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The use of generalized cell-survival data in a physiologically based objective function for hyperthermia treatment
D T Tompkins1, R Vanderby, S A Klein
1Department of Mechanical Engineering, University of Wisconsin-Madison 53792.
Purpose:
A physiologically based objective function for identifying a combination of ferromagnetic seed temperatures and locations that maximizes the fraction of tumor cells killed in pretreatment planning of local hyperthermia.
Methods And Materials:
An objective-function is developed and coupled to finite element software that solves the bioheat transfer equation. The sensitivity of the objective function is studied in the optimization of a ferromagnetic hyperthermia treatment. The objective function has several salient features including (a) a physiological basis that considers increasing the fraction of cells killed with increasing temperatures above a minimum therapeutic temperature (Tmin,thera), (b) a term to penalize for heating of normal tissues above Tmin,thera, and (c) a scalar weighting factor (gamma) that has treatment implications. Reasonable estimates for gamma are provided and their influence on the objective function is demonstrated. The cell-kill algorithm formulated in the objective function is based empirically upon the behavior of published hyperthermic cell-survival data. The objective function is shown to be independent of normal tissue size and shape when subjected to a known outer-surface, thermal boundary condition. Therefore, fractions of cells killed in tumors of different shapes and sizes can be compared to determine the relative performance of thermoseed arrays to heat different tumors.
Results:
In simulations with an idealized tissue model perfused by blood at various rates, maxima of the objective function are unique and identify seed spacings and Curie-point temperatures that maximize the fraction of tumor cells killed. In ferromagnetic hyperthermia treatment planning, seed spacing can be based on maximizing the minimum tumor temperature and minimizing the maximum normal tissue temperature. It is shown that this treatment plan is less effective than a plan based on seed spacings that maximize the objective function.
Conclusions:
It is shown that under the assumptions of the model and based on a desired therapeutic goal, the objective function identifies a combination of thermoseed temperatures and locations that maximizes the fraction of tumor cells killed.