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Intermediate Physics for Medicine and Biology - Russell K. Hobbie & Bradley J. Roth

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580 Appendix M. Joint Probability Distributions

FIGURE M.2. Perspective drawing of p(x, y).

M.2 Continuous Variables

When a variable can take on a continuous range of values, it is quite unlikely that the variable will have precisely the value x. Instead, there is a probability that it is in the interval (x, dx), meaning that it is between x and x + dx. For small values of dx, the probability that the value is in the interval is proportional to the width of the

interval. We will call it px(x)dx. The extension to joint probability in two dimensions is p(x, y)dxdy. This is the probability that x is in the interval (x, dx) and y is in the interval (y, dy). Figure M.1 shows each outcome of a joint measurement as a dot in the xy plane. The probability that x is in (x, dx) regardless of the value of y is

 

 

 

px(x)dx =

p(x, y)dy dx.

(M.3)

It is proportional to the total number of dots in the vertical strip in Fig. M.1. Normalization requires that

 

 

 

 

1 =

px(x)dx = dx

dy p(x, y).

(M.4)

The first strip could be taken horizontally:

1 = py (y)dy = dy dx p(x, y).

Figure M.2 shows a perspective drawing of p(x, y). The volume of the shaded column is p(x, y)dxdy. The volume of the slice is px(x)dx. The entire volume under the surface is equal to one.

Appendix N

Partial Derivatives

When a function depends on several variables, we may want to know how the value of the function changes when one or more of the variables is changed. For example, the volume of a cylinder is

V = πr2h.

How does V change when r is changed while the height of the cylinder is kept fixed?

V (r + ∆r) = π(r + ∆r)2h = π(r2 + 2rr + ∆r2)h.

Subtracting the original volume, we have

V = π(2rr + ∆r2)h.

In the limit of small ∆r, this is

dV = 2πhrdr.

This is the same answer we would have gotten if h had been regarded as a constant. The partial derivative of V with respect to r is defined to be

 

∂V

 

= lim

 

V (r + ∆r, h) − V (r, h)

 

= 2πrh.

 

 

 

 

 

∂r

h

r→0

 

r

 

The subscript h in the partial derivative symbol means that h is held fixed during the di erentiation. Sometimes it is omitted; when it is not there, it is understood that all variables except the one following the are held fixed.

If the cylinder radius is held fixed while the height is varied, we can write

V = V (r, h + ∆h) − V (r, h) = πr2h.

The partial derivative is

 

 

∂V

 

=

lim

 

V (r, h + ∆h) − V (r, h)

 

= πr2.

 

 

 

 

 

∂h

r

h→0

 

h

 

Suppose now that we allow small changes in both r and h. The di erence in volume is

V = V (r + ∆r, h + ∆h) − V (r, h).

We can add and subtract the term V (r, h + ∆h):

V = V (r + ∆r, h + ∆h) − V (r, h + ∆h)

 

 

+ V (r, h + ∆h) − V (r, h)

 

 

=

V (r + ∆r, h + ∆h) − V (r, h + ∆h)

r

 

 

r

 

 

 

+

V (r, h + ∆h) − V (r, h)

h.

 

 

h

 

 

 

 

 

In the limit as ∆r and ∆h → 0, the first term is

∂V

∂r h

r

evaluated at h + ∆h. If the derivatives are continuous at (r, h), the derivative evaluated at (r, h + ∆h) is negligibly di erent from the derivative evaluated at (r, h). Therefore, we can write

∂V

 

∂V

 

dV =

 

 

 

dr +

 

dh.

∂r

 

∂h

 

h

 

r

 

 

 

 

 

This result is true for several variables. For a function w(x, y, z)

∂w

∂w

 

∂w

 

dw =

 

 

dx +

 

 

dy +

 

 

 

dz. (N.1)

∂x y,z

∂y

 

∂z

 

 

x,z

 

x,y

582 Appendix N. Partial Derivatives

The derivatives are evaluated as though the variables being held fixed were ordinary constants. If w = 3x2yz4,

∂w

= 6xyz4,

 

∂x

y,z

The mixed partials are

2w

 

=

∂f

=

lim

 

f (x, y + ∆y) − f (x, y)

=

lim

∂y∂x

 

 

 

∂y

y→0

 

y

x→0

 

 

 

 

 

 

 

 

 

y→0

× w(x + ∆x, y + ∆y) − w(x, y + ∆y) − w(x + ∆x, y) + w(x, y) ∆x y

∂w

= 3x2z4

,

 

∂y

x,z

 

 

 

∂w

= 12x2yz3.

