Quantitative Analysis of Intravoxel Incoherent Motion (IVIM) Diffusion MRI using Total Variation and Huber Penalty Function

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Quantitative analysis in intravoxel incoherent motion (IVIM) imaging commonly uses voxel-wise estimation of the bi-exponential model, which might not be reliable for clinical interpretation. Improving model fitting performance and qualitative and quantitative parametric estimation, two novel methodologies are proposed here.


Five IVIM analyses methodologies: (a) Bi-exponential (BE) model, (b) Segmented BE method with two-parameter fitting (BEseg-2), (c) Segmented BE method with one-parameter fitting (BEseg-1), (d) BE with adaptive Total Variation penalty function (BE+TV) and (e) BE with adaptive Huber penalty function (BE+HPF) were evaluated. Relative root-mean-square error (RRMSE), relative bias (RB) and relative parameters Symbol were calculated to estimate the accuracy of methods in simulations. Empirical datasets from 14 patients with bone tumor were analyzed using these methodologies. Coefficient of variation (CV) were estimated for each IVIM parameter in tumor volume to measure the precision of the estimation methods in vivo.


Both BE+TV and BE+HPF showed consistently lower RRMSE (˜10–42%) and lower RB (−4 to 8%) at all noise levels, compared to BE, BEseg-2 and BEseg-1 (RRMSE: ˜15–120% and RB: −20 to 62%). Estimated Symbol for both BE+TV and BE+HPF methods were ˜1 (0.96–1.08), whereas BE, BEseg-2 and BEseg-1 showed sub-optimal parameter estimation (0.80–1.62). For clinical data BE+TV and BE+HPF showed 30–50% improved CV in estimating D, D*, and f than BE and improved CV in estimating D* (7–23%) and f (26–30%) than BEseg-2 and BEseg-1.


Bi-exponential model with penalty function showed quantitatively and qualitatively improved IVIM parameter estimation for both simulated and clinical dataset of bone tumors, thus potentially making this approach suitable for clinical applications in future.

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