Intermediate Physics for Medicine and Biology Book

Mechanics     1
Distances and Sizes     1
Forces and Translational Equilibrium     3
Rotational Equilibrium     4
Vector Product     5
Force in the Achilles Tendon     6
Forces on the Hip     7
The Use of a Cane     9
Work     10
Stress and Strain     12
Shear     13
Hydrostatics     13
Buoyancy     14
Compressibility     15
Viscosity     15
Viscous Flow in a Tube     15
Pressure-Volume Work     18
The Human Circulatory System     19
Turbulent Flow and the Reynolds Number     21
Symbols Used     23
Problems     24
References     29
Exponential Growth and Decay     31
Exponential Growth     31
Exponential Decay     33
Semilog Paper     34
Variable Rates     35
Clearance     36
Multiple Decay Paths     37
Decay Plus Input at a Constant Rate     38
Decay with Multiple Half-Lives and Fitting Exponentials     38
The Logistic Equation     39
Log-log Plots, Power Laws, and Scaling     39
Log-log Plots and Power Laws     39
Food Consumption, Basal Metabolic Rate, and Scaling     40
Symbols Used     42
Problems     42
References     47
Systems of Many Particles     49
Gas Molecules in a Box     50
Microstates and Macrostates     51
The Energy of a System: The First Law of Thermodynamics     53
Ensembles and the Basic Postulates     54
Thermal Equilibrium     56
Entropy     58
The Boltzmann Factor     58
The Nernst Equation     59
The Pressure Variation in the Atmosphere     60
Equipartition of Energy and Brownian Motion     60
Heat Capacity     61
Equilibrium When Particles Can Be Exchanged: The Chemical Potential     61
Concentration Dependence of the Chemical Potential     62
Systems That Can Exchange Volume     63
Extensive Variables and Generalized Forces     64
The General Thermodynamic Relationship     64
The Gibbs Free Energy     65
Gibbs Free Energy     65
An Example: Chemical Reactions      66
The Chemical Potential of a Solution     67
Transformation of Randomness to Order     69
Symbols Used     70
Problems     71
References     79
Transport in an Infinite Medium     81
Flux, Fluence, and Continuity     81
Definitions     81
The Continuity Equation in One Dimension     82
The Continuity Equation in Three Dimensions     82
The Integral Form of the Continuity Equation     83
The Differential Form of the Continuity Equation     84
The Continuity Equation with a Chemical Reaction     85
Drift or Solvent Drag     85
Brownian Motion     85
Motion in a Gas: Mean Free Path and Collision Time     85
Motion in a Liquid     86
Diffusion: Fick's First Law     87
The Einstein Relationship Between Diffusion and Viscosity     89
Fick's Second Law of Diffusion     91
Time-Independent Solutions     92
Example: Steady-State Diffusion to a Spherical Cell and End Effects     94
Diffusion Through a Collection of Pores, Corrected     95
Diffusion from a Sphere, Corrected     95
How Many Pores Are Needed?      96
Other Applications of the Model     96
Example: A Spherical Cell Producing a Substance     96
Drift and Diffusion in One Dimension     98
A General Solution for the Particle Concentration as a Function of Time     99
Diffusion as a Random Walk     100
Symbols Used     102
Problems     102
References     108
Transport Through Neutral Membranes     111
Membranes     111
Osmotic Pressure in an Ideal Gas     112
Osmotic Pressure in a Liquid     114
Some Clinical Examples     115
Edema Due to Heart Failure     116
Nephrotic Syndrome, Liver Disease, and Ascites     116
Edema of Inflammatory Reaction     116
Headaches in Renal Dialysis     116
Osmotic Diuresis     116
Osmotic Fragility of Red Cells     117
Volume Transport Through a Membrane     117
Solute Transport Through a Membrane     119
Example: The Artificial Kidney     120
Countercurrent Transport     121
A Continuum Model for Volume and Solute Transport in a Pore     122
Volume Transport     123
Solute Transport      124
Summary     127
Reflection Coefficient     127
