Compartmental System Analysis: State of the Art

IEEE Transactions on Biomedical Engineering

Volumn BME-27, Issue 1, 1980, Pages 1-11

  Brown, Reginald F ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

CHEMICAL REACTION KINETICS; COMPARTMENT MODEL; ECOLOGY; METABOLISM; NONBIOLOGICAL MODEL; PHARMACOKINETICS; REVIEW; THEORETICAL STUDY;

COMPUTERS; KINETICS; METABOLISM; MODELS, BIOLOGICAL; MODELS, CHEMICAL; MODELS, THEORETICAL; PHARMACEUTICAL PREPARATIONS; RANDOM ALLOCATION; STOCHASTIC PROCESSES; SYSTEMS ANALYSIS; SYSTEMS THEORY; TIME FACTORS;

CHEMICAL REACTIONS; ECOLOGY - MATHEMATICAL MODELS; MATHEMATICAL MODELS - REVIEWS;

COMPARTMENTAL MODELS; METABOLISM; PHARMACOKINETICS;

BIOMEDICAL ENGINEERING;

EID: 0019230974     PISSN: 00189294     EISSN: 15582531     Source Type: Journal    
DOI: 10.1109/TBME.1980.326685     Document Type: Article

References (140)

1. J. A. Jacquez, Compartmental Analysis in Biology and Medicine. Amsterdam, The Netherlands: Elsevier, 1972.
2. A. Rescigno and J. S. Beck, “Compartments,” in Foundations of Mathematical Biology, vol. 2, Cellular Systems, R. Rosen, Ed. New York: Academic, 1972, ch. 5, pp. 255–322.
3. J. G. Llaurado, “Compartmental approaches to water and electrolyte distribution,” in Engineering Principles in Physiology, vol. 2, J. H. U. Brown and D. S. Gann, Eds. New York: Academic, 1973, ch. 25, pp. 347–372.
4. I. W. Sandberg, “On the mathematical foundations of compartmental analysis in biology, medicine, and ecology,” IEEE Trans. Circuit Syst., vol. CAS-25, pp. 273–279, May 1978.
5. M. Gibaldi and D. Perrier, Pharmacokinetics. New York: Dekker, 1975.
6. J. G. Wagner, Fundamentals of Clinical Pharmacokinetics. Hamilton, IL: Drug Intelligence Publications, 1975.
7. T. Teorell, “Kinetics of distribution of substances administered to the body, I. The extravascular modes of administration,” Arch. Int. Pharmacodynamie Thérapie, vol. 57, pp. 205–225, 1937; “II. The intravascular modes of administration,” Arch. Int. Pharmacodynamie Thérapie, vol. 57, pp. 226–240, 1937.
8. C. W. Sheppard, “The theory of the study of transfers within a multi-compartment system using isotopic tracers,” J. Appl. Phys., vol. 19, pp. 70–76, Jan. 1948.
9. J. N. Kremer and S. W. Nixon, A Coastal Marine Ecosystem. Berlin, Germany: Springer, 1978.
10. L. J. Bledsoe, “Linear and nonlinear approaches for ecosystem dynamic modeling,” in Systems Analysis and Simulation in Ecology, vol. 4, B. C. Patten, Ed. New York: Academic, 1976, ch. 10, pp. 283–297.
11. A. R. Cooper and G. V. Jeffreys, Chemical Kinetics and Reactor Design. Edinburgh, Scotland: Oliver & Boyd, 1971, ch. 5, pp. 146–206.
12. E. P. Odum, Fundamentals of Ecology, 3rd ed. Philadelphia, PA: Saunders, 1971, p. 291.
13. M. T. Hays, “Kinetics of the human thyroid trap: A compartmental model,” J. Nucl. Med., vol. 19, pp. 789–795, July 1978.
