Fiber ball white matter modeling in focal epilepsy

Abstract Multicompartment diffusion magnetic resonance imaging (MRI) approaches are increasingly being applied to estimate intra‐axonal and extra‐axonal diffusion characteristics in the human brain. Fiber ball imaging (FBI) and its extension fiber ball white matter modeling (FBWM) are such recently described multicompartment approaches. However, these particular approaches have yet to be applied in clinical cohorts. The modeling of several diffusion parameters with interpretable biological meaning may offer the development of new, noninvasive biomarkers of pharmacoresistance in epilepsy. In the present study, we used FBI and FBWM to evaluate intra‐axonal and extra‐axonal diffusion properties of white matter tracts in patients with longstanding focal epilepsy. FBI/FBWM diffusion parameters were calculated along the length of 50 white matter tract bundles and statistically compared between patients with refractory epilepsy, nonrefractory epilepsy and controls. We report that patients with chronic epilepsy had a widespread distribution of extra‐axonal diffusivity relative to controls, particularly in circumscribed regions along white matter tracts projecting to cerebral cortex from thalamic, striatal, brainstem, and peduncular regions. Patients with refractory epilepsy had significantly greater markers of extra‐axonal diffusivity compared to those with nonrefractory epilepsy. The extra‐axonal diffusivity alterations in patients with epilepsy observed in the present study could be markers of neuroinflammatory processes or a reflection of reduced axonal density, both of which have been histologically demonstrated in focal epilepsy. FBI is a clinically feasible MRI approach that provides the basis for more interpretive conclusions about the microstructural environment of the brain and may represent a unique biomarker of pharmacoresistance in epilepsy.


| INTRODUCTION
Despite being classically considered to be a gray matter disorder, increasing evidence demonstrates cerebral white matter pathology in focal epilepsy. Epilepsy is a systems network brain disorder and is characterized by various neuropathological processes in the cerebral white matter, both in lesional and nonlesional cases (Concha, Livy, Beaulieu, Wheatley, & Gross, 2010;Deleo et al., 2018;Reeves et al., 2016). Identifying and characterizing these changes using noninvasive imaging techniques are important as this will provide deeper insights into the mechanisms of pathology in individual patients and potentially inform clinical and surgical decision-making. For example, reconstruction of white matter structural networks and connectivity using diffusion MRI (dMRI) has been demonstrated to be an effective imaging biomarker of postoperative outcome in focal epilepsy (Bonilha et al., 2013;Keller et al., 2015;Keller et al., 2017). Diffusion tensor imaging (DTI) and extensions of which, such as diffusion kurtosis imaging (DKI), have been widely used to study white matter alterations in patients with focal epilepsy. Typical findings show a pattern of reduced fractional anisotropy (FA) and increased mean diffusivity (MD) in patients with focal epilepsy (Concha, Beaulieu, & Gross, 2005;Gross, Concha, & Beaulieu, 2006;McDonald et al., 2008), and a more widespread pattern of altered kurtosis metrics, suggesting an increased sensitivity of DKI in detecting WM abnormalities in epilepsy (Bonilha, Lee, et al., 2015;Glenn et al., 2016;Lee et al., 2014). However, while both DTI and DKI are reasonably sensitive to changes in white matter microstructure, these parameters only describe the tissue environment in terms of diffusion physics, rather than in biological parameters. They therefore lack microstructural specificity, making biological interpretation difficult (Fieremans, Jensen, & Helpern, 2011). To overcome this limitation, several diffusion methods have been proposed that more directly relate parameters with clear biological meanings to the diffusion MRI signal (Jelescu & Budde, 2017;Novikov, Kiselev, & Jespersen, 2018).
These must necessarily introduce assumptions and approximations that explicitly connect water diffusion to microstructure. The simplest of such methods are based on the assumption that there are two nonexchanging water compartments within brain white matter: a fast (which models the less hindered extra-axonal water) and a slow (which models the more restricted intra-axonal water) diffusion compartment (Assaf, Freidlin, Rohde, & Basser, 2004;Fieremans et al., 2011;Kleban, Tax, Rudrapatna, Jones, & Bowtell, 2020).