 

∂z

x,y

 

It is also possible to take higher derivatives, such as 2w/∂x2 or 2w/∂x∂y. One important result is that the order of di erentiation is unimportant, if the function, its first derivatives, and the derivatives in question are continuous at the point where they are evaluated. Without filling in all the details of a rigorous proof, we will simply note that

2w = ∂g = lim

∂x∂y ∂x y→0 ∆x→0

×

w(x + ∆x, y + ∆y) − w(x + ∆x, y) − w(x, y + ∆y) + w(x, y) .

 

x y

 

The right side of each of these equations is the same, except for the order of the terms. Thus

 

∂ ∂w

=

∂ ∂w

 

 

 

 

 

 

 

 

∂x ∂y

∂y ∂x

 

 

Problems

 

 

 

 

f =

 

∂w

=

lim

 

 

w(x + ∆x, y) − w(x, y)

 

 

∂x

 

 

 

 

 

 

x→0

 

 

x

g =

∂w

 

=

lim

 

w(x, y + ∆y) − w(x, y)

.

∂y

 

 

 

y→0

 

 

 

y

Problem 1 If w = 12x3y+z, find the three partial derivatives ∂w/∂x, ∂w/∂y, and ∂w/∂z.

Problem 2 If V = xyz and x = 5, y = 6, z = 2, find dV when dx = 0.01, dy = 0.02, and dz = 0.03. Make a geometrical interpretation of each term.

Appendix O

Some Fundamental Constants and Conversion Factors

The values of the fundamental constants are from the 2002 least-squares adjustment, available at physics.nist.gov/PhysRefData/contents-constants.html.

Symbol

Constant

Value

 

 

 

SI units

c

 

Velocity of light in

2.997 925 ×

108

m s1

 

 

vacuum

1.602 177 ×

 

 

 

e

 

Elementary charge

1019

C

F

 

Faraday constant

9.648 53 × 104

C mol1

g

 

Standard acceleration

9.806 65

 

 

 

m s2

 

 

of free fall

6.626 069 ×

 

 

 

h

 

Planck’s constant

1034

J s

 

 

Planck’s constant

1.054 572 ×

1034

J s

 

 

(reduced)

6.582 119 ×

 

 

 

 

 

 

1016

eV s

kB

Boltzmann’s constant

1.380 651 ×

1023

J K1

 

 

 

8.617 343 ×

105

eV K1

me

Electron rest mass

9.109 382 ×

1031

kg

mec2

 

 

×

 

5

 

Electron rest energy

8.187 105

 

1014

J

 

 

 

5.109 99 × 10

 

eV

mp

Proton rest mass

1.672 622 ×

1027

kg

NA

Avogadro’s number

6.022 142 ×

1023

mol1

re

 

Classical electron radius

2.817 940 ×

1015

m

R

 

Gas constant

8.314 47

 

 

 

J mol1

 

2

Mass unit (12C standard)

 

×

 

8

K1

u

1.660 538

 

kg

 

 

1027

uc

 

Mass unit (energy units)

9.314 94 × 10

 

eV

0

 

Electrical permittivity

8.854 19 × 1012

C2 N1

 

 

of space

8.987 55 × 109

m2

1/4π 0

 

N m2 C2

σSB

Stefan Boltzmann

5.670 40 × 108

W m2

 

 

constant

2.426 31 × 1012

K4

λC

Compton wavelength

m

 

 

of electron

 

 

 

 

 

µB

Bohr magneton

9.274 009 ×

1024

J T1

µ0

Magnetic permeability

4π × 107

 

 

T m A1

 

 

of space

 

 

 

 

 

µN

Nuclear magneton

5.050 783 ×

1027

J T1

Some of the more useful conversion factors for converting from older units to SI units are listed. They are taken from Standard for Metric Practice, ASTM E 38076, Copyright 1976 by the American Society for Testing and Materials, Philadelphia.

