Next, the Cartesian coordinate system is aligned with the principal axes of the hydraulic conductivity tensor; this avoids the need for cross derivatives.
2.
Where \ mathbf \ Sigma _ i is the intracellular conductivity tensor, v is the transmembrane potential, I _ \ text { ion } is the transmembrane ionic current per unit area, C _ m is the membrane conductivity per unit area, \ lambda is the intra-to extracellular conductivity ratio, and \ chi is the membrane surface area per unit volume ( of tissue ).
3.
Where w _ m is the volumetric fraction of the total porosity occupied by the porous medium, \ Gamma _ { ex } is the internal fluid exchange rate ( e . g . surface water, wells, and tile drains ), Q is the external fluid outside of the model domain, \ theta _ s is the saturated water content, S _ w is the degree of saturation, \ textbf { K } is the hydraulic conductivity tensor, k _ r is the relative permeability of the medium calculated as a function of saturation, \ psi is the pressure head, and z is the elevation head.
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