Optimizing proton minibeam radiotherapy by interlacing and heterogeneous tumor dose on the basis of calculated clonogenic cell survival

Abstract

Proton minibeam radiotherapy (pMBRT) is a spatial fractionation method using sub-millimeter beams at center-to-center (ctc) distances of a few millimeters to widen the therapeutic index by reduction of side effects in normal tissues. Interlaced minibeams from two opposing or four orthogonal directions are calculated to minimize side effects. In particular, heterogeneous dose distributions applied to the tumor are investigated to evaluate optimized sparing capabilities of normal tissues at the close tumor surrounding. A 5 cm thick tumor is considered at 10 cm depth within a 25 cm thick water phantom. Pencil and planar minibeams are interlaced from two (opposing) directions as well as planar beams from four directions. An initial beam size of σ0 = 0.2 mm (standard deviation) is assumed in all cases. Tissue sparing potential is evaluated by calculating mean clonogenic cell survival using a linear-quadratic model on the calculated dose distributions. Interlacing proton minibeams for homogeneous irradiation of the tumor has only minor benefits for the mean clonogenic cell survival compared to unidirectional minibeam irradiation modes. Enhanced mean cell survival, however, is obtained when a heterogeneous dose distribution within the tumor is permitted. The benefits hold true even for an elevated mean tumor dose, which is necessary to avoid cold spots within the tumor in concerns of a prescribed dose. The heterogeneous irradiation of the tumor allows for larger ctc distances. Thus, a high mean cell survival of up to 47% is maintained even close to the tumor edges for single fraction doses in the tumor of at least 10 Gy. Similar benefits would result for heavy ion minibeams with the advantage of smaller minibeams in deep tissue potentially offering even increased tissue sparing. The enhanced mean clonogenic cell survival through large ctc distances for interlaced pMBRT with heterogeneous tumor dose distribution results in optimum tissue sparing potential. The calculations show the largest enhancement of the mean cell survival in normal tissue for high-dose fractions. Thus, hypo-fractionation or even single dose fractions become possible for tumor irradiation. A widened therapeutic index at big cost reductions is offered by interlaced proton or heavy ion minibeam therapy.

Longitudinally Heterogeneous Tumor Dose Optimizes Proton Broadbeam, Interlaced Minibeam, and FLASH Therapy

“…It covers the tumor homogeneously with the dose from each side. The considered proton energies and their relative weighting (see Table 1 ) is taken from previous studies [ 10 , 11 ]. The summed dose distribution fluctuates less than ±1% relative to D t ( 1.0%).…”

“…In addition, for each of the four depth-dose distributions, an optimized irradiation case is calculated utilizing the planar minibeams. The minimum dose criterion is taken here that any location in the tumor volume has to be covered with a dose D > 0.975 D t (here: D t = 10 Gy), as already introduced in [ 11 ]. An upper dose limit is not considered allowing highly modulated dose distributions within the tumor volume.…”

“…The irradiation scenario is a 25 cm-thick phantom which contains a 5 cm-thick tumor at the center of the phantom as discussed in [ 10 , 11 ]. Therefore, the irradiated healthy tissue is 10 cm thick from each direction.…”

“…The dose distributions for interlaced proton planar minibeams are calculated similarly to our previous studies using Matlab [ 12 ] where planar minibeams have shown to be the best option of increasing mean cell survival in the healthy tissue when applying longitudinally homogeneous mean depth-dose curves [ 11 ]. Here, in addition, longitudinally inhomogeneous dose distributions are considered as detailed in the results section.…”

“…The model parameters are taken from the PIDE database [ 20 ] as the mean values for human cells including tumor and healthy tissue cells waving any RBE effects in the first approximation. The LQ-model is appropriate as long as the percentage scale of cell survival is considered [ 11 ]. Thus, it is a good representation of the cell survival in the healthy tissue in the case of broadbeam irradiation modes where cell survivals of 10–20% are obtained for the considered 10 Gy tumor dose.…”