Room: Exhibit Hall | Forum 3
Purpose: To develop, parametrize and validate a mathematical model for the temporal behavior of prostate-specific antigen (PSA) in prostate cancer (PCa) patients treated with intensity modulated radiation therapy (IMRT) alone.
Methods: The model for PSA kinetics is composed of a logistic differential equation for cancer growth, the linear-quadratic (LQ) model for cell kill during radiotherapy (RT) and a fraction of quiescent cells created at every fraction, which die following a Poisson probability distribution. The PSA concentration is proportional to the number of viable and quiescent cells. For the parametrization of the model we used serial PSA data from 217 low-risk prostate patients treated at Houston Methodist Hospital with moderately hypo-fractionated IMRT alone, with a mean fraction dose of 2.19Gy and a median patient follow-up of 62 months. The differential equations were integrated semi-numerically. We used a non-linear least-squares fit of the data employing simulated annealing to evaluate the model parameters. We compared our results with published data from the literature for the natural history of early, localized prostate cancer and for the PSA kinetics during RT.
Results: We created an analytic model for the survival fraction of early, localized PCa patients using data from the literature which is fitted well using two Gaussian distributions for the linear growth parameter. We fitted individual patient PSA data for all patients using the numeric model. The linear growth parameter histogram for the RT patient and natural history data show similar behavior. The calculated mean survival fraction was 0.499, but the narrow range of clinical doses did not allow for an accurate estimation of the LQ model parameters.
Conclusion: The radiobiological model including quiescent cells accurately describes the patient data for PSA in low-risk prostate patients treated with RT alone. The growth parameter probability distributions for RT patients and natural history are consistent.