1.3 Forces and Translational Equilibrium
1.4 Rotational Equilibrium
1.6 Force in the Achilles Tendon
1.17 Viscous Flow in a Tube
1.18 Pressure
Volume Work
1.19 The Human Circulatory System
1.20 Turbulent Flow and the Reynolds Number
2 Exponential Growth and Decay
2.8 Decay Plus Input at a Constant Rate
2.9 Decay With Multiple Half-Lives and Fitting Exponentials
2.10 The Logistic Equation
2.11 Log
log Plots, Power Laws, and Scaling
2.11.1 Log
log Plots and Power Laws
2.11.2 Food Consumption, Basal Metabolic Rate, and Scaling
3 Systems of Many Particles
3.1 Gas Molecules in a Box
3.2 Microstates and Macrostates
3.3 The Energy of a System: The First Law of Thermodynamics
3.4 Ensembles and the Basic Postulates
3.10 Equipartition of Energy and Brownian Motion
3.9 The Pressure Variation in the Atmosphere
3.12 Equilibrium When Particles Can Be Exchanged: the Chemical Potential
3.13 Concentration Dependence of the Chemical Potential
3.14 Systems That Can Exchange Volume
3.15 Extensive Variables andGeneralized Forces
3.16 The General Thermodynamic Relationship
3.17 The Gibbs Free Energy
3.17.2 An Example: Chemical Reactions
3.18 The Chemical Potential of a Solution
3.19 Transformation of Randomness to Order
4 Transport in an Infinite Medium
4.1 Flux, Fluence, and Continuity
4.1.1 The Continuity Equation in One Dimension
4.1.2 The Continuity Equation in Three Dimensions
4.1.3 The Integral Form of the Continuity Equation
4.1.4 The Differential Form of the Continuity Equation
4.1.5 The Continuity Equation with a Chemical Reaction
4.2 Drift or Solvent Drag
4.4 Motion in a Gas: Mean Free Path and Collision Time
4.6 Diffusion: Fick's First Law
4.7 The Einstein Relationship Between Diffusion and Viscosity
4.8 Fick's Second Law of Diffusion
4.9 Time-Independent Solutions
4.10 Example: Steady-State Diffusion to a Spherical Cell and End Effects
4.10.1 Diffusion Through a Collection of Pores, Corrected
4.10.2 Diffusion from a Sphere, Corrected
4.10.3 How Many Pores Are Needed?
4.10.4 Other Applications of the Model
4.11 Example: A Spherical Cell Producing a Substance
4.12 Drift and Diffusion in One Dimension
4.13 A General Solution for the Particle Concentration as a Function of Time
4.14 Diffusion as a Random Walk
5 Transport Through Neutral Membranes
5.2 Osmotic Pressure in an Ideal Gas
5.3 Osmotic Pressure in a Liquid
5.4 Some Clinical Examples
5.4.1 Edema Due to Heart Failure
5.4.2 Nephrotic Syndrome, Liver Disease,and Ascites
5.4.3 Edema of Inflammatory Reaction
5.4.4 Headaches in Renal Dialysis
5.4.6 Osmotic Fragility of Red Cells
5.5 Volume Transport Through a Membrane
5.6 Solute Transport Through a Membrane
5.7 Example: The Artificial Kidney
5.8 Countercurrent Transport
5.9 A Continuum Model for Volume and Solute Transport in a Pore
5.9.4 Reflection Coefficient
5.9.5 The Effect of Pore Walls on Diffusion
5.9.6 Net Force on the Membrane
6 Impulses in Nerve and Muscle Cells
6.1 Physiology of Nerve and Muscle Cells
6.2 Coulomb's Law, Superposition, and the Electric Field
6.8 Current and Ohm's Law
6.9 The Application of Ohm's Law to Simple Circuits
6.10 Charge Distribution in the RestingNerve Cell
6.11 The Cable Model for an Axon
