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Advanced Analysis of the Water/Fat Distribution in Skeletal Muscle Tissue Using Magnetic Resonance Imaging in Patients With Neuromuscular Disease

Purpose: Neuromuscular diseases (NMDs) frequently cause severe disabilities. Magnetic resonance imaging (MRI)–based calculation of the so-called fat fraction (FF) in affected muscles was recently described as a reliable biomarker for monitoring progression of NMDs. This is of high interest as newly available modern gene therapies, currently subject to intensive investigations, may provide at least palliation of these severely disabling diseases. In this retrospective study feasibility of advanced image analysis, potentially extending the application of FF in lower limbs in patients suffering various NMDs was investigated. Methods: Patients receiving MRI due to manifestation of proven NMDs (amyotrophic lateral sclerosis [n = 6], spinobulbar muscular atrophy [n = 4], limb girdle muscular dystrophy [n = 5], metabolic myopathy [n = 2]) in lower limbs were compared to patients without NMD [n = 9]. FF and new parameters derived from an advanced image analysis with generation of standardized MRI feature–based matrices were correlated with clinical grades of strength obtained using the MRC scale (Medical Research Council for Muscle Strength). While FF displays the fat partition in muscles only, the advanced image analysis considers the full MR-image information. Here, principal (PCA) and independent component analyses (ICA) were employed to derive parameters describing the full data obtained in more detail. Results: PCA- and ICA-based full-image parameters remained strongly correlated with FF (Spearman coefficient 0.96–0.59), but generally showed stronger correlations with the MRC score in lower limbs (Spearman coefficient; FF = −0.71; PCA & ICA parameters = −0.76–0.78). So far, age was no significant confounder in full-image assessment. Conclusion: The proposed advanced image analysis in NMDs is technically feasible and seems to effectively extend the information of FF.


INTRODUCTION
Neuromuscular diseases (NMDs), although low in prevalence (1-3/100,000 persons), are known to show either slow or sometimes fast progression of symptoms leading to severe disabilities, currently without the opportunity of an effective treatment. Disease-modifying therapies are subject to intensive investigations in order to provide at least palliation of the often heavily disabling symptoms of NMDs [1]. In parallel, this requires the development of objective and sensitive methods enhancing the diagnostic algorithm and reliably measuring alterations in affected muscle tissue over time to prove effectiveness and validity of therapeutic interventions.
Magnetic resonance imaging (MRI)-based high-resolution myometry with quantification of the fat fraction (FF) was validated as a sensitive biomarker for both myopathies and neuropathies showing strong correlations with clinical and functional scores [2,3]. In this context, certain MRI techniques, as described by Dixon [4], enable the direct determination of signal contributions from either structurally bound or highly mobile protons. This allows the differentiation of muscular water and fat content, since signal from bound protons mainly represents fat and signal from highly mobile protons is primarily attributed to cellular and interstitial water components. In this way, separate water and fat images can be generated, where FF simply calculates the proportion of fat signal from the signal totally gained from both, i.e., water and fat, proton pools [5].
FF proved useful especially in slowly progressing NMDs leading to fatty infiltration of muscular tissue, but further alterations in the muscle tissue texture attributed to edema, a common pathological feature of neuropathies, may occur as well [6]. So far, patterns of regional muscular affections in various NMDs were analyzed. Typically, the specific appearance of muscle tissue in regions of interest (ROIs) drawn in representative MRI sections was rated by FF and compared with clinical findings [5,7,8]. This way, FF was established as standard parameter for MRI-based myometry and became a promising tool to play an important role in the assessment of disease state and progression [7,9].
However, as FF displays the proportion of fat signal only, we hypothesized that this does not fully account for all potentially meaningful information about relevant shifts in the global muscular water/fat distribution caused by NMDs. Therefore, we propose a novel, extended quantitative voxel-based assessment method for muscular tissue using principal component analysis (PCA) and independent component analysis (ICA) to analyze and describe the full, directly measured, muscular water/fat signal distribution in MRI. So far, PCA and ICA have already been used to extract certain features in (functional) MRI data. In contrast to PCA, ICA can be used to find a linear representation also of non-Gaussian data so that the components are statistically independent, or as independent as possible. Such a representation seems to be able to capture essential features of the data in various applications, including feature extraction and signal separation [10]. Although ICA is able to extract an unknown number of components, depending on the quality and amount of data, the exact or optimum number of components remains an issue [11,12]. In our application, the number of components is known and low, so we can expect robust results. This approach could provide a deeper insight into muscular tissue alterations in NMDs, which in turn could be used for a more detailed analysis of disease progression and response of NMDs to therapeutic efforts.

