Optimal mass transport kinetic modeling for head and neck DCE-MRI: Initial analysis

Abstract

Purpose: Current state-of-the-art models for estimating the pharmacokinetic parameters do not account for intervoxel movement of the contrast agent (CA). We introduce an optimal mass transport (OMT) formulation that naturally handles intervoxel CA movement and distinguishes between advective and diffusive flows.

Method: Ten patients with head and neck squamous cell carcinoma (HNSCC) were enrolled in the study between June 2014 and October 2015 and underwent DCE MRI imaging prior to beginning treatment. The CA tissue concentration information was taken as the input in the data-driven OMT model. The OMT approach was tested on HNSCC DCE data that provides quantitative information for forward flux ( ${\Phi }_F$ ) and backward flux ( ${\Phi }_B$ ). OMT-derived ${\Phi }_F$ was compared with the volume transfer constant for CA, $K^{\mathrm{trans}}$ , derived from the Extended Tofts Model (ETM).

Results: The OMT-derived flows showed a consistent jump in the CA diffusive behavior across the images in accordance with the known CA dynamics. The mean forward flux was 0.0082 ± 0.0091 ( $\stackrel{-1}{min}$ ) whereas the mean advective component was 0.0052 ± 0.0086 ( $\stackrel{-1}{min}$ ) in the HNSCC patients. The diffusive percentages in forward and backward flux ranged from 8.67% to 18.76% and 12.76% to 30.36%, respectively. The OMT model accounts for intervoxel CA movement and results show that the forward flux ( ${\Phi }_F$ ) is comparable with the ETM-derived $K^{\mathrm{trans}}$ .

Conclusions: This is a novel data-driven study based on optimal mass transport principles applied to patient DCE imaging to analyze CA flow in HNSCC.

Keywords: DCE pharmacokinetic modeling; advection; data-driven; diffusion; optimal mass transport.