By Anita T. Layton, Aurélie Edwards
With the provision of excessive pace pcs and advances in computational innovations, the appliance of mathematical modeling to organic structures is increasing. This finished and richly illustrated quantity presents up to date, wide-ranging fabric at the mathematical modeling of kidney body structure, together with medical information research and perform workouts. uncomplicated options and modeling ideas brought during this quantity might be utilized to different parts (or organs) of physiology.
The versions provided describe the most homeostatic features played by way of the kidney, together with blood filtration, excretion of water and salt, upkeep of electrolyte stability and rules of blood strain. every one bankruptcy comprises an creation to the elemental appropriate body structure, a derivation of the basic conservation equations after which a dialogue of a chain of mathematical types, with expanding point of complexity.
This quantity could be of curiosity to organic and mathematical scientists, in addition to physiologists and nephrologists, who would favor an creation to mathematical concepts that may be utilized to renal delivery and serve as. the cloth is written for college kids 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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Additional info for Mathematical Modeling in Renal Physiology
Such a solute can be NaCl or urea or protein. x/. x/. 3) are general and apply to all types of renal tubules. Of course, tubules in the kidney differ widely in their transport properties, and those differences are reflected in the flux terms JV and JS . 2 Water Fluxes Water can be driven through a cell membrane by hydrostatic pressure, oncotic pressure, and osmotic pressure. Oncotic pressure, discussed in Chap. 4, is exerted by proteins in blood plasma. Because in a healthy kidney, virtually no proteins are filtered by the glomerulus, oncotic pressure can be assumed to be zero along the loops of Henle and collecting ducts.
8 Probability density function for the lognormal and normal distributions of pore sizes. 20 Å p Note that the constant ” is not equal to 2 , as in standard probability theory, because the distribution is restricted to positive values of r. Instead, it depends on and , and must be evaluated so that g(r) satisfies the normalization condition Eq. 55). Examples of lognormal and normal distributions are plotted on Fig. 8. 3 Discrete Pore Size Distributions A popular alternative to these continuous distributions is the isoporous-plus-shunt model.
1 WS / exp . 7 cP at 37 ı C). 2 Hindrance Factors The theory of hindered transport was first elaborated in the 1950s by Pappenheimer, Renkin and colleagues (Pappenheimer et al. 1951), who sought to describe the passage of molecules across capillary walls. Since then, many theoretical studies have focused on predicting hindered transport coefficients based upon the shape, size, and electrical charge of both solutes and pores. A comprehensive review of these theoretical developments can be found in Dechadilok and Deen (2006).