6.12 Electrotonus or Passive Spread
6.13 The Hodgkin
Huxley Model for Membrane Current
6.13.1 Voltage Clamp Experiments
6.13.2 Potassium Conductance
6.13.3 Sodium Conductance
6.14 Voltage Changes in a Space-Clamped Axon
6.15 Propagating Nerve Impulse
6.16 Myelinated Fibers and Saltatory Conduction
6.17 Membrane Capacitance
6.18 Rhythmic Electrical Activity
6.19 The Relationship Between Capacitance, Resistance, and Diffusion
6.19.1 Capacitance and Resistance
6.19.2 Capacitance and Diffusion
7 The Exterior Potential and the Electrocardiogram
7.1 The Potential Outside a Long Cylindrical Axon
7.2 The Exterior Potential is Small
7.3 The Potential Far from the Axon
7.4 The Exterior Potential for an Arbitrary Pulse
7.5 Electrical Properties of the Heart
7.6 The Current-Dipole Vector of the Heart as a Function of Time
7.7 The Electrocardiographic Leads
7.8 Some Electrocardiograms
7.9 Refinements to the Model
7.9.1 The Fiber Has a Finite Radius
7.9.2 Nonuniform Exterior Conductivity
7.9.3 Anisotropic Conductivity: The Bidomain Model
7.10 Electrical Stimulation
7.11 The Electroencephalogram
8.1 The Magnetic Force on a Moving Charge
8.2 The Magnetic Field of a Moving Charge or a Current
8.2.1 The Divergence of the Magnetic Field is Zero
8.2.2 Ampere's Circuital Law
8.2.3 The Biot
Savart Law
8.2.4 The Displacement Current
8.3 The Magnetic Field Around an Axon
8.4 The Magnetocardiogram
8.5 The Magnetoencephalogram
8.6 Electromagnetic Induction
8.8 Magnetic Materials and Biological Systems
8.8.2 Measuring Magnetic Properties in People
8.8.3 Magnetic Orientation
8.8.4 Magnetic Nanoparticles
8.9 Detection of Weak Magnetic Fields
9 Electricity and Magnetism at the Cellular Level
9.2 Potential Change at an Interface: The Gouy
Chapman Model
9.3 Ions in Solution: The Debye
Hỹckel Model
9.4 Saturation of the Dielectric
9.5 Ion Movement in Solution: The Nernst
Planck Equation
9.6 Zero Total Current in a Constant-Field Membrane: The Goldman Equations
9.10 Possible Effects of Weak External Electric and Magnetic Fields
9.10.2 Power Frequency (50
60 Hz) Fields
9.10.2.1 Fields in Homes are Weak
9.10.2.2 Epidemiological Studies
9.10.2.3 Laboratory Studies
9.10.2.4 Reviews and Panel Reports
9.10.2.5 Electric Fields in the Body
9.10.2.6 Electric Fields in a Spherical Cell
9.10.3 Electrical Interactions and Noise
9.10.4 Magnetic Interactions and Noise
9.10.5 Microwaves, Mobile Phones, and Wi-Fi
10.1 Steady-State Relationships Among Variables
10.2 Determining the Operating Point
10.3 Regulation of a Variable and Open-Loop Gain
10.4 Approach to Equilibrium without Feedback
10.5 Approach to Equilibrium in a Feedback Loop with One Time Constant
10.6 A Feedback Loop with Two Time Constants
10.7 Proportional, Derivative, and Integral Control
10.8 Models Using Nonlinear Differential Equations
10.8.1 Describing a Nonlinear System
10.8.2 An Example of Phase Resetting: The Radial Isochron Clock
10.8.3 Stopping an Oscillator
10.9 Difference Equations and Chaotic Behavior
10.9.1 The Logistic Map: Period Doubling and Deterministic Chaos
10.9.2 The Bifurcation Diagram
10.10 A Feedback Loop with a Time Constant and a Fixed Delay
10.11 Negative Feedback Loops: A Summary
