Validation of an automated segmentation algorithm for lower leg MR images, applied to sodium quantification

Objective To develop and validate an automated segmentation algorithm for the lower leg using a multi-parametric magnetic resonance imaging protocol. Methods An automated algorithm combining active contour and intensity-based thresholding methods was developed to identify skin and muscle regions from proton Dixon MR images of the lower leg. Tissue sodium concentration was then computed using contemporaneously acquired sodium images with calibrated phantoms in the field of view. Resulting sodium concentration measurements were compared to a gold standard manual segmentation in 126 scans. Results Most cases had no observable errors in segmentation of muscle and skin. Six cases had minor errors that were not expected to affect quantification; in the worst, 126 mm2 (2%) of a muscle area of 8,042 mm2 was misclassified. In one case the algorithm failed to separate the tibia from the muscle compartment. Correlation between automated and manual measurements of sodium concentration was R2 = 0.84 for skin, R2 = 0.99 for muscle. Additionally, the RMSE was 2.4mM for skin and 0.5mM for muscle; the observed physiological range was 8.5 to 37.4mM. Conclusion For the purpose of estimating sodium concentrations in muscle and skin compartments, the automated segmentations provided equally accurate results compared to the more time-intensive manual segmentations. Sodium quantification serves as a biomarker for disease progression, which would assist with early diagnostic treatments. The proposed algorithm will improve workflow, reproducibility, and consistency in such studies.

3 49 Introduction 50 With technological advancements, biomedical application of sodium (Na) magnetic 51 resonance imaging is on the rise, as it provides unique and quantitative biochemical information 52 related to tissue viability, cell integrity and function [1][2][3][4][5][6][7]. The lower leg muscle and skin is of 53 particular interest because of the technical simplicity and speed of obtaining an MRI scan of the 54 calf [8].

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A straightforward approach to determine sodium levels based on the sodium magnetic 56 resonance images of the calf is to manually segment the desired regions. This process requires 57 meticulous attention and inconsistencies can be introduced via human error, which diminishes 58 reproducibility.

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An automated approach could address these problems, and consequently improve 60 workflow. A variety of automated methodologies have been developed to segment anatomical 61 magnetic resonance images of the leg. One approach has been to apply a fuzzy clustering method 62 to segment anatomical regions such as adipose tissue, cortical bone, and spongy bone in the lower 63 musculature of the leg [9] and in the thigh [  (1) ( , ) = 1 1 + |∇ ( * )| 2 6 115 where "G 0 " represents the image and "I" represents the smoothing factor. The curves that shape 116 the object are then minimized in order to closely identify the desired object. This is achieved by 117 integrating the edge indicator function using calculus of variance 118 (2) 119 which yields a mask of the desired object. More simply stated, the active contour model can be 120 thought of as creating a basic shape that encloses the object, then progressively moving closer to 121 the object until it reaches the edge, shaping the object's boundary (Fig 2). The automated quantification algorithm can be divided into four main phases: leg and 140 phantom segmentation, skin segmentation, muscle segmentation, and quantification of sodium 141 concentration.

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First, using the proton-density weighted image (Fig 4a) a 400-iteration active contour 143 Chan-Vese method [15] was used to identify the leg portion of the mask and phantoms from the 144 background (Fig. 4b). Nature of each segmented region was determined automatically based on 145 size (leg >2400 mm 2 , phantoms <1300 mm 2 ). The skin region was estimated by eroding the leg portion of the mask (Fig. 4b) by a 4 mm 154 radius circular kernel and subtracting the resulting image from the original leg portion of the 155 mask (Fig. 4b) to select approximately the outer 4 mm of the leg region (Fig. 4c). It should be 156 noted that this process assumes the skin thickness is similar in all participants. At the time of MR 157 acquisition, the posterior area of the leg was resting on the phantom holder surface and thus 158 aligned perpendicular to the slice direction such that through-plane partial volume effect was 159 minimized [22]. Therefore, the skin region was reduced to include only the portion in contact 160 with the surface of the phantom holder (Fig. 4d). The reduced skin region was parallel to the coil 8 161 surface and the tissue thickness was more stable. Then, the produced image was overlaid on the 162 sodium image (Fig. 4e) [17, 18].

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The muscle region was identified on the water-only image derived from the mDixon scan 164 (Fig. 3a) using a two-class global histogram based intensity thresholding method (Fig. 3) [19].
165 The estimated classification threshold was then reduced by 50% to account for intensity 166 inhomogeneity in the image. Both the resulting two class image (Fig. 4f) and the leg portion of 167 the mask (Fig. 4b)

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Of the 123 usable scans, 94% of the segmentations were highly accurate on visual 194 inspection, correctly identifying the muscle and skin while excluding the tibia (Fig. 4h-i). 5% In this study, we aimed to develop an algorithm that would allow us to streamline 249 23 NaMRI readings of the lower leg. Our data suggest that the sodium concentration 250 measurements obtained by the automated segmentation were of excellent quality, adequate to 251 replace those obtained by the gold standard manual segmentation method.

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Based on the Bland-Altman analysis of the muscle (Fig. 6b) the sodium concentration 266 measurements in this region were highly correlated. However, three cases fell outside of the limit 267 of agreement. One of these had high levels of intramuscular fat (Fig. 5b). In this scenario, the 268 manual approach which divides the muscles into five sub-compartments could possibly exclude 269 slightly more of the intramuscular fat tissue between compartments compared to the automated 270 method, resulting in a small bias towards lower muscle sodium concentration estimates by the 13 271 automated method. Another was the case where the tibia was erroneously included in the muscle 272 region due to poor estimation from the active contour model in the automated method, this 273 consequently yielded an underestimation of sodium concentrations. The manual segmentation 274 from the third case was performed on the first slice of the mDixon scan instead of the middle 275 slice, which was an accidental deviation from the protocol due to human error as is typical with 276 manual procedures.

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Overall, the inter-scan comparisons were comparable for both the regions and 278 segmentation methods (Fig. 7). The correlations between baseline and the follow up for the skin 279 region is slightly higher for the automated method, hence increased reproducibility, compared to 280 the manual method. Conversely, the correlations between baseline and the follow up for the muscle 281 region is the same in the automated and manual methods. It should be noted that the used sub-282 dataset is from an ongoing longitudinal study during which some subjects will experience 283 treatment and time effects, thus we are not strictly measuring reproducibility.

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Although the automated algorithm performed quite well, there are some limitations. First, 285 the MR imaging protocol it relies on is fast, but still moderately complex and multi-parametric, 286 requiring both proton-tuned and sodium-tuned coils. Also, the results still require manual quality 287 review to identify significant failures such as inclusion of the tibia. Finally, the algorithm did not 288 reliably exclude the fibula from the muscle region. However, the area of the fibula is relatively 289 quite small, and we used the median instead of the mean in the muscle region to summarize 290 sodium quantification more robustly in the presence of a small number of outlier voxels (fibula).
291 Observed results had trivial errors compared to the manual segmentation that consistently 292 excluded the fibula (Fig. 7).
14 293 The global intensity-based thresholding step can be confounded by intensity 294 inhomogeneity in the MR images, resulting in a threshold that excludes some muscle tissue in 295 lower intensity regions or includes some background voxels in higher intensity regions. Such 296 inhomogeneity was present in our data, but not to a degree that affected results compared to 297 manual segmentation. This issue could be more pronounced in data from other field strengths or