To convert from

To

Multiply by

 

 

 

angstrom

meter

1.000 000 × 1010

atmosphere (standard)

pascal

1.013 250 × 105

bar

pascal

1.000 000 × 105

barn

meter2

1.000 000 × 1028

calorie (thermochemical)

joule

4.184 000

centimeter of

pascal

1.333 22 × 103

mercury (0 C)

 

9.806 38 × 101

centimeter of

pascal

water (4 C)

 

1.000 000 × 103

centipoise

pascal second

curie

becquerel

3.700 000 × 1010

dyne

newton

1.000 000 × 105

electron volt

joule

1.602 18 × 1019

erg

joule

1.000 000 × 107

fermi (femtometer)

meter

1.000 000 × 1015

gauss

tesla

1.000 000 × 104

liter

meter3

1.000 000 × 103

mho

siemens

1.000 000

millimeter of mercury

pascal

1.333 22 × 102

poise

pascal second

1.000 000 × 101

roentgen

coulomb

2.58 × 104

 

per kilogram

1.333 22 × 102

torr

pascal

Index

A scan, 352

AAPM, 383, 384, 397, 445, 500 Abbey, H., 564

Abductor muscle, 7 Aberration

chromatic, 389 spherical, 389

Ablation, 381

Able, K. P., 217, 224

Able, M. A., 217, 224

Abramowitz, M., 199, 201, 250, 253, 338, 340 Absolute temperature, 57

Absorbed dose, 427 Absorption coe cient, 365 Absorption edge, 404 Acceleration, 547 Accommodation, 389 Acetabulum, 7

Acetylcholine, 104, 137, 185, 573 ACHD, 376

Achilles tendon, 6 Acoustic impedance, 346 Actinometry, 383 Action potential, 135

foot, 174

Gaussian approximation, 182 propagating, 159 space-clamped, 158

Activating function, 200 Active transport, 497 Activity, 76, 484, 489

cumulated, 488, 489 Activity vector, 180

Adair, R. K., 244, 247, 253, 317, 323 Adenosine triphosphate (ATP), 3 Adiabatic approximation, 416 Adiabatic process, 54

ADP, 67, 534 Afterloading, 504

Ahlen, S. P., 418, 420, 423, 434 Aine, C., 225

Air

acoustic impedance, 346 attenuation, 350

density and specific heat, 61 speed of sound, 345

Alberts, B., 459 Albumin, 129, 130 Aldroubi, A., 542 Algae, 217 Aliasing, 294, 309

in an image, 331 Allen, A. P., 47 Allen, R. D., 103 Allison, J., 542 Allos, S. H., 225

α particle, 424, 484, 505 Alternans, 282

Alveoli, 1, 19, 77, 104, 256

American Association of Physicists in Medicine, see AAPM

American Heart Association, 195 Ampere, 145

Ampere’s law, 206, 213, 216 and Biot-Savart law, 220

Amplitude attenuation coe cient, 350 Ampullae of Lorenzini, 244, 252 Anaplasia, 378

Anderka, M., 293, 323

Anderson, H. L., 357

Anderson, J. R., 513 Anesthetic, 163 Angelakos, J. D., 175 Angiography, 376, 453

586 Index

Angioplasty, 504

Angioscopy, 376 Angstrom, 3

Angular momentum, 516 Anisotropy, 191, 192 Annihilation radiation, 414, 488 Anode, 193

Anode break excitation, 173 Anomalous rectification, 251 Antineutrino, 486 Antiscatter grid, 450 Antonini, E., 76 Antzelevitch, C., 185, 201 Anumonwo, J. B., 165, 175 Aorta, 20, 456

