Biomedical Engineering Reference
In-Depth Information
7.1 INTRODUCTION
Compartmental modeling describes the movement of a substance from one compartment
to another. Its origins are based on the metabolism of tracer-labeled compound studies
in the 1920s. As we will see, compartmental modeling is a special case of physiological
modeling, which is covered elsewhere in this topic. Primarily, it is concerned with main-
taining correct chemical levels in the body and their correct fluid volumes. A compartment
can be a volume (or space) or the amount of a substance in a volume. Both representations
are commonly used. Here we use the amount of substance in a volume as a compartment,
with each compartment assumed to be homogeneous, as described later in the chapter. The
process of transfer of substance from one compartment to another is based on diffusion and
mass conservation. As shown, compartmental analysis provides a uniform theory that can
be systematically applied to many linear and nonlinear systems. While interest in compart-
mental analysis here is focused on the human body, other engineers and scientists use
this technique in studying evolution, carcinogenesis, chemical reactions, infectious disease
models, and even semiconductor design and fabrication.
Before investigating compartmental modeling, Fick's Law of diffusion and osmosis is
presented first from basic principles. Next, the volume of a cell and capillary diffusion
are discussed. The basics of compartmental modeling are described from simple to more
complex models that are increasingly more realistic. Much of the material in this chapter
is based on the topic by Godfrey.
7.
2 SOLUTES, COMPARTMENTS, AND VOLUME
S
When analyzing systems of the body characterized by a transfer of a solution from one
compartment to another, such as the respiratory and circulatory systems, it is convenient
to describe the system as a finite series of interconnected compartments. A
is
defined as a homogeneous mixture of two or more substances in any of the three states
of matter: gas, liquid, or solid. Within a solution, we may have a mixture of matter—for
instance, solid within a liquid, gas within a liquid, and so on. A solution is described by
a component called a solute and another called the solvent. While there are no absolute
rules regarding which component is the solute and which is the solvent, we typically call
the component in the lesser amount the solute and the other the solvent. For instance, blood
is a fluid that consists of 90 percent water with suspended cells such as red blood cells
(erythrocytes), white blood cells (leukocytes), platelets, small molecules (i.e., glucose and
carbon dioxide), large proteins, and electrolytes (i.e., sodium, calcium, magnesium, potas-
sium). The solute could be a particular protein, and the solvent is the blood minus the
protein.
The following are some of the readily identifiable compartments in the human body:
solution
Cell nucleus that is separated from the cytoplasm of the cell
Internal organelle volumes, such as the mitochondria, endoplasmic reticulum, and so on
that are separated from the cytoplasm
Cell volume that is separated from the extracellular space by the cell membrane
