Online Submission ID: 1096

Automated Analysis and Visualization ofRemyelination Therapy for Spinal Chord Injury

Category: Research

(a) (b) (c)

Fig. 1. Density of detected cells. Figure (a) shows images with manual count of axons of interest shown with red markers, (b) showsdensity image calculated using manual counts for corresponding image shown in (a); (c) is the density image using the proposedalgorithm. Blue regions mark areas having high density of axons of interest. Images (b) and (c) should be similar if the actual andthe manual counts closely match. The image similarity measure SSIM [27] with mean SSIM index=0.993 (an index of 1.0 indicatingidentical) indeed show that they are very similar.

Abstract— Demyelination – the loss of the myelin sheath that insulates axons, is a prominent feature in many neurological disordersand results in the disruption of signals within the axons. The lost myelin sheath can be replaced by a process called remyelination,used in cutting-edge research for treatment of spinal cord injury. In order to evaluate the effectiveness of new remyelination therapiesthe images of the cross-sections of the spinal cords of the treated rat subjects have to be analyzed and visualized as follows.The axons remyelinated due to a special kind of cells called oligodendrocyte have to be detected, separated from other cells, andthen clustered. The location and density of the clusters show the site and amount of remyelination, both important parameters tounderstand the effectiveness of the remyelination therapy.

In this paper, we propose an algorithm for efficient, accurate and automated analysis and visualization of remyelination therapy.First, we use a robust, shape-independent algorithm based on iso-contour analysis of the image at progressively increasing intensitylevels for contour detection of the boundaries of the cells. The detected boundaries of spatially clustered cells are then separated usingDelaunay triangulation based contour separation method resulting in a clear boundary for each cell. The therapeutically importantoligodendrocyte-remyelinated axons (OR-axons) are differentiated from all the other detected cells by their characteristically low G-ratio – the ratio of the thickness of the cell boundary to the cell diameter. Finally, we generate a density map for visualizing the locationand density of the OR-axons for efficacy analysis of the therapy.

Remyelination analysis, currently done manually, is a painfully tedious process prone to subjective errors in estimation and clas-sification of OR-axons. Our automated remyelination analysis thus results in an incredible increase in efficiency and significantlyreduces error due to human subjectivity. We corroborate the accuracy of the results of our algorithm by extensive cross-verificationby the domain experts.

Index Terms—medical visualization, cell structure analysis, cell counting, cytometry

1 INTRODUCTION

Demyelination – the loss of myelin sheath – is a prominent featurein many neurological disorders including multiple sclerosis (MS) andspinal cord injury (SCI) [21, 6] which results in the disruption of sig-nals within the axons. The lost myelin sheath can be replaced by a pro-cess called remyelination which wraps myelin sheath around the de-myelinated axons restoring the conduction of signals within the axons.Remyelination can be achieved by two kinds of cells, oligodendrocytesand Schwann cells [22, 5]. One of the many therapies being developed

to improve the remyelination include transplantation of oligodendro-cyte progenitor cells into the adult spinal cord of rats following SCIwhich helps in remyelination of the demyelinated axons. However,to study the progress of the therapy these OR-axons (OR-axons) dueto oligodendrocyte progenitor cell transplantation need to be distin-guished from the already myelinated axons or axons remylinated bythe Schwann cells already existing in the body. The OR-axons areidentified by their characteristically thin myelin sheaths relative to thediameter of the axons. This ratio of myelin sheath thickness to axondiameter is called the G-ratio [25, 13]. Following the identification of

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Normally remyelinated axons

Oligodendrocyte-remyelinated axons

Schwann cell-remyelinated axons

Fig. 2. Different kinds of cells in the image. Left and Middle shows images obtained with different staining processes and hence the overall colordifference. The right one is the zoomed in view of the middle image showing the different types of axons.

OR-axons, their distribution has to be analyzed by visualizing the size,location and density of its clusters of in the image. By tracking suchvisualizations of microscopic images periodically captured on differ-ent rat subjects before and after the treatment, one can understand thegrowth rate and site of the OR-axons and hence the effectiveness ofthe therapy.

