Heat Therapy for Tumors (UMAP)

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