The Effect of Pore Walls on Diffusion     128
Net Force on the Membrane     128
Symbols Used     129
Problems     129
References     133
Impulses in Nerve and Muscle Cells     135
Physiology of Nerve and Muscle Cells     135
Coulomb's Law, Superposition, and the Electric Field     137
Gauss's Law     138
Potential Difference     141
Conductors     142
Capacitance     143
Dielectrics     143
Current and Ohm's Law     145
The Application of Ohm's Law to Simple Circuits     146
Charge Distribution in the Resting Nerve Cell     148
The Cable Model for an Axon     149
Electrotonus or Passive Spread     153
The Hodgkin-Huxley Model for Membrane Current     154
Voltage Clamp Experiments     154
Potassium Conductance     156
Sodium Conductance     157
Leakage Current     158
Voltage Changes in a Space-Clamped Axon     158
Propagating Nerve Impulse     159
Myelinated Fibers and Saltatory Conduction      160
Membrane Capacitance     163
Rhythmic Electrical Activity     164
The Relationship Between Capacitance, Resistance, and Diffusion     165
Capacitance and Resistance     165
Capacitance and Diffusion     165
Symbols Used     167
Problems     168
References     175
The Exterior Potential and the Electrocardiogram     177
The Potential Outside a Long Cylindrical Axon     177
The Exterior Potential is Small     179
The Potential Far From the Axon     180
The Exterior Potential for an Arbitrary Pulse     181
Electrical Properties of the Heart     184
The Current-Dipole Vector of the Heart as a Function of Time     186
The Electrocardiographic Leads     186
Some Electrocardiograms     189
Refinements to the Model     189
The Axon Has a Finite Radius     190
Nonuniform Exterior Conductivity     191
Anisotropic Conductivity: The Bidomain Model     191
Electrical Stimulation     192
The Electroencephalogram     196
Symbols Used     196
Problems     197
References      201
Biomagnetism     203
The Magnetic Force on a Moving Charge     203
The Magnetic Field of a Moving Charge or a Current     205
The Divergence of the Magnetic Field Is Zero     205
Ampere's Circuital Law     205
The Biot-Savart Law     206
The Displacement Current     207
The Magnetic Field Around an Axon     208
The Magnetocardiogram     209
The Magnetoencephalogram     211
Electromagnetic Induction     213
Magnetic Stimulation     214
Magnetic Materials and Biological Systems     214
Magnetic Materials     215
Measuring Magnetic Properties in People     216
Magnetic Orientation     217
Detection of Weak Magnetic Fields     218
Symbols Used     219
Problems     220
References     224
Electricity and Magnetism at the Cellular Level     227
Donnan Equilibrium     227
Potential Change at an Interface: The Gouy-Chapman Model     229
Ions in Solution: The Debye-Huckel Model     231
Saturation of the Dielectric     233
Ion Movement in Solution: The Nernst-Planck Equation     234
Zero Total Current in a Constant-Field Membrane: The Goldman Equations     236
Membrane Channels     238
Noise     242
Shot Noise     242
Johnson Noise     242
Sensory Transducers     243
Possible Effects of Weak External Electric and Magnetic Fields     244
Introduction     244
Effects of Strong Fields     244
Fields in Homes are Weak     244
Epidemiological Studies     245
Laboratory Studies     245
Reviews and Panel Reports     245
Electric Fields in the Body     246
Electric Fields in a Spherical Cell     246
Electrical Interactions and Noise     247
Magnetic Interactions and Noise     247
Symbols Used     248
Problems     249
References     253
Feedback and Control     255
Steady-State Relationships Among Variables     256
Determining the Operating Point     257
Regulation of a Variable and Open-Loop Gain     257
Approach to Equilibrium without Feedback     259
Approach to Equilibrium in a Feedback Loop with One Time Constant     259
A Feedback Loop with Two Time Constants      262
Models Using Nonlinear Differential Equations     263
