Series in Modern Applied Mathematics - Vol. 1
MATHEMATICAL METHODS IN MEDICINE
by Richard Bellman (University of Southern California)
This book is intended for medical students and advanced undergraduates such as physicists and mathematicians with inter-disciplinary interests, biophysicists, medical physicists, applied mathematicians and others who wish to understand medicine in mathematical terms as well as current mathematical applications in physiology and medicine. The mathematical presentation is clear and self-contained.
This book, representing 15 years of work at RAND Corporation and USC on chemotherapy, pharmacokinetics and nuclear medicine, attempts to direct medical scientists towards mathematical aspects of problems in medicine. The book begins with an introduction to compartmental models and matrix theory, highlighting the advantages of the approach. Discussions on how questions in observations and testing lead to multi-point boundary value problems are presented. The potentials of the digital computer in the bio-medical field are examined. A new approach — dynamic programming — to overcome clinical constraints is covered in detail. The reader should obtain a broad impression of where future research opportunities in the biochemical field lie.
Contents:
- One- and Two-Compartmental Models
- Matrices and
Multi-Compartment Models
- Observation and Testing
- Pharmacokinetic Properties
- The Sorcerer's Apprentice
- The Digital Computer
- Numerical Algorithms
- Optimal Dosage and Control Theory
- Clinical Treatment and Constraints
- Decision Processes and Dynamic Programming
- Analytic and Computational Techniques
- Uncertainty
- Tumor Detection and Scan-Rescan Processes
- Radiotherapy and Radiative Transfer
| 268pp |
Pub. date: Apr 1983 |
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