Patients
In total, 22 consecutive patients receiving 26 MRI examinations due to suspected degenerative neuromuscular disease with primary manifestation at the lower limbs were included in this retrospective study. Five groups with two subgroups were differentiated, where in the reference group patients initially suspected for NMD, but during clinical workup identified as articular induced pain syndromes without degenerative muscle affection, were collected as controls (CO, control group; n = 9; male:female = 7:2; age: 55.3 ± 16.8 years). Next to this, two subgroups differentiating subjects from the cumulative control group by age were created. One subgroup included subjects younger than 50 years at the time of their examinations only (control subgroup: CO <50; n = 4; male:female= 3:1; age: 33.2 ± 3.4 years), while the other subgroup included only subjects older than 50 years (control subgroup: CO >50, n = 5; male:female = 4:1; age: 60.4 ± 4.0 years).
The clinical grade of muscle strength in the lower limbs at the time of MRI was assessed according to the Medical Research Council (MRC) scale for muscle strength in all patients employing the commonly used six grades (i.e., 5-0) scoring system, where grade 5 is assigned to full strength and grade 0 is given in case of complete paralysis [14,15].
The study was approved by the local institutional review board (NÖ Ethikkommission, trial: GS1-EK-4/597-2019) and conducted according to WMA guidelines in force at the time of patient data acquisition [16].

Magnetic Resonance Imaging
MRI simultaneously depicting both legs was performed on a clinical 1.5-T whole-body scanner (Magnetom Avanto, Siemens, Erlangen, Germany) using the system's standard peripheral angiography coil set with full coverage of both legs (Tim matrix coil system of about 1,000 mm length). The scan protocol included T 1 -weighted (T 1 w), three-dimensional (3D) gradient-echo (GE) imaging implemented as a two-point Dixon volumetric interpolated GE sequence (3D-Dixon-VIBEsequence). The 3D-Dixon sequence offers fast, high-resolution imaging of muscles through asymmetric k-space sampling and interpolation (voxel size = 1.2 × 1.2 × 5.0 mm; slices = 64; FOV = 380 mm; total scan time: 4:05 min) and allows generation of separate water-and fat-only images due to the incorporated dual echo Dixon technique (TE 1 = 2.39 ms; TE 2 = 4.78 ms; TR = 10 ms; NSA = 1).