Remyelination is analyzed on microscopic images of 5× 625µm2

areas aligned on a radial oriented line that originates from the centralcanal of the spinal cord and extends to the outermost limit of the spinalcord cross section. The current method for identifying remyelinatedaxons is the line sampling technique [6] that is achieved manually.There are two kinds of error introduced in manually estimating andclassifying the remyelinated axons. Since a manual process is verytedious, the OR-axons are only identified in approximately 15% of theactual area of pathology on an average. In the rest of the area, it isonly estimated. This leaves out a high percentage of area in which alarge amount of estimation error can be introduced in the data. Fur-ther, there is classification error because of the subjectivity involvedin the manual classification of the OR-axons. The G-ratio, which canbe used to classify OR-axons, is not calculated for every single axonbecause this would be a tedious and time intensive work. It is oftenassigned by relative measure through visual estimation. This againleads to more classification errors. It is not known how much erroris introduced to the data when there are multiple examiners countingthese axons. These errors can be reduced by increasing the percent-age of the actual area of pathology. But the sheer size of the numberof samples collected from the pathology makes this a daunting task.Typically, axons are identified in a 1µm thick slice every 2mm peranimal. Therefore, in projects involving many groups, the OR-axongrowth analysis can take several weeks. An increase in percentage ofcounted area would not only increase the analysis time, but might alsoincrease the error due to human factors including fatigue.

An automated method to analyze and visualize the distribution ofthe OR-axons can alleviate all the above problems and provide an in-credibly useful tool for research in these kinds of cutting edge therapy.Automated system will allow analysis of a higher percentage of areaof the pathology, at much frequent intervals, and at higher accuracydue to less subjectivity and human factor related errors. Thus, it is ev-ident that automated recognition and classification of the axons wouldbe imminent in reducing the turn-around-time and the subjective errorin this research.

1.1 Technical ChallengesAutomating the process of analysis and visualization of distribution ofthe OR-axons involves taking as input a microscopic image (Figure1a) and creating a density map (Figure 1c) where blue regions indicatehigh density clustering of OR-axons. The complexity of this automa-tion is compounded by the following facts.

• The microscopic image is littered with a large amount of ‘cel-lular debris’, i.e. proteins and other cell bodies that have to be

identified and rejected, or not identified at all.

• The oligodendrocyte cells do not conform to any particularshape. In fact, even basic shape properties like convexity can-not be assumed. This demands a shape independent classifier todistinguish the cells.

• The intensities of the input images might be different from sam-ple to sample, and also dependent on the staining process (Figure2a and 2b). Hence relating intensities across images for con-sistently identifying the cells is not possible, and this intensitythreshold for cell identification has to be learnt within each im-age.

1.2 Main ContributionMost existing methods for automatic cell analysis focus on large, cel-lular matrices [1]. However, in cases where the topology of the cellu-lar structures is not uniform, as it is typically the case in injury sites,methods for identification and quantification of individual cells mustbe employed. Our main contribution is in designing an end-to-endautomated process that analyzes the input microscopic image and re-turns an effective high-level visualization of the distribution of the OR-axons. We present a robust algorithm to handle noise, subjectivity andunder-sampling, by using efficient computational geometry and stablestatistical techniques. We believe this is one of the first methods inbiomedical processing and visualization that to combine these tech-niques for reliable and robust cell/axon detection and processing. Ourmethod consists of the following five key steps.

1. Contour Detection: First, we detect the myelin sheath surround-ing the axons using progressive isocontours with varying inten-sity levels (Section 3). This technique is shape independent pro-cess that makes use of the variational property of the intensi-ties of the cell structures. This also allows us to detect axonboundaries across images of different intensities and pathologiesstained by different dyes.

2. Contour Separation: Since the contour detection step does notconsider the shape of the axons, the boundaries detected by thisstep may include multiple axons. We use a Delaunay triangula-tion based method to separate these cells and define a clean andunique boundary for each of them (Section 4).

3. Noise Removal: The cells detected by the above steps may in-clude noise (e.g. cellular debris). In this step, we identify thisnoise and remove them (Section 5).

4. OR-Axon Classification: G-ratio is defined as the ratio of thecell boundary (myelin sheath) thickness to the cell diameter. Theremyelination due to different cells can be differentiated by theG-ratio of the cell. In this step, we design a method based on G-ratio computation and clustering to identify the OR-axons fromother axons (Section 6).

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Online Submission ID: 1096

Contour Separation

Oligodendrocyte-remyelinated

axon Classification

Noise Removal

Density MapGeneration

Non-redundant boundary-coupled valid sheath

Non-redundant boundary-coupled oligodendrocyteremyelinated axons

Oligodendrocyte remyelinated axon clusters

Non-redundant boundary-coupled sheath

Input Image

Non-redundant sheath

Sheath Detection

Fig. 3. The pipeline of our proposed algorithm.

5. Density Map Generation: Finally, we use the distribution of thedetected OR-axons in the image to generate a density map thatis effective in visualizing the size, location and density of theirclusters in the area of the pathology (Section 7).

The pipeline of the entire process, as described above, is illustrated inFigure 3. We corroborate our method by extensive cross-verificationby the domain experts to demonstrate its accuracy and robustness.

