Mathematical Modelling of Haemodialysis: Cardiovascular Response, Body Fluid Shifts, and Solute Kinetics

ISBN-13: 9783030214128 / Angielski / Miękka / 2020 / 156 str.

Leszek Pstras; Jacek Waniewski

Spis treści

Contents

1. INTRODUCTION ................................................................................................................................ 1

1.1. KIDNEY FUNCTION ....................................................................................................................... 1

1.2. CHRONIC KIDNEY FAILURE .......................................................................................................... 2

1.3. HAEMODIALYSIS .......................................................................................................................... 5

1.4. CLINICAL PROBLEMS IN HAEMODIALYSIS .................................................................................... 7

1.5. MATHEMATICAL MODELLING .................................................................................................... 10

REFERENCES ....................................................................................................................................... 13

2. MODEL DESCRIPTION ................................................................................................................... 17

2.1. OVERVIEW ................................................................................................................................. 17

2.2. CARDIOVASCULAR SYSTEM ....................................................................................................... 18

2.2.1. Cardiovascular compartments ..................................................................................... 18

2.2.2. Vascular resistance ...................................................................................................... 20

2.2.3. Cardiac output ............................................................................................................. 22

2.2.4. Baroreflex .................................................................................................................... 24

2.2.5. Haematocrit ................................................................................................................. 29

2.2.6. Arteriovenous access ................................................................................................... 31

2.2.7. Assumptions ................................................................................................................ 32

2.3. WATER AND SOLUTE KINETICS .................................................................................................. 33

2.3.1. Fluid compartments ..................................................................................................... 33

2.3.2. Small solute kinetics .................................................................................................... 34

2.3.3. Capillary filtration ....................................................................................................... 38

2.3.4. Protein transport .......................................................................................................... 42

2.3.5. Lymph flow ................................................................................................................. 43

2.3.6. Cellular water transport ............................................................................................... 44

2.3.7. Dialyzer mass exchange .............................................................................................. 46

2.3.8. Blood mixing ............................................................................................................... 47

2.4. MODEL INTEGRATION ................................................................................................................ 49

2.5. PARAMETERS ASSIGNMENT ........................................................................................................ 50

2.5.1. Cardiovascular system parameters .............................................................................. 50

2.5.2. Transport parameters ................................................................................................... 53

2.6. INITIAL CONDITIONS .................................................................................................................. 55

2.6.1. Normal man ................................................................................................................. 55

2.6.2. Patient before dialysis.................................................................................................. 59

2.7. HAEMODIALYSIS MODELLING .................................................................................................... 64

2.8. COMPUTATIONAL IMPLEMENTATION ......................................................................................... 66

REFERENCES ....................................................................................................................................... 67

3. MODEL ANALYSIS .......................................................................................................................... 77

3.1. SENSITIVITY ANALYSIS .............................................................................................................. 77

3.1.1. Overview ..................................................................................................................... 77

3.1.2. Sensitivity to assigned parameters ............................................................................... 81

3.1.3. Sensitivity to equation parameters ............................................................................... 85

3.2. MODEL VALIDATION .................................................................................................................. 88

3.2.1. Lublin data ................................................................................................................... 88

3.2.2. Literature data .............................................................................................................. 96

3.3. MODEL LIMITATIONS ............................................................................................................... 100

REFERENCES ..................................................................................................................................... 102

4. SIMULATION RESULTS ............................................................................................................... 104

4.1. HAEMODYNAMICS ................................................................................................................... 104

4.2. VASCULAR REFILLING ............................................................................................................. 107

4.3. WATER SHIFTS ......................................................................................................................... 110

4.4. SOLUTE KINETICS .................................................................................................................... 111

4.5. HAEMATOCRIT CHANGES ......................................................................................................... 114

4.6. IMPACT OF BAROREFLEX AND CARDIAC PARAMETERS ............................................................. 116

4.7. IMPACT OF DIALYSIS SETTINGS ................................................................................................ 121

REFERENCES ..................................................................................................................................... 122

5. CONCLUSIONS ............................................................................................................................... 124

REFERENCES ..................................................................................................................................... 126

O autorze

Leszek Pstras is an Assistant Professor at the Laboratory of Mathematical Modelling of Physiological Processes at the Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences. His research focuses on mathematical modelling of cardiovascular short-term regulatory mechanisms as well as fluid and solute transport kinetics during haemodialysis therapy.

Jacek Waniewski is a Professor of Biomedical Engineering and the Chairman of the Scientific Council at the Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences. His research focuses on mathematical modelling of membrane transport in medicine and biomedical engineering with a special interest in modelling transport processes during renal replacement therapies (both haemodialysis and peritoneal dialysis).

Blurb

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.