INDEX

ACSL (Advanced Continuous Simulation Language) software

use in human lactation studies, 28 use in large-scale modeling, 4 use in protein turnover analysis, 37-57

Albumin copper-binding activity, 272 liquid chromatrographic separation, 391

Aldehyde oxidase, 274 Algae, 13carbon-labelled, 371 Aluminum

accelerator mass spectrometric analysis, 407, 408 inductively coupled plasma mass spectrometric

analysis, 384 Aluminum isotopes, half-life, 408 Amine oxidases, 272 Amino acids, copper-binding activity, 272 p-Aminobenzoylglutamic acid, deuterium isotopic la-

bel exchange, 370 Anorexia nervosa, 289 Area under the concentration-time curve (AUC),

244,245,246 Area under the moment curve (AUMC), 244, 245, 246 Arsenic, inductively coupled plasma mass spectro­

metric analysis, 384, 390 Atmosphere, 14carbon content, 400

Barium, inductively coupled plasma mass spectro-metric analysis, 384

Bayesian methodology, 107 Beryllium isotopes, half-life, 408 Bioassay development and use, statistics, 173--190

assay controls, 183--186 assay setup and data description, 176 blocking, 188 calibration, 176--180

unknown samples, 176, 180 coefficient of variation, 175, 181-183, 188, 189 control samples, 183-186 fitting of standard curves, 179--180, 187 fixed bias, 175 fixed effects, 184 guidelines, 187-179 heteroscedasticity, 179, 183

Bioassay development and use, statistics (cont.) inter-assay precision, 175, 187, 188 intra-assay precision, 175, 176, 180-183, 187, 188

definition, 180-181 profile construction, 181-182 profile use, 182-183 quantitative assays, 173--190

iteratively reweighted least squares, 179--180 lower limit of detection, 175 lower quantitative limits, 175 minimum detectable concentration, 175 outliers, 180, 187 quantitative limits, 175 random errors, 175, 177 relative bias, 175 relative standard deviation, 175 replication, 184-186, 187, 188, 189 reporting and interpretation of results, 188--189 reporting of precision, 189 reproducibility, 175 response error relationship, 178 ruggedness, 175 sample submission strategies, 180, 188 semiquantitative assays, 174 sensitivity, 175, 187 specificity, 175 standard curve data, 174, 177-179 systemic errors, 175 terminology, 174-175 variance function, 177-179 weighted least squares, 179--180

Bismuth, inductively coupled plasma mass spectro-metric analysis, 384

Blank samples, 373 Blocking, 188 Blood clotting factor V, 272 Bone calcium metabolism, kinetic studies, in chil-

dren, 283-291 analytical methods, 285-286 compartmental models, 287 isotope selection, 286 mass spectrometry use, 284 neutron activation analysis, 284 study protocol, 284-285

411

Boron, inductively coupled plasma mass spectromet­ric analysis, 384, 386

Bovine somatotropin, 341 Breast cancer

fat intake-related, intake measurement instruments, 141-145

obesity-related, economic costs, 293 Bromine, inductively coupled plasma mass spectro­

metric analysis, 386

Cadmium, inductively coupled plasma mass spectro­metric analysis, 382-383, 386, 390, 391

Calcium inductively coupled plasma mass spectrometric

analysis, 382, 388 Recommended Dietary Allowance, 272

Calcium isotopes, half-life, 408 Calcium kinetic studies, in children, 283-291

analytical methods, 285-286 compartmental models, 287 isotope selection, 286 mass spectrometry, 284 neutron activation analysis, 284 study protocol, 284--285

Calibration, statistical models, 176-180 unknown samples, 176, 180

Cancer drugs, pharmacokinetic evaluation, induc­tively coupled plasma mass spectrometry, 383,390

Carbohydrates, rumen fermentation, 327-328 Carbon isotopes

accelerator mass spectrometric analysis, 406, 407

half-lives, 406, 409 I3Carbon isotopes, 368

background enrichment, 369 comparison with classical analysis of variation,

192 14Carbon, atmospheric concentration, 400 14Carbon isotopes, 363-364; see also Folate metabo­

lism, 14C_folic acid tracer study of accelerator mass spectrometric analysis, 398-

406 Cardiovascular disease

copper metabolism during, 273 obesity-related, economic costs, 293

~-Carotene, see also Vitamin A-I3-carotene metabolic relationship, compartmental models of

deuterated isotopomers, HPLC, 374--376 plasma dynamics, 208

Carotenodermia, 228, 232 Carboxylesterase, isotopic profile, 369 Cellulose, rumen fermentation, 327, 328 Cerium, inductively coupled plasma mass spectro­

metric analysis, 384 Ceruloplasmin, 272

deficiency, 273 normal serum range, 273

Cesium, inductively coupled plasma mass spectro­metric analysis, 384

Change-point models, 147, 157, 158

412

Chemical purity, 373 Chemical speciation, inductively coupled plasma

mass spectrometric analysis, 389-391, 392

Chemometrics and Intelligent Laboratory Systems, 190

Children, see also Infants; Premature infants calcium kinetic studies, 283-291

analytical methods, 285-286 compartmental models, 287 isotope selection, 286 mass spectrometry, 284 neutron activation analysis, 284 study protocol, 284--285

Chlorine accelerator mass spectrometric analysis, 406,

407 inductively coupled plasma mass spectrometric

analysis, 382, 386 Chlorine isotopes, half-life, 408 Cholesterol metabolism, copper, 273 Chromatograph

capillary colunm, interface with mass spectrome­ters,366

liquid, interface with mass spectrometers, 366 Chromatography, 174; see also High performance

liquid chromatography (HPLC) gas, comparison with inductively coupled plasma

mass spectrometry, 381, 382 gas-combustion-isotope ratio mass spectrometry,

367-368,369 liquid, use in albumin separation, 391 size exclusion, 391

on-line, 388 Cohort survival, response curve analysis, 191-

203 bandwidth estimation, 195 biological parameters, 196, 198, 202 comparisons using characteristic features,

