On the sensitivity of IMRT dose optimization to the mathematical form of a biological imaging-based prescription function

Voxel-based prescriptions of deliberately non-uniform dose distributions based on molecular imaging, so-called dose painting or theragnostic radiation therapy, require specification of a transformation that maps the image data intensities to prescribed doses. However, the functional form of this transformation is currently unknown. An investigation into the sensitivity of optimized dose distributions resulting from several possible prescription functions was conducted. Transformations between the radiotracer activity concentrations from Cu-ATSM PET images, as a surrogate of tumour hypoxia, and dose prescriptions were implemented to yield weighted distributions of prescribed dose boosts in high uptake regions. Dose escalation was constrained to reflect clinically realistic whole tumour doses and constant normal tissue doses. Optimized heterogeneous dose distributions were found by minimizing a voxel-by-voxel quadratic objective function in which all tumour voxels were given equal weight. Prescriptions based on a polynomial mapping function were found to be least constraining on their optimized plans, while prescriptions based on a sigmoid mapping function were the most demanding to deliver. A prescription formalism that fixed integral dose was less sensitive to errors in the choice of the mapping function than one that boosted integral dose. Integral doses to normal tissue and critical structures were insensitive to the shape of the prescription function. Planned target dose conformity improved with smaller beamlet dimensions until the inherent spatial resolution of the functional image was matched. Clinical implementation of dose painting depends on advances in absolute quantification of functional images and improvements in delivery techniques over smaller spatial scales.