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Modeling and Estimation for the Renal System

2021
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Release : 2021
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Book Synopsis Modeling and Estimation for the Renal System by : Benjamin James Czerwin

Download or read book Modeling and Estimation for the Renal System written by Benjamin James Czerwin. This book was released on 2021. Available in PDF, EPUB and Kindle. Book excerpt: Understanding how a therapy will impact the injured kidney before being administered would be an asset to the clinical world. The work in this thesis advances the field of mathematical modeling of the kidneys to aid in this cause. The objectives of this work are threefold: 1) to develop and personalize a model to specific patients in different diseased states, via parameter estimation, in order to test therapeutic trajectories, 2) to use parameter estimation to understand the cause of different kidney diseases, differentiate between potential kidney diseases, and facilitate targeted therapies, and 3) to push forward the understanding of kidney physiology via physiology-based mathematical modeling techniques. To accomplish these objectives, we have developed two models of the kidneys: 1) a broad, steady-state, closed-loop model of the entire kidney with human physiologic parameters, and 2) a detailed, dynamic model of the proximal tubule, an important part of kidney, with rat physiologic parameters.

Parameter Estimation for Mathematical Models of Ion Transport in the Renal System

2010 Biological transport
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Release : 2010
Genre : Biological transport
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Book Synopsis Parameter Estimation for Mathematical Models of Ion Transport in the Renal System by : Mónica A. Nadal Quirós

Download or read book Parameter Estimation for Mathematical Models of Ion Transport in the Renal System written by Mónica A. Nadal Quirós. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Modeling in Renal Physiology

2014-08-06 Mathematics
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Release : 2014-08-06
Genre : Mathematics
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Book Rating : 67X/5 ( reviews)

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Book Synopsis Mathematical Modeling in Renal Physiology by : Anita T. Layton

Download or read book Mathematical Modeling in Renal Physiology written by Anita T. Layton. This book was released on 2014-08-06. Available in PDF, EPUB and Kindle. Book excerpt: With the availability of high speed computers and advances in computational techniques, the application of mathematical modeling to biological systems is expanding. This comprehensive and richly illustrated volume provides up-to-date, wide-ranging material on the mathematical modeling of kidney physiology, including clinical data analysis and practice exercises. Basic concepts and modeling techniques introduced in this volume can be applied to other areas (or organs) of physiology. The models presented describe the main homeostatic functions performed by the kidney, including blood filtration, excretion of water and salt, maintenance of electrolyte balance and regulation of blood pressure. Each chapter includes an introduction to the basic relevant physiology, a derivation of the essential conservation equations and then a discussion of a series of mathematical models, with increasing level of complexity. This volume will be of interest to biological and mathematical scientists, as well as physiologists and nephrologists, who would like an introduction to mathematical techniques that can be applied to renal transport and function. The material is written for students who have had college-level calculus, but can be used in modeling courses in applied mathematics at all levels through early graduate courses.

Parameter Estimation of Renal Models

2012
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Release : 2012
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Book Synopsis Parameter Estimation of Renal Models by : Yanhong Wu

Download or read book Parameter Estimation of Renal Models written by Yanhong Wu. This book was released on 2012. Available in PDF, EPUB and Kindle. Book excerpt: Two parameters of the delay time and the feedback gain play important roles in understanding an important mechanism--Tubuloglomerular feedback in renal hemodynamics. A few mathematical models have been developed, where each emphasizes different parts of the renal system but all of them include these two parameters and they define these two parameters differently. An inverse problem, estimating the two parameters by combining the information of the experimental data and the simulated data from mathematical models has brought to our attention. Ditlevsen et al. estimated these two parameters by the least square distance between the spectral densities of experimental data and simulated data from their renal model for normatensive and hypertensive rats in 2005 and 2007. The main work of this thesis is to use different statistical estimation methods, Bayes linear method (BLM), maximal likelihood estimation method based on generalized-polynomial chaos expansion (MLE-GPC) and markov chain monte carlo method (MCMC), to estimate the delay time and the feedback gain in a partial differential equation model developed by Layton and Pitman. The idea of BLM is to update beliefs about adjusted expectations and adjusted variances of quantities. MLE-GPC and MCMC methods focus on probability density functions of quantities. Likely regions, consisting of plausible values of the parameters, are estimated instead of a single plausible value for each parameter and further confident intervals in Ditlevsen's papers.

Modeling and Simulating of the Human Renal System Mathematical Model

2011
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Release : 2011
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Book Synopsis Modeling and Simulating of the Human Renal System Mathematical Model by : Haydar A. Mahmoud

Download or read book Modeling and Simulating of the Human Renal System Mathematical Model written by Haydar A. Mahmoud. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this study is to present a functional approach to develop a computer program using Verilog programming language. This software is used to test and validate the overall mathematical model of the renal/body fluid system developed by Uttamsingh et al (1985). This approach can be used to develop advanced algorithms to simulate a wide range of biological systems that need to be investigated without the risk of using humans as experiment subjects; also it can be used to model physiological mechanisms related to medical disorders such as diabetic, cardiac disorders and many others. The Simulation results indicated that the model and the developed software system are in agreement with the responses presented in the literature of the real physiological system within adequate confines; therefore it's valid and suitable for hypothesis testing.

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