Describing a Nonlinear System     264
An Example of Phase Resetting: The Radial Isochron Clock     265
Stopping an Oscillator     268
Difference Equations and Chaotic Behavior     268
The Logistic Map: Period Doubling and Deterministic Chaos     269
The Bifurcation Diagram     270
Quasiperiodicity     271
A Feedback Loop with a Time Constant and a Fixed Delay     272
Negative Feedback Loops: A Summary     273
Additional Examples     274
Cheyne-Stokes Respiration     274
Hot Tubs and Heat Stroke     274
Pupil Size     274
Oscillating White-Blood-Cell Counts     275
Waves in Excitable Media     275
Period Doubling and Chaos in Heart Cells     276
Symbols Used     277
Problems     277
References     283
The Method of Least Squares and Signal Analysis     285
The Method of Least Squares and Polynomial Regression     285
The Simplest Example     285
A Linear Fit     286
A Polynomial Fit     287
Variable Weighting      288
Nonlinear Least Squares     288
The Presence of Many Frequencies in a Periodic Function     289
Fourier Series for Discrete Data     290
Introducing the Fourier Series     290
Equally Spaced Data Points Simplify the Equations     290
The Standard Form for the Discrete Fourier Transform     291
Complex Exponential Notation     291
Example: The Square Wave     292
Example: When the Sampling Time Is Not a Multiple of the Period of the Signal     292
Example: Spontaneous Births     293
Example: Photosynthesis in Plants     294
Pitfalls of Discrete Sampling: Aliasing     294
Fast Fourier Transform     295
Fourier Series for a Periodic Function     295
The Power Spectrum     296
Correlation Functions     298
Cross-Correlation of a Pulse     298
Cross-Correlation of a Nonpulse Signal     299
Cross-Correlation Example     299
Autocorrelation     299
Autocorrelation Examples     299
The Autocorrelation Function and the Power Spectrum     300
Nonperiodic Signals and Fourier Integrals     301
Introduce Negative Frequencies and Make the Coefficients Half as Large     301
Make the Period Infinite     302
Complex Notation     303
Example: The Exponential Pulse     303
The Delta Function     304
The Energy Spectrum of a Pulse and Parseval's Theorem     304
Parseval's Theorem     305
Example: The Exponential Pulse     305
The Autocorrelation of a Pulse and Its Relation to the Energy Spectrum     305
Noise     306
Correlation Functions and Noisy Signals     308
Detecting Signals in Noise     308
Signal Averaging     308
Power Spectral Density     309
Units     309
Frequency Response of a Linear System     310
Example of Calculating the Frequency Response     311
The Decibel     311
Example: Impulse Response     312
The Frequency Spectrum of Noise     312
Johnson Noise     312
Shot Noise     315
1/f Noise     315
Testing Data for Chaotic Behavior     316
Embedding     316
Surrogate Data     316
Stochastic Resonance     317
Threshold Detection     317
Feynman's Ratchet      318
Symbols Used     319
Problems     319
References     323
Images     325
The Convolution Integral and its Fourier Transform     325
One Dimension     325
Two Dimensions     326
The Relationship Between the Object and the Image     327
Point-Spread Function     327
Optical-, Modulation-, and Phase-Transfer Functions     328
Line- and Edge-Spread Functions     329
Spatial Frequencies in an Image     329
Summary     331
Two-Dimensional Image Reconstruction from Projections by Fourier Transform     331
Reconstruction from Projections by Filtered Back Projection     332
An Example of Filtered Back Projection     335
Symbols Used     337
Problems     337
References     340
Sound and Ultrasound     343
The Wave Equation     343
Plane Waves in an Elastic Rod     343
Plane Waves in a Fluid     344
Properties of the Wave Equation     345
Acoustic Impedance     346
Relationships Between Pressure, Displacement and Velocity in a Plane Wave     346
Reflection and Transmission of Sound at a Boundary     346
Comparing Intensities: Decibels     347