Depiction of the MRI-Based Muscular Water/Fat Distribution
All image data were translated to NIfTI-2 format for further processing [18]. A representative slice at the mid-level of all thighs and calves was selected from the 3D-Dixon sequences, and separate regions of interest indexed by distinct numbers for each depicted muscle (ROI m ) on each side were drawn by an experienced reader (U.K.) who was blinded to the respective NMD. All examinations were presented to him in random order. The respective slice was chosen in such a manner that as much of the cross-sectional muscle tissue was visible as possible for the assessment. The specific fascia defined the boundaries of each muscle ROI, thereby excluding large nerves, vessels, the skin, and the subcutaneous fat, as well as the bone structures from the evaluations. In this way, in thighs ROIs showing the rectus femoris muscle, the vastus medialis, intermedius and lateral muscles, the semimembranosus, the semitendinosus, the biceps femoris, the adductor magnus, and the sartorius and gracilis muscles were drawn at each side. In calves, the anterior tibial, the long peroneal, the lateral and medial gastrocnemii, the soleus, and the posterior tibial muscles were outlined on each side (Supplementary Figure 1). Subsequently, scripts written for the applied statistical software used the indexed ROI m to generate virtual cumulative ROIs for thigh (ROI T ) and calf muscles (ROI C ), which, in turn, were integrated into virtual cumulative master ROIs for assessment of the whole lower limbs (ROI LL ). Besides visual inspection of theROI m , they served also to correct for potential Dixon inversion artifacts by testing the plausibility of the signal relation between bone marrow and muscle signal encountered in both legs.
Signal intensities from water-and fat-only images were then normalized voxel-wise in all ROI T , ROI C , and ROI LL to their signal specific maximum: where w n and f n represent the normalized water and fat signal intensities, w s and f s the original signal, and w max and f max the respective ROI-specific maximum of water or fat signal. In order to generate comparable images of ROI-specific water/fat distributions (WFD ROI ), all values of w n and f n were resampled within discrete intervals of i = 0.01 and adjusted to the interval ]0, 1] by: where x n denotes the normalized water or fat signal values w n or f n and r (x n ) conforms to the rank of x n according to the used resampling interval i. Note that replacing equal or less than zero by i is a convenient way to correct for inconsistencies of the previous Dixon water-and fat-only image calculations and that these values were eliminated later by thresholding the noise in the various ROIs. Equation 2 was used to assign a distinct pair of ranks r (w n ) , r (f n ) to each voxel of the given ROI. Then, the absolute frequency of each r (w n ) , r (f n ) combination was determined leading to WFD ROI . After normalization of WFD ROI to its maximum, a k × l matrix M w/f was built from the normalized frequencies p r (wn) ,r (fn) using their ranks r (w n ) , r (f n ) as subscripts: r (w n ) i ∈ R w n k=1/i,...,1 = 1, . . . , i · k r (f n ) j ∈ R f n l=1,...,1/j = j · l, . . . , 1 In Equation (3), M w/f denotes the squared ROI-specific standardized WFD matrix. The number of rows k and columns l, where k = l, depends on the interval steps i defined in Equation 2. Symbols R w n k=1/i,...,1 and R f n l=1,...,1/j denote the ordered sequences of ranks r (w n ) and r (f n ) , which were used as subscripts of the elements of M w/f . All other symbols have the same meaning as in Equations 1 and 2. A full summary of the M w/f workup is given in Figure 1.
For further assessment of M w/f , the subscript or rank order, respectively, was set descending for water signal and ascending for fat signal. This is owed to the fact that in the following standardized WFD matrices M w/f were interpreted like images depicting the specific water/fat distribution of the various ROIs. These images may be visualized directly to depict a specific WFD in a certain NMD or can be stored in a database for further statistical image analysis.
In order to set any results derived from M w/f images in relation to established parameters, also the FF, as proposed in the literature [19], was calculated for all ROI T , ROI C , and ROI LL : where all symbols have the same meaning as in Equations (1-3).
FIGURE 1 | Flow chart showing the generation of standardized ROI-specific WFD matrices M w/f . The described process is essentially based on the normalization to the corresponding maximum of (1) water signal, (2) fat signal, and (3) the frequency of observed normalized water/fat signal pairs in the analyzed ROIs. Technically, this procedure may be applied to any combination of MR sequences without, in their effect, co-linear signal components.