We first discuss the relevant literature in Section 2. Then we presentthe four steps of our automated algorithm in Section 3 to 7. This is fol-lowed by experiments and analysis in Section 8. Finally, we concludein Section 9.

2 RELATED WORK

Digital image cytometry [12, 14, 31], the analysis of cell attributesfrom images, serves as an essential component of biological research.Correct detection of relevant cell structure and boundaries is a chal-lenging task in image cytometry because of the varying intensity lev-els in the images occurring from different staining protocols, varyingsizes of the specimen, difference in shapes across cell structures andthe presence of large number of cell debris.

Cell detection algorithms using image processing and computer vi-sion techniques continues to be a significant area of research [20, 14,31, 28, 7, 23, 10, 24, 4, 16, 30, 29]. Shape based analysis of cells isa common approach used by researchers [26, 9, 2] and is applicableto types of cells that conform to specific shapes. Since the OR-axonsaxons can be of any arbitrary shape, the shape dependent methods arenot useful and shape invariant analysis must be used for detection,identification and classification of axons.

Watershed segmentation is a widely used shape-independent ap-proach for cell detection [17, 11, 19]. But this algorithm is susceptibleto the presence of noise in the image. A single outlier can impact largegroups of pixels thereby making the watershed segmentation unstable.Most cell detection algorithms usually detect some cell structures thatare merged and need to be separated. Thus, segmentation or separa-tion of cell boundaries to detect individual cells is an active area ofresearch [15, 8, 14, 31]. Active contours method [30, 15, 8, 31] issuccessfully employed for cell analysis and usually produces robustboundaries even for noisy images. Zimmer et al. [31] uses an activecontour based cell segmentation approach to detect and track motilecells. They use an edge map computed from deviation between localintensities to detect low contrast boundaries. While active contours de-tects the cell structure by energy minimization subject to external andinternal constraints, our proposed approach uses different contours ofthe same image to classify a structure as a cell by analyzing the evolu-tion of boundaries detected by isocontour algorithm progressively.

In almost all applications, the nature of staining makes the nuclei ofcells more prominent compared to the outer cell boundaries. A goodcell segmentation algorithm has to correctly identify the separating re-gion between the adjacent cell nuclei. Using known cell nucleus, Joneset al. [14] used a non-Euclidean Voronoi diagrams on Riemannianmanifolds to detect cell boundaries and segment cells. The cell nucleusis not known in our applications, and hence the approach proposedin [14] is not applicable to our problem. We use an Euclidean-spaceDelaunay triangulation based approach to separate the detected axonboundary contours obtained from progressive isocontouring. Further-more, our method directly works on the geometry of the 2D cell struc-ture provided by the isocontouring algorithm, while [14] works onhigher dimensional space derived from the image parameters.

We introduce the concept of progressive isocontouring to detectall the cell structures followed by contour separation using Delaunaytriangulation. This allows us to detect event points when there is amorphological change in the shape of the isocontours which can sub-sequenly be used in the post processing stage to detect generic cellstructures.1 The detected cell structures, once identified as axons, areprocessed to identify the subset of OR-axons axons using robust geo-metrical and statistical methods.

3 CONTOUR DETECTION

Traditionally, axon detection algorithms use two techniques – shapedependent analysis and edge detection. Since the OR-axons can be ofany shape, typical shape matching algorithms cannot be used in ourapplications. Further, traditional edge detection methods also cannotbe used due to the presence of an abnormal number of debris in theimage, and the need for correct computation of relative size of thedetected boundaries in order to classify the axons.

The OR-axons sometimes can be classified by their lighter intensityvalues in the image slices. The intensity value at which these axonscan be detected can vary over the elapsed time since the remyelinationprocedure and also depends on the subjective manual staining processbefore the microscopic images are taken. Hence isocontouring at spe-cific intensity level will not be a feasible solution for this problem.

We present the progressive isocontouring technique – isocontour-ing at progressively increasing intensity levels – as a generic methodto detect possible axon structures. For this purpose, we first definethe axon structure in this context. Let us consider two simple closediso-contours at intensity i, I(i) and O(i). Let these two enclose regions

1Note that although the analysis of evolving topology and its events is alsothe basis of Morse theory [18], its application is limited in the context of med-ical image processing due to the complexity of the image content.

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O(i)

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T

AI(i)

AO(i)S(i)

S(i)=AO(i) - AI(i)

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O(i)O(j)

O(k)

O(i)

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i < j < k

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Fig. 4. (a) This illustrates the axon and sheath structures in the image.(b) This illustrates the redundant sheath structures in red. The bluesheath is the one detected at the lowest intensity and hence it is retainedas the non-redundant sheath structure.