The Decibel     347
Hearing Response     347
The Ear and Hearing     348
Attenuation     349
Medical Uses of Ultrasound     350
Ultrasound Transducers     350
Pulse Echo Techniques     352
The Doppler Effect     353
Symbols Used     354
Problems     354
References     357
Atoms and Light     359
The Nature of Light: Waves versus Photons     359
Atomic Energy Levels and Atomic Spectra     361
Molecular Energy Levels     362
Scattering and Absorption of Radiation; Cross Section     364
The Diffusion Approximation to Photon Transport     367
General Theory     367
Continuous Measurements     368
Pulsed Measurements     368
Refinements to the Model     369
Biological Applications of Infrared Scattering     369
Near Infrared (NIR)     369
Optical Coherence Tomography (OCT)     370
Raman Spectroscopy     371
Far Infrared or Terahertz Radiation     372
Thermal Radiation     372
Infrared Radiation from the Body     375
Atherosclerotic Coronary Heart Disease     376
Blue and Ultraviolet Radiation     377
Treatment of Neonatal Jaundice     377
The Ultraviolet Spectrum     377
Response of the Skin to Ultraviolet Light     378
Ultraviolet Light Causes Skin Cancer     380
Protection from Ultraviolet Light     380
Ultraviolet Light Damages the Eye     381
Ultraviolet Light Synthesizes Vitamin D     381
Ultraviolet Light Therapy     381
Heating Tissue with Light     381
Radiometry and Photometry     383
Radiometric Definitions     383
Photometric Definitions     387
Actinometric Definitions     388
The Eye     388
Quantum Effects in Dark-Adapted Vision     390
Symbols Used     392
Problems     393
References     397
Interaction of Photons and Charged Particles with Matter     401
Atomic Energy Levels and X-ray Absorption     401
Photon Interactions     403
Photoelectric Effect     403
Compton and Incoherent Scattering      403
Coherent Scattering     403
Inelastic Scattering     403
Pair Production     403
Energy Dependence     404
The Photoelectric Effect     404
Compton Scattering     405
Kinematics     405
Cross Section: Klein-Nishina Formula     406
Incoherent Scattering     406
Energy Transferred to the Electron     407
Coherent Scattering     407
Pair Production     407
The Photon Attenuation Coefficient     408
Compounds and Mixtures     410
Deexcitation of Atoms     410
Energy Transfer from Photons to Electrons     412
Charged-Particle Stopping Power     414
Interaction with Target Electrons     418
Scattering from the Nucleus     421
Stopping of Electrons     422
Compounds     422
Linear Energy Transfer and Restricted Collision Stopping Power     422
Range, Straggling, and Radiation Yield     423
Track Structure     424
Energy Transferred and Energy Imparted; Kerma and Absorbed Dose     425
An Example     425
Energy Transferred and Kerma     427
Energy Imparted and Absorbed Dose     427
Net Energy Transferred, Collision Kerma, and Radiative Kerma     428
Charged-Particle Equilibrium     428
Radiation Equilibrium     428
Charged-particle Equilibrium     428
Buildup     429
Symbols Used     430
Problems     431
References     434
Medical Use of X Rays     437
Production of X Rays     437
Characteristic X Rays     437
Bremsstrahlung     438
Quantities to Describe Radiation Interactions     439
Radiation Chemical Yield     439
Mean Energy per Ion Pair     439
Exposure     440
Detectors     440
Film and Screens     440
Scintillation Detectors     442
Gas Detectors     444
Semiconductor Detectors     445
Thermoluminescent Dosimeters     445
Chemical Dosimetry     445
Digital Detectors     446
The Diagnostic Radiograph     446
X-ray Tube and Filter     446
Collimation     447
Attenuation in the Patient: Contrast Material     447
Antiscatter Grid      450
Film-Screen Combination     450
Computed and Direct Radiography     450
Image Quality     450
Angiography and Digital Subtraction Angiography     453
Mammography     453
Fluoroscopy     454
Computed Tomography