14. J. G. Wagner, “Linear pharmacokinetic equations allowing direct calculation of many needed pharmacokinetic parameters from the coefficients and exponents of polyexponential equations which have been fitted to the data,” J. Pharmacokin. Biopharm., vol. 4, pp. 443–467, 1976.
15. K. R. Godfrey and R. F. Brown, “Practical aspects of the identification of process dynamics,” Trans. Instrum. Meas. Contr., vol. 1, pp. 85–95, Apr.–June 1979.
16. H. Maeda and S. Kodama, “Qualitative analysis of a class of nonlinear compartmental systems: Nonoscillation and asymptotic stability,” Math. Biosci., vol. 38, pp. 35–44, 1978.
17. R. Bellman, “Topics in pharmacokinetics 1: Concentration-dependent rates,” Biosci., vol. 6, pp. 13–17, 1970.
18. J. J. Di Stefano, “Tracer experiment design for unique identification of nonlinear physiological systems,” Amer. J. Physiol., vol. 230, pp. 476–485, Feb. 1976.
19. J. H. Matis and H. O. Hartley, “Stochastic compartmental analysis model and least squares estimation from time series data,” Biometrics, vol. 27, pp. 77–102, Mar. 1971.
20. J. H. Matis, R. L. Kodell, and M. Cardenas, “A note on the use of a stochastic mammillary compartmental model as an environmental safety model,” Bull. Math. Biol., vol. 38, pp. 467–478, 1976.
21. H. D. Tolley, D. Burdick, K. G. Manton, and E. Stallard, “A compartmental model approach to the estimation of tumor incidence and growth: Investigation of a model of cancer latency,” Biometrics, vol. 34, pp. 377–389, Sept. 1978.
22. R. F. Brown, “Case for improved measurements in compartmental modeling of metabolic systems,” Australasian Physical Sci. Med., vol. 2-1, pp. 7–28, Jan. 1979.
23. J. H. Matis, M. Cardenas, and R. L. Kodell, “On the probability of reaching a threshold in a stochastic mammillary system,” Bull. Math. Biol., vol. 36, pp. 445–454, 1974.
24. M. Cardenas and J. H. Matis, “On the stochastic theory of compartments: Solution for n-compartment systems with irreversible time-dependent transition probabilities,” Bull. Math. Biol., vol. 36, pp. 489–504, 1974.
25. —, “On the time-dependent reversible stochastic compartmental model-I. The general two-compartment system,” Bull. Math. Biol., vol. 37, pp. 505–519, 1975.
26. —, “On the time-dependent reversible stochastic compartmental model-II. A class of n-compartment systems,” Bull. Math. Biol., vol. 37, pp. 555–564, 1975.
27. A. K. Thakur, A. Rescigno, and D. E. Schafer, “On the stochastic theory of compartments: I. A single-compartment system,” Bull. Math. Biophys., vol. 34, pp. 53–63, 1972.
28. —, “On the stochastic theory of compartments: II. Multicompartment systems,” Bull. Math. Biol., vol. 35, pp. 263–271, 1973.
29. A. K. Thakur and A. Rescigno, “On the stochastic theory of compartments: III. General time-dependent reversible systems,” Bull. Math. Biol., vol. 40, pp. 237–246, 1978.
30. A. S. Kapadia and B. C. McInnis, “A stochastic compartmental model with continuous infusion,” Bull. Math. Biol., vol. 38, pp. 695–700, 1976.
31. P. Purdue, “Stochastic theory of compartments,” Bull. Math. Biol., vol. 36, pp. 305–309, 1974.
32. —, “Stochastic theory of compartments: One and two compartment systems,” Bull. Math. Biol., vol. 36, pp. 577–587, 1974.
33. —, “Stochastic theory of compartments: An open, two compartment, reversible system with independent Poisson arrivals,” Bull. Math. Biol., vol. 37, pp. 269–275, 1975.