Apoptosis, 458

Aquaspirillum magnetotacticum, 217 Aqueous, 388

Arai, S., 224

Armstrong, B. K., 380, 397 Arqueros, F., 425, 434, 494, 512 Arteriole, 20

Artificial insemination, 72 Artificial kidney, 120 Ascites, 116

Ashley, J. C., 435

Astigmatism, 389

Astumian, R. D., 244, 247, 252–254, 317–319, 323 Ataxia-tangliectasia, 461

Athens, J. W., 323

Atherosclerosis, 376

Atkins, P. W., 70, 79 Atmosphere, 43

pressure variation, 60, 75 Atmosphere (pressure unit), 14 Atomic deexcitation, 410 Atomic energy levels, 402 Atomic number, 482

Atoms per unit volume, 366 ATP, 67, 534

Atrioventricular node, see see AV node Attenuation

of sound wave, 349 water, 350

Attenuation coe cient, 365 amplitude, 350 e ective, 368

intensity, 350 linear, 409 mass, 409

Attenunator ladder, 171

Attix, F. H., 407, 414, 420, 422, 426, 429, 430, 434, 440, 445, 467, 477

Attractor, 262, 269

Auditory evoked response, 308

Auger electron, 410, 425, 485, 500, 504

cascade, 411, 438 Augmented limb leads, 188 Austin-Seymour, M., 478

Autocorrelation function, 299, 522 of exponential pulse, 305

and energy spectrum, 305 and power spectrum, 301 of noise, 314

of sine wave, 300 of square wave, 300

AV node, 185, 194 Average, 561

ensemble, 52 time, 52

Average reference recording, 196, 201 Avogadro’s number, 59, 85, 409

definition in SI units, 366 Axel, L., 526, 535, 542 Axelrod, D., 96, 108, 109 Axon, 2, 135

cable model, 149 electric field, 148

membrane capacitance, 149, 163

membrane capacitance and conductance, 150 membrane equivalent circuit, 155

membrane time constant, 150 myelinated, 136, 160 potassium gate, 157

potassium Nernst potential, 155 potential outside, 177

sodium conductance, 157 sodium gate, 158

sodium Nernst potential, 155 space-clamped, 154, 158 surface charge density, 149 unmyelinated, 136, 160 voltage-clamped, 154

Axoplasm, 136 Ayotte, P., 473, 477

B scan, 352, 356 Background

natural, 470 Backscatter

factor, 430 Backx, P. H., 202 Bacteria, 2

magnetotactic, 217, 222 orientation in a magnetic field, 223

Bacteriophage, 2 Badeer, H. S., 18, 29 Bainton, C. R., 261 Balduzzi, A., 398 Balloon angioplasty, 504 Bambynek, W., 411, 434 Banavar, J. R., 41, 47 Bank, R. A., 133

 

Index

587

Bar, 12

Berne, B. J., 372, 397

 

Barach, J. P., 212, 218, 221, 224

Bernoulli equation, 18

 

Barentsz, J., 542

Bernoulli process, 563

 

Barium, 449

Bernstein, M. A., 532, 533, 542

 

Barium fluorobromide, 446

Berry, E., 398, 399

 

Barker, A. T., 214, 224

Berson, A. S., 225

 

Barkovich, A. J., 542

Bessel function, 250, 338, 340, 352

 

Barlow, H. B., 392, 397

modified, 199

 

Barn (unit), 404

Beta decay, 484, 485

 

Barnes, F. S., 244, 253

spectrum, 487

 

Barneston, R. StC., 399

Bethe, H., 418

 

Barold, S. S., 194, 201

Bethe–Bloch formula, 420

 

Barr, G., 87, 108

Bevington, P. R., 289, 323

 

Barr, R. C., 154, 160, 175

Beyer, R. T., 350, 357

 

Barrett, H. H., 325, 333, 341

Bianchi, A. M., 308, 310, 323

 

Barrett, J. N., 240

Bicudo, C. E. M., 224

 

Barth, R. F., 467, 477

Bidomain model, 191, 192, 195, 199, 221

 

Bartlett, A. A., 39, 47, 274, 283

Bieber, M. T., 107, 108

 

Basal cell, 378, 381

Biersack, J. P., 415, 418–423, 435

 

Basal cell carcinoma, 464

Bifocal lenses, 389

 

Basal cell carcinoma (BCC), 380, 381

Bifurcation, 266

 

