The hydraulic conductivity (
L p) is a measure of the amount of fluid that passes through the cell layer or membrane and depends on the surface area of the confluent cell layer on the filter, volumetric flow rate, and pressure decrease. The resistance of the cell layer to flow is inversely related to the cellular hydraulic conductivity. As the resistance across the cell layer increases the cellular hydraulic conductivity decreases. The resistance of the cell layer is also inversely related to the area across which the fluid flows. These variables are related by
equation 1 .
\[L_{\mathrm{p}}{=}\frac{Q}{{\Delta}P{\cdot}A}.\]
To determine the resistance of the cell layer to flow, it is useful to draw parallels between fluid flow and basic electrical circuit theory. In electrical circuit theory,
where
V is the voltage or electromotive force,
I is the current, and
R is the resistance. The electromotive force is the difference in potential or voltage between two points and is analogous to the pressure difference, Δ
P, between the height of the fluid reservoir and the cell layer in the perfusion system that provides the driving force for fluid flow. Current is the rate of flow of electrical charge past a given point and can likewise be compared to the volumetric flow rate,
Q, across the cell layer. Therefore, this expression can be rewritten for fluid flow as
Combining
equations 1 and 3gives
\[R{=}\frac{{\Delta}P}{Q}{=}\frac{1}{L_{\mathrm{p}}A}\]
and
\[\frac{1}{L_{\mathrm{p}}}{=}\frac{{\Delta}PA}{Q}.\]
In calculating accurately the
L p of the cell layer alone, the resistance of the filter membrane must be accounted for. Although more permeable than the cell layer, it is possible that the filter membrane still has a significant resistance to fluid flow. In accounting for this, the
L p of the empty filter alone is calculated experimentally and accounted for in the electrical circuit analogy. In calculating how the hydraulic conductivity of the filter affects the total resistance, the cells and filters can be considered a pair of resistors in series. Drawing again from electrical circuit theory, the total resistance of resistors in series is given by the sum of the individual resistances
\[R_{\mathrm{total}}{=}R_{1}{+}R_{2}{+}R_{3}{+}{\ldots}\]
or
\[R_{\mathrm{cells}{+}\mathrm{filter}}{=}R_{\mathrm{cells}}{+}R_{\mathrm{filter}}\]
and
\[\frac{1}{L_{\mathrm{p,cells}{+}\mathrm{filter}}}{=}\frac{1}{L_{\mathrm{p,cells}}}{+}\frac{1}{L_{\mathrm{p,filter}}}.\]
Combining
equations 5 and 8and solving for
L p,cells gives
\[L_{\mathrm{p,cells}}{=}\frac{Q_{\mathrm{cells}{+}\mathrm{filter}}}{{\Delta}PA\left(1{-}\frac{Q_{\mathrm{cells}{+}\mathrm{filter}}}{Q_{\mathrm{filter}}}\right)}.\]
From this equation, the cellular hydraulic conductivity can be calculated because the surface area of the confluent cell layer is known and assumed to be equal to the filter. The transcellular pressure drop can be calculated based on the pressure across the cell layer plus filter, and atmospheric pressure (Δ
P transcellular =
P cell layer +filter −
P atmospheric). The flow rate across the cells and filter,
Q cells+filter, is calculated, and the flow rate across the filter,
Q filter, is measured experimentally by perfusing empty filters without cells and calculating the average volumetric flow rate and
L p across the filter alone.