Introduction to Mathematics in Physiology, Medicine, and Health Sciences
- 1st Edition - January 1, 2026
- Imprint: Academic Press
- Authors: Dhanjoo N. Ghista, Anacleto V. Mernone, Kayalvizhi Mohan, Jagannath Mazumdar
- Language: English
- Hardback ISBN:9 7 8 - 0 - 4 4 3 - 3 0 1 8 6 - 5
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 3 0 1 8 7 - 2
Introduction to Mathematics in Physiology, Medicine, and Health Sciences provides a quantitative handbook for physiology and biological systems, so researchers, practi… Read more
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Introduction to Mathematics in Physiology, Medicine, and Health Sciences provides a quantitative handbook for physiology and biological systems, so researchers, practitioners, and clinicians can have a quantitative foundation, and medicine can incorporate more precise diagnostics. This book’s purpose is to demonstrate how fundamental mathematics can be incorporated into biomedical engineering, physiology, medicine, and health sciences research, application, and clinical practice to make these disciplines more quantitative and computational, and hence more explanatory and informative. The book also provides more quantitative formulation of medical procedures, towards supporting the growing field of precision medicine. The book guides readers though the foundations of mathematics as it is applied to modeling of physiological systems, medicine, biology, and health sciences. Each chapter includes a robust introduction to the mathematical concepts and principles necessary to understand their application to the indicated medical and biological systems, beginning with the fundamental relationships among biological variables in Chapter 2, introduction to basic calculus and rate of change in biomedical variables in Chapter 3, and the principles of linear algebra and vectors applied to medicine in Chapter 4. Chapters 5-7 cover the fundamentals of exponential and logarithmic biomedical functions, maximum and minimum values of a function, and integration applications such as summation, area, and volume. Chapter 8 provides an in-depth look into biomedical applications of Ordinary and Partial Differential Equations, which are important modeling tools for flow and variable systems. Chapter 9 provides extensive coverage of Organ System Analyses, which is the core of the physiological system modeling in the book, with a wide range of applied examples. Chapters 10 and 11 extend the modeling applications to medical devices and signal processing. Each chapter provides in-depth guidance on the mathematical concepts, methodology, and procedures for applying the mathematical formulas and equations to the appropriate biomedical and physiological systems, as well as step-by-step procedures for creating models for a wealth of specific applications.
- Includes real-world examples and case studies that illustrate how mathematics is used in medical research, clinical practice, and healthcare management, making the content practical and relatable
- Equips the audience with the knowledge and tools to design experiments, collect data, and analyze results using mathematical techniques, potentially leading to more robust and impactful research outcomes
- Provides readers with a solid foundation in mathematical concepts and techniques relevant to physiology, medicine, and health sciences, making it accessible to students and professionals from various backgrounds
Biomedical engineers, biomedical and clinical researchers as well as biomedical and clinical professionals who are interested in pursuing further studies or research and need a stronger mathematical foundation
1. Preamble
2. Fundamental Relationships among Biological Variables
2.1 Relationships between Several Biomedical Variables
2.2 Meaning of Functions and Examples of Functional Relationship Between Biomedical Quantities
2.3 Types of Functions - Linear, Quadratic, Logarithmic, Exponential, Trigonometric and Polynomial
