Biomedical Engineering Reference
In-Depth Information
A model with a number of these reactors with different interconnections can
be similarly developed. Each tank is considered as a compartment (Figure 10.3).
The interconnections represent transfer of material (mass/time) which physiologi-
cally represents transport from one location to another, chemical transformation,
or both. However, it is difficult to have physiological/anatomical correlates for
every scenario. For example, if one were to use a single compartmental model for
clearance of a component in the kidney, the solution is identical to the single-tank
example. However, the physiological phenomenon is glomerular filtration not dilu-
tion within the tank. Nevertheless, the amount of a component absorbed per unit
time can be calculated within the model; alternatively, the change in chemical con-
centration in blood or the tissue representing the port of entry may be simulated
using appropriate equations.
There are various ways to classify compartmental models. However, typically
there can be either mechanistic models or physiological models. In physiologically
based compartmental models, compartments are described, as far as possible, with
respect to the actual anatomy and physiology of the test animal. Typically, physi-
ological systems are more complex and need more measurements to validate the
model. Very often analytical solutions are not possible and need computer pro-
grams to solve compartmental systems.
With the mechanistic compartmental models, concentration in tissue versus
time is determined by experiment and then described by the equations associated
with a particular model. For example, the body is described as consisting of two
compartments with appropriate intercompartmental transfer rate constants. The
model parameters, including the volumes of the compartments and the transfer rate
constants, are estimated by fitting the model to the data hence the term, data-based
compartmental models. The model parameters bear no direct correspondence with
actual tissue volumes or blood flow rates in the test animals.
10.2.1.1 Apparent Volume of Distribution
In the human body, determining the volume of the compartment is a significant
challenge. For example, when a therapeutic agent is administered to a 70-kg pa-
tient, one could assume 3L of plasma to be the volume of the compartment. How-
ever, not all of the plasma is available for dissolution of the therapeutic agent as
much of it could be circulating in other parts of the body. Further, the therapeutic
agent could bind to blood components and/or enters the various tissue compart-
ments where it may be dissolved in lipid and water components and be bound to
tissue macromolecules. An approach taken is determining the initial concentration
(
C
0
) of the drug at time zero and then estimating the apparent volume of distribu-
tion of the therapeutic agent using the dosage (in mass), given by the relation
Dose
[mass units]
V
=
D
C
0
As
V
D
relates the total amount of drug to the plasma concentration, it is also
useful in understanding the process of drug distribution in the body. Another
