing concept - "high-frequency equipment". 44. Physical processes in tissues that occur when exposed to current and electromagnetic fields All substances are composed of molecules, each of them is a system of charges. Therefore, the state of bodies essentially depends on the currents flowing through them and on the acting electromagnetic field. The electrical properties of biological bodies are more complex than the properties of inanimate objects, because an organism is also a collection of ions with a variable concentration in space. The primary mechanism of the impact of currents and electromagnetic fields on the body is physical. The primary action of direct current on body tissues. Galvanization. Electrophoresis of medicinal substances The human body largely consists of biological fluids containing a large number of ions that are involved in various metabolic processes. Under the influence of an electric field, ions move at different speeds and accumulate near cell membranes, forming a counter electric field, called polarization. Thus, the primary effect of direct current is associated with the movement of ions in different elements of tissues. The impact of direct current on the body depends on the strength of the current, so the electrical resistance of tissues, especially the skin, is of great importance. Moisture, sweat significantly reduce the resistance, which, even with a small voltage, can cause the passage of current through the body. Continuous direct current with a voltage of 60-80 V is used as a therapeutic method of physiotherapy (galvanization). The current source is a full-wave rectifier - a galvanization apparatus. For this, electrodes made of sheet lead with a thickness of 0,3-0,5 mm are used. Since the products of electrolysis of a sodium chloride solution contained in tissues cause cauterization, hydrophilic pads moistened with warm water are placed between the electrodes and the skin. Direct current is also used in medical practice for the introduction of drugs through the skin or mucous membranes. This method is called drug electrophoresis. For this purpose, they proceed in the same way as in galvanization, but the active electrode gasket is moistened with a solution of the corresponding medicinal substance. The drug is injected from the pole, the charge of which it has: anions are injected from the cathode, cations - from the anode. Galvanization and electrophoresis of medicinal substances can be carried out using liquid electrodes in the form of baths, in which the patient's limbs are immersed. 45. Impact of alternating (impulse) currents The effect of alternating current on the body essentially depends on its frequency. At low, sound and ultrasonic frequencies, alternating current, like direct current, has an irritating effect on biological tissues. This is due to the displacement of ions of electrolyte solutions, their separation, changes in their concentration in different parts of the cell and intercellular space. Tissue irritation also depends on the shape of the pulsed current, the duration of the pulse and its amplitude. So, for example, increasing the steepness of the pulse front reduces the threshold current strength, which causes muscle contraction. This indicates that the muscles adapt to changes in current strength, and ionic compensation processes begin. Since the specific physiological effect of electric current depends on the shape of the pulses, in medicine, to stimulate the central nervous system (electrosleep, electron anesthesia), the neuromuscular system, the cardiovascular system (pacemakers, defibrillators) and others, currents with different time dependence are used. Acting on the heart, the current can cause ventricular fibrillation, which leads to the death of a person. The threshold current strength that causes fibrillation depends on the density of the current flowing through the heart, the frequency and duration of its action. Current or electromagnetic wave has a thermal effect. Therapeutic heating with high-frequency electromagnetic oscillations has a number of advantages over the traditional and simple method - a heating pad. Warming up the internal organs with a heating pad is carried out due to the thermal conductivity of the external tissues - the skin and subcutaneous fatty tissue. High-frequency heating occurs due to the formation of heat in the internal parts of the body, i.e. it can be created where it is needed. Heating with high-frequency vibrations is also convenient because, by adjusting the power of the generator, it is possible to control the power of heat release in the internal organs, and in some procedures it is also possible to dose the heat. High-frequency currents are used to heat tissues with currents. The passage of high frequency current through the tissue is used in physiotherapeutic procedures called diathermy and local darsonvalization. During diathermy, a current with a frequency of about 1 MHz with weakly damped oscillations, a voltage of 100-150 V is used; current is a few amperes. Since skin, fat, bones, muscles have the greatest specific resistance, they heat up more. The least heating in organs rich in blood or lymph is the lungs, liver, and lymph nodes. The disadvantage of diathermy is that a large amount of heat is unproductively released in the skin layer and subcutaneous tissue. Recently, diathermy has been leaving therapeutic practice and being replaced by other methods of high-frequency exposure. High frequency currents are also used for surgical purposes (electrosurgery). They allow you to cauterize, "weld" tissues (diathermocoagulation) or dissect them (diathermotomy). 