2.3.1 Linear
2.3.2 Quadratic
2.3.3 Logarithmic
2.3.4 Exponential
2.3.5 Trigonometric
2.3.6 Polynomial
2.4 Sketching the graph of a given function; Maximum, minimum and point of inflection
2.5 Biomedical Applications
2.5.1 Celsius and Fahrenheit temperature scales
2.5.2 Cardiac Muscle force and shortening velocity
2.5.3 Pressure and Volume of a Gas
2.5.4 Cavitation
2.5.5 Glucose Tests
2.5.6 Renal Dialysis
2.5.7 Torque on a Long Tube and Resulting Shear Stress
2.5.8 Velocity of Enzyme Substrate reaction and the amount of Substrate
2.5.9 Wall stress and fluid pressure in fluid filled organ
2.5.10 Infant body weight and height vs Age
3. Introduction to Basic Calculus and Rate of Change of Biomedical Variables
3.1 Biomedical Applications
3.1.1 Change in pulse rate wrt the amount of drug
3.1.2 Rate of blood volume output during ejection period
3.1.3 Population (organism) growth rate
3.1.4 The half life and rate of decay of a radioactive substance
3.1.5 Definition of physical, biological and effective half life
3.1.6 Measurement of blood flow to limbs by measuring of rate of change of limb circumference
3.1.7 Compartmental modelling for studying drug transfer in the body
4. Introduction to Algebra, Linear Algebra and Vectors in Medicine
4.1 Biomedical Applications
4.1.1 Application of vectors in the musculo-skeleto system to determine muscle and joint force
5. Exponential and Logarithmic Biomedical Functions and their derivatives
5.1 Biomedical applications
5.1.1 Exponential growth models for bacteria and human populations
5.1.2 Radioactivity decay models, half life of a radioactive material
5.1.3 Definition of physical, biological and effective half life
5.1.4 Determination of the time of death of a person from body temperature and room temperature
6. Maximum and Minimum Value of a Function - Applications to Biomedical stability and instability
6.1 Biomedical Applications
6.1.1 Optimal design of bone from maximum strength and minimum weight
6.1.2 Optimal cardiovascular branching that minimises resistance to flow
6.1.3 How airways are optimally designed to expel air from the lungs most efficiently
6.1.4 How nerve fibres are optimally designed to maximise the impulse velocity
6.1.5 Delineating critical states of a patient’s medical condition
7. Integration - Summation, areas and volume applications
7.1 Biomedical Applications
7.1.1 Pressure-volume loop analysis in cardiology
7.1.2 To calculate the pumping work done by the heart at each stroke and its power
7.1.3 To calculate left ventricle (LV) volumes of end filling and end ejection from LV images, and hence determining stroke volume
7.1.4 PV loop analysis
7.1.5 PV loop changes for diverse cardiac abnormalities
7.1.6 To calculate the pumping work done by the heart at each stroke and its power
7.1.7 Numerical integration – to calculate cardiac output by dye- dilution method, from data on dye bolus injected and blood concentration time profile at a sampling rate
8. First and Second Order Ordinary Differential Equations (ODE) and Partial Differential Equations (PDE) for Modelling Physiological Processes and Medical Procedures
8.1 Biomedical Applications
8.1.1 Determination of the size of the tumour by mathematical modelling of tumour growth rate
8.1.2 Determination of the concentration of a solute in a cell membrane given the concentrations on either side of the membrane
8.1.3 Model for determining the flow to an organ by monitoring the concentrations of tracer flows into the organ
8.1.4 Diastolic and systolic blood pressure time variations in the aorta
8.1.5 Diffusion processes in medicine
9. Organ System Analyses (OSA)
9.1 Cardiovascular Systems Analysis
9.1.1 Treadmill test
9.1.2 Heart sounds
9.1.3 LV pressure development
9.1.4 Ventricular pressure
9.1.5 Aortic pressure development and monitoring
9.1.6 Pulsatile blood flow
9.1.7 Blood flow in the Cardiovascular system
9.1.8 Measurement of blood plasma volume
9.2 Pulmonary Systems Analysis
