The influence of timing on radiation damage to cell populations

When chemo/radiotherapy is administered, both cancer and normal cells are a ffected and destroyed. It would be optimal, then, to administer treatment t o minimize killing of normal cells and maximize killing of cancer cells. Be cause the schemes to kill cancer cells have been well explored, in this pap er we investigate only which dose distribution treatment could minimize the damage of normal cells. A dose refers to the total energy absorbed per uni t mass. In this paper, within a certain framework, it is proved that radiat ion with two split acute doses or at any continuous dose rate results in mo re damage to cell populations than one acute dose, provided the total dose is fixed and small. The mathematical model is a system of ordinary differen tial equations which represents proliferating cells in m cell compartments. We assume there is a unique nontrivial stable equilibrium and that the sys tem is linear near the equilibrium state. The damage criterion is the "accu mulated deficiency," i.e., the total deficiency of cell number caused by ra diation, integrated over time. At the end, we draw the conclusion that the acute dose delivery provides minimal killing of normal cells and maximal ki lling of cancer cells. It is also proved that the solution Z(t) to the linear system (Z)over dot(t ) = AZ(t), Z(0) = Z0 greater than or equal to 0 is strictly positive for t > 0 as long as -A is an M-matrix and one of the components of Z(0) is stric tly positive.