The recently developed fiber ball imaging (FBI) is one such twocompartment dMRI method (Jensen, Russell Glenn, & Helpern, 2016;Moss, McKinnon, Glenn, Helpern, & Jensen, 2019). FBI offers the ability to estimate the fiber orientation distribution function (fODF) of white matter fiber bundles along with related axon-specific microstructural parameters. This is achieved by using strong diffusion weightings (bvalue > > 2000 s/mm 2 ) to suppress the signal from the more mobile extra-axonal water pool. Thus, by employing high b-values FBI only needs to model the intra-axonal compartment, a major advantage of FBI over other two-compartment models. The main assumption of FBI is that water diffusion inside axons is accurately described by regarding axons as thin, straight, impermeable tubes. Compelling experimental evidence indicates that this is indeed a good approximation at least for myelinated axons (McKinnon, Jensen, Glenn, & Helpern, 2017;Moss et al., 2019;Veraart, Fieremans, & Novikov, 2019). Besides the fODF, FBI also allows estimation of the fractional anisotropy of the intra-axonal space (FAA) and ζ (a property related to the axonal water fraction; AWF). Fiber ball white matter modeling (FBWM; McKinnon, Helpern, & Jensen, 2018) builds upon the principles of FBI but uses both high and low diffusion weightings to model the extra-axonal space and the intra-axonal space.
FBWM therefore allows the estimation of additional microstructural parameters including the intrinsic intra-axonal diffusivity (D a ), the mean extra-axonal diffusivity (MD e ), the radial (D e , ⊥ ) and axial (D e,k ) extraaxonal diffusivity, the fractional anisotropy of the extra-axonal space (FAE), and the AWF (Table 1). FBWM requires more data and more assumptions than FBI so that there is a natural division between the two.
Specifically, FBWM is built by combining FBI and DKI data. Distinguishing FBI, DKI, and FBWM parameters emphasizes that they each have different biophysical underpinnings. FBI and FBWM have not previously been applied in patient cohorts.
Diffusion tractography provides the ability to reconstruct and assess diffusion characteristics averaged over whole white matter fiber bundles and along the longitudinal axis of tracts (along-tract). Alongtract analysis permits investigation of regionally specific alterations that may be more sensitive to regional pathology than averaging diffusion characteristics over entire tracts, particularly as tissue characteristics vary considerably along white matter tracts ( Figure 1). This is particularly important for the in vivo assessment of neuropathology in neurological disorders as some pathological alterations occur in circumscribed regions of tracts, which may be overlooked when averaging diffusion metrics over entire tracts . Alongtract approaches have demonstrated increased sensitivity for the identification of diffusion abnormalities in patients with temporal lobe epilepsy (Concha, Kim, Bernasconi, Bernhardt, & Bernasconi, 2012;Kreilkamp et al., 2019;Kreilkamp, Weber, Richardson, & Keller, 2017), high levels of sensitivity and specificity for the prediction of postoperative outcome , and greater yield of diffusion changes using DKI over conventional DTI . The use of FBI and FBWM combined with along-tract tractography offers the ability to investigate regional white matter tissue alterations with diffusion parameters that are biologically specific, which has not previously been possible using standard DTI approaches.
