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NUMERICAL SOLUTION OF RENAL TRANSPORT EQUATIONS

肾脏转运方程的数值解

基本信息

批准号：
3151075
负责人：
REGINALD P TEWARSON
金额：
$ 6.38万
依托单位：
STATE UNIVERSITY NEW YORK STONY BROOK
依托单位国家：
美国
项目类别：
财政年份：
1974
资助国家：
美国
起止时间：
1974-06-30 至 1987-03-31
项目状态：
已结题

来源：
https://reporter.nih.gov/project-details/3151075
关键词：
computer simulation mathematical model renal tubular transport

项目摘要

The overall long-term goal of this proposed research is to develop efficient algorithms which permit comprehensive computer simulation of renal function. It is proposed to continue the research that during the last nine years has led to very useful mathematical models of the medullary counter-flow system and the whole kidney. To make our models more comprehensive and realistic (e.g., simulate tracer washout curves and estimate membrane parameters), further improvements are required in our computer algorithms for the solution of the complicated systems of coupled, stiff, and nonlinear differential equations describing the models. It is hoped to increase the accuracy and stability of the algorithms through the use of piecewise polynomial approximations, Implicit Runge-Kutta methods, and optimum basis functions obtained from the analytic local solutions of conceptually simplified models, when transforming the model differential equations to their finite difference (or finite element) analogues. The use of parallel and multiple shooting, collocation, Rayleigh-Ritz and Galerkin, Invariant-Imbedding, Chebyshev expansion methods will be investigated. It is intended to achieve significant improvements in the efficiency of the algorithms by partitioning the equations in accordance with the physiological connectivity of the kidney, tearing the equations and variables that correspond to the solutes with minor effects on the water flow, the application of sparse matrix techniques, and the use of quasi Newton and projection methods to minimize the computer storage and run-times. It is expected that as a result of the continued successful application of the above techniques the models will progressively improve in sophistication and permit a serious attack on the problem of parameter estimation. For this purpose the use of experimental values, continuation, smoothing, minimization of energy requirements and related techniques is proposed. The methods already developed, as well as currently available experimental information about the parameters, flows, pressures, concentrations and architecture will be progressively incorporated in to our multinephron, multisolute, path following models.

这项拟议研究的总体长期目标是开发有效的算法，允许全面的计算机模拟，肾功能建议继续研究，在过去的九年里，我们已经建立了非常有用的骨髓数学模型，逆流系统和整个肾脏。让我们的模特全面和现实的（例如，模拟示踪剂冲刷曲线，估计膜参数），需要进一步改进我们的计算机算法的解决方案的复杂系统的耦合，刚性和非线性微分方程描述的模型。是希望通过提高算法的准确性和稳定性，使用分段多项式近似，隐式Runge-Kutta方法，和最佳基函数获得的解析局部解概念上简化的模型，当转换模型微分时方程到它们的有限差分（或有限元）类似物。的使用平行和多重拍摄，搭配，瑞利-里兹和 Galerkin，不变量嵌入，Chebyshev展开方法将是研究了其目的是实现重大改进，通过根据方程划分算法的效率与肾脏的生理连通性，以及对应于溶质的变量，这些变量对水流，稀疏矩阵技术的应用，以及拟牛顿法和投影法，以尽量减少计算机存储和运行时间。预计，由于持续的成功，应用上述技术，模型将逐步改进在复杂性和允许一个严重的攻击问题的参数估计。为此目的，使用实验值，延续，平滑化、能量需求最小化和相关技术，提出了已经开发的以及目前可用的方法关于参数、流量、压力集中和建筑将逐步纳入，我们的多肾多溶质路径跟踪模型