Analysis of the Muscular Water/Fat Distribution
First, PCA was performed on all matrices M w/f of ROIs: ROI T , ROI C , and ROI LL in the various groups. Matrices M w/f were noise-thresholded, and using the water-and fat-signal ranks, r (w n ) and r (f n ) , as dimensions, the quantity P (rw n ,r wn ) = p r (wn) ,r (fn) ∈ M w/f p r (wn) ,r (fn) ≥ 0.1 was generated. From PCA performed on P (rw n ,r wn ) , the rotation angle ϕ (w/f ) (unit: radiant) of the normalized first principal component eigenvector e 1 relative to the unit vector u: and the related scattering defined by the coherence were derived. In Equation (6), σ n denotes the components' standard deviations σ 1 and σ 2 , with n = 2 according to the number of dimensions of the PCA. All other symbols have the same meaning as in Equation (3). The constant c k×l is the product of the matrix dimensions of M w/f (here: c k×l = 100 2 ). Note that only measurements with the same values for c k×l are directly comparable. Assuming distinct shapes of WFD related either to regular or to non-regular (NMD) muscle tissue as depicted in M w/f , PCA and derived angles ϕ (w/f ) and scattering c ϕ (w/f ) , σ n were used to identify these two conditions constituting the shape of M w/f in the various groups and regions (cumulative group WFDs are displayed in Figures 2, 3

, and Supplementary Figures 2-4).
As PCA suggested distinctly different WFD patterns for (1) regular and (2) non-regular muscle tissue in matrices M w/f , ICA with separation of two components was performed to test the automatic separation of these. Similar to general image pattern recognition [20], we first transformed all matrices M w/f of dimension: k × l to one-dimensional vectors v (w n /f n ) of length: k · l. Vectors v (w n /f n ) were then used to generate separate s × k · l matrices S w/f for thighs, calves, and whole lower limbs, where the number of rows s conforms to the number of subjects (=observations) involved. To warrant a reproducible strength of pattern separation, correlation (Spearman's Rho, ρ ) of the two obtained component-vectors i 1 and i 2 derived from ICA was tested and ICA was performed repetitively until condition ρ < 0.3 was true. Component-vectors i 1 and i 2 were sorted such, that i 1 always applied to regular (1) and i 2 to non-regular (2) muscle tissue. Sorting was achieved by testing the location of the median crossing point m (w n ) ,m (f n ) after re-transformation of i 1 and i 2 to their corresponding matrix M w/f (Figure 4;  Supplementary Figure 5).
After this, vectors v (w n /f n ) of each case and region (thighs, calves, lower limbs) were analyzed for their correlation with i 1 and i 2 using Spearman rank correlation tests (Spearman's Rho: ρ) with calculation of ρ i 1 and ρ i 2 . To gain the same effect direction for ρ i 1 and ρ i 2 , correlations were always given as ρ 1 = 1 − ρ i 1 (complement of ρ i 1 ) and ρ 2 = ρ i 2 . Muscular MRI examinations using ICA were described by ρ 1 and ρ 2 , or, more comprehensively, by the scalar neuromuscular index NMi : = ρ 1 + ρ 2 .

Statistical Analysis of the Muscular Water/Fat Distribution
Since, clinically, no noticeable differences between left and right legs were assessable, and with respect to the small number of cases, only one MRC score was given for both lower limbs. Accordingly, image parameters also represent cumulative evaluations of both legs. Additionally, we assessed age as a possible confounder of FF and the newly introduced full imagerelated parameters using robust linear regression analysis (LRA) and calculation of group-differences with conservative correction for multiple comparisons.
Conformity of WFDs in the various ROIs m with the normal distribution was found in <5% of all cases (Shapiro-Wilk test, testing ROIs m : WFD conform with normal distribution: water signal = 4.62%, fat signal= 3.85%; p < 0.05). Thus, median-based tests were used for inferential statistics and the median, the median absolute deviation (MAD), and range [minmax] for descriptive statistics. Single subject analysis and group testing were based on rank correlation tests with calculation of Spearman's Rho.
Differences between groups were evaluated using Kruskal-Wallis tests (K-W test) with Dunnett's modified Tukey-Kramer pairwise multiple comparison tests (DTK) for post-hoc analysis [21]. Conservative correction for multiple comparisons (Bonferroni) was performed. A p < 0.05 was considered significant. Linear regression analysis was performed using least trimmed squares robust (high breakdown point) regression. All computations and statistical evaluations were performed using scripts written for cran-R involving packages AnalyzeFMRI, robustbase, fastICA, and DTK [21][22][23][24][25]. Since only one patient presented with MRC score 2, this patient was not included in the score-group comparison (detailed data are provided in Table 1).

