  Purpose:The recently proposed IPO-IMPT framework allows simultaneous
optimization of dose, dose rate, and LET for FLASH treatment planning. Finding
solutions to IPO-IMPT is difficult due to computational intensiveness.
Nevertheless, an inverse solution that simultaneously specifies the geometry of
a sparse filter and weights of a proton intensity map is desirable for both
clinical and preclinical applications. Such solutions can reduce effective
biological dose to organs at risk in cancer patients as well as reduce the
number of animal irradiations needed to derive extra biological dose models in
preclinical studies.
  Methods:Unlike our initial forward heuristic, this inverse IPO-IMPT solution
includes simultaneous optimization of sparse range compensation, sparse range
modulation, and spot intensity. The daunting computational tasks vital to this
endeavor were resolved iteratively with a distributed computing framework to
enable Simultaneous Intensity and Energy Modulation and Compensation (SIEMAC).
SIEMAC was demonstrated on a human lung cancer patient and a minipig.
  Results:SIEMAC improves maps of spot intensities and patient-field-specific
sparse range compensators and range modulators. For the lung cancer patient, at
our max nozzle current of 300 nA, dose rate coverage above 100 Gy/s increased
from 57% to 96% in the lung and from 93% to 100% in the heart, and LET coverage
above 4 keV/um dropped from 68% to 9% in the lung and from 26% to <1% in the
heart. For a simple minipig plan, the FWHM of the dose, dose rate, and LET
distributions decreased by 30%, 1.6%, and 57%, respectively, again with similar
target dose coverage, thus reducing uncertainty in these quantities for
preclinical studies.
  Conclusion:The inverse solution to IPO-IMPT demonstrated the capability to
simultaneously modulate sub-spot proton energy and intensity distributions for
clinical and preclinical studies.