34. T. T. Soong, “Pharmacokinetics with uncertainties in rate constants,” Math. Biosci., vol. 12, pp. 235–243, 1971.
35. T. T. Soong and J. W. Dowdee, “Pharmacokinetics with uncertainties in rate constants-III: The inverse problem,” Math. Biosci., vol. 19, pp. 343–353, 1974.
36. S. Chuang and H. H. Lloyd, “Analysis and identification of stochastic compartment models in pharmacokinetics: Implication for cancer chemotherapy,” Biosci., vol. 22, pp. 57–74, 1974.
37. L. Campello and C. Cobelli, “Parameter estimation of biological stochastic compartmental models—An application,” IEEE Trans. Biomed. Eng., vol. BME-25, pp. 139–146, Mar. 1978.
38. J. O. Tsokos and C. P. Tsokos, “Statistical modeling of pharmacokinetic systems,” J. Dynam. Syst. Meas. Contr. Trans. ASME, pp. 37–43, Mar. 1976.
39. J. Z. Hearon, “Theorems on linear systems, Article 1 (multi-compartment analysis of tracer experiments),” Ann. N.Y. Acad. Sci., vol. 108, pp. 36–91, 1963.
40. G. Aronsson and R. B. Kellogg, “On a differential equation arising from compartmental analysis,” Math. Biosci., vol. 38, pp. 113–122, 1978.
41. H. Maeda, S. Kodama, and F. Kajiya, “Compartmental system analysis: Realization of a class of linear systems with physical constraints,” IEEE Trans. Circuit Syst., vol. CAS-24, pp. 8–14, Jan. 1977.
42. C. D. Thron, “Structure and kinetic behavior of linear multicompartment systems,” Bull. Math. Biophys., vol. 34, pp. 277–291, 1972.
43. A. Mazanov, “Stability of multi-pool models with lags,” J. Theor. Biol., vol. 59, pp. 429–442, 1976.
44. R. J. Mulholland, “Analysis of linear compartment models for ecosystems,” J. Theor. Biol., vol. 44, pp. 105–116, 1974.
45. G. S. Ladde, “Cellular systems—I. Stability of chemical systems,” Math. Biosci., vol. 29, pp. 309–330, 1976.
46. —, “Cellular systems—II. Stability of compartmental systems,” Math. Biosci., vol. 30, pp. 1–21, 1976.
47. R. M. Zazworsky and H. K. Knudsen, “Controllability and observability of linear time-invariant compartmental models,” IEEE Trans. Automat. Contr., vol. AC-23, pp. 872–877, Oct. 1978.
48. C. Cobelli, A. Lepschy, and G. Romanin-Jacur, “Comments on ‘On the relationships between structural identifiability and the controllability, observability properties’” IEEE Trans. Automat. Contr., vol. AC-23, pp. 965–967, Oct. 1978.
49. —, “Structural identifiability of linear compartmental models of ecosystems,” in Theoretical System Ecology, E. Haflon, Ed. New York: Academic, to be published.
50. C. Cobelli and G. Romanin-Jacur, “Controllability, observability, and structural identifiability of multi input and multi output biological compartmental systems,” IEEE Trans. Biomed. Eng., vol. BME-23, pp. 93–100, Mar. 1976.
51. C. Cobelli, A. Polo, and G. Romanin-Jacur, “A computer program for the analysis of controllability, observability and structural identifiability of biological compartmental systems,” Comput. Programs Biomed., vol. 7, pp. 21–36, 1977.
52. R. M. Zazworsky and H. K. Knudsen, “Comments on ‘Control-ability, observability and structural identifiability of multi input and multi output biological compartmental systems,’” IEEE Trans. Biomed. Eng., vol. BME-24, pp. 495–496, Sept. 1977.
53. J. Delforge, “Comments on ‘Controllability, observability and structural identifiability of multi input and multi output biological compartment systems,’” IEEE Trans. Biomed. Eng., vol. BME-25, pp. 400–402, July 1978.
