By Anita T. Layton, Aurélie Edwards
With the supply of excessive velocity desktops and advances in computational strategies, the appliance of mathematical modeling to organic structures is increasing. This finished and richly illustrated quantity offers up to date, wide-ranging fabric at the mathematical modeling of kidney body structure, together with scientific facts research and perform workouts. simple thoughts and modeling options brought during this quantity should be utilized to different parts (or organs) of physiology.
The types awarded describe the most homeostatic features played by means of the kidney, together with blood filtration, excretion of water and salt, upkeep of electrolyte stability and rules of blood strain. each one bankruptcy comprises an creation to the fundamental proper body structure, a derivation of the fundamental conservation equations after which a dialogue of a sequence of mathematical versions, with expanding point of complexity.
This quantity can be of curiosity to organic and mathematical scientists, in addition to physiologists and nephrologists, who would prefer an creation to mathematical thoughts that may be utilized to renal delivery and serve as. the fabric 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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Extra resources for Mathematical Modeling in Renal Physiology
Cell biology of the glomerular podocyte. Physiol. Rev. : Independent two-photon measurements of albumin GSC give low values. Am. J. Physiol. Renal Physiol. : Porous substructure of the glomerular slit diaphragm in the rat and mouse. J. Cell Biol. : The normal kidney filters nephrotic levels of albumin retrieved by proximal tubule cells: retrieval is disrupted in nephrotic states. Kidney Int. : Effect of ACE inhibition on glomerular permselectivity and tubular albumin concentration in the renal ablation model.
Am. Soc. Nephrol. : Hindrance factors for diffusion and convection in pores. Ind. Eng. Chem. Res. : Heteroporous model of glomerular size selectivity: application to normal and nephrotic humans. Am. J. Physiol. Renal Physiol. : A model of glomerular ultrafiltration in the rat. Am. J. Physiol. : Structural determinants of glomerular permeability. Am. J. Physiol. Renal Physiol. : Structural determinants of glomerular hydraulic permeability. Am. J. Physiol. Renal Physiol. : Ultrastructural model for size selectivity in glomerular filtration.
The computations are complex, and the results are often presented in tabular form. The expressions for WS and HS developed by Bungay and Brenner by asymptotic matching are among the very few analytical correlations found to be accurate over the entire range of values (Bungay and Brenner 1973). 1 /2 Ks . 1 / 5=2 1 C 4 60 50; 400 C 4:0180 3:9788 1:9215 2 C 4:392 3 C 5:006 4 : Kt . 3 Ultrafiltration Coefficient The hydraulic conductivity of an isoporous capillary wall, LP , can also be calculated explicitly under certain assumptions.