Despite the growing research in free water elimination (FWE) methods with advanced diffusion acquisition protocols, the need for robust single-shell based FWE remains, as this is the standard acquisition protocol in the clinic. This is especially important in the characterization of peritumoral regions with infiltration. However, single-shell FWE is an ill-posed problem, dependent on parameter initialization, solutions to which often fail to obtain a balanced correction between healthy and abnormal tissue. We introduce FERNET, a robust FWE protocol for single-shell data with a comprehensive investigation of initialization parameters based on a software simulated phantom where the ground truth is known.
Data acquisition and preprocessing: T1 and dMRI data of 10 tumor (glioblastoma multiforme and metastasis) patients were selected (dMRI at TR/TE=5000/86ms, b=1000s/mm2, 30 gradient directions). T1 data was segmented using FSL-FAST to investigate tissue classes2.
FERNET: is a robust FWE method for clinically feasible diffusion acquisitions. This fits a two-compartment model per voxel1:
$$A_{i}(D,f)=fexp(-bq_i^T Dq_{i})+(1-f)exp(-bd)[1]$$
where the first term is the signal attenuation of the tissue compartment, modeled by a diffusion tensor, D; the second is the FW component; Ai is the signal attenuation of the ith diffusion weighted image; f is the contribution of the tissue compartment; qi is the ith gradient direction; b is the diffusion weighting; and d is the diffusivity (fixed at 3.0x10-3mm2/s) in the FW compartment. The bi-tensor model in [1] is an inverse problem with infinitely many solutions1, that we solve using a gradient-descent optimization after calculating an initial estimate of the solution. The initial estimate of attenuation in the tissue compartment $$$\hat{A}_{t}$$$ is crucial, but challenging for two reasons:
I- $$$\hat{A}_{t}$$$ is initialized based on estimating the contribution f to the diffusion signal per voxel, driven by an estimate of the representative unweighted signal in tissue and FW1 :
$$f (initial)= 1-\frac{log(\frac{S_{0}}{S_{t}})}{log(\frac{S_{w}}{S_{t}})} [2]$$
where S0, St, Sw correspond to the b0 signal, a representative b0 signal from the tissue compartment without free water, and a representative signal from pure FW compartment, respectively. Therefore, careful region-of-interest definition to obtain representative signals for each compartment is key for accurate FW estimation, leading to optimized estimation of tissue tensor D.
II- $$$\hat{A}_{t}$$$ is constrained by maximum (λmax) and minimum (λmin), the range of biologically plausible diffusivities in the tissue compartment1:
$$e^{-b\lambda_{max}}<\hat{A}_{t}<e^{-b\lambda_{min}}[3]$$
For (I), we estimate pure tissue signal as 95th percentile of b0 signal in a white matter (WM) mask (voxels with FA>0.70) and pure FW signal as the 95th percentile of voxels with high mean diffusivity (MD>2.8x10-3mm2/s). Initial restricted estimate of f by [3] prevents over-correction in healthy WM voxels. We verified that FERNET corrects only in edema regions with FW and not in tissue where FW is very low (contralateral cingulum and internal-capsule (IC)), by comparing FA values in these regions pre- and post-FERNET. These comparisons were repeated with previous single-shell FWE1 and its extension based on initializing with MD=0.8x10-3mm2/s. For (II), λmax and λmin were investigated using Phantomas, a software for simulating diffusion phantoms3. These parameter choices were based on mean square error (MSE) between FERNET output and ground truth values obtained by fitting a tensor to the same phantom, but without simulated edema (Fig.2). Due to the absence of ground truth in human data, we investigated voxels with MD outside a physiologically plausible range (0.4-1.2x10-3mm2/s) in WM, GM, and edema4.
Conclusion
We have proposed a FWE paradigm, FERNET, which addresses the known parameter dependence issues of single shell FWE methods, provides a robust selection of initialization parameters, and produces physiologically plausible solutions for the multi-compartment fit. As it separates the edema from the underlying tissue, this is a clinically viable paradigm for FWE that can be applied to clinical studies that have single-shell data and no means for advanced acquisition.1- Pasternak, O., et al., Free water elimination and mapping from diffusion MRI. Magnetic resonance in medicine: official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2009. 62: p. 717-30.
2- Zhang, Y., M. Brady, and S. Smith, Segmentation of brain MR images through a hidden Markov random field model and the expectation maximization algorithm. IEEE Transactions on Medical Imaging, 2001. 20(1): p. 45-57.
3- Caruyer, E., et al. Phantomas: a flexible software library to simulate diffusion MR phantoms. in ISMRM. 2014.
4- Helenius, J., et al., Diffusion-Weighted MR Imaging in Normal Human Brains in Various Age Groups. AJNR Am J Neuroradiol, 2002. 23(2): p. 194-199.