196-1090 comparisons using principal components, 198-

201 eigenfunctions, 198, 200, 202 functional data, 192 hazard rate functions, 193, 194, 196, 199 Karhunen--Loeve decomposition, 198, 200, 202 local quadratic polynomials, 195 multivariate analysis, 192, 202

Collagen, interaction with copper, 272-273 Colon cancer, obesity-related, economic costs, 293 Compartmental models, 132

accessible and nonaccessible compartments, 82 applications, 81 a priori identifiability, 88-89, 97, 98-99, 100 calcium kinetics, in children, 283-291

analytical methods, 285-286 compartmental models, 287 isotope selection, 286 mass spectrometry, 284 neutron activation analysis, 284 study protocol, 284--285

Compartmental models (cont.) copper metabolism, 271, 276-277, 279 definition, 79, 81,116 deterministic, 79, 81 endocrine-metabolic control systems, 81, 82, 85 estimation, 122-128

accuracy, 127-128 partial derivative, 125 steepest descent search technique, 124-128, 129 vector of rate parameters, 122-123

examples, 93-99 sum of exponentials, 93-96

glucose metabolism, 94-100 interconnectedness between compartments, 81,

82 lactation, human, 21-33

collection of system information, 23 derivation of model equations, 24-26 development of system diagram, 23 estimation of parametric values and initial con-

ditions, 26-28 experimental background, 21-22 fitting model to the data, 28-30 modeling process, 23-30

of lactation, ruminant, 330-343 acetate effects, 334, 335, 337, 338 acetate milk fat incorporation equation, 332 alternative feeding strategies effects, 339-343 arterio-venous nutrient uptake differences,

336-339 block diagram, 333 blood lipids milk fat incorporation equation, 332 as dynamic model, 326, 339, 340, 342-343 glucose oxidation effect, 334 glucose uptake, 337 lactate conversion rate, 335 lactose synthesis equation, 332 as mechanistic model, 340, 342-343 Michaelis-Menten equation, 333 milk protein synthesis equation, 330, 332 recombinant somatotropin effects, 341 state variables, 330

3-methylhistidine metabolism, 303-324 applications, 320-322 de novo production, 303-304, 310-312, 313 fractional breakdown rate calculations, 311-312,

314 fractional transfer rates, 315, 316 in humans, cattle and dogs, 303, 306, 313,

314-315,316,317,318,319,321,322 mass transfer rate, 317 minimal one-compartment model, 312, 315-318 modeling assumptions, 314 model parameters, 315, 316 prediction of muscle mass, 318-320 SAAM/CONSAM program, 303 in sheep, 303, 306-309, 311, 314-315, 316,

317-318, 322 species comparison, 314-315, 316, 317 steady-state compartment masses, 317 structure of tracer, 307

Compartmental models (cont.) 3-methylhistidine metabolism (cont.)

in swine, 303, 306-307, 310, 311, 312, 314-315,316,317,319,320,321,322

three-compartment model, 303, 306-312, 313, 314-315,316,317,318-320

model identification, 87-93 Akaike criteria, 92 a priori identifiability, 88-89 F-test,92 model quality assessment, 91-92 model validation, 91, 92-93 nonidentifiable models, 89 parameter estimation problem, 89-91 Schwarz criteria, 92 simulation, 93 weighted nonlinear least squares, 91, 92 weighted residual sum of squares minimization,

90-91,93,95-96 molybdenum metabolism, 271, 276-277, 278-

279 protein turnover, leucine radioisotope study, 345-

359 amino acid channeling, 345, 347, 348, 349-351,

352,353-354,355-356,357 amino acid recycling, 345-347, 348, 349-351,

352,353-354,355,356-357 description of compartmental model, 347-

350 experimental design, 350--354 extracellular leucine pool, 347, 348, 349, 350,

352,353,354,355 fractional synthesis rate, 347, 349-350, 351,

352,353,354 intracellular leucine pool, 345, 347, 348, 349,

350,351,353,354,355 leucyl tRNA pool, 347, 348, 349, 350, 351, 352,

353,354,355,356 sensitivity analysis, 349-350

protein turnover, whole-body, 36-57 Advanced Continuous Simulation Language

(ACSL) use, 37-57 continuous dose estimation technique, 35, 36,

37,40 flooding dose estimation technique, 35, 37, 39,

40,42--45 model description, 36 modeling process, 37--45

single-input multiple-output, SAAM II use, 59-77

forced functions-, 59-60, 61-64 fractional transfer coefficients, 62, 63 goodness-of-fit,74-76 model identifiability, 74-76 model structure postulation, 64-74

stochastic, 79, 81 theoretical basis, 81-85

differential equations, 118 irreversible losses, 118, 120 Michaelis-Menten kinetics, 121-122 rate constants, 117, 118, 120

413

Compartmental models (com.) theoretical basis (com.)

substance washout time calculation, 118--122 tracee models, 83-85 tracee steady states, 86-87 tracer models, 85---S6 tracer-tracee models, 86, 87-418

vitamin A-p-carotene metabolic relationship, 225-237

compartmental modeling methods, 228 isotope methods, 226-228 pre-formed vitamin A metabolism model,

229-232 SAAM II use, 228, 231 SLAMANGHI factors, 234 vitamin A formed from p-carotene model

232-235 well-mixed and kinetic heterogeneity, 81, 82-413 zinc metabolism, 253-269

computer fitting of data and model, 254, 264-266

development, 257-260 erythrocyte compartment, 258, 262, 263 fecal compartment, 256, 257, 258--259, 262,

263,267 fractional standard deviations, 265-266, 267 fractional transfer coefficients, 261,262,263,264 hepatic compartment, 257-259, 263 in infants, 388 manual fitting of data and model, 254, 261-264 objectives, 254 plasma compartment, 256, 257, 258, 262, 263 in premature infants, 386-387 SAAMICONSAM software use, 254, 261, 262,