9.2.1 Ventilation modelling and lung disease monitoring
9.2.2 Blood oxygenation
9.2.3 Cellular oxygenation
9.2.4 Mass transfer in the respiratory system
9.2.5 Ventilation/blood flow and gas exchange in the lungs
9.2.6 Oxygen uptake in the pulmonary capilliary
9.2.7 Krogh’s cylinder model, mathematical modelling for hypoxia
9.2.8 Ventilation modelling and lung disease monitoring
9.2.9 Blood oxygenation
9.2.10 Mass transfer in the respiratory system
9.2.11 Air Pollutants
9.2.12 Biological Responses of the Respiratory System to Air Pollutants
9.2.13 Lung Function Examination
9.2.14 Acute and Chronic Effects of Occupational Exposure on Pulmonary Function
9.2.15 Monitoring of Irritants
9.2.16 Studies of Acute, Temporary Lung Function Effects
9.2.17 Respiratory Irritants
9.2.18 Toxic Chemicals
9.2.19 Inhalation Fevers
9.2.20 Organic Dust Toxic Syndrome
9.2.21 Metal Fume Fever
9.2.22 Polymer Fume Fever
9.2.23 Occupational Asthma
9.2.24 Diseases Caused By Organic Dusts
9.2.25 Hazards
9.2.26 Pathogenesis
9.2.27 Histopathology
9.2.28 Clinical Manifestations
9.2.29 Safety and Health Measures
9.2.30 Pneumoconioses: Definition
9.2.31 Exposure-Dose-Response Relationships
9.2.32 Physicochemical Characteristics of Fibrogenic Dust Particles
9.2.33 Biological Mechanisms Inducing the Fundamental Lesions
9.2.34 Silicosis
9.2.35 Radiographic Patterns and Functional Pulmonary Abnormalities
9.2.36 Coal Workers' Lung Diseases
9.2.37 Progressive Massive Fibrosis
9.2.38 Obstructive Lung Disease
9.2.39 Chronic Bronchitis
9.2.40 Emphysema
9.2.41 Silicosis
9.2.42 Rheumatoid Pneumoconiosis
9.2.43 Lung Cancer
9.2.44 Regulatory Limits on Dust Exposure
9.2.45 Asbestos-Related Diseases
9.2.46 Hard Metal Disease
9.2.47 Respiratory System: The Variety Of Pneumoconioses
9.2.48 Chronic Obstructive Pulmonary Disease
9.2.49 Health Effects Of Man-Made Fibres
9.2.50 Respiratory Cancer
9.2.51 Ventilation/blood flow and gas exchange in the lungs
9.2.52 Oxygen uptake in the pulmonary capilliary
9.2.53 Krogh’s cylinder model, mathematical modelling for hypoxia
9.3 Diabetology Systems Analysis
9.3.1 Glucose regulation and glucose response to glucose administration in the glucose tolerance test
9.3.2 Glucose response to insulin administration
9.4 Digestive Systems Analysis
9.4.1 Flow of food/chyme and digestive juices in the gastrointestinal system
9.5 Renal System Analysis
9.5.1 Kidney function and renography
9.5.2 Urethral flow and propagation of stones to the bladder
9.5.3 Urine flows in the renal and urinary system
9.5.4 Mass transfer in the kidney
9.5.5 Peristaltic flow in the renal system
9.5.6 Kidney function and renography
9.5.7 Urethral flow, urinary tract obstruction, propagation of stones to the bladder
9.5.8 Urinary Tract Obstruction
9.5.9 Hydronephrosis: A Distended Kidney
9.6 Neural Systems Analysis
9.6.1 Action potential impulse propagation
9.6.2 Depolarisation wave propagation in heart and biopotentials in the neighbourhood leading to the basis of Einthoven triangle for VCG and ECG
9.7 Endocrine Systems Analysis 9.8 Reproductive Systems Analysis
10. Medical Devices
10.1 Biomedical Medical Devices In Common Clinical Practice
10.1.1 Stethoscope
10.1.2 Electroencephalography (EEG)
10.1.3 Electrocardiography (ECG)
10.1.4 Sphygmomanometer
10.1.5 Other medical devices
11. Elementary Signal processing, Wavelets and their Biomedical Applications
11.1 Fundamentals of Signal Processing and Transform
11.1.2 The Fourier Transform (FT)
11.1.3 The Short Time Fourier Transform (STFT)
11.1.4 The Wavelet Transform (WT)
11.2 Examples of Signal Processing in Biomedical Applications
11.2.1 Heart Sound Analysis Studies
11.2.2 Sleep Apneoa Studies
11.2.3 Other Studies
2. Fundamental Relationships among Biological Variables
2.1 Relationships between Several Biomedical Variables
2.2 Meaning of Functions and Examples of Functional Relationship Between Biomedical Quantities
2.3 Types of Functions - Linear, Quadratic, Logarithmic, Exponential, Trigonometric and Polynomial
2.3.1 Linear
