Table 1.

Parameter list, their units and values if known. All CPA specific and cell and system parameters are determined from previous studies. In particular, all cell specific parameter values are from Benson et al. [27] and Liu et al. [28] and the solute diffusivity values, their activation energies, and the tortuosity value are from Maroudas et al. [29] and Page et al.[30]. Note that the fitting parameters are all functionally related (see Section 2.3), and $\overline{A_{\text{is}}}$ is the sole fitting parameter of the model.

CPA specific Parameter	Parameter Name	Value (EG)	Value (DMSO)	Units
Lp	Hydraulic Conductivity at 22 °C	0.00375	0.00375	μm s−1 atm−1
Ps	Solute Permeability	0.105	0.132	μm s−1
$E_{\mathrm{a}}^{L_p}$	Activation energy of water permeability	11.69	12.43	kCal/mol
$E_{\mathrm{a}}^{P_s}$	Activation energy of Solute Mobility	20.35	18.34	kCal/mol
σ	Reflection coefficient	0.75	0.55	unitless
ω	Solute mobility (temperature dependent calculated value)	—		Ps = ωR̄T

Cell and system Parameter	Parameter Name	Value	Units
V	Cell volume (individual islet cell)	970	μm3
Vb	Osmotically inactive fraction of the cell	0.40	unitless
A	Surface area of cell (assumed constant)	408	μm2
λ	Tortuosity	1.44	unitless
D	Diffusivity of CPA in water at 22 °C	1100	μm/s2
D	Diffusivity of NaCl in water at 22 °C	1075	μm/s2
D̄	Diffusivity of solute in tissue	D̄= Dλ−2	μm/s2
$E_{\mathrm{a}}^D$	Activation energy of diffusivity	5.46	kCal/mol
R	Gas constant	0.0821	L atm K−1 mol−1

Fitting Parameters	Parameter Name	Units
δ	Effective channel radius	μm
Ac	Surface area of cell in contact with other cells	μm2
Ais	Surface area of cell in contact with intracellular media	μm2
$\overline{A_{\text{is}}}$	Normalized surface area of cell in contact with intracellular media	μm2

State Variables	Variable Name	Units
T	Temperature	K
S	Intracellular moles of permeating solute	mol
C	Intracellular CPA Concentration	mol/kg
K	Intracellular salt concentration	mol/kg
c	Extracellular CPA Concentration	mol/kg
k	Extracellular salt concentration	mol/kg
C̄	Mean CPA concentration	mol/kg
Js	Solute mole flux	mol/μm2/s
Jv	Volume flux 6	μm/s
t	Time	s
R	Radius of whole islet	μm
r	Radius from center of whole islet	μm