  Purpose: The FLASH effect, which reduces the radiosensitivity of healthy
tissue while maintaining tumor control at high dose rates, has shown potential
for improving radiation therapy. Conformal FLASH proton therapy involves
advanced beam-shaping technologies and specialized nozzle designs to confine
the dose to the target volume. Optimizing the spot delivery pattern and range
modulators can enhance the local dose rate, and genetic algorithms have been
used to optimize scan patterns for stereotactic FLASH proton therapy of
early-stage lung cancer and lung metastases. A fast and effective method based
on graph theory is proposed to optimize the dose rate in specific regions of
interest.
  Methods: We have created a graph-based algorithm to optimize the trajectory
of proton spots to maximize the 100th percentile dose rate. Since this problem
is NP-hard, we have employed an approximation algorithm that can solve this
kind of Traveling Salesman Problem efficiently.
  Results: When compared to a conventional serpentine pattern, the optimized
scanning trajectory led to a doubling of the median dose rate, but only a minor
increase in DR95. Our approach is more efficient and requires fewer evaluations
of the objective function and hyper-parameters compared to existing genetic
algorithms. Conclusions: The optimized scanning trajectory led to a doubling of
the median dose rate, but only a minor increase in DR95. The extent to which
the dose rate can be increased depends on the size and shape of the region of
interest. Future research could explore integrating FLASH objectives into
treatment planning and incorporating the proposed method into plan
optimization.
