Jd. Fenwick, PREDICTING THE RADIATION CONTROL PROBABILITY OF HETEROGENEOUS TUMOR ENSEMBLES - DATA-ANALYSIS AND PARAMETER-ESTIMATION USING A CLOSED-FORM EXPRESSION, Physics in medicine and biology, 43(8), 1998, pp. 2159-2178
A closed-form formula describing the tumour control probability (tcp)
of a heterogeneous collection of rumours has been obtained by analytic
ally averaging the homogeneous double-exponential tcp formula over int
er-tumour distributions of clonogen radiosensitivity, density and repo
pulation rate, tumour volume and dose. The formula can be straightforw
ardly and relatively quickly fitted to clinical data, yielding radiobi
ological parameter values for use in rep modelling. The formula was fi
tted to published tcp data which catalogued tumour control records gro
uped by dose and tumour volume, and treatment duration. Fitted paramet
er values, confidence intervals and goodness-of-fit statistics were de
termined. The sets of parameter values obtained are unique only to wit
hin a scaling factor. The formula provides non-rejectable fits to data
which grouped tcp by dose and volume when radiosensitivity parameters
take values close to laboratory estimates, the fitted volume dependen
ce parameter, however, taking rather high values. Good fits are obtain
able with the intuitively reasonable volume parameter value of one, bu
t with radiosensitivity values around one-third of their laboratory es
timates. Non-rejectable fits to data which grouped rep by dose and tre
atment duration may be obtained with radiosensitivity and repopulation
rate parameters lying close to laboratory estimates.