264--267 single-input multiple-output, 59-77 standard deviations, 265, 266, 267

CONSAM (conversational SAAM) software use in copper metabolism studies, 271, 277 use in molybdenum metabolism studies, 271, 277 Windows environment, 5; see also WinSAAM Pro-

ject Constrained modeling, in micro-scale modeling, 4 Contaminants, in tracer studies, 373-374 Continuous infusion technique, 35, 36, 37, 40 Control samples, 183-186 Copper

deficiency, 272 indices, 273

homeostasis, 276 inductively coupled plasma mass spectrometric

analysis, 384, 386, 387, 391 metabolism .

compartmental models, 271, 276-277, 279 conditions affecting, 273 kinetic models, 271

normal serum range, 273 physiological roles, 272-273 Recommended Dietary Allowance, 272 stable isotope studies, 275-278 toxicity, 273

414

Copper-binding proteins, 272 CSMP software, for large-scale modeling, 4 Curve data analysis, of cohort survival: see Response

curve analysis, cohort survival Cytochrome c oxidase, 272

copper deficiency indicator, 273

Decoupling, 4 forced functions, 59-60, 61-64

Deterministic models, of ruminant digestion and me­tabolism,326

Deterministic predictions, 116 Deuterium isotopes, 368

cost, 372 kinetic isotope effects, 371 placement/position stability, 369, 370 protium substitution, 371

Deuterium oxide isotope dilution, 21-33 Diabetes mellitus, obesity-related, economic costs,

293 Diamine oxidase, 272 Dietary intake, measurement instruments, 139-

145 Food Frequency Questionnaire, 139-140, 141-

142 new model, 142-145

Differential equations, 118 DNA assays, 173 Dopamine p-monooxygenase, 272 Dynamic models, ruminant digestion and metabo­

lism, 326, 339, 340, 342-343 Dynamic range, 366

Eigenfunctions, 198, 200, 202 Electrophoresis, capillary, 390-391 Elemental analysis, primary objectives, 380 Endocrine-metabolic control systems, compartmental

models, 81, 82, 85 Endocrine-nutrient models, 134 Enzyme-linked immunoabsorbent assays (ELISA),

methodology, 176 Enzymes

copper-containing, 272 molybdenum-containing, 274

Estimation, compartmental modeling, 122-128 accuracy, 127-128 partial derivative, 125 steepest descent search technique, 124-128, 129 vector of rate parameters, 122-123

Estrogens, effect on skeletal metabolism, 288 Evaporative light-scattering detection devices, 372 Experts, mathematical modeling, Internet access,

133

Faraday cup detectors, 368 Fast atom bombardment, 381, 385 Fat-free mass, 318

effect on resting energy expenditure, 294 Ferroxidases, copper-containing, 272 Fixed bias, 175 Flooding dose technique, 35, 37, 39, 41, 42-45

Fluorescence, 397-398 Folate depletion-repletion bioassay, statistical models,

147,148--171 descriptive plots, 149-151 experimental design, 149, 149 nonparametric approach, 159-167

assessment of curve estimators, 159-160 bandwidth selection, 159, 160-161 comparison with parametric fit, 165-167, 168 kernel smoothing, 148, 161-162 locally weighted least squares regression, 148,

162-165, 167 local vs. global fit, 159 saturation phenomenon, 163

parametric approach, 151-158 change-point models, 147, 157, 158 data distribution determination, 151-152 generalized linear model, 147, 151 modeling of over all regimes, 152-156 mUltiple linear squares, 151 nonlinear modeling of folate source interactions,

156-158 saturation phenomenon, 156, 157, 158 separate modeling of single-source regimes, 152 sum of weighted squares, 151

Folate metabolism, 14C-folic acid trace study, 239-251

accelerator mass spectrometry use, 239-251 areas under the concentration-time curve (AUC),

244,245,246 areas under the moment curve (AUMC), 244, 245,

246 14C-folate concentration kinetic profile, 245-246 cumulative loss and mass balance of 14C_folate,

246,247-249 erythrocyte analysis, 241, 242-243, 244, 245, 246,

249 experimental methods

specimen collection and handling, 242-243 subject, diet, and dose, 242 tracer synthesis, 241-242

fecal analysis, 241, 243-244, 245, 246, 247 laboratory analysis, 243-244 mean sojourn time (MST), 244, 245, 246, 249 plasma analysis, 241, 242, 244, 245, 248 results, 244-246

sensitivity and precision for tracer analysis, 244 subject and diet, 244 time course plots, 244-245

urine analysis, 241, 242-245, 246, 247-248, 249 Food Frequency Questionnaire, 139-140, 141-142 Forced functions, 59-60, 61-64 FORTRAN 85,149 Fourier transform ion cyclotron resonance instru­

ments, 385 Fractional breakdown rate, 311-312, 314 Fractional transfer coefficients, 62, 63, 261, 262, 263,

264 Fractional transfer rates, 315, 316 Fractional standard deviations, 265-266, 267 F-test,92

Gall bladder disease, obesity-related, economic costs, 293

Gasoline, lead isotope ratios, 387 Generalized linear model, 147, 151 Gibbs sampling, 107 Global Two-Stage method, 106 Glucose metabolism

compartmental models, 94-100 kinetic models, 115 minimal (cold) model, 80 in ruminants, 314, 317 use in population kinetic analysis, 110-112

Gold, inductively coupled plasma mass spectrometric analysis, 383, 384

Gold-drug therapy, inductively coupled plasma mass spectrometric analysis, 390

Growth curve, growth spurt, 196

Hazard rate functions, 193, 194, 196, 199 Hemicellulose, rumen fermentation, 327,328 Heteroscedasticity, 179, 183 High performance liquid chromatography (HPLC)

deuterated ~-carotene isotopomers, 374-376 eluent monitoring applications, 372 precision, 189

Hill equation, 84 Hydrogen isotopes, half-life, 408 Hypertension, obesity-related, economic costs, 293

Identifiability a priori, 88--89, 98--99, 100 micro-scale modeling, 4

Immunoassays,174 Infants

breast milk intake determination: see Lactation, compartmental models, human

premature: see Premature infants zinc metabolism modeling, 388

Infectious diseases, copper metabolism during, 273 Inflammatory conditions, copper metabolism during,

