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Consortium for Mathematics and its Applications

Product ID: 99714
Supplementary Print
Undergraduate

Heat Therapy for Tumors (UMAP)

Author: Leah Edelstein-Keshet


This module discusses calculus techniques to gain insight into a problem of clinical and medical significance. The methods used include triple (volume) integration in spherical coordinates and elementary Taylor series. They are applied to evaluating hyperthermia, a form of cancer therapy that has gained recognition and importance in the last decade.

Table of Contents:

INTRODUCTION

HYPERTHERMIA

MONITORING THE COURSE OF A TREATMENT

CHARACTERIZING TUMOR TEMPERATURES

MODELING THE PROCESS AND MAKING SIMPLIFYING ASSUMPTIONS

TUMOR GEOMETRY AS THE DOMINANT EFFECT
Spherical Tumor, Linear Temperature Profile
Nonspherical Tumor, Monotonic Temperature Profile

HEATING PATTERN AS THE DOMINANT EFFECT
Some Equitherms Are (Almost) Ellipsoidal
Some Equitherms Are (Almost) Parabolic
Estimating Heated Volume

EPILOGUE

SOLUTIONS TO THE EXERCISES

REFERENCES

ACKNOWLEDGEMENTS

ABOUT THE AUTHOR

©1992 by COMAP, Inc.
UMAP Module
32 pages

Mathematics Topics:

Calculus , Operations Research

Application Areas:

Life Sciences & Medicine

Prerequisites:

Equithermal surfaces; spherical and cylindrical coordinates; triple integration in spherical coordinates; Taylor series

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