An approach to the residence time distribution for stochastic multi-compartment models

Stochastic compartmental models are widely used in modeling processes such as drug kinetics in biological systems. This paper considers the distribution of the residence times for stochastic multi-compartment models, especially systems with non-exponential lifetime distributions. The paper first der...

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Bibliographic Details
Published in:Mathematical biosciences 2004-10, Vol.191 (2), p.185-205
Main Authors: Yu, Jihnhee, Wehrly, Thomas E.
Format: Article
Language:English
Subjects:
Anticholesteremic Agents - administration & dosage
Anticholesteremic Agents - pharmacology
Body Fluid Compartments
Cofactor rule
Feedback, Physiological - physiology
Humans
Hypercholesterolemia - drug therapy
Hypercholesterolemia - metabolism
Markov Chains
Models, Biological
Moment generating function
Pharmacokinetics
Pravastatin - administration & dosage
Pravastatin - pharmacokinetics
Residence time
Saddlepoint approximation
Semi-Markov process
Stochastic compartment model
Stochastic Processes
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Summary:Stochastic compartmental models are widely used in modeling processes such as drug kinetics in biological systems. This paper considers the distribution of the residence times for stochastic multi-compartment models, especially systems with non-exponential lifetime distributions. The paper first derives the moment generating function of the bivariate residence time distribution for the two-compartment model with general lifetimes and approximates the density of the residence time using the saddlepoint approximation. Then, it extends the distributional approach to the residence time for multi-compartment semi-Markov models combining the cofactor rule for a single destination and the analytic approach to the two-compartment model. This approach provides a complete specification of the residence time distribution based on the moment generating function and thus facilitates an easier calculation of high-order moments than the approach using the coefficient matrix. Applications to drug kinetics demonstrate the simplicity and usefulness of this approach.
ISSN:0025-5564
1879-3134
DOI:10.1016/j.mbs.2004.06.005