273 Insulin sensitivity, whole-body, 80 Internet, published mathematical model library,

131-\35 Intravenous glucose tolerance test

minimal (cold) glucose kinetics model, 110-112

tracers, 80 Iodine

accelerator mass spectrometric analysis, 407 inductively coupled plasma mass spectrometric

analysis, 384 Iodine isotopes, half-life, 408 Ion trap detection, 367, 385 Iron

accelerator mass spectrometric analysis, 407 inductively coupled plasma mass spectrometric

analysis, 382-383, 386, 387, 388, 390 Recommended Dietary Allowance, 272

Iron isotopes, half-life, 408 Iron metabolism, copper, 273

415

Irreversible loss, 118, 119 Isolation, tracer studies, 373-374 Isotope dilution methodology: see Tracer kinetic

studies Isotopes, see also specific isotopes

half-lives, 408 nuclear chemistry, 364 radioactive decay, 364

Isotopic purity, 373 Isotopic substitution, kinetic isotope effects, 371 Isotopomers, heavy, 368-369 Iterative Two-Step method, 106, 107 Iteratively reweighted least squares, 179-180

Karhunen--Loeve decomposition, 198, 200, 202 Kernel estimators, 148 Kernel smoothing, 148, 161-162 Kinetic isotope effects, 371

Lactation, compartmental models human, 21-33

collection of system information, 23 derivation of model equations, 24-26 development of system diagram, 23 estimation of parametric values and initial con-

ditions, 26-28 experimental background, 21-22 fitting model to the data, 28-30 modeling process, 23-30

ruminant, 330-343 acetate effects, 334, 335, 337, 338 acetate milk fat incorporation equation, 332 alternative feeding strategies effects, 339-343 arterio-venous nutrient uptake differences,

336-339 block diagram, 333 blood lipids milk fat incorporation equation,

332 as dynamic model, 326, 339, 340, 342-343 glucose oxidation effect, 334 glucose uptake, 337 lactate conversion rate, 335 lactose synthesis equation, 332 as mechanistic model, 340, 342-343 Michaelis-Menten equation, 333 milk protein synthesis equation, 330, 332 of recombinant somatotropin effects, 341 state variables, 330

Lanthanum, inductively coupled plasma mass spec­trometric analysis, 384

Lawrence Livermore National Laboratory, Center for Accelerator Mass Spectrometry, 399, 406, 407

Lead, inductively coupled plasma mass spectrometric analysis, 384, 386, 390

Lead isotopes, half-life, 408 Lead poisoning, inductively coupled plasma mass

spectrometric analysis, 387, 390 Library of Mathematical Models of Biological Sys­

tems, web address, 30-31 Lindstrom-Bates algorithm, 105, 107, 108, 110

416

Lithium, inductively coupled plasma mass spectro­metric analysis, 384, 386

Longitudinal data analysis: see Population kinetic analysis

Luminescence, 397-398 Lysyl oxidase, 272-273

copper deficiency indicator, 273

Magnesium, inductively coupled plasma mass spec­trometric analysis, 386

Manganese, inductively coupled plasma analysis, 382-383

Manganese isotopes, half-life, 408 Maple (computer language), 28, 89 Mass spectrometry, 174, 364, 365-366

accelerator, 365, 397--410 costs, 399, 405--405 properties, 400--404 sensitivity, 366, 367, 399, 403 specificity, 366-367, 368 use in 14carbon-labelled compound tracing,

398--406 use in elemental tracing, 406--408

automatic gain control function, 367 chemical ionization, 367

use with inductively coupled plasma mass spec­trometry, 385

comparison with radiometric detection, 365 electron impact, 366-367

use with inductively coupled plasma mass spec­trometry, 385

Faraday cup detectors, 368 fast atom bombardment

comparison with inductively coupled plasma mass spectrometry, 381, 385

use with inductively coupled plasma mass spec­trometry, 385

field desorption comparison with inductively coupled plasma

mass spectrometry, 385 use with inductively coupled plasma mass spec­

trometry, 385 gas chromatography, comparison with inductively

coupled plasma mass spectrometry, 381, 382

gas chromatography-combustion-isotope ratio, 367-368

isotopic background, 369 high specificity, 365, 365 inductively coupled plasma, 379-396

atomic emission; 381 comparison with fast bombardment mass spec­

trometry,38l comparison with gas chromatography mass

spectrometry, 381, 382 comparison with inductively coupled plasma

atomic emission mass spectrometry, 381 comparison with neutron activation analysis,

381,382,383 comparison with quadrupole thermal ionization

mass spectrometry, 381

Mass spectrometry (cant.) inductively coupled plasma (cant.)

comparison with thermal ionization mass spec-trometry, 381, 382

development of instrumentation, 385 double-focusing magnetic-sector, 381-382 external calibration, 385 in vivo uptake and retention studies, 385 neutron activation analysis, 385 polyatomic ion species overlap, 382-383 quantitative analysis, 382 sample carry over, 384 sample contamination, 384 spectral interference, 384, 385 stable isotope dilution analysis use with,

38()""38 I standard additions, 385 thermal ionization mass spectrometry use with,

385,386,387,391-392 toxicokinetics, 387-388, 390 toxicology, 387-388, 390 use in chemical speciation analysis, 389-391,

392 use with chemical ionization mass spectrometry,

385 use with electron impact mass spectrometry, 385 use with elemental mass spectrometry, 382 use with fast atom bombardment mass spec-

trometry,385 use with multiple isotope, 38()""38 I

ion trap, 366, 367 for vitamin A metabolism, 373-374

quadrupole, 366--367 selected ion monitoring, 366 selected ion storage scan function, 367 specificity, 365 thermal ionization

comparison with inductively coupled plasma mass spectrometry, 381, 382

use in copper metabolism studies, 275 use in molybdenum metabolism studies, 275 use with inductively coupled plasma mass spec-

trometry, 385, 386, 387, 391-392 use in calcium kinetic studies, 284 use in copper metabolism studies, 275 use in ecotoxicology, 387-388, 390

