One method embodiment of the present invention is a process for using deterministic methods to calculate dose distributions resulting from radiotherapy treatments, diagnostic imaging, or industrial sterilization, and for calculating scatter corrections used for image reconstruction. In one embodiment of the present invention, the method provides a means for constructing a deterministic computational grid from an acquired 3-D image representation, transport of an external radiation source through field shaping devices and into the computational grid, calculation of the radiation scatter and/or delivered dose in the computational grid, and subsequent transport of the scattered radiation to detectors external to the computational grid. In another embodiment of the present invention, the method includes a process, by solving the adjoint form of the transport equation, which can enable patient dose responses to be calculated independently of treatment parameters and prior to treatment planning, enabling patient dose fields to be accurately reconstructed during treatment planning and verification.