Second, the presence of cells and transport of water and CPA across
cell membranes affects the rate of transport through the extracellular space. Typically, cells would be expected to slow mass transfer
because the cell membranes provide an additional barrier. The third
effect is mediated by changes in cell size. As cells expand in a local
tissue region, they concentrate fixed charges, which would in turn
draw water to that region. In this way, cell size changes can lead to
overall changes in tissue size. Overall, the cell response is inherently
dependent on the tissue response and vice versa.
3 Tissue Mass Transfer Models
We restrict our discussion to mass transfer models in threedimensional tissues that are exposed to CPA only at the tissue
boundary. There are various considerations that can be used to
classify previously reported mathematical modeling approaches. A
key consideration is whether the model is capable of predicting
changes in the size of the tissue during CPA equilibration. The
most common approach for modeling mass transfer in tissues is to
use Fick’s law of diffusion, which assumes that the size of the tissue
remains constant, but other modeling approaches have been
reported that account for tissue size changes. Another distinction
we can make is whether the mass transfer driving forces are represented using a dilute (“ideal”) or non-dilute (“nonideal”)
approach. In general, as concentration increases, there is a departure of one or more constituent activity coefficients from unity, or
in other words a departure from solution ideality. Vitrification
methods typically involve the use of high CPA concentrations that
fall in the non-dilute regime. Another key consideration for modeling mass transfer in tissues is the modes of mass transfer that are
considered in the model. There are three main modes of mass
transfer: transport across the cell membrane from the intracellular
solution to the interstitial space, transport through the interstitial
space, and transport from cell to cell. The specific tissue one wants
to model dictates the importance of one transport mode over the
others. For instance, in a low-cell density tissue such as cartilage,
transport across the cell membrane and from cell to cell are of less
importance than interstitial transport. In a high-cell density tissue
such as ovarian tissue, the importance of the cell transport terms
would increase. In the discussion below, we present previously
reported tissue mass transfer models in the context of these modeling considerations.
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Ross M. Warner and Adam Z. Higgins
cell membranes affects the rate of transport through the extracellular space. Typically, cells would be expected to slow mass transfer
because the cell membranes provide an additional barrier. The third
effect is mediated by changes in cell size. As cells expand in a local
tissue region, they concentrate fixed charges, which would in turn
draw water to that region. In this way, cell size changes can lead to
overall changes in tissue size. Overall, the cell response is inherently
dependent on the tissue response and vice versa.
3 Tissue Mass Transfer Models
We restrict our discussion to mass transfer models in threedimensional tissues that are exposed to CPA only at the tissue
boundary. There are various considerations that can be used to
classify previously reported mathematical modeling approaches. A
key consideration is whether the model is capable of predicting
changes in the size of the tissue during CPA equilibration. The
most common approach for modeling mass transfer in tissues is to
use Fick’s law of diffusion, which assumes that the size of the tissue
remains constant, but other modeling approaches have been
reported that account for tissue size changes. Another distinction
we can make is whether the mass transfer driving forces are represented using a dilute (“ideal”) or non-dilute (“nonideal”)
approach. In general, as concentration increases, there is a departure of one or more constituent activity coefficients from unity, or
in other words a departure from solution ideality. Vitrification
methods typically involve the use of high CPA concentrations that
fall in the non-dilute regime. Another key consideration for modeling mass transfer in tissues is the modes of mass transfer that are
considered in the model. There are three main modes of mass
transfer: transport across the cell membrane from the intracellular
solution to the interstitial space, transport through the interstitial
space, and transport from cell to cell. The specific tissue one wants
to model dictates the importance of one transport mode over the
others. For instance, in a low-cell density tissue such as cartilage,
transport across the cell membrane and from cell to cell are of less
importance than interstitial transport. In a high-cell density tissue
such as ovarian tissue, the importance of the cell transport terms
would increase. In the discussion below, we present previously
reported tissue mass transfer models in the context of these modeling considerations.
180
Ross M. Warner and Adam Z. Higgins