Multi-compartment model

Abstract: Competing compartment models of different complexities have been used for the quantitative analysis of dynamic contrast-enhanced magnetic resonance imaging data. We present a spatial elastic net approach that allows to estimate the number of compartments for each voxel such that the model complexity is not fixed a priori. A multi-compartment approach is considered, which is translated into a restricted least square model selection problem. This is done by using a set of basis functions for a given set of candidate rate constants. The form of the basis functions is derived from a kinetic model and thus describes the contribution of a specific compartment. Using a spatial elastic net estimator, we chose a sparse set of basis functions per voxel, and hence, rate constants of compartments. The spatial penalty takes into account the voxel structure of an image and performs better than a penalty treating voxels independently. The proposed estimation method is evaluated for simulated images and applied to an in vivo dataset. Copyright © 2013 John Wiley & Sons, Ltd.

Abstract: It is well known in pharmacokinetics that exponential changes in blood concentrations of a drug are not related directly to the properties of the compartments that make up the system under study. A mathematical analysis is presented that permits treatment of the exponential components in a manner analogous to that of the hypothetical compartments. A simple treatment of cumulation processes in the central compartment is done to avoid full analysis of the system. For the circumstance when elimination is confined to the central compartment, total accumulation in the system and the exact volume of distribution are calculated from the blood concentration curve after a single i.v. injection. The method reduces complex accumulation calculations to the simplicity of single compartment formulae.

Abstract: Drug residence time in ''compartmentalized'' human body system had been studied from both deterministic and Markovian perspectives. However, probability and probability density functions for a drug molecule to be (1) in any compartment of study interest, (2) with any defined inter-compartment traveling route, and (3) with/without specified residence times in its visited compartments, has not been systemically reported. In Markovian view of compartmental system, mathematical solutions for the probability or probability density functions, for a drug molecule with any defined inter- compartment traveling routes in the system and/or with specified residence times in any visited compartments, are provided. Matrix convolution is defined and thus employed to facilitate methodology development. Laplace transformations are used to facilitate convolution operations in linear systems. This paper shows that the drug time-concentration function can be decomposed into the summation of a series of component functions, which is named as convolution expansion. The studied probability or probability density functions can be potentially engaged with physiological or pharmacological significances and thus be used to describe a broad range of drug exposure-response relationships.

Abstract: A technique for the determination of transfer rates and other parameters of biological systems is outlined The technique is designed for the presentation of solutions to the generalized equations in order to: determine an appropriate model that produces the same results as observed experimentally; determine the parameters of a specific model that best fit the data; vary the boundary conditions easily for matching or predicting what a particular model will do under other experimental circumstances; use and observe transient effects between compartments (assuming, however, instantaneous mixing in any compartment); and use, in a limited manner, of timevarying coefficients It is also pointed out that such a computer will allow the choice of different flow rates in different directions across the same boundary The model is designed to aid in determining what parameters are measurable or even controllable