Óscar Peña-Nogales^{1}, Rodrigo de Luis-Garcia^{1}, and Santiago Aja-Fernández^{1}

^{1}Laboratorio de Procesado de Imagen, Universidad de Valladolid, Valladolid, Spain

Estimation of Intravoxel Incoherent Motion (IVIM) parameter maps from a set of diffusion-weighted (DW) images acquired at multiple b-values usually suffers from low SNR, which may increase the variance of the estimated maps. Unfortunately, there is no consensus on the optimal b-values to maximize the noise performance of IVIM parameters. In this work, we determine the optimal b-values to maximize the performance of IVIM parameter mapping by using a Cramér-Rao Lower Bound approach under realistic noise assumptions. The reduction of the estimation variance on the IVIM parameters compared to state-of-the-art b-values suggests the utility of this approach to optimize DW-MRI.

Furthermore, optimal b-value sets obtained with the proposed approach were computed from parameters shown in Table 1 to study their distribution and properties.

Eq. 1: $$\begin{bmatrix}\sum\limits_{k=1}^{K}[fe^{-b_k\cdot\text{D}^*}+(1-f)e^{-b_k\cdot\text{D}}]^2\mathcal{I}_n(S(b_k),\sigma)&-\sum\limits_{k=1}^{K}S(b_k)(1-f)b_ke^{-b_k\cdot\text{D}}\mathcal{I}_n(S(b_k),\sigma)&\sum\limits_{k=1}^{K}S(b_k)[e^{-b_k\cdot\text{D}^*}-e^{-b_k\cdot\text{D}}]\mathcal{I}_n(S(b_k),\sigma)&-\sum\limits_{k=1}^{K}S(b_k)fb_ke^{-b_k\cdot\text{D}^*}\mathcal{I}_n(S(b_k),\sigma)\\-\sum\limits_{k=1}^{K}S(b_k)(1-f)b_ke^{-b_k\cdot\text{D}}\mathcal{I}_n(S(b_k),\sigma)&\sum\limits_{k=1}^{K}S^2_0(1-f)^2b^2_ke^{-2\cdot{b}_k\cdot\text{D}}\mathcal{I}_n(S(b_k),\sigma)&-\sum\limits_{k=1}^{K}S^2_0(1-f)b_k[e^{-b_k\cdot\text{D}^*}-e^{-b_k\cdot\text{D}}]e^{-b_k\cdot\text{D}}\mathcal{I}_n(S(b_k),\sigma)&\sum\limits_{k=1}^{K}S^2_0(f-f^2)b^2_ke^{-b_k\cdot(\text{D}+\text{D}^*)}\mathcal{I}_n(S(b_k),\sigma)\\\sum\limits_{k=1}^{K}S(b_k)[e^{-b_k\cdot\text{D}^*}-e^{-b_k\cdot\text{D}}]\mathcal{I}_n(S(b_k),\sigma)&-\sum\limits_{k=1}^{K}S^2_0(1-f)b_k[e^{-b_k\cdot\text{D}^*}-e^{-b_k\cdot\text{D}}]e^{-b_k\cdot\text{D}}\mathcal{I}_n(S(b_k),\sigma)&\sum\limits_{k=1}^{K}S^2_0[e^{-b_k\cdot\text{D}^*}-e^{-b_k\cdot\text{D}}]^2\mathcal{I}_n(S(b_k),\sigma)&-\sum\limits_{k=1}^{K}S^2_0fb_k[e^{-b_k\cdot\text{D}^*}-e^{-b_k\cdot\text{D}}]e^{-b_k\cdot\text{D}^*}\mathcal{I}_n(S(b_k),\sigma)\\-\sum\limits_{k=1}^{K}S(b_k)fb_ke^{-b_k\cdot\text{D}^*}\mathcal{I}_n(S(b_k),\sigma)&\sum\limits_{k=1}^{K}S^2_0(f-f^2)b^2_ke^{-b_k\cdot(\text{D}+\text{D}^*)}\mathcal{I}_n(S(b_k),\sigma)&-\sum\limits_{k=1}^{K}S^2_0fb_k[e^{-b_k\cdot\text{D}^*}-e^{-b_k\cdot\text{D}}]e^{-b_k\cdot\text{D}^*}\mathcal{I}_n(S(b_k),\sigma)&\sum\limits_{k=1}^{K}S^2_0f^2b^2_ke^{-2\cdot{b}_k\cdot\text{D}^*}\mathcal{I}_n(S(b_k),\sigma)\\\end{bmatrix}$$

Additionally, given a b-value set, corresponding DWI of an acquisition were selected for IVIM parameter estimation with a maximum likelihood estimator. However, if a b-value was repeated, the equivalent number of DWI of the consecutive repetitions were selected. This method was repeated 16 consecutive times, one per acquisition, obtaining a set of 16 repeated IVIM parameter maps. Then, we obtained the voxel-wise standard deviation statistics across all the estimated maps (σ

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**Table 2:** Description of the in-vivo IVIM liver DW-MRI acquisition, liver mean IVIM parameters and mean SNR value (mean ± std), and various sets of b-values used to compare the estimation variance (i.e., noise performance) of the IVIM parameter maps.

+Note that the acquisition was repeated 16 consecutive times to enable voxel-wise determination of IVIM parameters and SNR statistics.

++The optimal set of b-values is obtained with the proposed Four b-value Search algorithm under the Rician noise assumption by minimizing the CRLB_{𝛤} of the liver mean IVIM parameters and mean SNR value.