Radiotherapy planning for glioblastoma based on a tumor growth model: implications for spatial dose redistribution
Abstract
Gliomas differ from many other tumors as they grow infiltratively into the brain parenchyma rather than forming a solid tumor mass with a welldefined boundary. Tumor cells can be found several centimeters away from the central tumor mass that is visible using current imaging techniques. The infiltrative growth characteristics of gliomas question the concept of a radiotherapy target volume that is irradiated to a homogeneous dose—the standard in current clinical practice. We discuss the use of the FisherKolmogorov glioma growth model in radiotherapy treatment planning. The phenomenological tumor growth model assumes that tumor cells proliferate locally and migrate into neighboring brain tissue, which is mathematically described via a partial differential equation for the spatiotemporal evolution of the tumor cell density. In this model, the tumor cell density drops approximately exponentially with distance from the visible gross tumor volume, which is quantified by the infiltration length, a parameter describing the distance at which the tumor cell density drops by a factor of e. This paper discusses the implications for the prescribed dose distribution in the periphery of the tumor. In the context of the exponential cell kill model, an exponential falloff of the cell density suggests a linear falloff of the prescription dose with distance. We introduce the dose falloff rate, which quantifies the steepness of the prescription dose falloff in units of Gy mm^{1}. It is shown that the dose falloff rate is given by the inverse of the product of radiosensitivity and infiltration length. For an infiltration length of 3 mm and a surviving fraction of 50% at 2 Gy, this suggests a dose falloff of approximately 1 Gy mm^{1}. The concept is illustrated for two glioblastoma patients by optimizing intensitymodulated radiotherapy plans. The dose falloff rate concept reflects the idea that infiltrating gliomas lack a defined boundary and are characterized by a continuous falloff of the density of infiltrating tumor cells. The approach can potentially be used to individualize the prescribed dose distribution if better methods to estimate radiosensitivity and infiltration length on a patient by patient basis become available.
 Publication:

Physics in Medicine and Biology
 Pub Date:
 February 2014
 DOI:
 10.1088/00319155/59/3/771
 Bibcode:
 2014PMB....59..771U