10.12 Additional Examples
10.12.1 Cheyne
Stokes Respiration
10.12.2 Hot Tubs and Heat Stroke
10.12.4 Oscillating White-Blood-Cell Counts
10.12.5 Waves in Excitable Media
10.12.6 Period Doubling and Chaos in Heart Cells
11 The Method of Least Squares and Signal Analysis
11.1 The Method of Least Squares and Polynomial Regression
11.1.1 The Simplest Example
11.1.4 Variable Weighting
11.2 Nonlinear Least Squares
11.3 The Presence of Many Frequencies in a Periodic Function
11.4 Fourier Series for Discrete Data
11.4.1 Determining the Parameters
11.4.2 Equally Spaced Data Points Simplify the Equations
11.4.3 The Standard Form for the Discrete Fourier Transform
11.4.4 Complex Exponential Notation
11.4.5 Example: The Square Wave
11.4.6 Example: When the Sampling Time is not a Multiple of the Period of the Signal
11.4.7 Example: Spontaneous Births
11.4.8 Example: Photosynthesis in Plants
11.4.9 Pitfalls of Discrete Sampling: Aliasing
11.4.10 Fast Fourier Transform
11.5 Fourier Series for a Periodic Function
11.7 Correlation Functions
11.7.1 Cross-Correlation of a Pulse
11.7.2 Cross-Correlation of a Nonpulse Signal
11.7.3 Cross-Correlation Example
11.7.5 Autocorrelation Examples
11.8 The Autocorrelation Function and the Power Spectrum
11.9 Nonperiodic Signals and Fourier Integrals
11.9.1 Introduce Negative Frequencies and Make the Coefficients Half as Large
11.9.2 Make the Period Infinite
11.9.4 Example: The Exponential Pulse
11.11 The Energy Spectrum of a Pulse and Parseval's Theorem
11.11.1 Parseval's Theorem
11.11.2 Example: The Exponential Pulse
11.12 The Autocorrelation of a Pulse and its Relation to the Energy Spectrum
11.14 Correlation Functions and Noisy Signals
11.14.1 Detecting Signals in Noise
11.14.3 Power Spectral Density
11.15 Frequency Response of a Linear System
11.15.1 Example of Calculating the Frequency Response
11.15.3 Example: Impulse Response
11.16 The Frequency Spectrum of Noise
11.17 Testing Data for Chaotic Behavior
11.18 Stochastic Resonance
11.18.1 Threshold Detection
11.18.2 Feynman's Ratchet
12.1 The Convolution Integral and Its Fourier Transform
12.2 The Relationship Between the Object and the Image
12.2.1 Point Spread Function
12.2.2 Optical, Modulation, and Phase Transfer Functions
12.2.3 Line and Edge Spread Functions
12.3 Spatial Frequencies in an Image
12.4 Two-Dimensional Image Reconstruction from Projections by Fourier Transform
12.5 Reconstruction from Projections by Filtered Back Projection
12.6 An Example of Filtered Back Projection
13.1.1 Plane Waves in an Elastic Rod
13.1.2 Plane Waves in a Fluid
13.2 Properties of the Wave Equation
13.3.1 Relationships Between Pressure, Displacement and Velocity in a Plane Wave
13.3.2 Reflection and Transmission of Sound at a Boundary
13.4 Comparing Intensities: Decibels
13.4.2 Measuring Hearing Response
13.7 Diagnostic Uses of Ultrasound
13.7.1 Ultrasound Transducers
13.7.2 Pulse Echo Imaging
13.7.3 The Doppler Effect
13.8 Therapeutic Uses of Ultrasound
14.1 The Nature of Light: Waves and Photons
14.2 Electron Waves and Particles: The Electron Microscope
14.3 Atomic Energy Levels and Atomic Spectra
14.4 Molecular Energy Levels