Fig. 5. This figure shows all the invalid axons. Left: Invalid axons dueto self-intersecting boundary or intersecting inner and outer boundary;Middle: Invalid axon due to axon-within-axon structure; Right: Invalidaxon due to local discontinuity in sheath thickness.

AI(i) and AO(i) respectively such that AI(i)⊂ AO(i). Then AO(i) con-stitutes an axon and the region between the contours I(i) and O(i),given by AO(i)−AI(i), constitute the myelin sheath S(i). The thick-ness T (i) of S(i) is given by the average of the closest distance of allpoints in the inner boundary I(i) from the outer boundary O(i). Thisis illustrated in Figure 4.

We compute iso-contours progressively at different intensity levelsmoving from lower to higher intensities. A sheath S(i) detected at in-tensity level i signifies a valid structure if it obeys the rules describedbelow. These rules are framed based on our observations of the struc-ture of the axon and its surrounding myelin sheath in the images.

1. Boundary Coupling: There exists a one-to-one and onto relation-ship between the inner and outer boundaries of a sheath structureS(i). This maintains the invariance that every inner boundary hasa corresponding unique outer boundary and vice-versa.

2. Non-Redundant Sheath Structure: Since the myelin sheath is al-ways darker than both the interior and exterior of the axon, thethickness of the sheath detected at the intensity level i will be lessthan that of the sheath detected for the same axon at a higher in-tensity level. Let S(i) = AO(i)−AI(i) and S( j) = AO( j)−AI( j)be sheath structures at two different intensity levels i and j, i < j(Figure 4b). If AI( j)⊂ AI(i)⊂ AO(i)⊂ AO( j) then T (i) < T ( j).In this case both S(i) and S( j) represent the sheath structure ofthe same axon in the image, but are detected at different intensitylevels. The sheath S(i) with smaller thickness, T (i), is retainedand the sheath S( j) is rejected. Retaining the sheath structure atthe lowest intensity level allows us to have a standardized refer-ence to compare the sheath thickness across different axons inthe same image during subsequent classification. It also avoidsduplication in counting the number of axon structures. Hence wecall this sheath structure S(i) at the lowest intensity i as the non-redundant sheath structure. In our detection scheme, we wouldlike to identify each sheath structure in this non-redundant stage.

3. Valid Sheath Structure: To form a valid sheath structure, no axon

(a) (b) (c)

(d) (e) (f)

Fig. 6. Progressive Isoconturing: isocontours of the image at three dif-ferent intensity levels. The top row shows the isocontours at each in-tensity level, and the bottom row shows the identification of axon struc-tures (shown in blue). The isocontours (d) have multiple componentsand as intensity level increases progressively, complete axon structuresare formed (b), and valid axon structures get morphed and merged atstill higher intensity levels (c,f). When complete axon structures are de-tected at a particular intensity level, its geometry is preserved (d-f) andhence it is not affected by the subsequent morphing of the isocontours.

(a) (b) (c) (d)

Fig. 7. (a) Contour dilation process. (b-d)Problems with dilation basedaxon-separation. (b) The outer contour merges, even as the outer con-tour of one of the two sheaths has not been detected. (c) One of the in-ner contour that does not have a corresponding outer contour is dilatedto the minimum distance between itself and the merged outer contour.Note the thickness is much smaller than the reasonably correct shapegiven by the red contour. Such problems will skew the G-ratio of thisaxon, and hence its classification. (d) Our Delaunay based separationalgorithm computes the correct sheath shape.

structure AO(i) should be a subset of another axon structure de-tected at the same or a different intensity level ((Figure 5)). Thisensures that we do not detect an axon within another axon whichis a physical impossibility. Since S(i) ⊂ AO(i), this also assuresthat no sheath is contained within another sheath or another axon.Further, for valid sheath structures the inner and outer bound-aries, I(i) and O(i), should not be self-intersecting or intersectwith each other. Finally, the thickness T defined by the distancebetween I(i) and O(i) should be locally uniform across the entireboundary. Hence, the change in thickness, if existing, should besmooth.