The modeling of several diffusion parameters with interpretable biological meaning may offer the development of new, noninvasive biomarkers of pharmacoresistance in epilepsy. It is unclear why 30% of patients with focal epilepsy do not attain seizure control despite anti-epileptic drug (AED) treatment (Kwan & Brodie, 2000). The identification of a noninvasive imaging biomarker of treatment outcome would allow earlier stratification to more personalized treatment methods. However, there have been limited insights into the mechanisms and markers underlying pharmacoresistance using advanced MRI methods. Markers of hippocampal neuronal-glial changes have been associated with pharmacoresistance in patients with temporal lobe epilepsy using MR spectroscopy (Campos et al., 2010;Pimentel-Silva et al., 2020). Other studies have reported increased white matter and gray matter volumetric changes in patients with refractory relative to nonrefractory focal epilepsy using morphometric techniques applied to T1-weighted images Kim, Kim, Lee, & Park, 2017), which may relate to differences in functional connectivity between refractory and nonrefractory patients (Pressl et al., 2019). However, characterization of diffusion properties between patient groups using advanced methods that offer biological interpretation has not, to our knowledge, been performed. DTI and other traditional diffusion imaging methods provide indirect information about the underlying cellular microstructure. Diffusion metrics such as FA and MD represent the diffusion dynamics of all underlying compartments mixed together. Biophysical models, such as FBWM, attempt to separate the diffusion dynamics into different compartments (i.e., intra-axonal and extra-axonal) to get a more specific understanding of changes happening in the underlying microstructure.
This strategy is particularly useful when studying disease processes that affect microstructural compartments differently and could provide novel insights into pharmacoresistance in epilepsy.
In the present study, we have investigated intra-axonal and extraaxonal white matter diffusion alterations in patients with focal epilepsy by combining FBI and FBWM with an along-tract tractography approach. By specifically recruiting patients with either refractory or nonrefractory focal epilepsy, we sought to determine whether changes in the microscopic white matter environment may be a marker of pharmacoresistance. We expected to find differences between patient groups in FBI and FBWM metrics, which have a more easily understandable biological basis compared to standard DTI.

| Participants
Fifteen adults with focal epilepsy who had responded well to AED treatment (mean age = 41 years, SD = 12, eight female; hereon referred to as nonrefractory epilepsy), 15 adults with focal epilepsy who had refractory epilepsy (mean age = 38 years, SD = 12, eight T A B L E 1 Diffusion parameters determined by FBI and FBWM, their biophysical meanings and potential biological interpretations    (Greve & Fischl, 2009;Jenkinson, Bannister, Brady, & Smith, 2002;Jenkinson & Smith, 2001) and the MNI FA template available in FSL. and

| Statistical analysis
TractSeg permitted statistical analysis of FBI and FBWM parameter values along 100 points of each white matter tract and compared across three groups: controls, patients with refractory focal epilepsy and patients with nonrefractory focal epilepsy. Statistical analysis along-tracts was performed as per the tractometry documentation available online, 1 which is based on the statistical analysis approach described by Yeatman, Dougherty, Myall, Wandell, and Feldman (2012). This method uses a permutation based multiple comparison correction to appropriately adjust p-values given the correlation structure of the data (Nichols & Holmes, 2002). We adopted this approach and corrected for age, sex, and multiple comparisons using family wise error correction. Results were considered significant if the minimal p-value for each along-tract point was lower than the alpha value corrected for multiple comparison (Yeatman et al., 2012

All significant differences in FBI and FBWM parameters between
patients with refractory epilepsy, nonrefractory epilepsy and controls F I G U R E 2 (a) White matter tracts automatically segmented using TractSeg included in the present study. See Table 3

| DISCUSSION
This study is the first to apply FBI and FBWM to a clinical population.
We have used this advanced dMRI method together with along-tract tractography to investigate white matter microstructural changes in patients with longstanding focal epilepsy. By using FBI and FBWM, we are able make inferences about the biological processes underlying tissue diffusion changes, which has previously been difficult to do using conventional DTI. As expected, we found differences between patient groups and controls, and in accordance with previous literature we found increases in diffusivity parameters in patient groups. Note: The mean (SD) of the individual diffusion parameter, minimum p-value and its corresponding α value, t statistic, and Cohen's d for the peak of each significant tract are provided. Diffusivities are expressed in units of μm 2 /ms, while ζ values are in units of ms 1/2 / μm; all other quantities are dimensionless. Abbreviations for parameters are provided in Table 1 and for tracts in Table 3.
