  $\textbf{Purpose:}$ To assess the viability of a physics-based, deterministic
and adjoint-capable algorithm for performing treatment planning system
independent dose calculations and for computing dosimetric differences caused
by anatomical changes.
  $\textbf{Methods:}$ A semi-numerical approach is employed to solve two
partial differential equations for the proton phase-space density which
determines the deposited dose. Lateral hetereogeneities are accounted for by an
optimized (Gaussian) beam splitting scheme. Adjoint theory is applied to
approximate the change in the deposited dose caused by a new underlying patient
anatomy.
  $\textbf{Results:}$ The quality of the dose engine was benchmarked through
three-dimensional gamma index comparisons against Monte Carlo simulations done
in TOPAS. The worst passing rate for the gamma index with (1 mm, 1 %, 10 % dose
cut-off) criteria is 95.62 %. The effect of delivering treatment plans on
repeat CTs was also tested. For a non-robustly optimized plan the adjoint
component was accurate to 6.2 % while for a robustly optimized plan it was
accurate to 1 %.
  $\textbf{Conclusions:}$ YODA is capable of accurate dose computations in both
single and multi spot irradiations when compared to TOPAS. Moreover, it is able
to compute dosimetric differences due to anatomical changes with small to
moderate errors thereby facilitating its use for patient-specific quality
assurance in online adaptive proton therapy.