54. R. F. Brown, “The identifiability of nonlinear compartmental models,” presented at the 5th IFAC Symp. Ident. Syst. Parameter Estimation, Darmstadt, Germany, Sept. 1979.
55. R. Bellman and K. J. Åström, “On structural identifiability,” Math. Biosci., vol. 7, pp. 329–339, 1970.
56. M. Milanese and G. P. Molino, “Structural identifiability of compartmental models and pathophysiological information from the kinetics of drugs,” Math. Biosci., vol. 26, pp. 175–190, 1975.
57. K. R. Godfrey, R. P. Jones, and R. F. Brown, “The identifiability of linear compartmental models,” presented at the 5th IFAC Symp. Ident. Syst. Parameter Estimation, Darmstadt, Germany, Sept. 1979.
58. S. I. Rubinow and A. Winzer, “Compartment analysis: An inverse problem,” Biosci., vol. 11, pp. 203–247, 1971.
59. S. I. Rubinow, “On closed or almost closed compartment systems,” Math. Biosci., vol. 18, pp. 245–253, 1973.
60. H. Pohjanpalo, “System identifiability based on the power series expansion of the solution,” Math. Biosci., vol. 41, pp. 21–33, 1978.
61. C. Cobelli, A. Lepschy, and G. Romanin-Jacur, “Identifiability of time variant compartmental models of biological processes,” in A Link Between Science and Applications of Automatic Control, 7th IFAC Triennial World Congress, vol. 1, A. Niemi, B. Wahlström, and J. Virkkunen, Eds., Helsinki, Finland, 1978, pp. 205–224.
62. R. F. Brown and K. R. Godfrey, “Problems of determinacy in compartmental modeling with application to bilirubin kinetics,” Math. Biosci., vol. 40, pp. 205–224, 1978.
63. —, “Practical difficulties in testing identifiability of linear structural models,” IEEE Trans. Automat. Contr., vol. AC-23, pp. 1028–1030, Dec. 1978.
64. P. V. Pedersen, “General treatment of linear pharmacokinetics,” J. Pharmaceut. Sci., vol. 67, pp. 187–191, Feb. 1978.
65. H. Pohjanpalo and B. Wahlström, “On the uniqueness of linear compartmental systems,” Int. J. Syst. Sci., vol. 8, pp. 619–632, 1977.
66. M. Milanese and N. Sorrentino, “Decomposition methods for the identifiability analysis of large systems,” Int. J. Contr., vol. 28, pp. 71–79, 1978.
67. S. Niazi, “Application of a programmable calculator in data fitting according to one and two compartment open models in clinical pharmacokinetics,” Comput. Prog. Biomed., vol. 7, pp. 41–44, 1977.
68. D. A. Cook and G. S. Taylor, “The use of the APL/360 system in pharmacology: A computer assisted analysis of efflux data,” Comput. Biomed. Res., vol. 4, pp. 157–166, 1971.
69. J. D. Powers, T. E. Powers, J. D. Baggot, J. Kowalski, and K. Kerr, “Automated processing of data from pharmacokinetic investigations,” Comput. Biomed. Res., vol. 9, pp. 543–548, 1976.
70. R. H. Luecke and W. D. Wosilait, “A program to simulate drug elimination interactions: Warfarin and BSP-An illustrative example,” Comput. Prog. Biomed., vol. 8, pp. 35–43, 1978.
71. B. Kanyár and J. Erödi, “Program to estimate parameters of linear systems without numerical differentiation,” Comput. Prog. Biomed., vol. 8, pp. 135–140, 1978.
72. P. V. Pedersen, “Curve fitting and modeling in pharmacokinetics and some practical experiences with NONLIN and a new program FUNFIT,” J. Pharmacokin. Biopharm., vol. 5, pp. 513–531, 1977.
