Iterative optimization of relative stopping power by single detector based multi-projection proton radiography

In proton therapy, range uncertainties induced by the conversion from x-ray CT (xCT) Hounsfield units (HU) to relative stopping power (RSP) compromise the precision of dose delivery. To reduce range uncertainties induced by HU-converted RSPs, this study investigates optimizing the RSP of individual voxels in xCT iteratively based on multi-projection proton radiography (pRG) acquired using a single amorphous silicon flat panel imager. Time-resolved dose rate functions (DRF) were measured by the imager placed downstream of a test phantom consisting of tissue substitute materials. Water equivalent path lengths (WEPL) in the pRG were derived. By rotating the phantom, multiple pRG projections were acquired at angles from 0 to 358° with an increment of 2°. X-ray CT of the phantom was acquired and co-registered with the pRG acquisition coordinates. RSPs of individual xCT voxels were optimized iteratively by minimizing the difference between the measured WEPLs and the calculated WEPLs by ray tracing with HU-converted RSPs. Pixels in pRGs that exhibited severe proton range mixing were rejected for the optimization. Tikhonov regularization was applied under the assumption that HU-converted RSPs are inaccurate, but the inaccuracy is within a few percent. While ~50% of WEPL pixels were rejected due to severe range mixing in pRG, RSPs of  >90% CT voxels could still be optimized if multiple pRG projections, e.g.  ⩾12, around the phantom are utilized. For tissue substitute materials in a cylindrical phantom, percentage errors of RSPs were reduced from a range of  -8% to  +4% to be within  ±2%. Further optimization, achieved by implementing a material-specific regularization parameter, reduced percent errors to be within  ±0.5%. This study demonstrates the concept of optimizing RSPs of individual CT voxels with multi-projection pRGs acquired by a single flat panel imager, which could be further explored and implemented in proton therapy to reduce range uncertainties.