We detect iso-contour using standard iso-contour algorithms. Acontour is a closed polyline connecting a sequence of vertices. Nextwe perform a contour within contour test to decipher the inner andouter boundary contours. A contour I is within another contour O ifall vertices of I are inside O. A vertex v is inside a closed contour O, ifa ray shot from v to an arbitrary point well outside the bounding box ofO intersects O at an odd number of times. Hence the vertex-inside-a-closed-contour test needs a line-polygon intersection test. If a contourI lies inside another contour O, we identify I to be a inner boundaryand O to be its corresponding outer boundary. We perform progressive

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Online Submission ID: 1096

(a) (b) (c) (d) (e)

Fig. 8. Contour separation algorithm: (a) The pink outer boundary encloses multiple blue inner boundary violating the boundary coupling criterion.(b) The Delaunay triangulation of the vertices on inner and outer boundary contours. (b) The edges of the triangulation that connect any innerboundary vertex to an outer boundary vertex are retained. (d) The edges incident on each inner boundary that are statistical outliers with respectto edge length are shortened to match the average edge length of these edges. (e) The closed loop of vertices thus formed by the farther ends ofthe edges incident on each boundary forms the corresponding outer boundary thus separating the merged outer boundary contour.

isocontouring without violating the redundant sheath structures crite-rion by retaining the structure that is detected the earliest, as shown inFigure 6 on an example. Note that there can be multiple inner bound-aries associated with a single outer boundary violating the boundarycoupling criterion. These are handled in the contour separation step,as explained in Section 4. Further, there can also be multiple outerboundaries associated with a single inner boundary violating the validsheath structure criterion. These are handled in the noise removal step,as explained in Section 5.

The isocontours at specific intensity levels show the regions of theaxon in different topologies: the axon boundaries might have multi-ple components (Figure 6a) or multiple axons might be merged into asingle axon boundary (Figure 6c). On the other hand an analysis ofthe change in topology of the axon boundaries over the isocontours ofsmoothly varying intensity levels provides a wealth of information foridentifying the sheath structures accurately. This is the key observationbehind the progressive isocontouring method. We compute the curveswith same brightness (isocontours) in the image repeatedly for pro-gressively increasing intensity values (Figure 6). When the topologyof the isocontour changes over subsequent higher intensity levels, weanalyze it to detect the formation of new sheath structures (two closedcurves one containing the other). These sheaths identified at a specificintensity level (blue curves in Figure 6d-f), would be enclosed by theisocontours in the subsequent intensity level images (red curves in Fig-ure 6). These containments are detected and only the blue isocontours(with smaller sheath thickness) are retained as a non-redundant sheathstructure.

4 CONTOUR SEPARATION

After the first step of the pipeline we get non-redundant sheaths, butthey may not satisfy the boundary coupling criterion. There can bedetected outer boundary contours that enclose multiple smaller innerboundary contours. This is due to the fact that any pathology beingimaged by the microsope, though very thin, still has a non-zero thick-ness. Each cell seen in the image will have a slightly different depththan other. Though their mobility is restricted, they can sometime oc-clude parts of other cells merging visible outer boundaries.

Figure 8a illustrates the typical scenario of merged contours wherethe outer boundary of multiple myelin sheath structures are merged.This step of our algorithm divides the outer boundary into requirednumber of closed curves to match with each enclosed inner boundaries(Figure 8d).

One simpler and obvious solution to separate the contours is by di-lating the inner contour along the normal direction by the minimumdistance to the outer contour enclosing it (Figure 7a). This methodeven though works reasonably well in many cases, is not robust and issusceptible to noise (cellular debris) in the image and hence can leadto several situations where the constraints defining the boundary cou-pling can be violated. Some of these cases are illustrated in Figure 7b-d. Sometimes it may even lead to a sheath structure detection withinaccurate thickness and hence inaccurate G-ratio value and eventual

misclassification of the OR-axons.To avoid all these problems, we propose a robust Delaunay triangu-

lation based contour separation algorithm. A triangulation is if thereis no point inside the circumcircle of a triangle. Hence, a point isalways connected to closest point in Delaunay triangulation. Beforedetailing the algorithm, let us consider a sheath whose inner and outerboundaries, I and O are detected and coupled correctly. Let us con-sider a Delaunay triangulation of the vertices in the two boundaries,i.e. I∪O. If we retain the edges from this triangulation which connectpoints that both belong to the inner or both belong to outer boundarycontour, we get a set of edges corresponding to the sheath S in whichall edges have lengths close to the thickness of the sheath. Further, wealso notice empirically that all vertices in the inner contour are con-nected to at least one outer contour vertex. We use these observationsto handle situations where there are multiple inner contours within asingle outer contour (Figure ??).

The contour separation method takes as input N, N > 1, inner con-tours, denoted by Ik, 1≤ k≤N a single outer contour O. The output isN closed outer contours, Ok, one corresponding to each inner contourIk. The basic observation is the fact that around each inner contourIk, the outer contour O is well formed except in areas of concavitiesin O (Figure 8a). For this we first perform a Delaunay triangulationof all the points in Ik, 1 ≤ k ≤ N, and O (Figure 8a). Next, we retainthe edges connecting the inner boundary vertices to the outer bound-ary vertices (Figure 8b). Note that the edges of Delaunay triangula-tion connects two outer boundary vertices in concavities of the outerboundaries, which are removed in this step.

