Biomedical Engineering Reference
In-Depth Information
computed. To solve this problem Kleinhans (1998) developed a two-parameter
(2P) formalism that uses only two parameters: filtration and permeation. The
comparison of 2P and KK formalisms can be found in several papers (Katkov
2000; Chuenkhum and Cui 2006).
Both the KK and 2P formalisms describe global transport across mem-
branes and do not take into account possible inhomogeneities in the mem-
brane. Both methods are based on thermodynamical approach and they do
not consider the microscopic structure of the membrane. They yield only very
limited and indirect information on the details of transport mechanisms of
water and various solutes. On one hand that means that they are very general
and apply to a variety of membranes and membrane permeation mechanisms.
On the other hand, as our understanding of membrane structure and bio-
physical mechanisms of permeation of various substances improves, it makes
it dicult to relate the macroscopic description of membrane transport with
the microscopic details of transport mechanisms. The mechanistic formalism
(ME) proposed recently (Kargol 2002; Kargol and Kargol 2003, 2006) uses
several concepts of the KK formalism; however, it is based on a specific model
of a membrane, in which permeation of water and solutes takes place through
membrane pores. The aim of this formalism was to link the macroscopic trans-
port equations with the microscopic properties of a membrane described by a
specific, although very simplified, model.
In this chapter we describe the KK, 2P, and ME formalisms. We show
that the KK and ME formalisms are equivalent in the global form, but the
latter predict effects not detectable by the KK formalism, which may have
physiological significance. We discuss two applications of the KK and ME
equations in biology.
8.2 Thermodynamic KK Equations
Cell membrane forms a barrier separating the cytoplasm from the external
environment. It permits a controlled exchange of water and various chemical
compounds, as required for cell homeostasis and for all physiologic processes
the cell participates in. At the same time the membrane maintains proper gra-
dients of concentration, pressure, temperature, and electric potential between
the cytoplasm and the extracellular medium. These two fundamental func-
tions of the cell membrane can be described in terms of transport processes,
such as diffusion or osmosis.
Membrane transport processes, like most natural processes, are irre-
versible. On the basis of the linear thermodynamics of irreversible processes,
in 1958 Kedem and Katchalsky developed a formalism describing passive
membrane transport processes. It has been widely accepted and is commonly
 
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