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Large Scale Numerical Inversion of 4D Fully Coupled Convection-Diffusion Physical Model of Contrast Enhanced Ultrasound Results in Reproducible Quantitative Parameters Correlated to Microvascular Density and Sensitive to Anti-Angiogenic Treatments

D Hristov1*, L Mustonen1, J Zhou1, A El Kaffas1, (1) Stanford University, Palo Alto, CA


(Sunday, 7/12/2020) 11:30 AM - 12:30 PM [Eastern Time (GMT-4)]

Room: Track 2

Purpose: To implement and evaluate first principle, physically motivated analysis of 4D contrast enhanced ultrasound (CEUS) imaging data.

Methods: We formulate a discretized, fully coupled convection-diffusion model for the contrast propagation observed with 4D CEUS. Model unknowns include a velocity field which determines convective blood flow and a diffusivity field (symmetric tensor or a scalar) that describes (an)isotropic pseudo-diffusion arising from apparently random capillary flow. The unknown model fields are inversely reconstructed from 4D CEUS imaging data with an iterative sparse-least squares algorithm. We validated our model-based analysis on synthetic flow data and then applied it to serial 4D CEUS data from mice with LS174T tumors. From reconstructed velocity/diffusivity fields spatially averaged blood transport (flow) and diffusivity were calculated. These parameters were assessed against conventional ones such as Peak Enhancement (PE) and others. The sensitivity of the imaging parameters to treatment was evaluated with a mixed effects model in a group comprising control (n=11) and treated (n=10) mice imaged on days 0, 1, 3, 7, 10 and treated with saline/bevacizumab on days 0, 3, and 7. Reproducibility was evaluated with Concordance Correlation Coefficient (CCC) in 20 mice imaged twice within a day. Correlation of imaging parameters to microvascular density (MVD) was assessed with the Spearman Correlation Coefficient (SCC) with data from 10 mice.

Results: On synthetic data the relative error of the reconstructed fields was within 10% for 80% of the voxels. From the conventional parameters, only PE was sensitive to treatment (p=0.022) while having good reproducibility (CCC=0.768). However, PE was not correlated to MVD (SCC=0.19). In contrast, model-derived diffusivity was sensitive to treatment (p<0.0001), with excellent reproducibility (CCC=0.879) and strongly correlated to MVD (SCC=-0.86).

Conclusion: Numerical inversion of a fully coupled convection-diffusion model of 4D CEUS data results in reproducible parameters correlated to MVD and sensitive to anti-angiogenic treatments.

Funding Support, Disclosures, and Conflict of Interest: This work was partially supported by NIH R01 CA195453.


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