73. H. A. Feldman, “A short parameter-fitting routine for compartmental models,” Comput. Prog. Biomed., vol. 7, pp. 135–144, 1977.
74. A. Silvers and W. J. Sanders, “Digital online computer display to investigate the structure of metabolic systems,” Comput. Biomed. Res., vol. 3, pp. 133–145, 1970.
75. A. Lemaitre and J.-P. Malengé, “An efficient method for multiexponential fitting with a computer,” Comput. Biomed. Res., vol. 4, pp. 555–560, 1971.
76. R. H. Davis and J. H. Ottaway, “Application of optimization procedures to tracer kinetic data. Math. Biosci., vol. 13, pp. 265–282, 1972.
77. A. J. Sedman and J. G. Wagner, “CSTRIP, a Fortran IV computer program for obtaining initial polyexponential parameter estimates,” J. Pharmaceut. Sci., vol. 65, pp. 1006–1010, 1976.
78. J. Markham, D. L. Snyder, and J. R. Cox, “A numerical implementation of the maximum-likelihood method of parameter estimation for tracer-kinetic data,” Math. Biosci., vol. 28, pp. 275–300, 1976.
79. R. L. Kodell and J. H. Matis, “Estimating the rate constants in a two-compartment stochastic model,” Biometrics, vol. 32, pp. 377–400, June 1976.
80. C. G. Källström, T. Essebo, and K. J. Åström, “A computer program for maximum likelihood identification of linear multivariable stochastic systems,” in 4th IFAC Symp. Ident. Syst. Parameter Estimation, Tbilisi, U.S.S.R., paper 12.1, Sept. 1976, pp. 508–521.
81. C. E. Minder and I. McMillan, “Estimation of linear compartmental model parameters using marginal likelihood,” Biometrics, vol. 33, pp. 333–341, June 1977.
82. E. Ranjbaran and R. W. McLaren, “Modeling, testing, simulation, and optimization of digitalis pharmacokinetics,” in IEEE Int. Conf. Cybern. Soc., Washington, DC, 1976, pp. 361–367.
83. J. Buell, R. Jelliffe, R. Kalaba, and R. Sridhar, “Modern control theory and optimal drug regimens, I: The plateau effect,” Math. Biosci., vol. 5, pp. 285–296, 1969.
84. —, “Modern control theory and optimal drug regimens, II: Combination therapy,” Math. Biosci., vol. 6, pp. 67–74, 1970.
85. R. W. Jelliffe, J. Buell, R. Kalaba, R. Sridhar, and R. Rockwell, “A computer program for digitalis dosage regimens,” Math. Biosci., vol. 9, pp. 179–193, 1970.
86. L. B. Sheiner, B. Rosenberg, and K. L. Melmon, “Modelling of individual pharmacokinetics for computer-aided drug dosage,” Comput. Biomed. Res., vol. 5, pp. 441–459, 1972.
87. T. T. Soong, “Pharmacokinetics with uncertainties in rate constants-II: Sensitivity analysis and optimal dosage control,” Math. Biosci., vol. 13, pp. 391–396, 1972.
88. J. G. Pierce and A Schumitzky, “Optimal impulsive control of compartment models, I: Qualitative aspects,” J. Optimiz. Theory Appl., vol. 18, pp. 537–554, Apr. 1976.
89. Y. Biran and B. McInnis, “Optimal control of bilinear systems to identify time varying effects of antitumor drugs,” in A Link Between Science and Applications of Automatic Control, 7th IFAC Triennial World Congress, vol. 1, A. Niemi, B. Wahlström, and J. Virkkunen, Eds., Helsinki, Finland, 1978, pp. 549–555.
90. M. Gibaldi, Biopharmaceutics and Clinical Pharmacokinetics, 2nd ed. Philadelphia, PA: Lea & Febiger, 1977.
91. W. L. Chiou, M. A. F. Gadalla, and G. W. Peng, “Method for the rapid estimation of the total body drug clearance and adjustment of dosage regimens in patients during a constant-rate intravenous infusion,” J. Pharmacokin. Biopharm., vol. 6, pp. 135–151, 1978.
