Solution of a multinephron, multisolute model of the mammalian kidney by Newton and continuation methods

DOI10.1016/0025-5564(84)90036-1zbMath0562.92002OpenAlexW2005530933MaRDI QIDQ1057200

Raymond Mejia, John L. Stephenson

Publication date: 1984

Published in: Mathematical Biosciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0025-5564(84)90036-1

zbMATH Keywords

continuation methodNewton methodsteady state solutionskidney modelsmultinephron, multisolute model

Mathematics Subject Classification ID

Physiological flows (76Z05) Biological fluid mechanics (76Z99) Basic methods in fluid mechanics (76M99) Computational methods for problems pertaining to biology (92-08) Physiological, cellular and medical topics (92Cxx)

Related Items (13)

An efficient parallel algorithm for solving \(n\)-nephron models of the renal inner medulla ⋮ A dynamic numerical method for models of renal tubules ⋮ Existence and uniqueness of solutions to a mathematical model of the urine concentrating mechanism ⋮ Parallel algorithms for multinephron renal medullary models ⋮ Renal concentrating mechanism: Central core and vasa recta models ⋮ Efficient solution of differential equations for kidney concentrating mechanism analyses ⋮ Distributed solute and water reabsorption in a central core model of the renal medulla ⋮ A comparison of multinephron and shunt models of the renal concentrating mechanism ⋮ A mathematical modeling technique for renal counterflow systems ⋮ Multi-nephron and multi-vasa recta models of the inner medullary rental concentrating mechanism ⋮ A complete steady state model of solute and water transport in the kidney ⋮ The kidney model as an inverse problem ⋮ CONKUB: A conversational path-follower for systems of nonlinear equations

Uses Software

• MACSYMA

Cites Work

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• Free-energy balance in renal counterflow systems
• Solute concentration in the kidney. I: A model of the renal medulla and its limit cases
• Solute concentration in the kidney. II: Input-output studies on a central core model
• Comparison of numerical methods for renal network flows
• A note on solution of large sparse systems of nonlinear equations
• Bifurcation, perturbation of simple eigenvalues, and linearized stability
• Algorithm 502: Dependence of Solution of Nonlinear Systems on a Parameter [C5]
• Model of solute and water movement in the kidney.
• Finding Zeroes of Maps: Homotopy Methods That are Constructive With Probability One
• Quantitative Analysis of Mass and Energy Balance in Non-Ideal Models of the Renal Counterflow System

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