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Analysis of the transient behavior of kidney models

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Abstract

Non-steady-state equations for kidney models are stated. General conservation relations for these equations are derived. Transient equations for the central core model of the renal medulla are developed. Solution of the equations by Laplace transform methods for time invariant volume flows is discussed. The general theory of solving models with time dependent flows by finite difference methods is developed.

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Literature

  • Ang, P., H. D. Landahl and E. Bartoli. 1973. “Steady-State and Non-Steady-State Simulation of Transport in the Nephron.”Biophys. Soc. Abstr.,13, 36a.

    Google Scholar 

  • Hubbard, B. E. 1976. “Computing Transient Solutions for Certain Renal Counterflow Systems.”Proceedings of the 1976 Summer Computer Simulation. pp. 507–510. Conference Simulation Councils, Inc., P. O. Box 2228, LaJolla, California.

    Google Scholar 

  • Keller, H. B. 1974. “Accurate Difference Methods for Nonlinear Two-Point Boundary Value Problems.”SIAM J. Numer. Anal.,11, 305–320.

    Article  MATH  MathSciNet  Google Scholar 

  • Kellogg, B. 1975a. “Osmotic Flow in a Tube with Stagnant Points.” Report BN-818. University of Maryland. College Park, MD: IFDAM.

    Google Scholar 

  • — 1975b. “Uniqueness in the Schauder Fixed Point Theorem.” Technical Note BN-822. University of Maryland, College Park, MD: IFDAM.

    Google Scholar 

  • Mejia, R., R. B. Kellogg and J. L. Stephenson. 1976. “Comparison of Numerical Methods for Renal Network Flows.”J. Comp. Phys.,23, 53–62.

    Google Scholar 

  • Palatt, P. J. and G. M. Saidel. 1973. “An Analysis of Countercurrent Exchange With Emphasis on Renal Function.”Bull. Math. Biol.,35, 275–286.

    MATH  Google Scholar 

  • Rheinboldt, W. C. and C. K. Mesztenyi. 1973. “Arc Graphs and Their Possible Application to Sparse Matrix Problems.” Technical Report TR-238. Computer Science Center, University of Maryland, College Park, MD.

    Google Scholar 

  • Stephenson, J. L. 1969. “A Model for the Non-Steady-State Countercurrent Multiplier”.Biophys. Soc. Abstr.,9, A-74.

    Google Scholar 

  • — 1972. “Concentration of Urine in a Central Core Model of the Renal Counterflow System”.Kidney Int.,2, 85–94.

    Google Scholar 

  • — 1973a. “Transient Behavior of the Single Loop Solute Cycling Countercurrent Multiplier”.Bull. Math. Biol.,35, 183–194.

    Article  Google Scholar 

  • — 1973b. “Concentrating Engines and the Kidney: I. Central Core Model of the Renal Medulla”.Biophys. J.,13, 512–545.

    Google Scholar 

  • — 1973c. “Concentrating Engines and the Kidney: II. Multisolute Central Core Systems”.Biophys. J.,13, 546–567.

    Article  Google Scholar 

  • — and J. Chen. 1974. “Role of Hydrostatic and Oncotic Pressure in the Concentration of Urine”.Fedn Proc.,33, 1514.

    Google Scholar 

  • — and R. Mejia. 1974. “Transient Behavior of Non-Ideal Models of the Renal Counterflow System”.Bull. Am. Phys. Soc. II,19, 604.

    Google Scholar 

  • — R. Mejia and R. P. Tewarson. 1976. “Model of Solute and Water Movement in the Kidney”.Proc. Natn. Acad. Sci. U.S.A.,73, 252–256.

    Article  MATH  Google Scholar 

  • — R. P. Tewarson and R. Mejia. 1974. “Quantitative Analysis of Mass and Energy Balance in Non-Ideal Models of the Renal Counterflow System”.Proc. Natn. Acad. Sci. U.S.A.,71, 1618–1622.

    Article  MATH  Google Scholar 

  • Tewarson, R. P., J. L. Stephenson, A. Kydes and R. Mejia. 1976. “Use of Sparse Matrix Methods in Numerical Solution of Differential Equations for Renal Counterflow Systems”.Comp. Biomed. Res.,9, 507–520.

    Article  Google Scholar 

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Stephenson, J.L. Analysis of the transient behavior of kidney models. Bltn Mathcal Biology 40, 211–221 (1978). https://doi.org/10.1007/BF02461436

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  • DOI: https://doi.org/10.1007/BF02461436

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