In an ideal cell with coupled inner and outer boundary contours,the Delaunay edges incident on the inner boundary vertices are all ofsimilar lengths. So, we find the edges incident on each Ik that arestatistical outliers in terms of their length. These are usually the edgeswhich couple an inner boundary vertex to an incorrect vertex in theouter boundary or a different inner boundary. Hence, we shorten thelengths of these edges to be the average of the length of all the othernon-outlier edges incident on Ik (Figure 8c). The outer boundary Ok isnow formed by connecting the farther end points of the edges incidenton Ik in order (Figure 8d).

This Delaunay based contour separation method is extremely ro-bust. This algorithm is also provably correct as it retains only thoseDelaunay triangles whose circumcenter is close to the medial axis [3]formed by the coupled inner-outer contour pair points, thus establish-ing the one-to-one and onto correspondence between the inner andouter contours as prescribed by the boundary coupling criteria for thedefinition of a sheath structure. Further the lengths of the edges re-tained in this Delaunay triangulation provide a very good estimate ofsheath thickness which is later used in our G-ratio computation andclassification (Section 6).

5 NOISE REMOVAL

Following the contour separation step, we get non-redundant bound-ary coupled sheath structure, but we still have many invalid sheath

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structures detected due to cellular debris. In this step we identify suchcellular debris and remove them. The remaining sheath structures thenare both valid and non-redundant satisfying boundary coupling prop-erties.

Sheath structures that have self-intersecting boundaries and inter-secting inner and outer boundaries can be identified using simpleline-polygon intersection algorithms and removed. The invalidity dueto axon within axon (Figure 5)is detected using the same contourwithin contour test as used to differentiate inner boundaries from outerboundaries in Section 3. Note that axon-within-axon noise structuresare different from structures that require axon separation. The formerstructure has multiple axons (with both inner and outer contours) in-side another axon (again with both inner and outer contours), whilethe latter has multiple inner contours inside a single outer contour.

The last case of invalid sheath structure is one with locally non-uniform sheath thickness. This is detected using an algorithm similarto the one proposed for contour-separation. We find the Delaunay tri-angulation of the inner contour I and outer contour O and retain onlythe edges that connect inner boundary vertices to outer boundary ver-tices. If the function of the lengths of these edges in sequence is notderivative continuous then it indicates an invalid sheath (Figure ??).

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Fig. 9. K-means clustering algorithm for Axon Classification: The Y-axisshows the G-ratio of the axons. The X-axis is the intensity level at whichspecific axons were detected using the progressive isocontour process.The blue points represents the OR-axons (true positives), the magenta,red and black points represent the false positives, false negatives andtrue negatives respectively. The data is accumulated over many micro-scopic images spanning different staining intensities, and with differentnumbers of axons.

6 OLIGODENDROCYTE-REMYELINATED AXON CLASSIFICA-TION

The identification and classification of oligidendrocyte-remyelinatedaxons are done based on a parameter called G-ratio. The G-ratio is de-fined as the ratio of the sheath thickness to the axon diameter. To findthe sheath thickness, we perform the Delaunay triangulation of its in-ner and outer boundary vertices and retain only the edges that connectthe inner boundary vertices to the outer boundary vertices. The meanlength of these retained edges approximates the sheath thickness. Theaxon diameter is computed as the largest distance between any twopoints in the inner boundary I.

There are three kinds of myelinated axons: (a) normally myelinatedaxons are those that were not affected during the spinal cord injury,(b) the axons that were remyelinated by the Schwann cells and (c) theaxons that were remyelinated by the oligodendrocyte cells that wereinjected in the course of therapy. Our goal is to detect and count theOR-axons in order to monitor the progress of oligodendrocyte based

remyelination which is a critical step in estimating the efficacy ofthe therapy. Oligodendrocyte remyelinated axons are characterizedby lower G-ratios than the normally or Schwann remyelinated axons.Hence, to classify these therapeutically important axons we performk-means clustering of the G-ratios with number of clusters set to two.The axons corresponding to the cluster with lower G-ratio are the OR-axons.

