By Anita T. Layton, Aurélie Edwards

With the provision of excessive pace pcs and advances in computational strategies, the appliance of mathematical modeling to organic platforms is increasing. This accomplished and richly illustrated quantity presents updated, wide-ranging fabric at the mathematical modeling of kidney body structure, together with scientific info research and perform routines. easy suggestions and modeling ideas brought during this quantity should be utilized to different parts (or organs) of physiology.

The versions provided describe the most homeostatic services played by way of the kidney, together with blood filtration, excretion of water and salt, upkeep of electrolyte stability and law of blood strain. each one bankruptcy contains an advent to the elemental suitable body structure, a derivation of the basic conservation equations after which a dialogue of a sequence of mathematical types, with expanding point of complexity.

This quantity should be of curiosity to organic and mathematical scientists, in addition to physiologists and nephrologists, who would favor an advent to mathematical suggestions that may be utilized to renal shipping and serve as. the cloth is written for college students who've had college-level calculus, yet can be utilized in modeling classes in utilized arithmetic in any respect degrees via early graduate courses.

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**Mathematical Modeling in Renal Physiology**

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Endothelium Assuming that the endothelial fenestrae are filled with water, the pressure and velocity profiles in each fenestra are obtained by solving the Stokes and continuity equations (Eqs. 82) in the computational domains shown in Fig. 9. The no-slip boundary condition must be satisfied at the fenestra walls (at the interface with the endothelial cells), and the pressure at the entrance of the fenestra is set to the luminal pressure. At the interface between the fenestrae and the basement membrane, the pressure, velocities and viscous stress must match.

As described below, it is also helpful to express the Péclet number as a function of ro . Substituting Eqs. 51) into the expression for Pe (Eq. 4 Fitting the Model to Experimental Data In the isoporous model, the capillary wall is essentially characterized by one parameter, ro . If the ultrafiltration coefficient cannot be estimated, the pore surface area-to-length ratio constitutes another unknown. This (or these) parameter(s) are chosen so as to minimize the difference between model predictions and experimental data.

The factor WS accounts for the fact that the solute velocity (evaluated at the particle center) differs from that of the fluid; this factor is equivalent to (1 S ). eff The factor HS is the ratio of the pore-to-bulk fluid solute diffusivity, DS /D1 . 42) where f is the fraction of the capillary surface area that is occupied by pores. This factor is needed to distinguish JS from the local solute flux within a pore; the volume flux JV in Eq. 42) is also expressed per unit capillary surface area. By similarity with Eq.