Mathematical Modeling in Renal Physiology by Anita T. Layton, Aurélie Edwards
By Anita T. Layton, Aurélie Edwards
With the supply of excessive pace pcs and advances in computational concepts, the applying of mathematical modeling to organic platforms 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 routines. uncomplicated options and modeling options brought during this quantity could be utilized to different parts (or organs) of physiology.
The versions offered describe the most homeostatic services played through 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 fundamental correct body structure, a derivation of the fundamental conservation equations after which a dialogue of a sequence of mathematical types, with expanding point of complexity.
This quantity might be of curiosity to organic and mathematical scientists, in addition to physiologists and nephrologists, who would favor an advent to mathematical strategies that may be utilized to renal delivery and serve as. the fabric 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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3. 17 Â Pe D r2 8Á ÃÂ WS HS DS1 Ã P …A pr exp . r/ D 1 exp . 1 exp . 1 WS / exp . 78) The overall sieving coefficient is then determined by integrating over all pore sizes (Eq. 63). How big are the errors using this approximate method? Deen et al. 7 %. Once mass balance equations are integrated following either of these three approaches, model parameters are adjusted by minimizing the sum of squared errors (SSE in Eq. 3) as described above. 5 Heteroporous Model Performance What can these pore models tell us about changes in the properties of the capillary wall in disease states?
At a given position x, the volume flux JV (x) is calculated using Eq. 35). – Assuming a continuous distribution g(r), NV (x, r) and NS (x, r) are then determined for each value of r with Eqs. 58). The solute flux JS (x) is subsequently obtained by integrating NS (x, r) over all the r values (Eq. 61). – Assuming an isoporous-plus-shunt representation, the solute flux is calculated based upon Eq. 68) instead. Knowing JV and JS , the plasma and solute flows at the next step can be determined. Once the mass balance equations are integrated along the entire x axis, the overall sieving coefficient is determined using Eq.
Therapeutic advantage of converting enzyme inhibitors in arresting progressive renal disease associated with systemic hypertension in the rat. J. Clin. Invest. : The dynamics of glomerular ultrafiltration in the rat. J. Clin. Invest. : The motion of a closely-fitting sphere in a fluid-filled tube. Int. J. Multiphase Flow. : Permselectivity of the glomerular capillary wall to macromolecules. I. Theoretical considerations. Biophys. J. : Resolved: normal glomeruli filter nephrotic levels of albumin.