Since, typically during manual counting, it is prohibitively tediousto measure G-ratios for all the detected sheaths, the conventionalway to identify an OR-axon is by the lighter intensity of its myelinsheath when compared to the darker, more compact, Schwann cell-remyelinated axons [25, 13]. Since we can accurately measure G-ratioautomatically, we use this for clustering the OR-axons. However, wemake an interesting observation from this classification. While it istrue that all cells with lighter intensity sheaths are OR-axons, the con-verse is not true – not all OR-axons have lighter intensity sheaths.Hence, intensity based manual classification is prone to errors. Fur-ther, the intensity levels at which the axons are detected change basedon the staining process before the microscopic images are taken. Thismakes intensity based manual classification subjective. Our automatedG-ratio based classification thus reduces classification errors signifi-cantly.

The results of this clustering method for several images are shownin Figure 9. In this figure we plot the G-ratio of the axons (Y-axis)against the intensity levels (X-axis) of the progressive isocontouringalgorithm at which the axon was detected. The image shows the plotof cells in over 15 images with variable staining intensity and differ-ent number of recognizable cells. Aggregated statistics from all theseimages are the following: all the cells recognized at an intensity levelabove 130 are oligodendrocyte remyelinated axons – so are all the cellswith G-ratio below 0.2. Further all the cells with G-ratio above 0.35are non-oligodendrocyte myelinated axons. The region of confusion isin the rectangular range of intensity less than 130 and the G-ratio be-tween 0.2 and 0.35. The blue points in the figure denote the OR-axonsand the black points mark all other cells. The false positives and falsenegatives are shown in magenta and red respectively. Further analysisof these results is given in Section 8.

7 DENSITY MAP GENERATION

To evaluate the effectiveness of the remyelination therapy it is impor-tant to identify the regions of the image where large clusters of highdensity OR-axons occur. The size and density of these clusters indi-cate the rate of progress and the location indicates the appropriatenessof the targeted cite of the therapy.

To facilitate this process we calculate a density map as follows: thecentroids of all the detected oligodendrocyte-remyelinated cells wereidentified, and for each pixel in the image, the average distance to its knearest centroids were calculated. Color coding of these values givesthe density image that visually represents the relative concentration ofthe detected cells. Lower values indicate higher concentration of OR-axons and vice versa. Hence, cooler colors (blue) indicate the citesof remyelination due to oligodendrocytes and warmer colors (yellowand red) indicates lack thereoff. Figures 1c and 10c shows the den-sity maps thus calculated from the input image in Figures 1a and 10arespectively.

8 RESULTS AND ANALYSIS

We used Sprague Dawley female adult rats with 200 KiloDyne forcespinal cord contusion injury. All tissues were fixed and processed asdescribed in [25]. The images of these tissues were used as input to oursystem. The implementation of the algorithm was prototyped usingMatlab and the images used had different intensities and cell shapesand scale also varied across images. The remyelination analysis thatwe automated were also carried on manually by experts prior to andwithout the knowledge of the results of the automated process. Theexperts were also consulted to review the results of the automated pro-cess.

Sample classification results with manual count and automaticcounts are demonstrated in Figure 11. The left column of Figure11

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Online Submission ID: 1096

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(a) (b) (c)

Fig. 10. Density of detected cells: Figures (a) shows the image with manual count of oligo cells shown in red markers, (b) shows the density imagecalculated using manual counts for corresponding images shown in a); (c) shows the density image using automated counts. Blue regions markareas having high density of oligo cells in all density images. The density image for manual and automatic count should be similar if the actual andthe manual counts closely match. Using image similarity measure SSIM [27], we show that the two sets density images are indeed very similar(mean mean SSIM =0.982).

denotes the greyscale images with manual counts marked with red andthe right column denotes the results from our automatic classificationwith the detected cells marked in cyan. In Figure 12, we also showother analysis of our automatic classification in one of the examples.False negatives are denoted by red and false positives by magenta.

Some of the sample results of the manual and automatic counts areshown in Figure 11 and Table 1. Although manual counting by expertssuffers from classification error due to the subjective nature of the task,all the statistics and analysis has been done assuming that the expertcounting for the first time (before seeing the results of the automatedprocess) is the ground truth (Column 1 of Table 1). The same imageswere then processed using our method and the automatic count of OR-axons were reported in Table 1. Correctly classified OR-axons wereconsidered to be true positives (denoted by blue in Figure 9), and thecells that are chosen by the system but not by the experts are falsepositive (denoted by magenta in Figure 9).

Actual Countof Axons

AutomatedCount ofAxons

Hit Rate Excess Rate

68 65 94.12 1.478 80 92.31 10.296 100 91.67 12.535 38 94.29 14.2825 30 96 24

Table 1. Empirical performance evaluation using domain expert’s countas ground truth: OR-axons detected by our algorithm closely matchesthe ground truth, demonstrated by the high hit rate.

