where f c represents the change in concentration with time of the
extracellular space due to exchange with the intracellular space. A
key assumption of their model which enables prediction of changes
in islet volume is that cells always occupy 80% of the islet volume.
This somewhat arbitrary assumption creates a direct link between
changes in the volume of islet cells and the resulting change in the
size of the whole islet. While this assumption is consistent with
experimental data for islets, it does not have a physical basis and
thus may not be generally extensible to the full range of conditions
encountered during CPA equilibration for islets as well as other
tissue types. The model is also limited because it is based on the
assumption of an ideal and dilute solution.
3.2.2 Network
Thermodynamic Model
Another example of a model that enables prediction of tissue volume changes based on coupled interstitial transport and cell membrane transport comes from de Freitas and colleagues [30]. In their
work, a network thermodynamic model is presented to describe the
behavior of a pancreatic islet during CPA equilibration. The pancreatic islet was subdivided into two cellular compartments—one
representing cells near the islet surface and the other representing
islet cells near the center—as well as interstitial compartments
alongside and between the cellular compartments. Flow of water
and CPA from the cellular compartments to the interstitial space
was modeled based on chemical potential driving forces using the
general theory of irreversible thermodynamics. The resulting equations are similar to the Kedem-Katchalsky equations, but the kinetic
parameters are specific to the cellular compartments in the model,
which are larger than individual islet cells. Flow of water and CPA
between adjacent interstitial compartments was assumed to be
proportional to their respective chemical potential differences.
Interaction between the flow of water and CPA in the interstitial
space was neglected. This model enables prediction of islet size
changes in terms of the sum of the cell size changes and changes
in the volume of the interstitial space. In contrast to the model of
Benson et al. [37], the model of de Freitas and colleagues enables
prediction of changes in the volume of the interstitial space directly
based on the calculated flows of water and CPA through the interstitial space. However, the mechanical effects of changes in islet size
are not considered in the model, and dilute approximations for the
chemical potentials were used.
3.2.3 Non-dilute
Biomechanical
Transport Model
The model developed by Abazari et al. [22] leverages the biomechanical triphasic theory of articular cartilage as proposed by
Lai et al. [29]. In the triphasic theory, cartilage is approximated as a
continuum of water, salt, and the extracellular matrix (solids).
Abazari et al. added a fourth phase to the theory: CPA. Much like
in the Maxwell-Stefan diffusion formalism, the thermodynamic
driving force for species movement is balanced by the frictional
184
Ross M. Warner and Adam Z. Higgins
extracellular space due to exchange with the intracellular space. A
key assumption of their model which enables prediction of changes
in islet volume is that cells always occupy 80% of the islet volume.
This somewhat arbitrary assumption creates a direct link between
changes in the volume of islet cells and the resulting change in the
size of the whole islet. While this assumption is consistent with
experimental data for islets, it does not have a physical basis and
thus may not be generally extensible to the full range of conditions
encountered during CPA equilibration for islets as well as other
tissue types. The model is also limited because it is based on the
assumption of an ideal and dilute solution.
3.2.2 Network
Thermodynamic Model
Another example of a model that enables prediction of tissue volume changes based on coupled interstitial transport and cell membrane transport comes from de Freitas and colleagues [30]. In their
work, a network thermodynamic model is presented to describe the
behavior of a pancreatic islet during CPA equilibration. The pancreatic islet was subdivided into two cellular compartments—one
representing cells near the islet surface and the other representing
islet cells near the center—as well as interstitial compartments
alongside and between the cellular compartments. Flow of water
and CPA from the cellular compartments to the interstitial space
was modeled based on chemical potential driving forces using the
general theory of irreversible thermodynamics. The resulting equations are similar to the Kedem-Katchalsky equations, but the kinetic
parameters are specific to the cellular compartments in the model,
which are larger than individual islet cells. Flow of water and CPA
between adjacent interstitial compartments was assumed to be
proportional to their respective chemical potential differences.
Interaction between the flow of water and CPA in the interstitial
space was neglected. This model enables prediction of islet size
changes in terms of the sum of the cell size changes and changes
in the volume of the interstitial space. In contrast to the model of
Benson et al. [37], the model of de Freitas and colleagues enables
prediction of changes in the volume of the interstitial space directly
based on the calculated flows of water and CPA through the interstitial space. However, the mechanical effects of changes in islet size
are not considered in the model, and dilute approximations for the
chemical potentials were used.
3.2.3 Non-dilute
Biomechanical
Transport Model
The model developed by Abazari et al. [22] leverages the biomechanical triphasic theory of articular cartilage as proposed by
Lai et al. [29]. In the triphasic theory, cartilage is approximated as a
continuum of water, salt, and the extracellular matrix (solids).
Abazari et al. added a fourth phase to the theory: CPA. Much like
in the Maxwell-Stefan diffusion formalism, the thermodynamic
driving force for species movement is balanced by the frictional
184
Ross M. Warner and Adam Z. Higgins