Basal metabolic rate, 61

diagram, 270

 

Base, 549

Bilirubin, 377

 

Basilar membrane, 349

Binding energy

 

Basin of attraction, 266

electronic, 484

 

Bass, M., 397, 399

nuclear, 483

 

Basser, P. J., 104, 108, 130, 133, 537, 542

per nucleon, 483

 

Bastian, J., 243, 253

Binomial probability distribution, 51, 101, 563

 

Battocletti, J. H., 535, 542

Bioheat equation, 382

 

Baum, M. J., 398

Biot-Savart law, 206

 

Baumgertner, C., 225

and Ampere’s law, 220

 

Baylor, D. A., 392, 399

and magnetic field around an axon, 208

 

Bazylinski, D. A., 217, 224

current in, 207

 

Beam hardening, 448

Bipolar electrode, 194

 

Bean, C. P., 87, 108, 123, 127, 128, 133

Birch, R., 439, 477

 

Beaurepaire, E., 399

Bird, R. B., 90

 

Beck, R. E., 128, 133

Birds, 217

 

Becker, D. V., 500

Birefringence, 371

 

Becklund, O. A., 328, 341

Births, 321

 

Becquerel (unit), 472, 489

spontaneous, 293, 294

 

Bee, 217, 222

Bishop, C. R., 323

 

Beer’s law, 365

Blackbody, 372

 

Begon, M., 266, 283

Blackbody radiation

 

BEIR, 471–473, 477, 505, 506, 512

and heat loss, 375

 

Bell, C., 542

vs. frequency, 375

 

Bell, G. I., 313

vs. wavelength, 373

 

Bellon, E. M., 224

Blackford, B., 225

 

Belousov–Zhabotinsky reaction, 275

Blackman, R. B., 295, 323

 

Bender, M. A., 511

Blackman-Tukey method, 309

 

Benedek, G. B., 10, 29, 90, 91, 100, 108

Blair, D. F., 96, 109

 

Bennison, L. J., 44

Blakemore, N., 217

 

Berg, H. C., 96, 108

Blakemore, R. P., 217, 224

 

Berg, M. J., 44, 47

Blank, M., 253, 254

 

Berger, M. J., 494, 512

Bloch equations, 519

 

Berggren, K-F., 434

Bloch, F., 418, 519

 

Bergmanson, J. P. G., 381, 397

Blood flow

 

Berlinger, W. G., 47

pulmonary artery, 296

 

588 Index

Blood pressure, 255 Blood-brain barrier, 116 Blount, W. P., 10 Blume, S., 376, 397 Boas, D. A., 398 Boccara, A. C., 399

Bockris, J. O’M., 234, 253 Bodenschatz, E., 283 Bohr, N., 418

Boice, J. D., 468, 477

BOLD (Blood Oxygen Level Dependent), 523, 536 Boltzmann factor, 54, 58–62, 85, 227, 372, 517 Boltzmann’s constant, 57

Bone scan, 501 Boone, J. M., 414, 434 Borgstede, J. P., 542

Born charging energy, 144, 234 Born, C. G., 466

Boron neutron capture therapy (BNCT), 467 Borthakur, A., 254

Bostrom, R. G., 480 Bouma, B. E., 370, 397, 399

Boundary-element method, 191 Bourland, J. D., 193, 201, 202, 534, 542 Boyd, I. A., 573

Bracewell, R. N., 295, 323 Brachytherapy, 461, 467, 503

high-dose-rate, 504 Bradley, W. G., 542 Bradshaw, L. A., 225 Bradshaw, P., 23, 29 Bradycardia, 194 Bragg peak, 466, 477 Bragg rule, 422

Bragg-Gray relationship, 468 Bramson, M. A., 373, 397 Brandts, B., 225

Brauer, F., 225 Braun, T. J., 274, 283 Breathing

energy loss due to, 61 Bremsstrahlung, 413, 417, 437

energy fluence, 438 Bren, S. P. A., 245, 253 Brennan, J. N., 224 Brenner, D. J., 472, 477 Bˇrezina, V., 295 Bˇrezina, V., 294, 323 Briggs, E. A., 434 Brightness contrast, 451 Brill, A. B., 500