2.3.2 Quadratic
2.3.3 Logarithmic
2.3.4 Exponential
2.3.5 Trigonometric
2.3.6 Polynomial
2.4 Sketching the graph of a given function; Maximum, minimum and point of inflection
2.5 Biomedical Applications
2.5.1 Celsius and Fahrenheit temperature scales
2.5.2 Cardiac Muscle force and shortening velocity
2.5.3 Pressure and Volume of a Gas
2.5.4 Cavitation
2.5.5 Glucose Tests
2.5.6 Renal Dialysis
2.5.7 Torque on a Long Tube and Resulting Shear Stress
2.5.8 Velocity of Enzyme Substrate reaction and the amount of Substrate
2.5.9 Wall stress and fluid pressure in fluid filled organ
2.5.10 Infant body weight and height vs Age
3. Introduction to Basic Calculus and Rate of Change of Biomedical Variables
3.1 Biomedical Applications
3.1.1 Change in pulse rate wrt the amount of drug
3.1.2 Rate of blood volume output during ejection period
3.1.3 Population (organism) growth rate
3.1.4 The half life and rate of decay of a radioactive substance
3.1.5 Definition of physical, biological and effective half life
3.1.6 Measurement of blood flow to limbs by measuring of rate of change of limb circumference
3.1.7 Compartmental modelling for studying drug transfer in the body
4. Introduction to Algebra, Linear Algebra and Vectors in Medicine
4.1 Biomedical Applications
4.1.1 Application of vectors in the musculo-skeleto system to determine muscle and joint force
5. Exponential and Logarithmic Biomedical Functions and their derivatives
5.1 Biomedical applications
5.1.1 Exponential growth models for bacteria and human populations
5.1.2 Radioactivity decay models, half life of a radioactive material
5.1.3 Definition of physical, biological and effective half life
5.1.4 Determination of the time of death of a person from body temperature and room temperature
6. Maximum and Minimum Value of a Function - Applications to Biomedical stability and instability
6.1 Biomedical Applications
6.1.1 Optimal design of bone from maximum strength and minimum weight
6.1.2 Optimal cardiovascular branching that minimises resistance to flow
6.1.3 How airways are optimally designed to expel air from the lungs most efficiently
6.1.4 How nerve fibres are optimally designed to maximise the impulse velocity
6.1.5 Delineating critical states of a patient’s medical condition
7. Integration - Summation, areas and volume applications
7.1 Biomedical Applications
7.1.1 Pressure-volume loop analysis in cardiology
7.1.2 To calculate the pumping work done by the heart at each stroke and its power
7.1.3 To calculate left ventricle (LV) volumes of end filling and end ejection from LV images, and hence determining stroke volume
7.1.4 PV loop analysis
7.1.5 PV loop changes for diverse cardiac abnormalities
7.1.6 To calculate the pumping work done by the heart at each stroke and its power
7.1.7 Numerical integration – to calculate cardiac output by dye- dilution method, from data on dye bolus injected and blood concentration time profile at a sampling rate
8. First and Second Order Ordinary Differential Equations (ODE) and Partial Differential Equations (PDE) for Modelling Physiological Processes and Medical Procedures
8.1 Biomedical Applications
8.1.1 Determination of the size of the tumour by mathematical modelling of tumour growth rate
8.1.2 Determination of the concentration of a solute in a cell membrane given the concentrations on either side of the membrane
8.1.3 Model for determining the flow to an organ by monitoring the concentrations of tracer flows into the organ
8.1.4 Diastolic and systolic blood pressure time variations in the aorta
8.1.5 Diffusion processes in medicine
9. Organ System Analyses (OSA)
9.1 Cardiovascular Systems Analysis
9.1.1 Treadmill test
9.1.2 Heart sounds
9.1.3 LV pressure development
9.1.4 Ventricular pressure
9.1.5 Aortic pressure development and monitoring
9.1.6 Pulsatile blood flow
9.1.7 Blood flow in the Cardiovascular system
9.1.8 Measurement of blood plasma volume
9.2 Pulmonary Systems Analysis
9.2.1 Ventilation modelling and lung disease monitoring