Mathematica, 28 Mathematical models, see also Compartmental mod-

els; Statistical models cellular applications, 3, 4 large-scale, 4 quality assessment, 91-92 rationale, 3--4 underutilization, 131, 132 validation, 92-93

Mathematical Models of Biological Systems Library, 3()""31, 131-135

Mean squared error, 159-160, 161 Mean sojourn time, 244, 245, 246, 249 Measurement precision, 366 Mechanistic models, 132

Mediterranean fruit flies, cohort survival curve analy-sis, 191-203

bandwidth estimation, 195 biological parameters, 196, 198, 202 comparisons using characteristic features, 196--198 comparisons using principal components, 198-20 I comparison with classical analysis of variation,

192 eigenfunctions, 198, 200, 202 functional data, 192 hazard rate functions, 193, 194, 196, 199 Karkunen-Loeve decomposition, 198, 200, 202 local quadratic polynomials, 195 multivariate data analysis and, 192, 202

Melanin pigment, formation, 273 Menkes' disease, 273 Mercury, inductively coupled plasma mass spectro­

metric analysis, 384, 390 Metal-containing compounds, inductively coupled

plasma mass spectrometric analysis, 379-380

Metallothioneins, 272 3-Methylhistidine metabolism, compartmental

model, 303-324 applications, 32()""322 de novo production, 303-304, 31()""312, 313 fractional breakdown rate, 311-312, 314 fractional transfer rate, 315, 316 in humans, cattle, and dogs, 303, 306, 313,

314-315,316,317,318,319,321,322 mass transfer rate, 317 minimal one-compartment model, 312, 315--318 modeling assumptions, 314 model parameters, 315, 316 prediction of muscle mass, 318-320 SAAM/CONSAM programs, 303 in sheep, 303, 306--309, 310, 311, 314-315, 316,

317-318,322 species comparison, 314-315, 316,317 steady-state compartment masses, 317 structure of tracer, 307 in swine, 303, 306--307, 310, 311, 312, 314-315,

316,317,319,320,321,322 three-compartment model, 303, 306--312, 313,

314-315,316,317,318-320 Methyl imidazoquinoxaline

accelerator mass spectrometric analysis, 402--404, 405--406

high performance liquid chromatographic analysis, 401--402

Michaelis-Menten equation, 84,121-122,333 Micro-scale modeling, 4

SAAM software use, 4-19 Minimal modeling, in micro-scale modeling, 4 Minimum detectable concentration, 175 Minitab program, 128 Model reduction, 4 Models, see also Compartmental models; Mathemati­

cal models definition, 115 prediction/control-related, 115--116

417

Molybdenum accelerator mass spectrometric analysis, 407 deficiency, 274-275 homeostasis, 276 inductively coupled plasma mass spectrometric

analysis, 384, 386 metabolism of, compartmental models, 271,

276-277,278-279 physiological roles, 274 Recommended Dietary Allowance, 272 stable isotope studies, 275-277, 278 toxicity, 274

Molybdenum cofactor deficiency, 274-275 Molybdenum isotopes, half-life, 408 Monoamine oxidase, 272 Monophenol monooxygenase, 272 Monte Carlo Simulation, 127, 128 Muscle mass, 3-methylhistidine isotope prediction

method,318-320 Muscle proteolysis, 3-methylhistidine compartment

model, 303--324 applications, 320-322 de novo production, 303--304, 310-312, 313 fractional breakdown rate, 311-312, 314 fractional transfer rate, 315, 316 in humans, cattle, and dogs, 303, 306, 313,

314-315,316,317,318,319,321,322 mass transfer rate, 317 minimal one-compartment mode, 312, 315-318 modeling assumptions, 314 model parameters, 315, 316 prediction of muscle mass, 318-320 SAAMICONSAM program, 303 in sheep, 303, 306-309, 310, 311, 314-315, 316,

317-318,322 species comparisons, 314-315, 316, 317 steady-state compartment masses, 317 structure of tracer, 307 in swine, 303, 306-307, 310, 311, 312, 314-315,

316,317,319,320,321,322 three-compartment model, 303, 306-312, 313,

314-315,316,317,318-320

National Institute of Health, WinSAAM Project, 3, 5-19

dynamic linking libraries, 6, 8 graphic text editor, 9, 11 methods, 5-9

design basis, 7-8 design objectives, 5-7

new directions, 14, 16-19 data exchange with other software, 6-7,17 input units, 16 modeling project, 16 third-party component modeling, 6, 17-19

Neodynium, inductively coupled plasma mass spec­trometric analysis, 384

Neutron activation analysis comparison with inductively coupled plasma mass

spectrometry, 381, 382, 383

418

Neutron activation analysis (cant.) use in calcium kinetic studies, 284 use with inductively coupled plasma mass spec­

trometry,385 Nickel

accelerator mass spectrometric analysis, 407 inductively coupled plasma mass spectrometric

analysis, 383 Nickel isotopes, half-life, 408 Nonparametric analysis, 147

convolution-based kernel estimators, 148 in folate depletion--repletion bioassays, 159-

167 assessment of curve estimators, 159-160 bandwidth selection, 159, 160-161 comparison with parametric fit, 165-167, 168 locally weighted least squares regression, 148,

162-165,167 local vs. global fit, 159 saturation phenomenon, 163

weighted local linear fitting, 147 Nuclear magnetic resonance (NMR) spectra, 372

Obesity, 293 Oral glucose tolerance test, tracers, 80 Osmium, inductively coupled plasma mass spectro-

metric analysis, 384, 386 Outliers, 180, 187 Oxygen, inductively coupled plasma analysis, 382 Oxygen-18 isotope, placement/position stability, 369,

370

Parametric analysis, application to folate deple-tion--repletion bioassays, 151-158

change point-models, 147, 157, 158 data distribution determination, 151-152 generalized linear model, 147, 151 modeling over all regimes, 152-156 multiple linear squares, 151 nonlinear modeling of folate source interactions,