Brittenham, G. N., 217, 224 Broad, W. J., 455, 477 Broad-beam geometry, 408 Bronzino, J. D., 308, 310, 323 Brooks, A. L., 471, 478 Brooks, R. A., 455, 457, 478

Brown, B., 225

Brown, J. H., 42, 47, 79 Brown, J. H. U., 399 Brown, R., 85

Brown, R. T., 434

Brownian motion, 61, 85, 312 Bruglio, A., 398

Bub, G., 275, 283 Buchanan, J. W., 500, 513 Buchsbaum, D., 505, 512 Bucky, G., 450

Budd, T., 425, 434

Budinger, T. F., 488, 490, 491, 498, 513 Bu er

calcium, 104 Buildup factor, 429, 494 Buka, R.L., 380, 397 Bundle branch block, 189 Bundle of His, 185 Buoyancy, 14

Burch, W. M., 103 Burnes, J. E., 191, 202 Bush, D. A., 479 Bystander e ect, 460, 500

Cable equation, 152

and ladder attenuator, 171 Cable model, 149

Cabral, J. M., 253

Cadene, M., 254 Calamante, F., 542 Calcaneus, 6 Calcium, 279

-induced calcium release, 105 di usion, 105

waves, 105 Calland, C. H., 120, 133 Calore, E., 398

Calorie, 54, 75

dietary, see Kilocalorie Calorimetry, 475

Cameron, J. R., 348, 349, 378, 397 Campbell, D. L., 185, 201

Cancer

prostate, 536

Cancer and power-line-frequency fields, 244 Candle (unit), 387

Capacitance, 143

concentric cylinders, 169 cylindrical membrane, 174 membrane, 163

resistance and di usion, 165 Capillary, 2, 20, 104, 115 Capillary blockade, 497 Carbohydrate, 3

11C, 502

14C dating, 512

Carbon dioxide production, 256

regulation, 257, 259, 261 Carbon monoxide, 74 Carbonyl group, 240 Carcinoma

basal cell, 380, 464 squamous cell, 380

Cardiac arrest, 72 Cardiac cell, 2 Cardiac output, 21 Carlsson, C. A., 434

Carlsson, G. A., 407, 434 Caro, C. G., 23, 29

Carr–Purcell (CP) Sequence, 526 Carr–Purcell–Meiboom–Gill (CPMG) Sequence, 527 Carslaw, H. S., 91, 94, 100, 106, 108

Carstensen, E. L., 245, 253 Cartilage

articular, 130 Casper, B. M., 68, 79 Castelli, W. P., 47 Catalyst, 74

Catfish, 243

Catheter, 376

Cathode, 194 virtual, 194

“dog bone”, 196 Cathode-ray tube, 203 Cavitation, 353

Cavity radiation, see Blackbody radiation Cebeci, T., 23, 29

Cell

eukaryotic, 2 membrane, 3

producing or absorbing a substance, 96 prokaryotic, 2

size, 2

Cell culture, 458 Cell sorting, 223 Cell survival

fractionation curve, 460 Cella, L., 479

Cellular automata, 275, 282 Center of gravity, 3

Center of mass, 362 Central slice theorem, 331 Centrifuge, 26, 75 Cerebral cortex, 212 Cerutti, S., 308, 310, 323 Cesaro, S., 398

Cesium iodide, 446 Chait, B. T., 253, 254

Chamberlain, J. M., 398, 399

Chance, B., 367–369, 398, 399 Chand, B., 435

Chandler, W. K., 250, 253

Index 589

Chang, S-B. R., 225 Chang, W., 398 Channel

selectivity, 240 Channels

calcium, 238 chloride, 238 delayed rectifier, 238 potassium, 238 sodium, 238 two-state model, 240

Chaos, 316

deterministic, 264, 270 in heart cells, 276

Chaotic behavior, 269 Characteristic x rays, 438, 485 Charcoal, activated, 44 Charge

free and bound, 144 Charge distribution

cylindrically symmetric, 139 line, 139

on cell membrane, 141 plane sheet, 139 point, 139

spherically symmetric, 139 Charge screening, 403 Charged-particle equilibrium, 428, 440 Charman, W. N., 390, 397

