Mathematical Modeling Of Commercial Kidney Dialysis

Hemodialysis is a widely used clinical procedure to treat patients who suffer from acute renal failure. The primary component in this procedure is an artificial kidney or dialyzer that removes waste products from the patient's blood. Many mathematical models have been proposed during the past four decades to model hemodialysis but none have addressed in detail the mass transport associated with the multiple passage of blood through the dialyzer. The motivation behind this investigation is to contribute to the development of a mathematical model which could easily interface with the clinical hemodialysis procedure.

Beginning with an introduction to kidney function, renal replacement therapies, and an overview of clinical problems associated with haemodialysis, this book explores the principles of the short-term baroreflex regulation of the cardiovascular system and the mechanisms of water and solute transport across the human body from a mathematical model perspective. It synthesizes theoretical physiological concepts and practical aspects of mathematical modelling needed for simulation and quantitative analysis of the haemodynamic response to dialysis therapy. Including an up-to-date review of the literature concerning the modelled physiological mechanisms and processes, the book serves both as an overview of transport and regulatory mechanisms related to the cardiovascular system and body fluids and as a useful reference for the study and development of mathematical models of dynamic physiological processes. Mathematical Modelling of Haemodialysis: Cardiovascular Response, Body Fluid Shifts, and Solute Kinetics is intended for researchers and graduate students in biomedical engineering, physiology, or medicine interested in mathematical modelling of cardiovascular dynamics and fluid and solute transport across the human body, both under physiological conditions and during haemodialysis therapy.

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.

What regulation shall we have for the operation? Shall a man transfuse he knows not what. to correct he knows not what. God knows how (l)? Dr. Henry Stubbs Royal College of Physicians circa 1670 If dialysis therapy were a new phannaceutical product being evaluated by the FDA now, it might not be approved for marketing. The recommended dose, its potential toxicity, the side effects of under-or over-dialysis as well as its efficacy have been the subject of very few studies. The high mortality rate associated with the treatment may raise a few eyebrows. That it is a life-saving modality of treatment is undoubtedly true for more than 100,000 patients in the United States and for more than a million patients world wide. Because dialysis has extended the lives of many people by a variable period of time, most nephrologists have "rested on their laurels" and did not vigorously pursue studies to optimize these treatments. But facts have a way of intruding in all our lives and the facts are that the overall mortality rate of dialysis patients in the United States is rising and stands close to 25% per year and is closer to 33% per year for patients between the ages of 65 and 74 (2). These mortality figures are considerably higher for age-adjusted dialysis populations in Europe and particu larly in Japan, and certainly for the age-adjusted nonnal population.

Mathematical modeling of real life phenomena is a powerful tool in analyzing and describing their dynamical behavior. These models can be optimized and controlled using appropriate optimization methods and optimal control theory. Different characterization techniques are used to explain a real natural phenomenon by numerical simulations or experimental approximations.

The advent of the Middle Molecule Theory of Uremic Toxicity has introduced the need for hemodialyzers capable of efficiently removing metabolites with molecular weights between 300 and 2000. The rate at which these solutes can be removed from the body depends not only upon the efficiency of the dialyzer, but also upon the ability of the metabolites to diffuse from innerbody compartments into the patient's blood stream. In an effort to characterize innerbody transport during hemodialysis, a multicompartmental patient-artificial kidney model has been developed. In vivo clinical data in the form of solute-plasma concentration decline measurements following an impulse IV injection of Dextran-1500 (1500 molecular weight dextran fraction) and Vitamin B-12 have been obtained. These data were used to determine model parameters in the form of compartmental volumes and intercompartmental mass transfer coefficients. Analysis of the dextran data indicated that two intracellular pools, the interstitial pool, and the plasma pool were involved in DX-1500 solute kinetics. Further analysis of the data yielded a transcapillary mass transfer coefficient of 502 ml/min and two transcellular coefficients of 141 and 7 ml/min. The Vitamin B-12 data produced a similar compartmental arrangement. A transcapillary mass transfer coefficient of 470 ml/min and two transcellular coefficients of 30 ml/min and 5 ml/min were obtained. The DX-1500 parameters were used to simulate various modes of dialysis. The model predicted that innerbody mass transfer barriers begin to limit solute removal even for moderate dialyzer clearances. In contrast to this, the model predicted that innerbody mass transfer has little effect on the dialysis of urea.

Advances in Mathematical Modeling for Reliability discusses fundamental issues on mathematical modeling in reliability theory and its applications. Beginning with an extensive discussion of graphical modeling and Bayesian networks, the focus shifts towards repairable systems: a discussion about how sensitive availability calculations parameter choices, and emulators provide the potential to perform such calculations on complicated systems to a fair degree of accuracy and in a computationally efficient manner. Another issue that is addressed is how competing risks arise in reliability and maintenance analysis through the ways in which data is censored. Mixture failure rate modeling is also a point of discussion, as well as the signature of systems, where the properties of the system through the signature from the probability distributions on the lifetime of the components are distinguished. The last three topics of discussion are relations among aging and stochastic dependence, theoretical advances in modeling, inference and computation, and recent advances in recurrent event modeling and inference.