92. R. E. Notari, A. M. Burkman, and W. K. van Tyle, “Structural effects in drug distribution: Whole animal pharmacokinetics,” J. Pharm. Pharmac., vol. 26, pp. 481–492, 1974.
93. S. A. Glantz, R. Kernoff, and R. H. Goldman, “Age-related changes in ouabain pharmacology,” Circ. Res., vol. 39, pp. 407–414, Sept. 1976.
94. L. Létourneau-Saheb, L. Lapierre, R. Daigneault, M. Prud’Homme, G. St-Louis, and G. Sirois, “Gentamicin pharmacokinetics during hemodialysis in patients suffering from chronic renal failure,” Int. J. Clin. Pharmacol, vol. 15, pp. 116–120, 1977.
95. J. J. Schentag, W. J.Jusko, J.W. Vance, T.J. Gumbo, E. Abrutyn, M. DeLattre, and L. M. Gerbracht, “Gentamicin disposition and tissue accumulation on multiple dosing,” J. Pharmacokin. Biopharm., vol. 5, pp. 559–577, 1977.
96. S. K. Chandrasekaran, W. Bayne, and J. E. Shaw, “Pharmacokinetics of drug permeation through human skin,” J. Pharmaceut. Sci., vol. 67, pp. 1370–1374, Oct. 1978.
97. S. M. Bryson, B. Whiting, and J. R. Lawrence, “Disopyramide serum and pharmacologic effect kinetics applied to the assessment of bioavailability,” Brit. J. Clin. Pharmac., vol. 6, pp. 409–419, 1978.
98. S. Niazi and W. L. Chiou, “Fluorocarbon aerosol propellants XI: Pharmacokinetics of dichlorodifluoromethane in dogs following single and multiple dosing,” J. Pharmaceut. Sci, vol. 66, pp. 49–53, Jan. 1977.
99. A. J. McLean, P. J. McNamara, P. du Souich, M. Gibaldi, and D. Lalka, “Food, splanchnic blood flow and bioavailability of drugs subject to first-pass metabolism,” Clin. Pharmacol Ther., vol. 24, pp. 5–10, July 1978.
100. L. I. Harrison and M. Gibaldi, “Physiologically based pharmacokinetic model for digoxin disposition in dogs and its preliminary application to humans,” J. Pharmaceut. Sci, vol. 66, pp. 1679–1683, Dec. 1977.
101. Y. -J. Lin, D. J. Weidler, D. C. Garg, and J. G. Wagner, “Novel method of estimating volume of distribution of a drug obeying Michaelis-Menten elimination kinetics,” J. Pharmacokin. Biopharm., vol. 6, pp. 197–207, 1978.
102. J. G. Wagner, “Time to reach steady state and prediction of steady state concentrations for drugs obeying Michaelis-Menten elimination kinetics,” J. Pharmacokin. Biopharm., vol. 6, pp. 209–225, 1978.
103. L. Z. Benet, “General treatment of linear mammillary models with elimination from any compartment as used in pharmacokinetics,” J. Pharmaceut. Sci., vol. 61, pp. 536–541, Apr. 1972.
104. D. P. Vaughan and A. Trainor, “Derivation of general equations for linear mammillary models when the drug is administered by different routes,” J. Pharmocokin. Biopharm., vol. 3, pp. 203–218, 1975.
105. V. F. Smolen, “Theoretical and computational basis for drug bioavailability determinations using pharmacological data. II. Drug input ⇄ response relationships,” J. Pharmacokin. Biopharm., vol. 4, pp. 355–375, 1976.
106. J. G. Wagner, “Linear pharmacokinetic models and vanishing exponential terms: Implications in pharmacokinetics,” J. Pharmacokin. Biopharm., vol. 4, pp. 395–425, 1976.
