CONTENTS
PREFACE ....................................................................................................9
MODULUS 1. Mathematical processing of medical and biological data .12
LECTURE SECTION 1..............................................................................12
CHAPTER 1.1. Mathematical methods of computing medical
and biological information (principles of calculus)...........12
1.1.1. Elements of differential calculus ...........................................12
1.1.2. Elements of integral calculus ................................................22
1.1.3. Elements of theory of differential equations. ........................28
CHAPTER 1.2. Fundamentals of the theory of probability and mathematical statistics .............................................32
1.2.1. Fundamentals of the theory of probability............................32
1.2.2. Sampling method.
Finding of characteristics of distribution...............................48
1.2.3. Elements of theory of correlation.
Correlation and statistical dependence ................................50
PRACTICAL SECTION 1..........................................................................52
PRACTICAL WORK 1.1. Elements of differential calculation..........52
Practical work 1.2. Elements of integral calculation ..............66
Practical work 1.3. Elements of the theory of differential equations .....................75
Practical WORK 1.4. Elements of the probability theory...........80
Practical WORK 1.5. Elements of mathematical statistics........86
MODULUS 2. Principles of biological physics..........................................90
LECTURE SECTION 2..............................................................................90
CHAPTER 2.1. Essential principles of biomechanics...............................90
2.1.1. Mechanical properties of biological tissues..........................92
2.1.2. Deformation of biological tissue ...........................................98
CHAPTER 2.2. Fluidity of viscous fluids in biological systems ..............100
2.2.1. Fluid viscosity .....................................................................101
2.2.2. Blood viscosity....................................................................103
2.2.3. Viscoelastic properties of biological tissues.......................104
2.2.4. Basic equations of fluid flow...............................................107
2.2.5. Criteria of mechanical affinity of flowing fluids ...................115
2.2.6. Pulse waves ........................................................................117
CHAPTER 2.3. Mechanical oscillations ..................................................120
2.3.1. Harmonic oscillations and their principle parameters.........120
2.3.2. Damped oscillations and aperiodic motion ........................124
2.3.3. Forced oscillations ..............................................................127
2.3.4. Resonance phenomenon and auto-oscillations .................128
2.3.5. Addition of harmonic oscillations ........................................130
CHAPTER 2.4. Mechanical waves .........................................................133
2.4.1. Wave equation. Longitudinal and transverse waves ..........134
2.4.2. Wave energy flow. Umov vector .........................................135
CHAPTER 2.5. Acoustics. Elements of hearing physics.Fundamentals of audiometry ................136
2.5.1. Sound nature, its main characteristics  (objective and subjective) .........................137
2.5.2. Weber-Fechner law .............................................................141
2.5.3. Ultrasound ..........................................................................144
2.5.4. Infrasound ...........................................................................146
CHAPTER 2.6. Structure and properties of biologic membranes ..........146
2.6.1. Passive transport of uncharged molecules.........................152
2.6.2. Passive transport of ions ....................................................155
2.6.3. Active transport ...................................................................159
CHAPTER 2.7. Biological potentials .......................................................161
2.7.1. Nernst equilibrium membrane potential ..............................163
2.7.2. Diffusion potential ...............................................................164
2.7.3. Donnan’s potential. Donnan’s equilibrium ..........................166
2.7.4. Stationary potential of Goldman-Hodgkin-Katz..................169
2.7.5. Action potential. Mechanism of generation  and propagation of nerve impulse ..................172
CHAPTER 2.8. Elements of dental material science ..............................178
PRACTICAL SECTION 2 ........................................................................191
LABORATORY WORK 2.1. Measurement of hearing threshold by audiometric method .......................191
LABORATORY WORK 2.2. Study of elastic properties  of biological tissues ...............................198
LABORATORY WORK 2.3. Determination of dependence  of liquid's surface tension coefficient on  temperature and surface-active substances ...204
LABORATORY WORK 2.4. Measurement of coefficient  of viscosity ...........210
LABORATORY WORK 2.5. Measurement of concentration  potential using compensation method ..........216
COMPUTER SECTION 2 ........................................................................222
COMPUTER PROGRAM 1. Haemodynamics ...............................222
COMPUTER PROGRAM 2. Structure and transport  properties of membranes ................229
COMPUTER PROGRAM 3. Rest and action electrical  potentials of membranes ..................244
MODULUS 3. Principles of medical physics ..........................................258
LECTURE SECTION 3 ............................................................................259
CHAPTER 3.1. Electrostatics .................................................................259
3.1.1. Major characteristics of electric field ..................................259
3.1.2. Electric dipole .....................................................................262
3.1.3. Dielectrics, dielectric polarization .......................................264
3.1.4. Dielectric properties of biological tissues ...........................268
3.1.5. Piezoelectric effect ..............................................................270
CHAPTER 3.2. Continuous (direct) current. Conductivity of biological tissue. Alternating current
and impedance of biological tissues .............................271
3.2.1. Characteristics of electric current .......................................271
3.2.2. Conductivity of biological tissues and fluids.......................272
3.2.3. Action of electric current on living organism ......................275
3.2.4. Equation of electric oscillations ..........................................277