9.2.2 Blood oxygenation
9.2.3 Cellular oxygenation
9.2.4 Mass transfer in the respiratory system
9.2.5 Ventilation/blood flow and gas exchange in the lungs
9.2.6 Oxygen uptake in the pulmonary capilliary
9.2.7 Krogh’s cylinder model, mathematical modelling for hypoxia
9.2.8 Ventilation modelling and lung disease monitoring
9.2.9 Blood oxygenation
9.2.10 Mass transfer in the respiratory system
9.2.11 Air Pollutants
9.2.12 Biological Responses of the Respiratory System to Air Pollutants
9.2.13 Lung Function Examination
9.2.14 Acute and Chronic Effects of Occupational Exposure on Pulmonary Function
9.2.15 Monitoring of Irritants
9.2.16 Studies of Acute, Temporary Lung Function Effects
9.2.17 Respiratory Irritants
9.2.18 Toxic Chemicals
9.2.19 Inhalation Fevers
9.2.20 Organic Dust Toxic Syndrome
9.2.21 Metal Fume Fever
9.2.22 Polymer Fume Fever
9.2.23 Occupational Asthma
9.2.24 Diseases Caused By Organic Dusts
9.2.25 Hazards
9.2.26 Pathogenesis
9.2.27 Histopathology
9.2.28 Clinical Manifestations
9.2.29 Safety and Health Measures
9.2.30 Pneumoconioses: Definition
9.2.31 Exposure-Dose-Response Relationships
9.2.32 Physicochemical Characteristics of Fibrogenic Dust Particles
9.2.33 Biological Mechanisms Inducing the Fundamental Lesions
9.2.34 Silicosis
9.2.35 Radiographic Patterns and Functional Pulmonary Abnormalities
9.2.36 Coal Workers' Lung Diseases
9.2.37 Progressive Massive Fibrosis
9.2.38 Obstructive Lung Disease
9.2.39 Chronic Bronchitis
9.2.40 Emphysema
9.2.41 Silicosis
9.2.42 Rheumatoid Pneumoconiosis
9.2.43 Lung Cancer
9.2.44 Regulatory Limits on Dust Exposure
9.2.45 Asbestos-Related Diseases
9.2.46 Hard Metal Disease
9.2.47 Respiratory System: The Variety Of Pneumoconioses
9.2.48 Chronic Obstructive Pulmonary Disease
9.2.49 Health Effects Of Man-Made Fibres
9.2.50 Respiratory Cancer
9.2.51 Ventilation/blood flow and gas exchange in the lungs
9.2.52 Oxygen uptake in the pulmonary capilliary
9.2.53 Krogh’s cylinder model, mathematical modelling for hypoxia
9.3 Diabetology Systems Analysis
9.3.1 Glucose regulation and glucose response to glucose administration in the glucose tolerance test
9.3.2 Glucose response to insulin administration
9.4 Digestive Systems Analysis
9.4.1 Flow of food/chyme and digestive juices in the gastrointestinal system
9.5 Renal System Analysis
9.5.1 Kidney function and renography
9.5.2 Urethral flow and propagation of stones to the bladder
9.5.3 Urine flows in the renal and urinary system
9.5.4 Mass transfer in the kidney
9.5.5 Peristaltic flow in the renal system
9.5.6 Kidney function and renography
9.5.7 Urethral flow, urinary tract obstruction, propagation of stones to the bladder
9.5.8 Urinary Tract Obstruction
9.5.9 Hydronephrosis: A Distended Kidney
9.6 Neural Systems Analysis
9.6.1 Action potential impulse propagation
9.6.2 Depolarisation wave propagation in heart and biopotentials in the neighbourhood leading to the basis of Einthoven triangle for VCG and ECG
9.7 Endocrine Systems Analysis 9.8 Reproductive Systems Analysis
10. Medical Devices
10.1 Biomedical Medical Devices In Common Clinical Practice
10.1.1 Stethoscope
10.1.2 Electroencephalography (EEG)
10.1.3 Electrocardiography (ECG)
10.1.4 Sphygmomanometer
10.1.5 Other medical devices
11. Elementary Signal processing, Wavelets and their Biomedical Applications
11.1 Fundamentals of Signal Processing and Transform
11.1.2 The Fourier Transform (FT)
11.1.3 The Short Time Fourier Transform (STFT)
11.1.4 The Wavelet Transform (WT)
11.2 Examples of Signal Processing in Biomedical Applications
11.2.1 Heart Sound Analysis Studies
11.2.2 Sleep Apneoa Studies
11.2.3 Other Studies
- Edition: 1
- Published: January 1, 2026
- Imprint: Academic Press
- Language: English
DG
Dhanjoo N. Ghista
