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Improved models of tumour cure

S L Tucker¹, J M Taylor

¹Department of Biomathematics, University of Texas, M.D. Anderson Cancer Center, Houston 77030, USA.

International Journal of Radiation Biology

|November 1, 1996

Summary

The standard Poisson model for tumor cure is inaccurate when tumor cell proliferation occurs during radiotherapy. New models (GS, PS, GS+) offer improved accuracy for predicting tumor cure rates, especially in fractionated radiotherapy.

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Area of Science:

Radiation oncology
Mathematical modeling
Cancer biology

Background:

The Poisson model is the standard for predicting tumor cure probability.
This model assumes surviving clonogens follow a Poisson distribution, which is inaccurate if proliferation occurs during treatment.

Purpose of the Study:

To investigate the magnitude of error in the Poisson model due to tumor cell proliferation during fractionated radiotherapy.
To propose and evaluate new models for predicting tumor cure rates.

Main Methods:

Investigated errors in the Poisson model for conventional and split-course radiotherapy.
Developed and tested three new models: GS, PS, and GS+.
Assessed model accuracy against simulated tumor cure rates.

Main Results:

The Poisson model can have significant errors (up to 100%) when proliferation occurs, particularly for small tumors.
Errors can reach 40% for larger tumors (> or = 10^6 clonogens).
The GS and PS models demonstrated improved accuracy over the Poisson model.
The GS+ model provided the most accurate cure rate estimates but is more complex.

Conclusions:

Tumor cell proliferation during radiotherapy significantly impacts cure probability, rendering the standard Poisson model inaccurate.
The proposed GS and PS models offer better predictions for tumor cure rates in fractionated radiotherapy.
No single model based on effective clonogen doubling time is universally accurate; cure rate depends on detailed cell kinetics.

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