Methods for Evaluating Gray Matter Contour Similarity in Transverse Slices of the Mammalian Spinal Cord

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The spinal cord may be divided into segments. The neural networks of different segment groups control, in particular, locomotion and visceral functions. Spinal cord segments serve as critical topographic landmarks for both experimental and therapeutic interventions. However, accurate identification of segment positions in vivo, particularly through automated methods, remains challenging: in mammals, some spinal cord segments are displaced rostrally (ascend) relative to their corresponding vertebrae, and the extent of this displacement varies even within a single species. One solution to this problem may be the use of reference images of slices of segments taken, for example, from histological atlases of the spinal cord. In this paper, we investigate various methods for analyzing the similarity of gray matter contours in transverse slices of the mammalian spinal cord, which allow us to determine whether a slice belongs to a certain segment. We consider the methods for analyzing slices obtained from one animal (based on the Jaccard coefficient, the metric of distances between contours, correlation analysis of R-φ curves, or Hu invariant moments), as well as the methods for comparing images of spinal cord segments with reference ones (correlation analysis of R-φ curves, Hu invariant moments). The results obtained allow us to assume that the method of determining segments by comparing tomographic or histological images of spinal cord transverse slices at different levels with a certain database containing a set of reference images of slices of specific segments, based on Hu invariant moments, is the most effective of those considered.

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V. Lyakhovetskii

Pavlov Institute of Physiology of the Russian Academy of Sciences

Email: mer-natalia@yandex.ru
俄罗斯联邦, St. Petersburg

P. Shkorbatova

Pavlov Institute of Physiology of the Russian Academy of Sciences

Email: mer-natalia@yandex.ru
俄罗斯联邦, St. Petersburg

A. Veshchitskii

Pavlov Institute of Physiology of the Russian Academy of Sciences

Email: mer-natalia@yandex.ru
俄罗斯联邦, St. Petersburg

N. Merkulyeva

Pavlov Institute of Physiology of the Russian Academy of Sciences

编辑信件的主要联系方式.
Email: mer-natalia@yandex.ru
俄罗斯联邦, St. Petersburg

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2. Fig. 1. (a) – Examples of variability of the skeletotopy of the lumbar segments of the cat spinal cord (for individual animals Q8 and Q17) in relation to the vertebrae (according to [11]). Methods for assessing the similarity of the gray matter of different segments of the spinal cord (b) and (c), examples of binarized images of the gray matter of the spinal cord (segments L1 – L7) from atlases [16] and [19]. A white dashed horizontal line is drawn through the center of the central canal, dividing the gray matter into two analyzed areas: the dorsal and ventral parts.

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3. Fig. 2. Calculation of the similarity of gray matter images of spinal cord sections using the Jaccard coefficient (using sections of segments L1 and L7 from the atlas [19] as an example). (a) Sections of segments L1 and L7, aligned by the position of the central canal; (b) intersection (IntersectImg) and union (UnionImg) of regions; (c) heat map of the results of the analysis of atlas sections.

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4. Fig. 3. Calculation of the similarity of spinal cord gray matter slice images in the C2Cdist distance metric between contours (using L1 and L7 segment slices from the atlas [19] as an example). (a) – Obtaining a gray matter contour from a binarized image of a slice of segment L7; (b) – obtaining a distance matrix to the gray matter contour of segment L1; (c) – projection of the gray matter contour of slice L7 onto the distance matrix to the gray matter contour of slice L1; (d) – heat map of the results of the atlas slice analysis.

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5. Fig. 4. Correlation analysis of the contours delimiting the gray matter of the sections. (a) – Calculation of the correlation coefficient between the contours delimiting the gray matter of the sections taken from two atlases [16] (red) and [19] (blue). The diagrams show a set of distances in pixels from the center of the central canal of the spinal cord to the most distant points of the gray matter from it – using the example of sections of the L1 segment of atlases [16] and [19], φ is the angle from the center of the central canal. On the left is the dorsal region of interest, on the right is the ventral region of interest. (b) – Heat map of the results of the analysis of sections of atlas [19]. (c) – Results of the correlation analysis: average values of Pearson correlations between all segments (L1 – L7) of atlases [16] and [19]. The large symbol for each segment of the atlas [16] indicates the segment of the atlas [19] that has the greatest similarity to it.

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6. Fig. 5. Analysis of the contours bounding the gray matter of slices based on Hu's invariant moments. (a) – Heat map of the results of the analysis of slices from the atlas [19]; (b) – average contour discrepancy for all segments (L1 – L7) of the atlases [16] and [19], calculated based on the Hu's invariant moments. The segment of the atlas [19] with the smallest difference from it is highlighted with a large symbol for each segment of the atlas [16]; (c) – average contour discrepancy for the segments (L4 – L7) from the work [5] with the segments L1 – L7 of the atlas [19]. The values of the mean ± standard deviation are given.

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