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Case studies in mathematical modeling for medical devices : how pulse oximeters and doppler ultrasound fetal heart rate monitors work.

Bibliographic Details
Main Author: Crowe, John
Corporate Author: ScienceDirect (Online service)
Format: eBook
Language:English
Published: Chantilly : Elsevier Science & Technology, 2024.
Subjects:
Medical instruments and apparatus > Mathematical models.
Pulse oximeters.
Fetal heart rate monitoring > Equipment and supplies.
Médecine > Appareils et instruments > Modèles mathématiques.
Oxymètres de pouls.
Cardiotocographie > Appareils et matériel.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Front Cover
  • Case Studies in Mathematical Modeling for Medical Devices
  • Copyright
  • Contents
  • Preface
  • Acknowledgments
  • Introduction to the book
  • 1 Maths for oximetry
  • List of symbols and abbreviations
  • 1 Introduction
  • 1.1 Oximetry
  • 1.2 Probability
  • 2 Discrete probability distributions
  • 2.1 Dice throwing and the probability mass function
  • 2.1.1 Notation
  • 2.1.2 Some "rules" of probability
  • 2.2 Example: coin tossing
  • 2.3 Cumulative distribution function
  • 2.4 Summary
  • 2.5 Problems
  • 3 Continuous probability distributions
  • 3.1 Pathlengths through a scattering sample
  • 3.1.1 Bar chart of counts
  • 3.1.2 Probability mass
  • 3.1.3 Probability density
  • 3.2 Probability density function
  • 3.2.1 Pathlength simulation
  • 3.3 Cumulative distribution function
  • 3.4 Example: uniform distribution
  • 3.5 Summary
  • 3.6 Problems
  • 4 Summary statistics, moments, and cumulants
  • 4.1 The mean and its synonyms
  • 4.2 Calculating the mean: discrete data
  • 4.2.1 Two dice
  • 4.2.2 Three coins
  • 4.3 Higher order and central moments
  • 4.3.1 Raw moments
  • 4.3.2 Central moments
  • 4.4 Variance: discrete data
  • 4.4.1 Variance - the second central moment
  • 4.4.2 Variance examples: dice and coins
  • 4.5 Mean and variance: continuous data
  • 4.5.1 Example: uniform distribution
  • 4.5.1.1 Mean
  • 4.5.1.2 Variance
  • 4.6 Moment generating function
  • 4.6.1 Introduction
  • 4.6.2 MGF in series form
  • 4.6.2.1 Extraction of the moments
  • 4.6.3 Discrete example: coin tossing
  • 4.6.4 Continuous example: uniform distribution
  • 4.6.4.1 First moment: [mu]
  • 4.7 Cumulant generating function
  • 4.8 Moments and cumulants
  • 4.9 Summary
  • 4.10 Problems
  • 5 Commonly encountered distributions
  • 5.1 Introduction
  • 5.2 Uniform distribution
  • 5.3 Binomial distribution
  • 5.3.1 Moment generating function
  • 5.3.2 Mean and variance
  • 5.4 Poisson distribution
  • 5.4.1 Derivation
  • 5.4.1.1 Limits
  • 5.4.2 Mean and variance
  • 5.4.3 Moment generating function
  • 5.5 Exponential distribution
  • 5.5.1 Mean and variance
  • 5.5.2 Cumulants
  • 5.5.3 Exponential and Poisson relationship
  • 5.6 Gaussian distribution
  • 5.6.1 Moment and cumulant generating function
  • 5.7 Wald distribution
  • 5.7.1 Gaussian and Wald relationship
  • 5.8 Summary
  • 5.9 Problems
  • 6 Shifting and scaling distributions
  • 6.1 Summary statistics-PDF and CDF
  • 6.1.1 Expectation value: E(Y)
  • 6.1.2 Variance
  • 6.1.3 CDF
  • 6.1.4 PDF
  • 6.2 Example 1: uniform distribution
  • 6.3 Example 2: Gaussian distribution
  • 6.4 Summary
  • 7 Random samples from distributions
  • 7.1 Sampling from a discrete distribution
  • 7.2 Sampling from a continuous distribution
  • 7.2.1 How it works
  • 7.2.2 Observations to use
  • 7.2.2.1 Invertible and monotonic CDF
  • 7.2.2.2 The CDF of a uniform distribution
  • 7.2.3 Derivation of the inverse CDF
  • 7.3 Examples
  • 7.3.1 Example: uniform random variates
  • 7.3.2 Example: simple continuous distribution.