46. Exposure to an alternating magnetic field In massive conducting bodies in an alternating field, eddy currents arise. These currents can be used to heat biological tissues and organs. Such a treatment method - inductothermy - has a number of advantages over the diathermy method. With inductothermy, the amount of heat released in the tissues is proportional to the squares of the frequency and induction of the alternating magnetic field and inversely proportional to the resistivity. Therefore, tissues rich in blood vessels (for example, muscles) will be heated more strongly than fatty ones. Treatment with eddy currents is also possible with general darsonvalization. In this case, the patient is placed in a solenoid cage, through the coils of which a high-frequency pulsed current is passed. Exposure to an alternating electric field. In tissues in an alternating electric field, displacement currents and conduction currents arise. Usually, ultra-high frequency electric fields are used for this purpose, so the corresponding physiotherapeutic method is called UHF therapy. It is customary to use a frequency of 40,58 MHz in UHF devices; at currents of this frequency, the dielectric tissues of the body heat up more intensively than conductive ones. Exposure to electromagnetic waves. Physiotherapeutic methods based on the use of electromagnetic waves in the microwave range, depending on the wavelength, received two names: "microwave therapy" and "DCV therapy". At present, the most developed theory is the thermal effect of microwave fields on biological objects. An electromagnetic wave polarizes the molecules of a substance and periodically reorients them as electric dipoles. In addition, an electromagnetic wave affects the ions of biological systems and causes an alternating conduction current. All this leads to heating of the substance. Electromagnetic waves can influence biological processes by breaking hydrogen bonds and affecting the orientation of DNA and RNA macromolecules. When an electromagnetic wave hits a part of the body, it is partially reflected from the surface of the skin. The degree of reflection depends on the difference in the dielectric constants of air and biological tissues. The depth of penetration of electromagnetic waves into biological tissues depends on the ability of these tissues to absorb wave energy, which in turn is determined by both the structure of tissues (mainly water content) and the frequency of electromagnetic waves. So, centimeter electromagnetic waves used in physiotherapy penetrate into muscles, skin, biological fluids to a depth of about 2 cm, and into fat and bones - about 10 cm. Taking into account the complex composition of tissues, it is conventionally considered that during microwave therapy the penetration depth of electromagnetic waves is 3-5 cm from the body surface, and during DCV therapy - up to 9 cm. 47. Electronics Electronics is a concept that is widespread at the present time. Electronics is based primarily on the achievements of physics. Today, without electronic equipment, neither the diagnosis of diseases nor their effective treatment is possible. The term "electronics" is largely arbitrary. It is most correct to understand electronics as the field of science and technology, in which the work and application of electrovacuum, ionic and semiconductor devices (devices) are considered. They single out physical electronics, meaning the section of physics that considers the electrical conductivity of bodies, contact and thermionic phenomena. Technical electronics is understood as those sections that describe the devices of devices and apparatuses and their switching circuits. Semiconductor electronics is what refers to the use of semiconductor devices, etc. Sometimes all electronics is divided into three major areas: vacuum electronics, which covers the creation and application of electrovacuum devices (such as vacuum tubes, photoelectronic devices, x-ray tubes, gas discharge devices); solid-state electronics, which covers the creation and application of semiconductor devices, including integrated circuits; quantum electronics - a specific branch of electronics related to lasers. Electronics is a dynamic branch of science and technology. On the basis of new effects (phenomena), electronic devices are created, including those that are used in biology and medicine. Any technical (radiotechnical or electronic) device is being upgraded, made smaller, etc. However, difficulties arise in this. So, for example, reducing the dimensions of a product can reduce its reliability, etc. A significant shift in the miniaturization of electronic devices was the introduction of semiconductor diodes and triodes, which made it possible to bring the density of electronic devices to 2-3 elements per 1 cm3. The next stage in the miniaturization of electronics, which is still developing at the present time, is the creation of integrated circuits. This is a miniature electronic device in which all elements (or part of them) are inseparably connected structurally and electrically interconnected. There are two main types of integrated circuits: semiconductor and film. Semiconductor integrated circuits are made from highly pure semiconductors. By thermal, diffuse and other processing, the crystal lattice of a semiconductor is changed so that its individual regions become different elements of the circuit. Film integrated circuits are made by vacuum deposition of various materials on suitable substrates. Hybrid integrated circuits are also used - a combination of semiconductor and film circuits. 