NUMERICAL SOLUTION OF RENAL TRANSPORT EQUATIONS

肾脏转运方程的数值解

• 批准号: 3225793
• 负责人: REGINALD P TEWARSON
• 金额: $ 8.31万
• 依托单位: STATE UNIVERSITY NEW YORK STONY BROOK
• 依托单位国家: 美国
• 财政年份: 1974
• 资助国家: 美国
• 起止时间: 1974-06-30 至 1993-03-31
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/3225793
• 关键词: computer program /software; mathematical model; model design /development; renal tubular transport

(Adapted from applicant's abstract): The overall goal of this continuing project is to develop efficient algorithms that will permit the development of mathematical models that relate normal and pathological renal function to the underlying membrane transport and flow processes in the renal tubules and their associated vasculature. The primary thrust of this research during the next period will be: To extend our present models at the physiological level to include: (a) Additional architectural features particularly a more detailed representation of the relation of vascular and tubular elements. (b) A more detailed representation of the transmural movement of water and solutes that takes into account both cellular and paracellular pathways. (c) The addition of the solutes H+, HCO3-, HPO4--, H2PO4-, NH4+, CO2, and certain of the organic osmolytes found in the medulla to the Na+, K+, Cl-, and urea already included in the models. (d) The exchange of electrolytes and water between red blood cells and plasma in the vasa recta. (e) A more detailed analysis of time dependent behavior, in particular the transition from diuresis to antidiuresis, and control of the excretion of Na, K, urea, and water by ADH, ANF, and aldosterone, To vectorize the present algorithms in a way that permits the efficient application of the parallel processing capabilities of supercomputer facilities. (a) Improve the stability (and, if necessary, the accuracy) of the numerical methods. (b) Develop hierarchal solution strategies of Multigrid type. (c) Develop general purpose algorithms that will guarantee the convergence of iterative schemes for the solution of model equations by using continuation and smoothing methods. (d) Develop improved methods for estimating the ranges of the significant parameters of the kidney. MINOS - the constrained nonlinear optimization package - will continue to be used on preliminary studies. A complementary aim is to make the non-linear Schur Complement type methods developed by us readily available to other biomedical modelers, and thus, to implement a variety of models on whole kidney and medulla. (b) Models of isolated perfused kidney. (c) Models of epithelia and isolated perfused tubules. (d) A multi-cell model of the macula densa of the cortical ascending limb and its role in the transmission of the tubuloglomerular feedback response. (e) Models for verifying by quantitative simulations hypotheses for mechanisms of neuronal function.

（改编自申请人的摘要）：本次持续性研究的总体目标 项目是开发有效的算法，允许开发 关联正常和病理肾功能的数学模型 肾脏中潜在的膜运输和流动过程 肾小管及其相关的脉管系统。 本次活动的主要目的是 下一阶段的研究将是： 扩展我们目前的模型 生理层面包括： (a) 额外的架构特征 特别是更详细地表示了血管和 管状元件。 (b) 更详细地表示透壁 考虑到细胞和溶质的水和溶质的运动 细胞旁路。 (c) 溶质 H+、HCO3-、HPO4-- 的添加， H2PO4-、NH4+、CO2 和某些存在于水中的有机渗透剂 髓质中的 Na+、K+、Cl- 和尿素已包含在模型中。 (四) 红细胞和血浆之间电解质和水的交换 在直肠血管中。 (e) 更详细的时间依赖性分析 行为，特别是从利尿到抗利尿的转变，以及 ADH、ANF 和 ANF 控制 Na、K、尿素和水的排泄 醛固酮，以允许 并行处理能力的有效应用 超级计算机设施。 (a) 提高稳定性（如有必要， 数值方法的准确性）。 (b) 制定分层解决方案 多重网格类型的策略。 (c) 开发通用算法 将保证迭代方案的收敛性 使用连续和平滑方法建立模型方程。 (d) 发展 改进的重要参数范围估计方法 肾脏。 MINOS - 约束非线性优化包 - 将 继续用于初步研究。 一个互补的目标是使 我们轻易开发的非线性Schur补类型方法 可供其他生物医学建模者使用，从而实现各种 整个肾脏和髓质的模型。 (b) 分离灌注模型 肾。 (c) 上皮细胞和孤立的灌注小管模型。 （四）A 皮质升肢致密斑多细胞模型及其 在肾小球反馈反应的传递中发挥作用。 （五） 通过定量模拟验证机制假设的模型 的神经元功能。