Steepness of the radiation dose-response curve for dose-per-fraction escalation keeping the number of fractions fixed

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Abstract
Clinically, there is growing interest in strategies for intensifying radiation therapy by escalating the dose per fraction. This paper considers the steepness of the dose-response curve in this case. The steepness of a radiation dose-response curve is most conveniently quantified by the normalized dose-response gradient, gamma. Under the assumption of a linear-quadratic dose-effect model, a simple analytical relationship is derived between the gamma-value for a dose-response curve generated by varying the total dose while keeping the number of fractions constant, i.e. escalating the dose per fraction, and the gamma-value for a dose-response curve generated by varying the total dose while keeping the dose per fraction constant. This formulation is compared with clinical dose-response data from the literature and shown to be in good agreement with the observations. Some implications of this formulation for non-uniform dose distributions delivered using 3D conformal radiotherapy or intensity modulated radiotherapy (IMRT) are briefly discussed.