48. Medical electronics One of the common uses of electronic devices is related to the diagnosis and treatment of diseases. Sections of electronics, which consider the features of the use of electronic systems for solving biomedical problems, as well as the device of the corresponding equipment, are called medical electronics. Medical electronics is based on information from physics, mathematics, engineering, medicine, biology, physiology and other sciences, it includes biological and physiological electronics. Currently, many traditionally "non-electrical" characteristics (temperature, body displacement, biochemical parameters, etc.) are being measured during measurements to be converted into an electrical signal. Information represented by an electrical signal can be conveniently transmitted over a distance and reliably recorded. We can distinguish the following main groups of electronic devices and apparatus used for biomedical purposes. 1. Devices for receiving (scheme), transmission and registration of biomedical information. Such information can be not only about the processes occurring in the body (in biological tissue, organs, systems), but also about the state of the environment (sanitary and hygienic purpose), about the processes occurring in prostheses, etc. This includes a large part of diagnostic equipment: ballistocardiographs, phonocardiographs, etc. 2. Electronic devices that provide dosing effects on the body by various physical factors (such as ultrasound, electric current, electromagnetic fields, etc.) for the purpose of treatment: microwave therapy devices, electrosurgical devices, pacemakers, etc. 3. Cybernetic electronic devices: 1) electronic computers for processing, storing and automatic analysis of biomedical information; 2) devices for controlling life processes and automatic regulation of the human environment; 3) electronic models of biological processes, etc. One of the important issues related to the device electronic medical equipment is its electrical safety for both patients and medical personnel. In an electric network and in technical devices, an electric voltage is usually set, but an electric current, that is, a charge flowing through a biological object per unit time, has an effect on the body or organs. The resistance of the human body between two touches (electrodes) is the sum of the resistance of internal tissues and organs and the resistance of the skin. The main and main requirement is to make it inaccessible to touch the equipment under voltage. To do this, first of all, parts of devices and apparatuses under voltage are isolated from each other and from the body of the equipment. 49. How is the reliability of medical equipment ensured When carrying out procedures using electrodes applied to the patient, it is difficult to foresee many options for creating an electrically hazardous situation, so you should clearly follow the instructions for this procedure without making any deviations from it. Reliability of medical equipment. Medical equipment must function normally. The ability of a product not to fail in operation under specified operating conditions and to maintain its performance for a given time interval is characterized by a general term - "reliability". For medical equipment, the problem of reliability is especially relevant, since the failure of devices and devices can lead not only to economic losses, but also to the death of patients. The ability of the equipment to fail-safe operation depends on many reasons, the effect of which is practically impossible to take into account, therefore, the quantitative assessment of reliability is of a probabilistic nature. So, for example, an important parameter is the probability of failure-free operation. It is estimated experimentally by the ratio of the number of working (not spoiled) products for a certain time to the total number of tested products. This characteristic evaluates the ability of the product to maintain operability in a given time interval. Another quantitative indicator of reliability is the failure rate. Depending on the possible consequences of a failure during operation, medical devices are divided into four classes. A - products, the failure of which poses an immediate danger to the life of the patient or personnel. Products of this class include devices for monitoring the vital functions of the patient, artificial respiration and circulatory apparatus. B - products, the failure of which causes a distortion of information about the state of the body or the environment, which does not lead to an immediate danger to the life of the patient or personnel, or necessitates the immediate use of a device similar in function to the standby mode. These products include systems that monitor the patient, devices for stimulating cardiac activity. B - products, the failure of which reduces the effectiveness or delays the treatment and diagnostic process in non-critical situations, or increases the burden on medical or maintenance personnel, or leads only to material damage. This class includes most of the diagnostic and physiotherapeutic equipment, tools, etc. G - products that do not contain fail-safe parts. Electromedical equipment does not belong to this class. 