156-158 saturation phenomenon, 156, 157, 158 separate modeling of single-source regimes,

152 sum of weighted squares, 151

Parametric estimation problem, model identification, 89-91

"Paranoid Laboratory Practice;' 403 Parathyroid hormone, effect on skeletal metabolism,

288-289 Pectin, rumen fermentation, 327 Peptides, copper-binding activity, 272 Peptidylglycine-ex-amodating monooxygenase,

272 Pesticides, copper-containing, 273 Pharmacokinetics, use in population kinetic analysis,

103--113 Phosphorus, inductively coupled plasma mass spec­

trometric analysis, 382 Platinum, inductively coupled plasma mass spectro­

metric analysis, 383, 390, 391

Platinum-based drugs, inductively coupled plasma mass spectrometry, 390

Population kinetic analysis averaging, 105 background and history, 105-107 Bayesian methodology, 107 case studies, 108-112 definition, 103-104 Gibbs sampling, 107 Global Two-Stage method, 106 intersubject variability focus, 103-104 Iterative Two-Step method, 106, 107 Lindstrom-Bates algorithm, 105, 107, 108, 110 maximum likelihood basis, 107 mixed effects models, 104--105 pooling, 105 software, 107 standard Two-Stage method, 105, 106

Potassium, inductively coupled plasma mass spectro­metric analysis, 382, 386

Precision high performance liquid chromatogrpahy, 189 inter-assay, 175, 187, 188 intra-assay, 175, 176, 180--183

definition, 180--181 profile construction, 181-182 profile use, 182-183

reporting of bioassay results, 189 Predictions, 115-116

deterministic, 116 model-based, 132 statistical, 116

Pregnancy, copper metabolism during, 273 Premature infants, calcium kinetic studies, 283-291

analytical methods, 285-286 compartmental models, 287 isotope selection, 286 mass spectrometry, 284 neutron activation analysis, 284 study protocol, 284--285

Principal component analysis, 198-201, 202 Principles and Practice ofImmunoassay (Price and

Newmaneds.),189--190 Protein fractional synthesis rate, estimation, 35

continuous infusion technique, 35, 36, 37, 40 flooding dose technique, 35, 37, 39, 40, 42-45

Protein turnover modeling, 35-57 14C-Ieucine/3H-leucine radioisotope study, 345-

359 amino acid channeling, 345, 347, 348, 349--351,

355-356,357 amino acid recycling, 345-347, 348, 349--351,

353,354,355,356-357 description of compartmental model, 347-350 experimental design, 350--354 extracellular leucine pool, 347, 348, 30, 351,

352,353,354,355 fractional synthesis rate, 347, 349--350, 351, 24,

353,354 intracellular leucine pool, 345, 347, 348,349,

350,351,353,354,355

Protein turnover modeling (cant.) 14C-leucinePH-leucine radioisotope study (cant.)

leucyl tRNA pool, 347, 348, 349, 350, 351, 352, 353,354,355,356

sensitivity analysis, 349--350 in muscle, 3-methylhistidine compartment model,

303--324 applications, 320--322 de novo production, 303-304, 310--312, 313 fractional breakdown rate, 311-312, 314 fractional transfer rate, 315, 316 in humans, cattle, and dogs, 303, 306, 313,

314--315,316,317,318,319,321,322 mass transfer rate, 317 minimal one-compartment model, 312, 315-

318 modeling assumptions, 314 model parameters, 315, 316 prediction of muscle mass, 318-320 SAAM/CONSAM programs, 303 in sheep, 303, 306-309, 310,311,314--315,316,

317-318,322 species comparison, 314--315, 316, 317 steady-state compartment masses, 317 structure of tracer, 307 in swine, 303, 306-307, 311, 312, 314--315,

316,317,319,320,321,322 protein fractional synthesis rate, 35

continuous infusion estimation, 35, 37, 40 flooding dose estimation, 35, 37, 39, 40, 42-

45 two-pool model

diagram, 38 equations, 38-39 evaluation, 44-45 independent data, 42-44 initial values, 40 model description, 36 objective, 37 sensitivity analysis, 40-42

whole-body, Advanced Continuous Simulation Language (ACSL) use, 37-57

continuous dose estimation technique, 35, 36, 37,40

flooding dose estimation technique, 35, 37, 39, 40,42-45

model description, 36 modeling process, 37-45

Protein Turnover in Mammaliam TIssues in the Whole Body (Waterlow et al.), 36

Protium substitution, deuterium, 371 Purification, tracer studies, 373-374

Q-Qplots, 151-152, 154 Quantitation limit, 175, 366

lower, 175 Quantitative bioassays, statistical models, 147-

171 generalized linear model, 147 multiple linear/polynomial regression, 147 nonlinear regression, 148

419

Quantitative bioassays, statistical models (cant.) nonparametric models, 147

convolution-based kernel estimators, 148 locally weighted linear regression, 148 weighted local linear fitting, 147

parametric models, 147, 148, 151-158 change models, 147, 148, 158 data distribution detennination, 151-152 generalized linear model, 147, 151 modeling over all regimes, 152-156 multiple linear squares, 151 nonlinear modeling of folate source interactions,

156-158 saturation phenomenon, 156, 157, 158 separate modeling of single-source regimes, 152 sum of weighted squares, 151

Radioactive waste and handling, 404, 405 Radiocarbon dating, 400-401 Radioisotope labeling, see also specific radioisotopes

specificity, sensitivity, and integrity, 397-398 Radioisotopes, radiation hazards, 398 Random errors, 175, 177 Reduce (computer language), 89 Refractive index, 372 Relative bias, 175 Relative standard deviations, 175,366 Relaxin bioassays, 177-178, 182-183 Repeated measurement analysis: see Population ki-

netic analysis Replication, 184-186, 187, 188, 189 Reproducibility, 175 Response curve analysis, of cohort survival, 191-203

bandwidth estimation, 195 comparisons using characteristic features, 196-198 comparisons using principal components, 198-20 I comparison with classical analysis of variation,