Dr. Dhanjoo N. Ghista is President of the University 2020 Foundation and a world authority in Biomedical Engineering. Dr. Ghista is author and editor of numerous books on subjects ranging from Biomedical Engineering to Cardiology science and technology, and he is the inventor of novel medical diagnostic and surgical procedures. Dr. Ghista is a pioneer in the field of Biomedical Engineering in Translational Medicine. He promotes a new STEMbased model of Medicine for precision medicine and surgery, as well as the role of universities in contributing sustainable community development. Dr. Ghista has an international standing in academia, having set up programs and departments at universities in responsible academic-administrative positions (from Department Head to CAO/Provost), and has even been involved in planning universities. Dr. Ghista has taught courses in Engineering, Physics, Biomedical Engineering, medical sciences, sports science, and hospital management. His research involvements and publications include Biomedical Engineering, Medicine, Cognitive Science and therapy, sports science, sustainable communities, and the role of university in society. Dr. Ghista is the author/editor of Biomedical Engineering Modeling for Medical Assessment, Volumes 1-3, Springer; Coronary Artery Bypass Grafting Design Simulations, Lambert Academic Publishing; Cardiac Perfusion and Pumping Engineering, World Scientific Publishing; Applied Biomedical Engineering Mechanics, CRC Press; and Orthopaedic Mechanics Procedures and Devices, Academic Press; among many others.
Affiliations and expertise
President, University 2020 Foundation, USAAM
Anacleto V. Mernone
Anacleto V. Mernone is a Researcher at the University of Adelaide and The Queen Elizabeth Hospital with a remarkable background in technical writing, primarily focused on the engineering and scientific domains, and boasting extensive experience within the defense and medical industries. With a diverse skill set encompassing modeling, simulation, analysis, systems engineering, software engineering, and design. He was research associate to Dr. Jagannath Mazumdar at the Centre for Biomedical Engineering, University of Adelaide.
Affiliations and expertise
The Queen Elizabeth Hospital, North Western Adelaide Health Service, AustraliaKM
Kayalvizhi Mohan
Dr. Kayalvizhi Mohan is an experienced Head of Department with a demonstrated history of working in the higher education industry. Skilled in Cognitive Science, Biomedical Engineering, Cognitive Neuroscience, Matlab, and Research, he is a strong education professional with a Doctor of Philosophy (Ph.D.) focused in Biomedical/Medical Engineering from Madras Institute of Technology campus Anna University.
Affiliations and expertise
Chennai Institute of Technology, Anna University, IndiaJM
Jagannath Mazumdar
Dr. Jagannath Mazumdar (deceased) was Emeritus Director of the Centre for Biomedical Engineering, University of Adelaide. After receiving bachelor’s and master’s degrees in applied mathematics from Patna University, India, he proceeded to Moscow State University to complete his Ph.D. in Solid Mechanics. He was also conferred an honorary Ph.D. degree by the University of Adelaide, Australia. Dr. Mazumdar has done some interesting research for the non-invasive study of heart valves tissue pathology by spectral analysis of heart sounds as well as by two-dimensional sector-scan echocardiography. This study gave us precise indication of the normality or abnormality of the stiffness property and hence, of the pathology of the valve leaflet material. He has also done some interesting study of vibrations of tympanic membrane (ear drum) by time-averaged holography which has been published in the Journal of Otolaryngological Society of Australia. Dr. Mazumdar worked in the field of Tissue Engineering and NanoBioscience. In acknowledgement of his contributions, Dr. Mazumdar was elected a Fellow of the Institution of Engineering, Australia. He was a Fellow of Australian Mathematical Society and a Fellow of Australian College of Physical Scientists and Engineers in Medicine.
Affiliations and expertise
Emeritus Director, Centre for Biomedical Engineering, University of Adelaide, Australia