F I G U R E 3 Statistically significant (red peaks) along-tract differences in FBWM diffusion properties in refractory patients compared to controls. 3D plots show Cohen's d values projected onto the relevant tracts with significant region highlighted by red boxes. Effect sizes greater than and equal to 1 are shown in dark red, with those less than and equal to −1 shown in dark blue. Significantly different ζ in regions of the right SLF III and right UF not illustrated (see Table 4 was substantially more revealing than conventional DTI metrics. We discuss the biological and clinical significance of these findings before highlighting pertinent methodological issues.

| Biological and clinical implications
The FBI/FBWM two compartment model permits separation of intraaxonal and extra-axonal water diffusion. MD e is a measure of extraaxonal diffusivity, which is similar to MD but only for the extra-axonal diffusion compartment. Similarly, D e,⊥ is analogous to RD using conventional DTI, but for the extra-axonal compartment. An increase in extra-axonal space has been argued to reflect an increase in neuroinflammation via microglial activation (Pasternak et al., 2012;Schwartz, Butovsky, Bruck, & Hanisch, 2006). Neuroinflammation is known to have an important role in epilepsy (Amhaoul, Staelens, & Dedeurwaerdere, 2014). Neuroinflammation has been studied exten-  (Amhaoul et al., 2015). In people with well circumscribed and phenotyped focal epilepsy, neuroinflammatory changes have been demonstrated in regions beyond the presumed seizure focus. For example, increased TSPO uptake has been demonstrated in temporal and extra-temporal lobe regions, ipsilateral and contralateral to the presumed seizure focus, in patients with TLE (Gershen et al., 2015;Hirvonen et al., 2012). Increased neuroinflammatory changes have been reported in a case study of post-ictal human focal epilepsy using PET (Butler et al., 2016). Interestingly, previous work has demonstrated increased uptake of (R)-[11C]PK11195 in rats with persistent seizures despite phenobarbital treatment compared to rats that responded well to treatment (Bogdanovic et al., 2014). Taken  zures for an average of over 3 years (Table 2) also showed evidence of more restricted pattern of extra-axonal diffusion compared to controls ( Figure 4).
An alternative explanation is that increased extra-axonal space is directly due to axonal degeneration (Rodriguez-Cruces & Concha, 2015). Reduced myelin content and axonal density of myelinated and nonmyelinated axons has been reported in refractory focal epilepsy (Garbelli et al., 2012), and reduced cumulative axonal membrane circumference is associated with reduced FA in WM tracts in close proximity to the epileptogenic zone (Concha et al., 2010).
Reduced axonal density inherently generates increased extra-axonal space (Rodriguez-Cruces & Concha, 2015), and this process could be driving increased extra-axonal diffusion in patients with epilepsy.
Most studies examining axonal density in refractory focal epilepsy naturally restrict analysis to the presumed epileptogenic zone (given the opportunity to perform histological studies on resected specimens). Whether the same neuropathology extends to axons extending distally across the brain as we have shown here is a more contentious issue. We report extra-axonal diffusivity alterations across many WM tracts that are presumably not part of the epileptogenic zone. The underlying histological cause of these changes remain unknown.
