Case Studies in Mathematical Modeling for Medical Devices : How Pulse Oximeters and Doppler Ultrasound Fetal Heart Rate Monitors Work

著者名：Crowe, John

Academic Press（2024/11/12発売）

• 言語：ENG
• ISBN：9780323954723
• eISBN：9780323954730

Description

Case Studies in Mathematical Modelling for Medical Devices: How Pulse Oximeters and Doppler Ultrasound Fetal Heart Rate Monitors Work focuses on two medical devices: pulse oximeters and Doppler ultrasound fetal heart rate monitors. The mathematical topics needed to explain their operation from first principles are introduced. These broadly cover the statistics of random processes and Fourier based signal processing. They are used to explain the devices' operation from first principles to how clinically relevant information is extracted from the devices' raw outputs. .The book is for MSc and PhD students working in the area who want a quick, clear introduction to the topics, upper-division undergrads as part of biomedical engineering or applied math degree courses, biomedical engineers looking for a quick "refresher course" and clinicians interested in the operation of the instruments they use.- Describes, from first principles, the operation of two medical diagnostic devices- Introduces diverse and widely used mathematical topics- Uses this knowledge to model the physical processes that underpin the devices' operation- Explains how clinically relevant information is obtained from the monitors' raw outputs.

Table of Contents

Preface ixAcknowledgments xiIntroduction to the book xiiiPART 1 Maths for oximetryList of symbols and abbreviations 31. Introduction 72. Discrete probability distributions 93. Continuous probability distributions 174. Summary statistics, moments, and cumulants 295. Commonly encountered distributions 436. Shifting and scaling distributions 617. Random samples fromdistributions 67PART 2 Oximeters8. Introduction: oximetry 799. Absorption coefficients 8910. Lambert–Beer law 9711. Oximetry on non-scattering samples 10512. Scattering and the Lambert–Beer law 11313. Attenuation versus absorption—a theoretical derivation 12314. Pulse oximetry 13515. Pulse oximetry on a population 14716. TheMasimo Corporation's oximeters 15317. Modeling light propagation 16318. The oximeter zoo 177PART 3 Appendices for oximeters19. Variance via raw moments 19720. Taylor series 19921. Binomial coefficients and series 20122. Calculus 20523. Derivatives of attenuation versus absorbance 21524. Modeling the PPG 21725. Fluorescence lifetimemeasurements 21926. Logarithms 223PART 4 Maths for DUS-FHRList of symbols and abbreviations 22927. Introduction 23128. Waves 23729. Sinusoids 24130. Beats 24931. Fourier analysis 25332. Frequency domain filtering 26333. Hilbert transform and the analytic signal 26934. Convolution 27935. Modulation 28536. Sampling 29337. Autocorrelation 299PART 5 DUS-FHR38. Fetal heart rate monitoring 30739. Ultrasound 31340. Doppler ultrasound 31741. Doppler shift extraction 32942. DUS-FHRmonitoring 35543. Bandpass sampling 37144. Pulsed operation 387PART 6 Appendices for DUS-FHR45. Compound angle identities 39546. Complex numbers 39747. Modeling with Matlab® 399Bibliography 409Index 413