50. System for obtaining medical and biological information Any biomedical research is associated with the acquisition and registration of missing information. In order to receive and record information about the state and parameters of a biomedical system, it is necessary to have a whole set of devices. The primary element of this set - the sensitive element of the measuring instrument, called the pickup device - certainly contacts or interacts with the system itself. In medical electronics devices, the sensing element either directly outputs an electrical signal, or changes such a signal under the influence of a biological system. The pickup device converts the information of biomedical and physiological content into a signal of an electronic device. There are two types of pickup devices used in medical electronics: electrodes and sensors. Electrodes are specially shaped conductors that connect the measuring circuit to the biological system. When diagnosing, electrodes are used not only to pick up an electrical signal, but also to bring in an external electromagnetic effect (for example, in rheography). In medicine, electrodes are also used to provide electromagnetic effects for the purpose of treatment and electrical stimulation. Many biomedical characteristics cannot be "recorded" by electrodes, since they are not reflected by a bioelectrical signal: blood pressure, temperature, heart sounds, and many others. In some cases, biomedical information is associated with an electrical signal; in these cases, sensors (measuring transducers) are used. A sensor is a device that converts a measured or controlled value into a signal that is convenient for transmission, further conversion or registration. Sensors are divided into generator and parametric. Generator - these are sensors that, under the influence of the measured signal, directly generate voltage or current. These types of sensors include: 1) piezoelectric; 2) thermoelectric; 3) induction; 4) photovoltaic. Parametric - these are sensors in which, under the influence of the measured signal, any parameter changes. These sensors include: 1) capacitive; 2) rheostatic; 3) inductive. Depending on the energy that is the carrier of information, there are mechanical, acoustic (sound), temperature, electrical, optical and other sensors. Bioelectric potentials are an essential diagnostic indicator of many diseases. Therefore, it is very important to correctly register these potentials and extract the necessary medical information. 51. Amplifier-oscillators Amplifiers of electrical signals, or electronic amplifiers, are devices that convert the energy of DC voltage sources into the energy of electromagnetic oscillations of various forms. According to the principle of operation, generators with self-excitation and generators with external excitation are distinguished, which are essentially high-frequency power amplifiers. Generators are subdivided according to the frequency and power of oscillations. In medicine, electronic generators find three main applications: in physiotherapeutic electronic equipment; in electronic stimulators; in separate diagnostic devices, for example, in a rheograph. All generators are divided into low-frequency and high-frequency. Medical devices - generators of harmonic and pulsed low-frequency electromagnetic oscillations combine two large groups of devices that are difficult to clearly distinguish: electronic stimulators (electrostimulators) and physiotherapy devices. At low frequencies, the most significant is the specific, and not the thermal, effect of the current. Current treatment has the character of stimulating some effect, therefore, there is a kind of confusion between the concepts of "treatment device" and "electrostimulator". Electrostimulators are divided into stationary, wearable and implantable (implanted). A wearable and often implantable pacemaker is the EKSR-01 implantable radio frequency pacemaker. The receiver receives radio signals from an external transmitter. These signals are perceived inside the patient's body by the implantable part and are sent to the heart in the form of impulses through electrodes. The technical devices for electrical stimulation also include electrodes for supplying an electrical signal to a biological system. In many cases, electrical stimulation is carried out by plate electrodes, which are applied to the human body like electrodes for electrocardiography. A large group of medical devices - generators of electromagnetic oscillations and waves - operates in the range of ultrasonic, high, ultra-high frequencies and is called the general term "high-frequency electronic equipment". With UHF therapy, the part of the body to be heated is placed between disc-shaped metal electrodes covered with an insulator layer. When exposed to electromagnetic waves, the emitter of these waves is brought closer to the body. Other physiotherapy devices include: 1) apparatus "Iskra-1" - a high-frequency generator operating in a pulsed mode and used for local darsonvalization; 2) apparatus IKV-4 for inductothermy, operating at a frequency of 13,56 MHz; 3) portable apparatus for UHF-therapy - UHF-66; 4) apparatus for microwave therapy "Luch-58". Electrosurgery devices (high-frequency surgery) are also referred to as high-frequency electronic medical equipment. 52. Optics Optics is a branch of physics that deals with the laws of radiation, absorption and propagation of light. The law of rectilinear propagation of light. Light in a transparent homogeneous medium propagates in a straight line. A light beam is an infinitely thin beam of light propagating in a straight line, this is a line indicating the direction of propagation of light energy. Flat mirror. If the incident parallel rays remain parallel after reflection from a flat surface, then such a reflection is called a specular reflection, and the reflecting surface is a flat mirror. Laws of refraction of light. The incident and refracted rays and the normal to the interface between the media at the point of incidence lie in the same plane. sinα /sinβ = n, where α is the angle between the incident beam and the normal; β is the angle between the refracted beam and the normal. Absolute and relative refractive indices. Relative refractive index of light n = n1/ n2, where n1 and n2 - absolute refractive indices of two media, equal to the ratio of the speed of light in vacuum to the speed of light in the