Case Studies in Mathematical Modelling for Medical Devices
How Pulse Oximeters and Doppler Ultrasound Fetal Heart Rate Monitors Work
- 1st Edition - November 1, 2024
- Author: John Crowe
- Language: English
- Paperback ISBN:9 7 8 - 0 - 3 2 3 - 9 5 4 7 2 - 3
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 9 5 4 7 3 - 0
Case Studies in Mathematical Modelling for Medical Devices: How Pulse Oximeters and Doppler Ultrasound Fetal Heart Rate Monitors Work focuses on three medical devices used to mon… Read more
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Request a sales quoteCase Studies in Mathematical Modelling for Medical Devices: How Pulse Oximeters and Doppler Ultrasound Fetal Heart Rate Monitors Work focuses on three medical devices used to monitor some aspect of physiological status: pulse oximetry, laser Doppler flowmetry and Doppler ultrasound fetal heart rate monitoring. The book's three case studies serve as the basis for readers to be able to generalize modeling to other medical devices. It introduces mathematical topics that appear in many areas of science and engineering by demonstrating the value of being able to model how devices work. This requires a brief description of their operating principles before appropriate mathematics. Containing three parts about each medical device, the book begins with a chapter on probability distributions that will be used in oximetry and laser Doppler flowmetry parts. This book is for MSc and PhD students in biomedical engineering and those interested in the mathematics behind the design of the instrumentation that they use.
- Demonstrates the value of analyzing three medical diagnostic devices and their operation using mathematics
- Looks at numerous, diverse mathematical topics that illustrate how math can be used to completely understand an instrument’s operation
- Models the physical processes that underpin devices operation to the principles of the processing applied to extract clinically relevant data from raw outputs
MsC and PhD students working in the area who want a quick, clear introduction to the topics, upper-division undergrads as part of applied mathematics or biomedical engineering degree course, Biomedical engineers looking for a quick "refresher course"
1 Probability Distributions
11.1 Introduction
1.2 Discrete Probability Distributions
1.3 Cumulative Distribution Function (CDF)
1.4 Summary Statistics
1.5 Probability Density Function
1.6 PDFs used
1.7 Summary
I Oximetry
2 Introduction
2.1 What Oximetry Measures
2.2 Structure
3 Lambert Beer Law
3.1 Introduction
3.2 Cross sections and the absorption coefficient
3.3 Derivation
3.4 Mean Free Path
3.5 Scattering processes
3.6 Summary
4 Chromophores and Absorption Coefficients
4.1 Introduction
4.2 Chromophores in tissue
4.3 Molar / specific absorption coefficient
4.4 Summary
5 Oximetry on non-Scattering Samples
5.1 Introduction
5.2 Definition of Oxygen Saturation
5.3 Single Wavelength Oximetry
5.4 Two wavelength oximetry
5.5 Practical concerns for scattering media
6 Modelling Photon Propagation in scattering media
6.1 Introduction
6.2 Model Parameters
6.3 Overview
6.4 Monte Carlo Modelling
6.5 Applying Monte Carlo to tissue modelling
6.6 Scattering
6.7 Results
6.8 Summary and Observations
7 Theory of light attenuation in scattering and absorbing media
7.1 Introduction
7.2 Lambert-Beer law
7.3 Attenuation vs. ma
7.4 Summary
8 Pulse Oximetry
8.1 Optical measurements on tissue
8.2 Pulse Oximetry
9 Summary
II Doppler Ultrasound Fetal Heart Rate Monitoring
10 Introduction
11 Continuous wave operation
11.1 Introduction
12 Example Motions
12.1 Case 1 : Static reflector
12.2 Case 2 : Reflector with constant velocity
12.3 Case 3 : Reflector undergoing sinusoidal motion
12.4 Case 4 : Idealised cardiac motion
12.5 Summary
13 Production of Intermediate Frequency (IF) ultrasound signal
13.1 Introduction
13.2 Mixing with LO
13.3 Ambiguity with heterodyne detection: and its resolution
13.4 FFT demodulation
14 Demodulation and Instantaneous Frequency
14.1 Introduction: Fetal monitor operation
14.2 Instantaneous Frequency
14.3 Graphical interpretation of Instantaneous Frequency
15 Pulsed Systems
16 Model 77
16.1 CW operation
16.2 Pulsed operation
III Laser Doppler Flowmetry
17 Laser Doppler Flowmetry
11.1 Introduction
1.2 Discrete Probability Distributions
1.3 Cumulative Distribution Function (CDF)
1.4 Summary Statistics
1.5 Probability Density Function
1.6 PDFs used
1.7 Summary
I Oximetry
2 Introduction
2.1 What Oximetry Measures
2.2 Structure
3 Lambert Beer Law
3.1 Introduction
3.2 Cross sections and the absorption coefficient
3.3 Derivation
3.4 Mean Free Path
3.5 Scattering processes
3.6 Summary
4 Chromophores and Absorption Coefficients
4.1 Introduction
4.2 Chromophores in tissue
4.3 Molar / specific absorption coefficient
4.4 Summary
5 Oximetry on non-Scattering Samples
5.1 Introduction
5.2 Definition of Oxygen Saturation
5.3 Single Wavelength Oximetry
5.4 Two wavelength oximetry
5.5 Practical concerns for scattering media
6 Modelling Photon Propagation in scattering media
6.1 Introduction
6.2 Model Parameters
6.3 Overview
6.4 Monte Carlo Modelling
6.5 Applying Monte Carlo to tissue modelling
6.6 Scattering
6.7 Results
6.8 Summary and Observations
7 Theory of light attenuation in scattering and absorbing media
7.1 Introduction
7.2 Lambert-Beer law
7.3 Attenuation vs. ma
7.4 Summary
8 Pulse Oximetry
8.1 Optical measurements on tissue
8.2 Pulse Oximetry
9 Summary
II Doppler Ultrasound Fetal Heart Rate Monitoring
10 Introduction
11 Continuous wave operation
11.1 Introduction
12 Example Motions
12.1 Case 1 : Static reflector
12.2 Case 2 : Reflector with constant velocity
12.3 Case 3 : Reflector undergoing sinusoidal motion
12.4 Case 4 : Idealised cardiac motion
12.5 Summary
13 Production of Intermediate Frequency (IF) ultrasound signal
13.1 Introduction
13.2 Mixing with LO
13.3 Ambiguity with heterodyne detection: and its resolution
13.4 FFT demodulation
14 Demodulation and Instantaneous Frequency
14.1 Introduction: Fetal monitor operation
14.2 Instantaneous Frequency
14.3 Graphical interpretation of Instantaneous Frequency
15 Pulsed Systems
16 Model 77
16.1 CW operation
16.2 Pulsed operation
III Laser Doppler Flowmetry
17 Laser Doppler Flowmetry
- No. of pages: 250
- Language: English
- Edition: 1
- Published: November 1, 2024
- Imprint: Academic Press
- Paperback ISBN: 9780323954723
JC
John Crowe
John Crowe retired in 2020 after working as a biomedical engineer in academia for 40 years. During this time, he worked on the development of numerous medical devices with a couple leading to the formation of spin out companies. He previously co-authored the Introduction to Digital Electronics (1998).
Affiliations and expertise
Professor Emeritus of Biomedical Engineering, Faculty of Engineering, University of Nottingham, UK