Author: Aditya P. Apte, Xinan Chen, Joseph O. Deasy, Ramesh Paudyal, Kyung Peck, Amita Shukla-Dave, Nathaniel Swinburne, Robert J. Young 👨🔬
Affiliation: Department of Radiology, Memorial Sloan Kettering Cancer Center, Department of Medical Physics, Memorial Sloan Kettering Cancer Center 🌍
Purpose: We apply our novel formulation of unbalanced-regularized-optimal-mass-transport (urOMT) theory to brain DCE-MRI data to quantify and visualize the behaviors of fluid flows in post-treatment follow-up scans with an aim to differentiate tumor recurrence from radiation necrosis.
Methods: We utilized a novel mathematical model in computational fluid dynamics, which we developed called the unbalanced-regularized-optimal-mass-transport (urOMT). The urOMT model characterizes the transport behaviors of fluids with an advection-diffusion differential equation and minimizes a pre-defined total energy of the entire transport process. We applied urOMT to a DCE-MRI dataset acquired using a standard imaging protocol at our center from 46 patients with brain metastases who were treated with radiotherapy. Subjects were previously classified as either tumor recurrence (N=33) or necrosis (N=13) based on surgical pathology. For each DCE-MRI study, we first converted the MRI signal into estimates of contrast agent concentration. The temporal 3D images within a region of interest were then fed into the urOMT algorithm, which was solved and analyzed to yield quantitative transport metrics, including speed, influx, efflux, and pathlines.
Results: urOMT showed the directional trends of cross-voxel flows associated with vascular and microvascular flow patterns, including quantification of the fluid transport kinetics. Compared to radiation necrosis cases, tumor recurrence cases exhibit, on average, more active fluid transport. Both the influx (p=0.037) and efflux (p=0.038) were higher in recurrence cases compared to radionecrosis cases, consistent with vasculature with stronger functioning in tumors.
Conclusion:
Our physics-motivated urOMT model accounts for cross-voxel transport measured by advection (bulk flows) and diffusion, creating a continuous map of intra-voxel fluid flows. As indicated by our preliminary results, the derived metrics are relevant to distinguishing between radionecrosis and tumor recurrence in DCE-MRIs in the future. One limitation of the current urOMT formulation is that it effectively smooths out small details of the microvascular flows.