Compartmental Modeling - Introduction to Biomedical Engineering - page 365

TABLE 7.2 Approximate Intracellular (Cytoplasm) and Extracellular
Concentrations of the Important Ions across a Mammalian Cell Membrane

Ion Intracellular (mM/L) Extracellular (mM/L)

K þ

140 4

Na þ 10 142

Cl 4 103

Ca þþ 0.0001 2.4

capillary is about the same size as a red blood cell, red blood cell movement through the
capillary involves significant contact with the wall.
Pores in the capillary wall between cells allow movement between the interstitial volume
and blood volume. Water freely moves through the capillary membrane. In fact, all other
components of the plasma easily move through the capillary membrane except for some
proteins such as albumin. While the interstitial fluid is similar to the plasma except for
some proteins, movement of fluid through the interstitial volume is much slower than
through the plasma. This is due to the structure of the interstitium that is maintained by
collagen fiber bundles and proteoglycan filaments. Fluid flow through the network of
filaments is mostly driven by diffusion. We will return to diffusion in capillaries in
Section 7.3.5.
In this section we presented the cell as a static structure. In actuality, the cell is dynamic,
and rapid changes in ionic concentrations are possible. The amount of water that moves in
and out of the cell each second is 100 times the volume of the cell; this process is balanced
so there is no net movement of water. Chapter 12 describes the neuron, which, when sig-
naling, involves the rapid movement of sodium and potassium across the membrane.
Chapter 4 describes the muscle and muscle contraction involving the rapid movement of
calcium across the membrane.

7.3.2 Fick's Law of Diffusion
Fick's Law of diffusion describes the time course of the transfer of a solute between two
compartments that are separated by a thin membrane, given by

dq

dt ¼ DA dc

ð 7 : 1 Þ

dx

where

q ¼ quantity of solute

A ¼ membrane surface area

c ¼ concentration

D ¼ diffusion coefficient

dx ¼ membrane thickness

dc
dx ¼

concentration gradient