RESULTS
FF, PCA-derived angle ϕ (w/f ) , and scattering c ϕ (w/f ) , σ n in lower limbs (ROI LL ) were correlated strongly with ρ = FIGURE 2 | Cumulative standardized WFD matrices M w/f of lower limbs from subjects without NMD. The left image displays subjects younger than 50 years, while on the right side subjects older than 50 years are shown. The area including 95% of all cases without NMD is marked in green color with green lines denoting the median of water and fat signals of all non-NMD cases. Generally, the WFDs in these subjects represent regular muscle tissue, which seems rather homogeneous and shows a greater variance of the water signal with, in its effect perpendicular to this, only minimal fat signal variances. Accordingly, eigenvectors in M w/f were nearly parallel to the main signal axes (blue and red arrows: eigenvectors multiplied by corresponding standard deviations arbitrarily drawn in the middle of M w/f showing the variance size and direction of the principal components). Also, the PCA-derived angle ϕ (w/f) and scattering c ϕ (w/f ) , σ n are given. The slightly higher scattering in older subjects was not significantly different from younger ones. 0.888 and 0.886 (Spearman's Rho), respectively. Correlations between FF, ϕ (w/f ) , and c ϕ (w/f ) , σ n in thighs (ROI T ) were even stronger with ρ = 0.962 and ρ = 0.938 (Spearman's Rho), respectively. In calves (ROI C ), the correlations between FF, ϕ (w/f ) , and c ϕ (w/f ) , σ n were still strong with ρ = 0.745 and 0.742 (Spearman's Rho), respectively. Also, the ICA-based parameters ρ 1 , ρ 2 , and NMi were strongly correlated with FF in lower limbs with ρ = 0.819, 0.826, and 0.828 (Spearman's Rho), respectively. The same was true in thighs, where strong correlations of FF with ρ 1 , ρ 2 , and NMi with ρ = 0.849, 0.875, and 0.878 (Spearman's Rho), respectively, were found. Correlations between FF and ρ 1 , ρ 2 , and NMi in calves were rather moderate with ρ = 0.621, 0.611, and 0.588 (Spearman's Rho), respectively.
The already visually different WFD patterns of regular and non-regular muscle tissue were investigated further, and the relation between the ICA-derived coefficients ρ 1 and ρ 2 was assessed using a robust linear regression model after transformation of ρ 2 to the logarithmic scale. Using the model ρ 1 : = a · log(ρ 2 ) + b, regression analysis revealed that the loss of regular muscular tissue was strongly correlated with an exponential increase in non-regular muscular tissue (LRA; loglinear model; R 2 [adjusted]: ROI T : 0.981, ROI C : 0.964, ROI LL : 0.966; p < 2.2 × 10 −16 ) (Figure 5; Supplementary Figure 6). Additionally, depending on the MRC score, PCA-derived angles ϕ (w/f ) and scattering c ϕ (w/f ) , σ n showed distinctly different distributions of NMDs with primary neuronal degeneration and those primary leading to fatty degeneration of the muscle tissue (Figure 6).
Concerning disability, the MRC score in LGMD patients was significantly lower compared to the control groups (K-W test: MRC, post-hoc: DTK [corr.], p = 0.002), while for the rest of the NMD groups no significant differences were found. In lower limbs, FF was also significantly different between the LGMD and control groups only : Bonferroni], p = 0.028). Otherwise, there were no significant differences found between the various groups, especially when testing the cumulative and the young and older control groups separately against the NMD groups. Additionally, linear regression analysis testing the influence of age on the various muscle parameters in the cumulative control group CO revealed that age was no LGMD (right lower image) were clearly more inhomogeneous and rotated into the direction of the fat signal, which is also supported by angles ϕ (w/f) and scatteringc ϕ (w/f ) , σ n . Note that the latter two parameters are clearly higher in NMD patients than in controls.