14.5 Scattering and Absorption of Radiation; Cross Section
14.6 The Diffusion Approximation to Photon Transport
14.6.1 Diffusion Approximation
14.6.2 Continuous Measurements
14.6.3 Pulsed Measurements
14.6.4 Refinements to the Model
14.7 Biological Applications of Infrared Scattering
14.7.1 Near Infrared (NIR)
14.7.2 Optical Coherence Tomography (OCT)
14.7.3 Raman Spectroscopy
14.7.4 Far Infrared or Terahertz Radiation
14.9 Infrared Radiation from the Body
14.9.1 Atherosclerotic Coronary Heart Disease
14.9.2 Photodynamic Therapy
14.10 Blue and Ultraviolet Radiation
14.10.1 Treatment of Neonatal Jaundice
14.10.2 The Ultraviolet Spectrum
14.10.3 Response of the Skin to Ultraviolet Light
14.10.4 Ultraviolet Light Causes Skin Cancer
14.10.5 Protection From Ultraviolet Light
14.10.6 Ultraviolet Light Damages the Eye
14.10.7 Ultraviolet Light Therapy
14.11 Heating Tissue with Light
14.12 Radiometry and Photometry
14.12.1 Radiometric Definitions
14.12.1.1 Radiant Energy and Power
14.12.1.2 Point Source: Radiant Intensity
14.12.1.3 Extended Source: Radiance
14.12.1.4 Energy Striking a Surface: Irradiance
14.12.1.5 Plane-Wave Relationships
14.12.1.6 Isotropic Radiation: Lambert's Law
14.12.2 Photometric Definitions
14.12.3 Actinometric Definitions
14.14 Quantum Effects in Dark-Adapted Vision
15 Interaction of Photons and Charged Particles with Matter
15.1 Atomic Energy Levels and X-ray Absorption
15.2.1 Photoelectric Effect
15.2.2 Compton and Incoherent Scattering
15.2.3 Coherent Scattering
15.2.4 Inelastic Scattering
15.3 The Photoelectric Effect
15.4.2 Cross Section: Klein
Nishina Formula
15.4.3 Incoherent Scattering
15.4.4 Energy Transferred to the Electron
15.7 The Photon Attenuation Coefficient
15.8 Compounds and Mixtures
15.9 Deexcitation of Atoms
15.10 Energy Transfer from Photons to Electrons
15.11 Charged-Particle Stopping Power
15.11.1 Interaction with Target Electrons
15.11.2 Scattering from the Nucleus
15.11.3 Stopping of Electrons
15.12 Linear Energy Transfer and Restricted Collision Stopping Power
15.13 Range, Straggling, and Radiation Yield
15.15 Energy Transferred and Energy Imparted; Kerma and Absorbed Dose
15.15.2 Energy Transferred and Kerma
15.15.3 Energy Imparted and Absorbed Dose
15.15.4 Net Energy Transferred, Collision Kerma and Radiative Kerma
15.16 Charged-Particle Equilibrium
15.16.1 Radiation Equilibrium
15.16.2 Charged-Particle Equilibrium
16 Medical Uses of X-Rays
16.1 Production of X-Rays
16.1.1 Characteristic X-Rays
16.2 Quantities to Describe Radiation Interactions
16.2.1 Radiation Chemical Yield
16.2.2 Mean Energy per Ion Pair
16.3.2 Scintillation Detectors
16.3.4 Semiconductor Detectors
16.3.5 Thermoluminescent Dosimeters
16.3.6 Chemical Dosimetry
16.4 The Diagnostic Radiograph
16.4.1 X-Ray Tube and Filter
16.4.3 Attenuation in the Patient: Contrast Material
16.6 Angiography and Digital Subtraction Angiography
16.9 Biological Effects of Radiation
16.9.1 Cell-Culture Experiments
16.9.3 The Linear-Quadratic Model
16.9.4 The Bystander Effect
16.9.5 Tissue Irradiation
16.9.6 A Model for Tumor Eradication
16.10.1 Classical Radiation Therapy
16.10.2 Modern X-Ray Therapy
16.10.3 Charged Particles and Neutrons