3.2.5. Forced electric oscillations, alternating current ..................279
3.2.6. Total resistance of alternating current circuit  (impedance). Ohm’s law for alternating current circuit ..282
3.2.7. Impedance of biological tissues .........................................284
3.2.8. Electromagnetic waves. Bias current .................................287
3.2.9. Maxwell’s equations ........................................................289
3.2.10. Plane electromagnetic waves. Umov-Poynting vector ....291
3.2.11. Electromagnetic spectrum ...............................................293
CHAPTER 3.3. Magnetic field ................................................................296
3.3.1. Magnetic field in vacuum and its characteristics ................296
3.3.2. Biot-Savart-Laplace’s law ...................................................298
3.3.3. Action of magnetic field on movable electric charge.  Ampere force, Lorentz force ...........299
3.3.4. Magnetic properties of substances ....................................302
3.3.5. Magnetic properties of biological tissues,  physical bases of magnetobiology. ...................306
CHAPTER 3.4. Medical electronic equipment ........................................308
3.4.1. General information of medical  electronic equipment (MEE) ............................308
3.4.2. Classification of medical electronic equipment ..................309
3.4.3. MEE performance specification ..........................................310
CHAPTER 3.5. Physycal principles of optical microscopy, refractometry and polarimetry ............313
3.5.1. Geometrical optics ...........................................................313
3.5.2. Ideal centered optical system ..........................................313
3.5.3. Optical microscopy ..........................................................316
3.5.4. Light polarization..............................................................319
3.5.5. Light polarization at reflection and refraction ..................320
3.5.6. Polarization at double refraction in crystal .......................321
3.5.7. Light polarization at passing through an  absorbing anisotropic substance .........323
3.5.8. Plane-of-polarization rotation by an optically  active substance .......324
3.5.9. Interaction of light with substance. Light absorption .......326
3.5.10. Light scattering ................................................................329
CHAPTER 3.6. Physical foundations of thermography, laws of heat radiation ........331
3.6.1. Heat (temperature) radiation ...............................................331
3.6.2. Kirchhoff’s law of spectral radiation ...................................333
3.6.3. Planck’s radiation law .........................................................334
3.6.4. Stefan-Boltzmann’s law ......................................................335
3.6.5. Wien displacement law .......................................................336
3.6.6. Infrared radiation .................................................................338
3.6.7. Ultraviolet radiation .............................................................339
CHAPTER 3.7. Notations of quantum mechanics ..................................339
3.7.1. The place of quantum mechanics in scientific  system of body motion .........339
3.7.2. De Broglie’s hypothesis ......................................................341
3.7.3. Heisenberg’s uncertainty relation .......................................344
3.7.4. Fundamental equation of quantum mechanics – Schrödinger equation ...............345
3.7.5. Schrödinger equation for hydrogen atom ...........................347
CHAPTER 3.8. Energy radiation and absorption by atoms and molecules ..............349
3.8.1. Atomic spectrum ..............................................................349
3.8.2. Molecular spectra ............................................................351
3.8.3. Luminescence ..................................................................355
3.8.4. Luminescence types ........................................................355
3.8.5. Photoluminescence. Stokes law ......................................356
3.8.6. Luminescence mechanisms ............................................358
3.8.7. Induced radiation .............................................................360
3.8.8. Equilibrium and inverse dependence ...............................360
3.8.9. Structure and principle of laser’s operation .....................362
3.8.10. Electronic paramagnetic resonance, nuclear magnetic  resonance and their medico-biological application .363
3.8.11. Method of electron paramagnetic resonance ..................364
3.8.12. Method of nuclear magnetic resonance ..........................368
CHAPTER 3.9. The nature and generation of X-ray beams ...................372
3.9.1. Deceleration X-ray radiation ............................................374
3.9.2. Characteristic X-ray radiation, its nature .........................375
3.9.3. Radioactivity, its properties .............................................377
3.9.4. Principle law of radioactive decay,  half-life period, activity .............380
3.9.5. The rules of shift, spectra specific feature  at the time of radioactive decay ...............384
3.9.6. Exposure dose, its rate, units ..........................................387
3.9.7. Absorbed dose, its rate, units ..........................................389
3.9.8. Equivalent dose, its rate, units .........................................391
3.9.9. Dosimeters .......................................................................393
3.9.10. Primary physical mechanisms of interaction  of X-ray radiation with substance ...........395
3.9.11. Primary mechanisms of radioactive radiation  and particle flux effect on substance ............399
PRACTICAL SECTION 3 ........................................................................403
LABORATORY WORK 3.1. Operation of electrocardiograph .......403
LABORATORY WORK 3.2. Operation of rheograph .....................411
LABORATORY WORK 3.3. Study of electrical impedance  of biological tissues ...............419
PRACTICAL LESSON. Interaction of electromagnetic field with biological tissues ...............425
LABORATORY WORK 3.4. Physiotherapeutic  equipment operation ..............435
LABORATORY WORK 3.5. Study of microscope  and measurement of microobjects .................446
LABORATORY WORK 3.6. Study of solution  concentration by refractometric method ..........450
LABORATORY WORK 3.7. Study of solution  concentration by polarimetric method ........454
LABORATORY WORK 3.8. Study of laser operation ....................460
LABORATORY WORK 3.9. Measurement of linear damping coefficient of gamma radiation ........464
INDEX OF SUBJECTS ...........................................................................471
INDEX OF NAMES .................................................................................474