Abdol Aziz Ould Ismail^{1}, Drew Parker^{1}, Simon Alexander^{2}, Emmanuel Caruyer^{3}, Ofer Pasternak^{4}, and Ragini Verma^{1}

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/mm

** FERNET:**
is
a robust FWE method for clinically feasible diffusion acquisitions. This fits a
two-compartment model per voxel

$$A_{i}(D,f)=fexp(-bq_i^T Dq_{i})+(1-f)exp(-bd)[1]$$

where the first term is the signal attenuation of the tissue
compartment, modeled by a diffusion tensor, *D*; the second is the FW component; *A _{i} *is
the signal attenuation of the

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 FW^{1} :

$$f (initial)= 1-\frac{log(\frac{S_{0}}{S_{t}})}{log(\frac{S_{w}}{S_{t}})} [2]$$

where* S _{0},
S_{t}, S_{w}* correspond to the

II- $$$\hat{A}_{t}$$$
is constrained by maximum (λ_{max}) and minimum (λ_{min}),
the range of biologically plausible diffusivities in the tissue compartment^{1}:

$$e^{-b\lambda_{max}}<\hat{A}_{t}<e^{-b\lambda_{min}}[3]$$

For (I), we estimate pure tissue signal as
95^{th} percentile of *b _{0}* signal in a white matter (WM) mask (voxels
with FA>0.70) and pure FW signal as the 95

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.

Figure 1: Comparison between existing and proposed
FWE techniques: (row 1) in-house implementation of^{1}, a fixed MD value for
initializing the corrected tensors (2^{nd} row), and FERNET (3^{rd}
row). FA values in cingulum, internal
capsule, and edema were compared between pre- and post-free water correction, and FA difference maps were calculated (4^{th }column). Results demonstrate that, unlike
the other methods, FERNET did not over correct in WM regions where free water
is limited. This is also reflected in the FA difference maps, where FERNET
FA map only corrects in the edema mask.

Figure 2: A ground truth phantom was simulated to
assess the quality of the free water estimation. The phantom was simulated^{3} with SNR=40 and 30 gradient directions, matching the investigated human data.
The FA of simulated WM was 0.40. Edema simulation in WM and GM was carried out using
free water volume fraction that increased from 0.20 to 0.80. 4900 FWE
experiments (70x70 for λ_{max}, λ_{min}) were performed to
investigate the sensitivity of these parameters in different tissue types and
for both healthy and contaminated tissues. Maintaining the integrity of the healthy tissue, parameters suggested from the phantoms are λ_{min}=0.6
and λ_{max}=2.5.

In order to investigate the physiological
plausibility of FERNET fits, FWE was performed for λ_{min} from 0.1 to 1.0
on the human dataset. We computed the percentage of voxels located outside the
known range of diffusivities^{5} in WM, GM and edema. Voxels with MD<0.4
(artifactual voxels) were obtained at the lower end of the range of λ_{min}
(1^{st} column). These percentages rapidly decreased near the value
suggested by the phantom (0.6). On increasing λ_{min}, we observed an
increase in the MD values above 1.2 across tissue types (2^{nd}
column), not reflective of healthy tissue. These findings are consistent with
observations from the phantom.