DISCUSSION
PCA and ICA were used to extend the widely accepted and validated MRI-based scalar quantity FF. Though FF is a robust biomarker, reliably assessing progression and stage of NMDs [2,3,26], we aimed to demonstrate the feasibility of statistical methods known from image analysis and pattern recognition to provide an even deeper insight into pathological alterations depicted by MRI in muscles. In contrast to FF, the quantitative methods proposed in this study rely on the assessment of the entire water-and fat-related signal acquired by muscular MRI in the lower limbs considering a wider range of MRI-accessible information. The proposed PCA-and ICA-derived parameters remained related to FF, but exhibited stronger correlations with muscle strength in lower limbs indicating a potentially higher clinical relevance of these methods in the assessment of the course and progression of NMDs.
FF considers the relative amount of the fat-attributed muscular tissue partition in MRI only, while the full range of the water/fat signal is used to correct for possible signal variations of the measurement. Though this warrants robust results [27], on the one hand, this could mask meaningful information about subtle shifts in the water/fat relation in muscles, on the other hand. Thus, the complete distribution of all water/fat signal pairs, the so-called WFD, encountered in MRI of lower limb muscles was evaluated in this study. In case of a high number of voxels with strong signal from stationary protons, much of the WFD is explained by muscular fat content, which rotates the preferential axes of the WFD in M w/f into the direction of the fat signal, and vice versa (Figures 2, 3). Consequently, the specific information of the FF-correlated fat content is conserved in PCA and ICA, while all the water-attributable signal information is added to the analysis. This assertion is clearly supported by the strong correlation between PCA-or ICA-derived parameters and the corresponding FF. Nevertheless, the correlation between the MRC score and PCA-and ICA-derived parameters was in large part stronger than that found for FF (Table 4), which indicates that FF may not reveal all the information about subtle but relevant alterations in the muscular texture depicted in MRI. Thus, the advanced analysis of muscular MRI stressed in this study seems to further extend the accuracy of FF.
As the WFD constitutes from the linear combinations of the underlying water/fat signal, PCA was used to calculate eigenvectors and values of the specific distribution. From the eigenvector of the main principal component, the rotation angle ϕ (w/f ) relative to the virtual y-axis of M w/f was computed to quantify the excursion of the measured signal distribution in the direction of either the water or fat signal. Additionally, scattering described by the coherence function c ϕ (w/f ) , σ n was evaluated in order to estimate the impact of variances of the acquired water and fat signals on the respective WFD. Further investigation of ϕ (w/f ) and c ϕ (w/f ) , σ n revealed that all patients with regular muscle strength, independently of their diagnosis, presented with small values for ϕ (w/f ) and c ϕ (w/f ) , σ n . This induced a certain WFD pattern of water/fat signal pairs densely packed near the virtual y-axis of M w/f , where the eigenvector of the major component was nearly parallel to this axis and pointed clearly into the direction of the water signal (Figure 2). In patients with reduced strength grades, the WFD patterns were more heterogeneous. They presented with a more or less widespread distribution of water/fat signal pairs around the virtual diagonal spanned between the extremes of M w/f . Due to the clearly stronger excursions of their WFD into the direction of the fatrelated signal with much larger variations of the encountered signal components, values found for ϕ (w/f ) and c ϕ (w/f ) , σ n were significantly higher than those in patients with regular muscle strength. Compared to FF, differentiation of patients with various MRC scores in thighs and lower limbs was in favor of the PCA-derived parameters, since correlations were stronger and the ability to separate patients from different groups was better defined using angles ϕ (w/f ) and/or scattering c ϕ (w/f ) , σ n ( Table 4). According to this, PCA parameters were strongly correlated with the MRC score and were significantly different in patients grouped by this score. This implies an improved discrimination of various stages of disease by the PCA parameters with preservation of the properties of FF, as the correlation with FF was strong. In this way, angles ϕ (w/f ) and an inherent part of the coherence function c ϕ (w/f ) , σ n , the product of standard deviations (σ product), theoretically, could serve automatic classification of NMDs in future trials on big data using artificial intelligence based approaches (Figure 6). Generally, two distinct WFD patterns, one typical for regular and the other for non-regular muscular tissue, with only a small overlap between the two patterns, were found (Figures 2, 3,  Supplementary Figures 2-4). This encouraged the use of ICA for automatic separation of these distinctly different patterns. A WFD can be seen as an image displaying a specific distribution of regular and non-regular muscle components, or, more precisely, it is a combination of at least two "sub-images" each depicting either regular or non-regular muscle tissue. These sub-images are represented by component vectors, which neither share a collinear statistical effect, as shown by ϕ (w/f ) , nor conform to the normal distribution in statistical testing. Thus, both components or sub-images may be assumed as non-Gaussian linear representations of water/fat signals of different disease conditions, which can be decomposed by ICA as statistically independent components hidden in the full WFD image. This assumption is proven by our results exhibiting a robust decomposition of the postulated two-characteristic-patterns using ICA.