16.12 The Risk of Radiation
16.12.1 Equivalent and Effective Dose
16.12.1.1 Equivalent Dose
16.12.1.2 Detriment and Effective Dose
16.12.2 Comparison With Natural Background
16.12.3.1 The Linear No-Threshold Model and Collective Dose
17 Nuclear Physics and Nuclear Medicine
17.2 Nuclear Decay: Decay Rate and Half-Life
17.3 Gamma Decay and Internal Conversion
17.5 Beta Decay and Electron Capture
17.6 Calculating the Absorbed Dose from Radioactive Nuclei within the Body: the MIRD Method
17.6.1 Activity and Cumulated Activity
17.6.1.1 The General Distribution Problem: Residence Time
17.6.1.2 Immediate Uptake with No Biological Excretion
17.6.1.3 Immediate Uptake with Exponential Biological Excretion
17.6.1.4 Immediate Uptake Moving through Two Compartments
17.6.1.5 More Complicated Situations
17.6.1.6 Activity per Unit Mass
17.6.2 Mean Energy Emitted Per Unit Cumulated Activity
17.6.3 Calculation of the Absorbed Fraction
17.6.3.1 Nonpenetrating Radiation
17.6.3.2 Infinite Source in an Infinite Medium
17.6.3.3 Point Source of Monoenergetic Photons in Empty Space
17.6.3.4 Point Source of Monoenergetic Photons in an Infinite Isotropic Absorber
17.6.3.5 More Complicated Casesthe MIRD Tables
17.6.4 Sample Dose Calculation
17.7 Radiopharmaceuticals and Tracers
17.7.1 Physical Properties
17.7.2 Biological Properties
17.8 Detectors; The Gamma Camera
17.9 Single-Photon Emission Computed Tomography
17.10 Positron Emission Tomography
17.11 Brachytherapy and Internal Radiotherapy
18 Magnetic Resonance Imaging
18.1 Magnetic Moments in an External Magnetic Field
18.2 The Source of the Magnetic Moment
18.4 Behavior of the Magnetization Vector
18.5 A Rotating Coordinate System
18.5.1 Transforming to the Rotating Coordinate System
18.5.2 An Additional Oscillating Field
18.7 Detecting the Magnetic Resonance Signal
18.8 Some Useful Pulse Sequences
18.8.1 Free-Induction-Decay (FID) Sequence
18.8.2 Inversion-Recovery (IR) Sequence
18.8.3 Spin-Echo (SE) Sequence
18.8.4 Carr
Purcell (CP) Sequence
18.8.5 Carr
Purcell
Meiboom
Gill (CPMG) Sequence
18.9.2 Readout in the Direction
18.9.3 Projection Reconstruction
18.9.5 Other Pulse Sequences
18.9.6 Image Contrast and the Pulse Parameters
18.13 Diffusion and Diffusion Tensor MRI
18.14 Hyperpolarized MRI of the Lung
A Appendix A Plane and Solid Angles
B Appendix B Vectors; Displacement, Velocity, and Acceleration
B.1 Vectors and Vector Addition
B.2 Components of Vectors
B.3 Position, Velocity, and Acceleration
C Appendix C Properties of Exponents and Logarithms
D Appendix D Taylor's Series
E Appendix E Some Integrals of Sines and Cosines
F Appendix F Linear Differential Equations with Constant Coefficients
F.2 Second-Order Equation
G Appendix G The Mean and Standard Deviation
H Appendix H The Binomial Probability Distribution
I Appendix I The Gaussian Probability Distribution
J Appendix J The Poisson Distribution
K Appendix K Integrals Involving e-ax2
L Appendix L Spherical and Cylindrical Coordinates
M Appendix M Joint Probability Distributions
N Appendix N Partial Derivatives
O Appendix O Some Fundamental Constants and Conversion Factors
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