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 (ΦF) and backward flux (ΦB). OMT‐derived ΦF was compared with the volume transfer constant for CA, normalKtrans, 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 (min-1) whereas the mean advective component was 0.0052 ± 0.0086 (min-1) 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 (ΦF) is comparable with the ETM‐derived normalKtrans. 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.

Current status in spatiotemporal analysis of contrast‐based perfusion MRI

“…For vascular input, the model applies an AIF‐based approach. It, therefore, extends the approach proposed by Pellerin et al 27 with interstitial convection, or generalizes the model in Elkin et al 47 with a global AIF.…”

“…Elkin et al 47 reduce the scale of the inverse problem by asserting the contrast agent mass density can be written as a function of velocity. For optimization, an operator splitting method followed by a Gauss–Newton minimization is applied 58 .…”

“…In 2019, Elkin et al 47 introduced a one‐compartment model with interstitial convection and diffusion (Figure 2B ). The model applies interstitial diffusion and convection parameters to distribute contrast agent through the interstitium between adjoining voxels.…”

Magnetic Resonance Imaging and Modeling of the Glymphatic System

“…In the most recent paper of vascular investigation by Elkin et al, fluid motion was described by applying an OMT regularized model to the human MRI data of ten patients with head and neck squamous cell carcinoma. The advantages of this model are that it provides quantitative information for the fluid flow with and without considering diffusion into account and it provides a clear signal between the neighboring voxels instead of ignoring intervoxel contrast agent movements [130]. This model can be further used to track the glymphatic pathways, thus showing both bulk flow and diffusion values, which are both critical for the complete understanding of the glymphatic system.…”

Identifiability of spatiotemporal tissue perfusion models

“…In theory, this bias can be removed by the use of spatiotemporal PK models (Sourbron 2014). Implementations of this approach have mainly focused on one-compartment models with transport by diffusion (Koh 2013), convection (Zhou et al 2021, Zhang et al 2023, or both (Sourbron 2015, Elkin et al 2019, Zhang et al 2022. Hybrid approaches have also been proposed, coupling a one-compartment spatiotemporal model for interstitial transport with vascular delivery modeled by a single, global AIF (Pellerin et al 2007, Fluckiger et al 2013, Sinno et al 2021, Sainz-DeMena et al 2022, Sinno et al 2022.…”