  PULSAR (personalized ultrafractionated stereotactic adaptive radiotherapy) is
a form of radiotherapy method where a patient is given a large dose or pulse of
radiation a couple of weeks apart rather than daily small doses. The tumor
response is then monitored to determine when the subsequent pulse should be
given. Pre-clinical trials have shown better tumor response in mice that
received immunotherapy along with pulses spaced 10 days apart. However, this
was not the case when the pulses were 1 day apart. Therefore, a synergistic
effect between immunotherapy and PULSAR is observed when the pulses are spaced
out by a certain number of days. In our study, we aimed to develop a
mathematical model that can capture the synergistic effect by considering a
time-dependent weight function that takes into account the spacing between
pulses. By determining feasible parameters, and applying reasonable conditions,
we utilize our model to simulate murine trials with varying sequencing of
pulses. We successfully demonstrate that our model is simple to implement and
can generate tumor volume data that is consistent with the pre-clinical trial
data. Our model has the potential to aid in the development of clinical trials
of PULSAR therapy.