107. D. J. Cutler, “On the definition of the compartment concept in pharmacokinetics,” J. Theor. Biol., vol. 73, pp. 329–345, 1978.
108. W. A. Colburn, A. R. Di Santo, and M. Gibaldi, “Pharmacokinetics of erythromycin on repetitive dosing,” J. Clin. Pharmacol., vol. 17, pp. 592–600, 1977.
109. E. R. Carson, C. Cobelli, and L. Finkelstein, “The identification of metabolic systems-A review,” presented at the 5th IFAC Symp. Ident. Syst. Parameter Estimation, Darmstadt, Germany, Sept. 1979.
110. R. F. Brown, E. R. Carson, L. Finkelstein, K. R. Godfrey, and R. P. Jones, “Adequacy of measurements in compartmental modelling of metabolic systems,” Med. Biol. Eng. Comput., vol. 17, pp. 216–222, Mar. 1979.
111. J. J. Di Stefano and F. Mori, “Parameter identifiability and experiment design: Thyroid hormone metabolism parameters,” Amer. J. Physiol., vol. 233, pp. R134-R144, 1977.
112. M. L. Sanfelippo, W. E. Walker, D. A. Hall, and R. S. Swenson, “Clinical application of a single compartment model to urea and creatinine kinetics in dialysis therapy,” Comput. Programs Biomed., vol. 8, pp. 44–50, 1978.
113. H. Freund and P. Gendry, “Lactate kinetics after short strenuous exercise in man,” European J. Appl. Physiol., vol. 39, pp. 123–135, 1978.
114. C. Cobelli, M. Frezza, and C. Tiribelli, “Modeling, identification and parameter estimation of bilirubin kinetics in normal, hemolytic and Gilbert’s states,” Comput. Biomed. Res., vol. 8, pp. 522–537, 1975.
115. A. D. Waxman, P. A. Leins, and J. K. Siemsen, “Invivo dynamic studies of hepatocyte function: A computer method for the interpretation of rose bengal kinetics,” Comput. Biomed. Res., vol. 5, pp. 1–13, 1972.
116. P. A. Insel, J. E. Liljenquist, J. D. Tobin, R. S. Sherwin, P. Watkins, R. Andres, and M. Berman, “Insulin control of glucose metabolism in man,” J. Clin. Invest., vol. 55, pp. 1057–1066, May 1975.
117. L. H. M. van Stekelenburg, N. Al, A. Kooman, and J. F. W. Tertoolen, “A three-compartment model for the transport and distribution of hippuran,” Phys. Med. Biol., vol. 21, pp. 74–84, 1976.
118. L. Krishnan, E. C. Krishnan, and W. R. Jewell, “Theoretical treatment of the distribution and degradation of vascular, interstitial and intracellular albumin,” J. Theor. Biol., vol. 67, pp. 609–623, 1977.
119. C. H. G. Irvine, “Four compartment model of thyroxine metabolism,” in Proc. Int. Conf. Thyroid Hormone Metabolism, Glasgow, Scotland, 1974. London, England: Pergamon, 1975, ch. 10.
120. R. Kroker, M. S. Anwer, and D. Hegner, “A compartmental model for hepatic transport of taurocholic acid in isolated perfused rat liver,” Arch. Pharmacol., vol. 303, pp. 287–293, July 1978.
121. R. G. Brown, K. R. Godfrey, and A. Knell, “Compartmental modelling based on methionine tolerance test data: A case study,” Med. Biol Eng. Comput., vol. 17, pp. 223–229, Mar. 1979.
122. K. Šudová and P. Langer, “Iodine kinetics and hypothalamo-pituitary regulation of thyroid function following its shortterm inhibition: Simulation with the aid of compartmental system modelling (COSMO), Comput. Biomed. Res., vol. 8, pp. 88–96, 1975.