The match of individual WFD image vectors with regular or non-regular muscle tissue component vectors i 1 and i 2 was quantified by computing the rank correlation coefficients ρ 1 and ρ 2 and their sum: NMi. In patients with reduced MRC scores suffering from long-lasting, i.e., already progressed NMDs (e.g., SBMA and LGMD patients), an exponential increase in nonregular muscle tissue was found. Patients with reduced muscle strength in rapidly progressing NMDs (e.g., ALS) and, therefore, shorter disease durations showed by far less reorganization of the muscle texture. However, both conditions were significantly different from patients without strength constraint. Accordingly, the ICA-derived parameters showed much stronger correlations with MRC scores than FF, though FF was still strongly correlated to ρ 1 , ρ 2 , and NMi. These findings emphasize the ability of ICA to robustly decompose regular and non-regular muscle components depicted in M w/f with preserving the information inherent to FF. However, the MRC scores were explained better by ICA-based parameters than by FF. Since the number of cases in this study was rather small, we did not try to separate other components by ICA, especially from the non-regular sub-image pattern of WFD. Nevertheless, separation of other components appears promising in larger and more homogenous (sub)samples, where ICA could FIGURE 6 | Behavior of PCA-derived parameters: ϕ (w/f) (y-axis) and the so-called σ -product (x-axis), an inherent part of scattering defined by the coherence function c ϕ (w/f ) , σ n , in the various NMD groups (indicated by different colors; numbers indicate the MRC score). Alterations in the muscular water/fat texture with higher fat partitions shift the measurements to the right and upward. Especially, an increased heterogeneity of the WFD indicated by the σ product was related to reduced MRC scores in muscles of lower limbs. As this suggests an excellent differentiation of alterations attributed predominantly to fatty infiltration from those primarily caused by denervation, this could serve automatic classification of NMDs in future trials. Note that younger and older controls share the same behavior suggesting nearly no effect of age on the measurements. be used to objectively explore conceivable further subtypes of NMD-induced muscle alterations.
It has to be noted that standardized M w/f matrices may contain-in principle-any combination of different MR signals. Three-point-, proton-density-, or T2-weighted Dixon techniques, which seem to offer more stable results for quantification of the muscular fat content [27], could also help to differentiate the various muscular conditions in NMDs, like fatty degeneration, denervation edema or fibrosis, which could further expand the power of our methods.
Though our preliminary results underline the advantages of sampling the full WFD, several limitations have to be considered. The sample size of our NMD cohort is quite small and most of our observations remain yet to be proven in larger NMD cohorts. Our results may, therefore, suffer from heterogeneity, where effects from, e.g., age, training state, or the body mass index, could not be considered entirely. On the other hand, given the very low prevalence of the investigated NMDs, the number of cases presented here appears at least fair to prove the feasibility of the proposed analysis methods. Even in our small sample of NMD patients, assessment using the proposed standardized matrices M w/f seemed to offer a valuable extension to FF. As the PCA-and ICA-derived parameters remained strongly correlated to FF, the proposed methods should still compare to FF. Despite this, we were able to demonstrate that, for instance, age was no significant confounder in our analysis, though some studies reported a relevant, but mostly weak, influence from age on FF. However, several other studies did not confirm this finding [3,28] and, accordingly, no significant influence from age on the assessed parameters was found in this study (compare Supplementary Figure 7). For the moment our approach, which primarily aims to demonstrate the feasibility of PCA-and ICAbased assessment of the proposed standardized WFD matrices, appears rather robust to influences of patients' age. As our sample consisted of several different NMDs, another limitation of this study was the need to abstain from commonly recognized clinical and functional scales describing special features of a particular NMD in more detail than the proposed assessment based on the MRC score. The MRC score helped to preserve comparability of clinical assessment and to reduce effects from the heterogeneity of the various NMDs in our sample. Additionally, MRC grading is a commonly accepted clinical tool validated to reliably measure strength in the lower limbs. However, the generally weaker relation between PCA, ICA, and FF and their weaker correlation to the MRC score in calves in our sample could also result from deficiencies of this score system. Actually, this system tests the ability to move the lower limbs against gravity, which does not require too much function of calf muscles. The overall smaller muscle volumes in calves, potentially inducing greater variances in the measurements, could also contribute to this. Moreover, as our methods indicate a higher sensitivity to detect subtle shifts in the muscular water/fat-content in NMDs, one also has to consider that alterations in MRI may precede the clinical deterioration of a patient. Obviously, this is not fully described by the MRC score and requires a closer analysis of the exact relation between changing of ICA-and PCA-based parameter values and the correlated clinical presentation of a patient. Finally, since we evaluated the full WFD without correction, we assume our measurements to be prone to bias from inhomogeneities of B 0 and geometrical properties of the used coil system. As all data was recorded on a single scanner using the same coil system, this seemed not to have played a major role. However, this needs to be investigated further, especially when assessing regions with smaller muscle volumes, as in the neck or the arms, with expectedly higher distortions of the magnetic field. Also, differences in data quality performed on different MR scanners or with higher field strengths and improved sequence techniques (e.g., 3-point Dixon sequence) is to be expected, potentially leading to improved spatial resolution and discrimination power.

