SU‐DD‐A2‐03: Anisotropic Edema Modelling for Permanent Prostate Implants

Abstract

Purpose: To develop an edema model for application in permanent prostate implant dosimetry that reflects edema spatial anisotropy and time‐resolution behaviors observed in clinical MRI data. Method and Materials: The basic manifestation of edema was represented as a trio of variations in Cartesian components of the distance, ri(t); i=1:3, from a radioactive seed to a dose calculation point; specifically . Here (r0)i are distance components in the absence of edema, fi(t) edema time‐resolution functions, and αi quantifiers of the directional contributions to edema volume subject to the constraint . Serial MRI data from our institution for n=40 prostate implant patients is well characterized by the parameters , and the function ; t<T; i=1:3. Hence these parameters and time‐resolution function were incorporated in the model. Next, the cumulative dose from a seed to a calculation point was expressed according to the TG‐43 formalism (using the anisotropy constant) as , where λ is the radionuclide decay constant and the other variables are defined as per TG‐43. The integrand was then expanded in even powers of |r⃗(t)|, and the resulting integral in each term of the expansion evaluated to yield either a closed‐form analytic function or a convergent series. Numerical evaluation of constituent terms in the dose expansion was done in MatLab to assess functional behavior. Results: The number of terms in the expansion of D(r⃗) are few, and all are well‐behaved numerically. For those terms involving convergent series, convergence is rapid and so only a small number of terms need to be evaluated. Based on these favorable properties, MatLab‐based dose calculation software is currently being developed to investigate applications to clinical dosimetry. Conclusion: A new edema model for permanent prostate implant dosimetry incorporating spatial anisotropy has been formulated. Clinical application is pending.