123. C. Berzuini, P. C. Franzone, M. Stefanelli, and C. Viganotti, “Iron kinetics: Modelling and parameter estimation in normal and anemic states,” Comput. Biomed. Res., vol. 11, pp. 209–227, 1978.
124. C. C. Schwartz, M. Berman, Z. R. Vlahcevic, L. G. Halloran, D. H. Gregory, and L. Swell, J. Clin. Invest., vol. 61, pp. 408–423, Feb. 1978.
125. A Rescigno and E. Gurpide, “Estimation of average times of residence, recycle and interconversion of blood-borne compounds using tracer methods,” J. Clin Endocrinol Metab., vol. 36, pp. 263–276, 1973.
126. E. Gurpide, Tracer Methods in Hormone Research, vol 8, Monographs on Endocrinology. Berlin, Germany: Springer, 1975.
127. R. Navalesi, A. Pilo, and E. Ferrannini, “Kinetic analysis of plasma insulin disappearance in nonketotic diabetic patients and in normal subjects,” J. Clin. Invest., vol. 61, pp. 197–208, Jan. 1978.
128. A. Jung, P. Bartholdi, B. Mermillod, J. Reeve, and R. Neer, “Critical analysis of methods for analysing human calcium kinetics,” J. Theor. Biol., vol. 73, pp. 131–157, 1978.
129. L. J. Bledsoe and G. M. van Dyne, “A compartment model simulation of secondary succession,” in Systems Analysis and Simulation in Ecology, vol. 1, B. C. Patten, Ed. New York: Academic, 1971, ch. 8, pp. 479–511.
130. R. A. Kelly, “Conceptual ecological model of the Delaware estuary,” in Systems Analysis and Simulation in Ecology, vol. IV, B. C. Patten, Ed. New York: Academic, 1976, ch. 1, pp. 3–45.
131. R. J. Mulholland and C. S. Sims, “Control theory and the regulation of ecosystems,” in Systems Analysis and Simulation in Ecology, vol. IV, B. C. Patten, Ed. New York: Academic, 1976, ch. 14, pp. 373–388.
132. M. D. Kamen, Isotopic Tracers in Biology, 3rd ed. New York: Academic, 1957.
133. S. M. Walas, Reaction Kinetics for Chemical Engineers. New York: McGraw-Hill, 1959.
134. G. R. Gavalas, Nonlinear Differential Equations of Chemically Reacting Systems. New York: Springer, 1968.
135. M. Berman, J. O. Eichling, A. M. Harper, and K. L. Zierler, “Panel discussion on ‘The best present method for summarizing the results of dynamic tracer studies is multicompartmental analysis,’ ” in Computer Processing of Dynamic Images from an Anger Scintillation Camera, K. B. Larson and J. R. Cox, Eds. New York: Society of Nuclear Medicine, 1974, ch. 11, pp. 152–168.
136. R. F. Brown and K. R. Godfrey, “Comments on ‘Some observations on the physical realizability of compartmental models with delays,’” IEEE Trans. Biomed. Eng., vol. BME-26, pp. 646–648, Nov. 1979.
137. R. M. Lewis and B. D. O. Anderson, “Insensitivity of a class of nonlinear compartmental systems to the introduction of arbitrary time delays,” IEEE Trans. Circuit Syst., to be published.
138. R. F. Brown and J. P. Norton,” Identifiability of large compartmental models,” to be presented at the 2nd IFAC Symp. Large Scale Syst. Theory Appl., Toulouse, France, June 1980.
139. D. Z. D’Argenio and A. Schumitzky, “A program package for simulation and parameter estimation in pharmacokinetic systems,” Comput. Prog. Biomed., vol. 9, pp. 115–134, Mar. 1979.
140. J. G. Pierce and A. Schumitzky, “Optimal control of compartment models, II: Algorithm,” J. Optimiz. Theory Appl., vol. 26, pp. 581–599, Dec. 1978.