Conclusion
PCA was found promising to allow robust classification of patients according to their stage of NMD, thereby extending the possibilities of FF. ICA enabled an apparently robust separation of regular from non-regular muscle components in the proposed standardized MRI feature-based matrices M w/f , which could offer a practical way for automatic identification of pathologically altered muscle tissue and possible NMD subgroups. Compared to FF, our preliminary results suggest a higher power of PCA-and ICA-derived parameters to detect subtle shifts in the MRI water/fat signal relation in NMDs, which encourages the conduction of further trials to overcome limitations of this study. PCA-and ICA-driven statistical assessment of neuromuscular MRI may, therefore, be used to substantially improve the diagnostic workup and monitoring of disease progression in NMDs.

DATA AVAILABILITY STATEMENT
The datasets generated for this study are available on request to the corresponding author.

ETHICS STATEMENT
The studies involving human participants were reviewed and approved by NÖ-Ethikkommission. The patients/participants provided their written informed consent to participate in this study.

AUTHOR CONTRIBUTIONS
CN, UK, HC, and WS conducted the data collection. CN conceptualized the study and method design. CN and EM contributed to the analysis and interpretation of the data. CN drafted the paper. All other authors revised it critically and approved the final version and agreed to be accountable for all aspects of this work.

FUNDING
No external funding was received for this study. Institutional infrastructure support was provided by the various departments participating in the study.