We additionally report increases in regional white matter MD in patients with refractory epilepsy compared to those with nonrefractory epilepsy. MD is a measure of all diffusion which is directionally averaged and may in itself be a marker of cellularity, edema and necrosis (Alexander et al., 2011). Increased MD is often reported in many dMRI studies of epilepsy (Concha, Beaulieu, Collins, & Gross, 2009;Jiang et al., 2017;McDonald et al., 2008). Moreover, MD was found to be superior to other conventional diffusion metrics in predicting postoperative seizure outcome from preoperative DTI in patients with TLE  Parkinson's disease (Planetta et al., 2016), and concussion (Pasternak et al., 2014). Neurite orientation dispersion and density imaging (NODDI) (Zhang, Schneider, Wheeler-Kingshott, & Alexander, 2012) has been used to demonstrate alterations in intracellular volume fraction, a marker of neurite density, in malformed brain regions causing epilepsy (Winston et al., 2014) and in widespread temporal and extratemporal brain regions in TLE (Winston et al., 2020). Other work has reported that NODDI-derived orientation dispersion index maps reveal cortical and subcortical abnormalities in patients with nonlesional focal epilepsy (Rostampour, Hashemi, Najibi, & Oghabian, 2018). Multicompartment models are better able to understand the biological processes driving changes in diffusion parameters (Winston et al., 2020). By modeling diffusion with two −/multicompartment models, evidence suggests that improved detection of focal abnormalities and further insights into the underlying microstructure of the brain is possible. While these models have provided important insights into microstructural brain changes associated with neuropathology, there are notable issues with many dMRI tissue models. These include problems with nonlinear fitting algorithms, on which many of these models are based, which can lead to increased computational times, sensitivity to noise and imaging artifacts, and issues related to the accuracy of the underlying idealizations (Novikov et al., 2018). FBWM mitigates these difficulties with a twocompartment model based on well-supported assumptions and a simple computational scheme involving a straightforward linear transformation of the dMRI signal together with a one-dimensional numerical optimization. Further, FBWM improves substantially upon the white matter tract integrity (WMTI) method (Fieremans et al., 2011). The WMTI method (Fieremans et al., 2011) assumes that all axons in a given voxel are approximately aligned in the same direction, which creates issues in regions of crossing fibers. FBWM overcomes this by using the fODF from FBI rather than assuming a particular geometric arrangement of axons and, as such, should more accurately model regions with crossing fibers.
Rather than averaging diffusion metrics over each reconstructed white matter tract we chose to utilize an along-tract approach. Given that white matter tissue diffusional characteristics vary long the length of tracts, it is advantageous to capture this variation in clinical studies as averaging across whole tracts may obscure regionally specific and pathologically relevant diffusion alterations (Figure 1). This is especially important for the development of imaging markers of treatment outcome in epilepsy; only by quantifying diffusion changes along tracts did a previous study identify preoperative markers of excellent and suboptimal postoperative seizure outcomes in patients with refractory TLE . In the present study, we were able to identify the circumscribed region of principle difference in extraaxonal diffusivity within tracts between patient groups and controls.
Moreover, given the inconsistent regional differences in diffusion metrics within tracts between refractory and nonrefractory patients ( Figure 5), we would be unable to identify significant differences in tract characteristics if diffusion measures were averaged over the entire tracts. In order to further improve upon this method, future work could make use of the fODFs generated directly from FBI. These are expected to yield improved tractography results over fODFs from standard DTI Moss et al., 2019). Our data suggest that dMRI two-compartment models analyzed over the length of tracts may be a noninvasive marker of pharmacoresistance in patients with epilepsy. It is possible to use alternative image analysis techniques to examine microstructural properties of white matter pathways, such as tract-based spatial statistics (TBSS). TBSS offers the opportunity to perform voxel-based analyses of representative regions while minimizing multiple comparisons by evaluating voxels constrained to a core white matter skeleton in standard space. However, we chose to apply a tractography approach that offers increased patient-constrained neuroanatomical precision and permits comprehensive profiling of microstructural properties along full white matter tracts, which we suggest may provide the best opportunity to identify individualistic diffusion-based biomarkers of treatment outcome . Finally, despite that this application of FBI and FBWM modeling is the first in a clinical cohort and has demonstrated robust extra-axonal alterations in patients recruited according to treatment response, it has done so in a modest sized cohort. Further insights into treatment response and patient cognitive profiles may be achieved in larger prospective studies.

| CONCLUSIONS
This is the first clinical application of FBI and FBWM. The twocompartment diffusion model has provided the means to separate intra-axonal and extra-axonal diffusion alterations in patients with longstanding epilepsy. The strongest findings were with parameters sensitive to extra-axonal diffusion, which may suggest significant neuroinflammatory processes and/or axonal degeneration. This work demonstrates that these changes are more widespread in patients with refractory epilepsy compared to those with wellcontrolled seizures located along eloquent white matter tracts not considered to be part of the epileptogenic zone in patients with focal seizures.