192 functional data, 192 hazard rate functions, 193, 194, 196, 199 local quadratic polynomials, 195 mulitvariate data analysis, 347-350

experimental design, 350-354 extracellular leucine pool, 347, 348,30,351,

352,353,354,355 fractional synthesis rate, 347, 349-350, 351,24,

353,354 intracellular leucine pool, 345, 347, 348, 349,

350,351,353,354,355 leucyl tRNA pool, 347, 348, 349, 350, 351, 352,

353,354,355,356 sensitivity analysis, 349-350

RNA assays, 173 Rubidium, inductively coupled plasma mass spectro­

metric analysis, 386 Ruggedness, 175 Ruminant digestion and metabolism models,

325-343 aggregation levels, 325-326 detenninistic models, 326 dynamic models, 326, 339

420

Ruminant digestion and metabolism models (cant.) empirical regression equations, 326-327 lactating cow model, 330-343

acetate effects, 334, 335, 337, 338 acetate milk fat incorporation equation, 332 alternative feeding strategies effects, 339-343 arterio-venous nutrient uptake differences,

336-339 block diagram, 333 blood lipids milk fat incorporation equation, 332 as dynamic model, 340, 342-343 glucose oxidation effects, 334 lactate conversion rate, 335 lactose synthesis equation, 332 as mechanistic model, 340, 342-343 Michaelis-Menten equation, 333 milk protein synthesis equation, 330, 332 recombinant somatotropin effects, 341 state variables, 330

SAAM (simulation, analysis, and modeling soft-ware),93

Extended Multiple Studinear model, 147 in micro-scale modeling, 4-19 multiple linear/polynomial regression, 147 nonlinear regression, 148 nonparametric mode 4-19 use in vitamin A-[3-carotene metabolism studies,

228,231 use in zinc metabolism studies, 254, 258, 262-

263 Windows environment, 3; see also WinSAAM

Project SAAM31, application to human lactation compart­

mental modeling, 24-25 26, 28 SAAM 11,28,79,99

definition, 93 new features, 100 objective (cost) function, 93 use for Internet mathematical models access, 134 use in single-input multiple-output models, 59-77 Windows environment, 4-5; see also WinSAAM

Project Saturation phenomenon, 156, 157, 158 Scientist software, 4, 6 Scintillation counting, 364 Selenium

accelerator mass spectrometric analysis, 407 inductively coupled plasma mass spectrometric

analysis, 382-383, 386, 390, 391 Selenium isotopes, half-life, 408 Sensitivity, 175, 187,397,398

accelerator mass spectrometry, 366, 367, 399,403 Short-bowel syndrome, 306 Sieverts, 404, 405 Silicon, inductively coupled plasma mass spectromet­

ric analysis, 384 Silicon isotopes, half-life, 408 Silver, inductively coupled plasma mass spectromet­

ric analysis, 384 Simulation, 93

Single-input multiple-output models, use with SAAM II, 59-77

forced functions, 59-{j0, 61--64 fractional transfer coefficients, 62, 63 goodness-of-fit, 74-76 model identifiability, 74-76 model structure postulation, 64-74

liver subsystem model, 67, 69 red blood cell subsystem model, 61--66 system model, 69-70, 71-74 urinary subsystem model, 61, 62, 63, 66--67,68

SLAMANGHI factors, 234 Sodium, inductively coupled plasma analysis, 382 Specificity, 175

accelerator mass speciation kinetic analysis, 366-367,368

Standard curves assay run, 181 bioassay development and use, 176

in data modeling, 177-179 default choice, 187 fitting, 179-180

definition, 174 Starch, rumen fermentation, 327 Statistical models, quantitative bioassays, 147-

171 generalized linear model, 147 mUltiple linear/polynomial regression, 147 nonlinear regression, 148 nonparametric models, 147, 159-167

convolution-based kernel estimators, 148 locally weighted linear regression, 148 weighted local linear fitting, 147

parametric models, 147, 148, 151-158 change-point models, 147, 148, 158 data distribution determination, 151-152 generalized linear model, 147, 151 modeling over all regimes, 152-156 multiple linear squares, 151 saturation phenomenon, 156, 157, 158 separate modeling of single-source regimes, 152 sum of weighted squares, 151

Statistics, bioassay development and use, 173--190 assay controls, 183--186 assay setup and data description, 176 blocking, 188 calibration, 176-180 coefficient of variation, 175, 181-183, 188, 189 control samples, 183--195 fitting of standard curves, 179-180, 187 fixed bias, 175 fixed effects, 184 guidelines, 187-189 heteroscedasticity, 179, 183 inter-assay precision, 175, 187, 188 intra-assay precision, 175, 176, 180-183, 187, 188 iteratively reweighted least squares, 179-180 lower limit of detection, 175 lower quantitative limits, 175 minimum detectable concentration, 175 outliers, 180, 187

Statistics, of bioassay development and use (cant.) quantitative limit, 175 quantitative assays, 173--190 random errors, 175, 177 relative bias, 175 relative standard deviation, 175 replication, 184-186, 187, 188, 189 reporting and interpretation of results, 188-189 reporting of precision, 189 reproducibility, 175 response error relationship, 178 ruggedness, 175 sample submission strategies, 180, 188 semiquantitative assays, 174 sensitivity, 175, 187 specificity, 175 standard curve data, 174, 177-179 systemic error, 175 terminology, 174-175 unknown samples, 176 variance function, 177-179 weighted least squares, 179-180