Charnov, E. L., 79 Charra, B., 133 Chavez, A. E., 414, 434 Cheeseman, J., 380, 397

Chemical dosimeter, 445

Chemical potential, 62, 88, 114, 115 ideal gas, 62

solute, 62, 69 water, 69

Chemical shift, 534, 541 images, 535

Chemotaxis, 94, 96

Chemotherapy, 42

Chen, C. N., 542 Chen, J., 254 Chen, P.-S., 283 Chen, W., 536, 542

Cherry, S. R., 501, 502, 511, 513 Cheyne–Stokes respiration, 274 Chick embryo, 213

Chick, W. L., 279 Chien, A., 478 Chileuitt, L., 542 Chittka, L., 398 Cho, Z. H., 335

Cho, Z.-H., 331, 341, 455, 478, 527, 542 Cholesterol

Raman spectrum, 372

590 Index

Christodolou, E., 478 Chromatic aberration, 389 Chromosome, 458, 459 Chronaxie, 171, 193

Chronic granulocytic leukemia, 275 Chung, S-H., 254

CIE, 379, 387 Cilia, 349 Circulation, 20, 278

Circulatory system, 20

Clark, J., 182, 183, 191, 199, 201, 209 Clark, J. W., 175

Clark, V. A., 36, 47

Clarke, G. D., 542

Clarke, J., 218, 224

Classical electron radius, 406, 419 Clausius-Clapeyron equation, 78 Clearance, 36, 278, 382 Clostridium, 146

Cloud chamber, 425 Cocco, C., 398 Cochlea, 349 Cochlear duct, 349 Cochlear implant, 192

Cochran, W. W., 217, 224 Co ey, J. L., 495, 513 Cohen, A., 309, 310, 323

Cohen, B. L., 472, 473, 478, 506 Cohen, D., 216, 224

Cohen, L., 478

Cohen, L. G., 214, 224, 225 Cohen, S. L., 253

Cohen, Y., 542

Coherence, 370

Coherent scattering, 403, 407 Cokelet, G. R., 133 Collagen, 130

Collective dose, 471 Collimator, 447

gamma camera, 501, 510, 511 multi-leaf, 464

Collision kerma, 440 Collision time, 86 Color blindness, 72 Colton, C. K., 133 Colyvan, M., 281, 283 Comer, M. B., 201

Commission Internationale de l’Eclairage, see CIE Common bundle, 185

Compass

in birds, 217

Competitive binding assay, 481 Complex exponential, 291 Complex notation, 303 Complex numbers, 291 Compound interest, 32 Compound microscope, 396

Compounds and mixtures, 410 Compressibility, 15, 344 Compressive strength, 12 Compton scattering, 403, 405, 442

cross section, 406 di erential cross section, 406

Compton wavelength, 405 Computed radiography, 450 Computed tomography

spiral, 455 Concentration

and potential di erence, 228 Concentration work, 63 Conductance, 145

Conduction system, 185, 194 Conduction velocity

myelinated, 160, 162 unmyelinated, 160, 162

Conductivity anisotropic, 191, 192

interior and exterior, 181 non-uniform, 191

tensor, 191 Conductor, 142

Cones (retinal), 387, 390 Conformal radiation therapy

three-dimensional, 465 Congestive heart failure, 35 Conjunctivitis, 381 Constant-field model, 235 Contact lens, 107, 381 Continuity equation, 82

di erential form, 84 integral form, 83

with creation or destruction, 85 Continuous slowing down approximation, 423 Contrast

brightness, 451 exposure, 451 film, 441

noise brightness, 451 noise exposure, 451

Contrast agent, 448 Convection coe cient, 76 Conversion factors, 583 Convolution, 326, 327

theorem, 326, 328 Cook, G., 77, 79

Cook, G. J. R., 536, 542

Cooley, J. W., 295, 323 Coordinate system

rotating, 519 64Cu, 44

Cormack, A. M., 455, 478 Cornea, 107, 381, 388 Cornsweet, T. N., 390, 397 Correlation function, 298