medium: n=c/v1, N2= c/v2 The course of rays in a prism. The law of light refraction makes it possible to calculate the course of rays in various optical devices, in particular in a triangular prism. total beam deflection d = a1 + b2 ×w, w=b1 + a2. If w is small, then: d = (n-1) h w, where n is the refractive index of the prism material. Phenomena of total internal reflection. If the beam goes from a medium that is optically denser (with a higher refractive index) to a medium that is optically less dense, then:  At a certain value of the angle of incidence a0, the refracted beam slides along the interface between the medium и β = n/2, then sinα0 = n1/ n2 53. Wave optics Wave properties of light. Light is electromagnetic waves in the frequency range 13 x 1014-8 x h 1014 Hz perceived by the human eye, i.e. the wavelength is 380 x 770 nm. Light has all the properties of electromagnetic waves: reflection, refraction, interference, diffraction, polarization. electromagnetic nature of light. Until the middle of the XNUMXth century, the question of the nature of light remained practically unresolved. The answer to it was found by J. Maxwell, who substantiated the general laws of the electromagnetic field. From the theory of J. Maxwell, the conclusion was that light is electromagnetic waves of a certain range. The speed of light in a homogeneous medium. The speed of light is determined by the electrical and magnetic properties of the medium. This is confirmed by the coincidence of the speed of light in vacuum with the electrodynamic constant:  (ε0 - electrical constant, m0 is the magnetic constant). The speed of light in a homogeneous medium, as is known, is determined by the refractive index of the medium n. The speed of light in a substance: υ=c/n where c is the speed of light in vacuum. From Maxwell's theory follows:  i.e., the refractive index and, consequently, the velocity in the medium are determined by the dielectric and magnetic permeability of the medium:  Interference is the addition of waves from two or more sources, when, as a result of addition, the principle of superposition of intensities is violated. The energy density in an electromagnetic wave is proportional to the square of the wave amplitude and determines the intensity of the light wave, which the human eye evaluates as illumination. Diffraction of light - the phenomenon of deviation of light from a rectilinear direction when passing at the edge of an obstacle. Wave diffraction is a set of phenomena observed during the passage of waves in inhomogeneous media, leading to the deviation of waves from the original rectilinear propagation. Huygens-Fresnel principle. Each point of the surface that the wave has reached at a given moment serves as a point source of secondary spherical waves, which are coherent: the wave surface at any time is not just an envelope of secondary waves, but the result of their interference. Fresnel zone method. For a point source in a homogeneous and isotropic medium, the wave surfaces have a spherical shape. Fresnel proposed to divide the wave surface into separate sections, called Fresnel zones, so that the oscillations coming from two adjacent zones to the observation point cancel each other out when added. 54. Light polarization Light is transverse electromagnetic waves. Polarization of light - ordering in the orientation of the vectors of strengths of the electric and magnetic fields of a light wave in a plane perpendicular to the light beam. Natural light (sunlight, incandescent lamps) is unpolarized, i.e., all directions of oscillation of the electric and magnetic vectors perpendicular to the light rays are equal. There are devices called polarizers, which have the ability to pass through themselves light rays with one direction of oscillation of the electric vector E, so that at the output of the polarizer, the light becomes plane (linearly) polarized. For an arbitrary angle a between the directions of the analyzer and the polarizer, the amplitude of the light oscillations emerging from the analyzer is equal to: Ea = En cos a, where En is the amplitude of the oscillations at the output of the polarizer. In an electromagnetic wave, the energy density (intensity) is proportional to the square of the oscillation amplitude E, i.e. In -E2n и Ia -E2a. Based on this, we get: Ia = In cos2 a. This relation is called the Malus law. The degree of light polarization (maximum and minimum) is equal to the intensity of partially polarized light transmitted by the analyzer. Polarization also occurs at the interface between two isotropic dielectrics. If the incident light is natural, then the refracted and reflected rays are partially polarized, and the predominant direction of oscillation of the electric vector of the refracted wave lies in the plane of incidence, and the reflected one is perpendicular to it. The degree of polarization depends on the refractive index of the second medium relative to the first: n21 = n2/n1 and on the angle of incidence a, moreover, at the angle of incidence ab, for which tg aБ = n21 (Brewster's law), the reflected beam is almost completely polarized, and the degree of polarization of the refracted beam is maximum. Birefringence is the ability of some substances, in particular crystals, to split an incident light beam into two beams - ordinary (O) and extraordinary (E), which propagate in different directions with different phase velocities and are polarized in mutually perpendicular planes. When light passes through some substances, called optically active, the plane of polarization of light rotates around the direction of the beam. The angle of rotation f of the plane of polarization is proportional to the path I traveled by light in an