Statistics for Analytical Chemists (Caulcutt and Boddy), 190

Steepest descent search technique, 124-128, 129 Stella software, 4 Stochastic models, 79, 81 Strontium, inductively coupled plasma mass spectro-

metric analysis, 386 Substance washout time, 118-122 Sulfate oxidase, 274 Sulfur, inductively coupled plasma analysis, 382 Sum of weighted squares, 151 Superoxide dismutase, 272

deficiency, 273 Survival, effect of nutrition, response curve analysis,

191-203 bandwidth estimation, 195 biological parameters, 196, 198, 202 comparisons using characteristic features, 196-198 comparisons using principal components, 198--201 comparison with classical analysis of variance, 192 eigenfunctions, 198, 200, 202 functional data, 192 hazard rate functions, 193, 194, 196, 199 Karhunen-Loeve decomposition, 198,200,202 local quadratic polynomials, 195

Systemic error, 174

T2 test, 192 Tautomerization,370 Tellurium, inductively coupled plasma mass spectro­

metric analysis, 390 Thallium, inductively coupled plasma mass spectro­

metric analysis, 384 Thorium, inductively coupled plasma mass spectro­

metric analysis, 383, 386 Time of flight instruments, 385 Tin, inductively coupled plasma mass spectrometric

analysis, 384, 390 Tin isotopes, half-life, 408

421

Titanium, inductively coupled plasma mass spectro­metric analysis, 384

Tracee definition, 363 steady states, 8~7

Trace elements accelerator mass spectrometric measurement,

406-408 inductively coupled plasma mass spectrometric

analysis, 379-396 stable isotope analysis, 380-381

Tracee models, 83-85 Tracer, definition, 363 Tracer kinetic studies

advantages, 80 protocol development, 363-378

examples, 373-376 gas chromatography-combustion-isotope ratio

mass spectrometry use, 367-368 isolation and purification issues, 372-373 mass spectrometry use, 365--367 nuclear chemistry basis, 364 stable vs. radioactive isotope use, 365 tracer selection, 368--372 use in ion trap detection, 367

tracer selection, 368--372 isotope costs, 372 isotope placement/poistion stability, 369-370 isotopic effects on reaction rates/adverse effects,

371 number of heavy isotopes per compound, 368--

369 Tracer models, 85-86 Tracer-tracee models, 86, 87--88 Tracer/tracee ratio, 363, 365 Transcuprein, 272 Tritium isotope, 363-364

accelerator mass spectrometric quantification, 406 Turner's syndrome, 289

University of Washington, Resource Facility for Ki­netic Analysis, 107, 109

Unknown samples bioassays, control samples, 183-186 calibration for analysis, 176, 180 mass spectrometric analysis of, limitations, 365

Uranium, inductively coupled plasma mass spectro­metric analysis, 383, 386

Vanadium, inductively coupled plasma mass spectro-metric analysis, 382-383, 390

Variance function, 177-179 Vitamin A, silyl derivative mass profile, 368, 369 Vitamin A-j3-carotene metabolic relationship, com-

partmental models, 225--237 compartmental modeling methods, 228 isotope methods, 226--228 pre-formed vitamin A metabolic model, 229-232 SAAM II use, 228, 231 SLAMANGHI factors, 234 vitamin A formed from j3-carotene model, 232-235

422

Vitamin A metabolism, compartmental models of in men, 207-223

"Atomium" model, 217, 218, 220, 221 CONSAM 31 use, 209, 217, 221 development of model, 211-221 experimental data, 208--209 hepatic vitamin A kinetics, 207, 210, 211-212,

213,215,217-219 modeling methodology, 209-210 vitamin A metabolism overview, 210

use in selected ion storage scan, 373 in women, 225--237

j3-carotene isotope methods, 227-228 vitamin A isotope methods, 226--227

use in linear-beam quadrupole mass spectrometry, 373--376

Washout time, 118--122 Weighted least squares, 179-180

locally, 162-167 nonlinear, 91, 92

Weighted residual sum of squares minimization, 90-91,93,95--96

Weighted squares, sum, 151 Weight loss, effect on resting energy expenditures

(REE), 293-302 equations, 295--296, 297, 298 model development, 294--299 model hypothesis testing, 300-301 total energy expenditure, 296, 298

Western Human Nutrition Research Center, 226, 271, 276

Wilson's disease, 273 Windows, SAAM use: see WinSAAM Project WinSAAM (Windows simulation analysis, and mod-

eling software) Project, 3,5--19 dynamic linking libraries, 6, 8 graphic text editor, 9, II methods, 5--9

design basis, 7-8 design objectives, 5--7

new directions, 14, 16--19 data exchange with other software, 6--7, 17 input units, 16 modeling project, 16 third-party component modeling, 6, 17-

19 notebook-oriented spreadsheet output, 9, 12 processing results, 9, 13--14 statistical package (STATA), 14, 15 terminal window, 9, 10 WinSAAM architecture, 8--9

Women, vitamin A and j3-carotene metabolism, 225--237

Women's Health Trial Vanguard Study, 140, 141, 143-144

Xanthine oxidase, 274

Zinc, inductively coupled plasma mass spectrometric analysis, 384, 386, 387, 390, 391

Zinc metabolism, compartmental modeling, 253-269

a priori identifiability, 253, 260---261, 266---267 computer fitting of data and model, 254, 264-

266 development, 257-260 erythrocyte compartment, 258, 262, 263 fractional standard deviations, 265-266, 267 fractional transfer coefficients, 261, 262, 263,

264 fecal compartment, 256, 257,258-259,262,263,

267 hepatic compartment, 257-259, 263 in infants, 388 manual fitting of data and model, 254, 261-264 objectives, 254 plasma compartment, 256, 257, 258, 262, 263 in premature infants, 386---387

Zinc metabolism, compartmental modeling (cant.) SAAMICONSAM programs use, 254, 261, 262,

264-267 single-input multiple-output models, with SAAM

II, 59-77 forcing functions, 59-60, 61-64 goodness-of-fit,74-76 liver subsystem model, 67, 68 model identifiability, 74-76 plasma subsystem model, 70---71 postulating of system model structure, 69-74 red blood cell subsystem model, 61-66 urinary subsystem model, 61, 62, 63, 66-67, 68

standard deviations, 265, 266, 267 urinary compartment, 256, 258-259, 261, 262,

263,267 Zireonium, inductively coupled plasma mass spectro­

metric analysis, 384

423