Optimal dose distribution for eradication of heterogeneous tumours.

The traditional single hit multitarget theory has been applied on the probability of eradication of an organ or a tumor and the probability for causing complications in normal tissue. This simple theory predicts a decreasing possibility to achieve uncomplicated tumor control with increasing tumor size and maintained irradiation technique, because the control curve moves to higher doses and the complication curve to lower doses as the tumor size increases. This simple result is shown to be consistent with clinically observed dose response relations for small and large tumors. The optimal dose distribution for eradication of a heterogeneous tumor is derived on the assumption that a uniform minimal recurrence probability is most advantageous for the patient. The optimal dose distribution is proportional to the spatial variation of the local D0 value and the logarithm of the tumor cell density. Various techniques to measure the density of tumor cells and the different possibilities to deliver non-uniform dose distributions to the target volume are also discussed.