optically active substance: where a is a constant of rotation, depending on the properties f = ai, substances and wavelengths of light  55. Optical system of the eye and some of its features The human eye is a kind of optical device that occupies a special place in optics. For physicians, the eye is not only an organ capable of functional disorders and diseases, but also a source of information about some non-ocular diseases. Let us dwell briefly on the structure of the human eye. The eye itself is the eyeball, which has a not quite regular spherical shape. The walls of the eye consist of three concentrically arranged shells: outer, middle and inner. The outer protein shell - the sclera - in the front of the eye turns into a transparent convex cornea - the cornea. In terms of optical properties, the cornea is the most refractive part of the eye. It is like a window through which rays of light pass into the eye. The outer covering of the cornea passes into the conjunctiva attached to the eyelids. The choroid is adjacent to the sclera, the inner surface of which is lined with a layer of dark pigment cells that prevent internal diffuse scattering of light in the eye. In front of the eye, the choroid passes into the iris, in which there is a round hole - the pupil. Directly to the pupil on the inside of the eye adjoins the lens - a transparent and elastic body, similar to a biconvex lens. The lens diameter is 8-10 mm, the radius of curvature of the anterior surface is on average 10 mm, the posterior surface is 6 mm. The refractive index of the lens substance is slightly higher - 11,4. The structure of the lens resembles the layered structure of an onion, and the refractive index of the layers is not the same. Between the cornea and the lens is the anterior chamber of the eye, it is filled with moisture - a liquid similar in optical properties to water. The entire inner part of the eye from the lens to the back wall is occupied by a transparent gelatinous mass called the vitreous body. The refractive index of the vitreous body is the same as that of aqueous humor. The elements of the eye discussed above mainly relate to its light-conducting apparatus. The optic nerve enters the eyeball through the back wall; branching, it passes into the innermost layer of the eye - the retina, or retina, which is the light-perceiving (receptor) apparatus of the eye. The retina consists of several layers and is not the same in its thickness and sensitivity to light; it contains light-sensitive visual cells, the peripheral ends of which have a different shape. At the site of entry of the optic nerve is a blind spot that is not sensitive to light. The eye can be represented as a centered optical system formed by the cornea, the fluid of the anterior chamber and the lens (four refractive surfaces) and bounded in front by the air medium, behind by the vitreous body. The main optical axis passes through the geometric centers of the cornea, pupil and lens. In addition, the visual axis of the eye is also distinguished, which determines the direction of the greatest photosensitivity and passes through the centers of the lens and the macula. 56. Thermal radiation of bodies Of all the variety of electromagnetic radiation, visible or invisible to the human eye, one can be distinguished, which is inherent in all bodies. This is the radiation of heated bodies, or thermal radiation. During thermal radiation, energy is transferred from one body to another due to the emission and absorption of electromagnetic waves. Thermal radiation of heated bodies occurs at any temperature, therefore it is emitted by all bodies. Equilibrium (black) radiation is radiation that is in thermodynamic equilibrium with bodies having a certain temperature. A black body is a body that completely absorbs any electromagnetic radiation incident on its surface, regardless of the temperature of the body. For a completely black body, the absorption capacity (the ratio of the absorbed energy to the energy of the incident radiation) is equal to one. According to its characteristics, such radiation obeys Planck's law of radiation, which determines the emissivity and energy brightness of a black body. He put forward a hypothesis, from which it followed that the black body radiates and absorbs energy not continuously, but in certain portions, quanta. Kirchgaard's law establishes a quantitative relationship between radiation and absorption - at the same energy luminosity density to the monochromatic light absorption coefficient for any bodies, including black ones. Kirchgaard's law establishes that the ratio of the emissivity r of a body to its absorption capacity of a black body f(w, T) at the same values of temperature and frequency:  where w is the frequency of the wave. Stefan-Boltzmann's law: the energy integral luminosity R (T) of a blackbody is proportional to the fourth power of absolute temperature: R(T) = QT4. The numerical value of the constant Q, called the Stefan-Boltzmann constant, is:  Wip's displacement law - the length lm, which accounts for the maximum radiation energy of a completely black body, is inversely proportional to the absolute temperature T. The value of Wiep's constant is 2,898 × 10-3 μK. μK is Wip's constant. This law is also valid for gray bodies. The manifestation of Vipa's law is known from ordinary observations. At room temperature, the thermal radiation of bodies is mainly in the infrared region and is not perceived by the human eye. If the temperature rises, then the bodies begin to glow with a dark red light, and at a very high temperature - white with a bluish tint, the feeling of body heating increases. Author: Podkolzina V.A.
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