Biomedical Engineering Reference
In-Depth Information
Equation (7.28) is useful in studying the effects of pathological conditions. In some types of
trauma,
D
p
A
increases, causing an interstitial volume increase (swelling). If plasma protein
concentration,
c
C
, increases, then the flow rate into the interstitial volume decreases.
7.4 COMPARTMENTAL MODELING BASICS
In the previous section, we worked from basic principles to examine diffusion and
osmosis. Here we use a systematic approach called compartmental modeling to describe
the movement of a solute through a system. Compartmental modeling involves describing
a system with a finite number of compartments, each connected by a flow of solute from
one compartment to another. Movement of the solute can be any of the following:
1.
Among organelles in a cell
2.
A cell and the extracellular space
3.
An organ and the interstitial space
4.
Among organs through the circulatory system
In modeling a system with compartments in this chapter, we consider a lumped param-
eter system rather than a distributed system. Therefore, we work with ordinary differential
equations. More accurate distributed system models have solutions that involve partial dif-
ferential equations. In many cases, however, we will find that the more complex distributed
system models are quite accurately described by compartmental models using a large num-
ber of compartments.
Compartmental modeling applied to the human body is usually a gross simplification of
the inherent underlying processes, and there may be a limited anatomical relationship
between the true system and the model. For example, we may define the compartments
of the body as the plasma compartment (that includes all noncellular fluids in all the blood
vessels), tissue compartment (that includes the fluid in 75 trillion cells), interstitial compart-
ment, and the lymph compartment, as illustrated in Figure 7.1. Naturally, the tissue com-
partment can be further divided into organs and so forth, and the plasma compartment
can be further divided into arteries, veins, and progressively smaller vessels. Nevertheless, we
will see that compartmental modeling is very useful in describing the movement of a solute
through the body, especially when small perturbations from steady-state are considered.
Many important applications of compartmental analysis are found in pharmacokinetics.
The alternative to compartmental modeling involves modeling the system via a fluid
model of the blood and lymph systems, and the transport phenomena of the solute in each
organ. The problem with this approach is finding a model that is time dependent, 3-D, and
distributed. The solute is not homogeneously distributed in the organs, and we do not have
detailed information about the parameters that describe the model.
As usual in physiological modeling, identifying the number of compartments and the
connections between compartments is the most difficult challenge, along with collecting
appropriate data. Regardless of the simplicity of the model, there should be some relation-
ship between the model and the system being modeled based on a priori knowledge.
Furthermore, it should be possible to test the model after collecting data and compare its
performance to the real system. After testing, the model is usually modified, typically