Traditionally, the success of an automated method is defined by thehit rate given by

hit rate =Number of true positives

Manual count of OR axons. (1)

This is usually accompanied by a false alarm rate given by

false alarm rate =Number of false positives

Manual count of non-OR axons. (2)

However, since the non-OR axons are of no importance in the contextof remyelination, manual count for non-OR cells are not available forus to calculate false alarm rate. Hence, we define a new term calledexcess rate as

excess rate =Number of false positivesManual count of OR axons

. (3)

A high hit rate signifies effective classification of OR axons while alow excess rate signifies effective rejection of non-OR axons. Hence,the hit rate together with the excess rate provides an important indica-tor for the accuracy of the automated remyelination analysis. A highhit-rate (> 90%) accompanied by a low excess rate (< 25%) signifiesa successful automated analysis.

The false positives (shown in magenta in Figure 9) either have highintensity or have very low G-ratio values indicating that they are in-deed within the statistical range of correct OR-axons. Interestingly, onshowing the results of the automatic cell detection, the experts con-curred that over 95% of false positives (cells chosen by us but not theexperts) were actually true positives. These true positives were misseddue to several human factors like subjectivity and fatigue. This demon-strates the need for automated analysis and also validates a higher ac-curacy for our automated analysis by increasing the hit rates and re-ducing the excess rates.

On the other hand, the false negatives (shown in red) which deter-mines the miss ratio (i.e. 1-hit ratio),in Figure 9, is in the boundary oftrue positives (shown in blue) and true negatives (shown in black) andhence are difficult to automatically label them correctly using onlyG-ratio and intensity. Similar pattern is observed when consideringsingle images, as shown in Figure 12. Interestingly, classification ofthe false negatives was also subjective among human experts and themisclassification by the automated system is well within the varianceexperienced in human counting.

The most important validation of the success of the automated anal-ysis would be in comparing a density map generated from the clusterscreated by the automated process with the one that is created from theclusters marked by manual process since this is the visualization thatis ultimately used for detecting the growth and site of remyelination.Figure 10 shows an example of density images for both manual countand automatic count for two sets of images. The number of k near-est neighbors was fixed at 1/4th of the number of cells in the manualcount. Blue regions in the density image denotes areas having higherdensity of detected cells (Figures 10a and 10d).

In order to quantify the image similarity between the density im-ages from the manual and automated counts, we use a well establishedimage similarity measure, Structural SIMilarity (SSIM) index [27].SSIM is an objective method for assessing perceptual image qualityusing structural similarity between images. The mean SSIM indexvalue of 1.0 between two images denotes two identical images. For thetwo images shown in Figure 10, the mean SSIM index value betweenthe density images corresponding to manual and automated count is0.993 and 0.982 respectively. The mean SSIM index for all the imagesreported in Table 1 is 0.97(±0.02). Thus the method not only countsthe desired cells with high degree of accuracy, but also identifies, clas-

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(a) (b)

60 70 80 90 100 110 120 130 140 150 1600

0.1

0.2

0.3

0.4

0.5

0.6

Intensity

g−ra

tio

(c)

Fig. 12. False positives (in magenta) , false negatives (in red) and true positives (in cyan and blue) as determined by the comparison of theautomatically classified image (a) with one of the manual classification images (b). Plot (c) shows the k-mean classification of the cells. Note thatfalse negatives is in the boundary of true positives and true negatives and hence are difficult to automatically label them correctly using only G-ratioand intensity.

sifies, and labels individual axons with very high confidence.

9 CONCLUSION

We have presented an end-to-end process for accurate analysis and vi-sualization of the clusters of OR-axons critical to evaluate the progressof remyelination therapy. Our automated cell classification always cor-rectly identifies the region populated by the OR-axons, and closelymatches the manual classification. Furthermore, the automated iden-tification has a natural advantage of objectively classifying the ax-ons. This automated remyelination analysis and visualization has alsoinjected a lot of excitement among our neurobiologist collaborators.This project will relieve them of several weeks of pain-staking routine,repetitive, and mundane task that consumes several hours of trainedman power. By virtue of its accuracy in detection and classificationof axons, we hope this method will find widespread applicability thusreducing the turnaround time of the neurobiology research.

Though specific in application, there are several components of thealgorithm that are generic and can be applied in different types of med-ical image analysis and visualization. The progressive isocontouringalgorithm is a simple and generic image processing technique that candetect closed shapes in general stained microscopic images. In ad-dition, this method also detects event points when the shape topologychanges. Any application specific post-processing method can processjust these events to detect the required cells. Our Delaunay triangula-tion based geometric processing contour separation and noise removalmight evoke great interest in the newly developing bio-geometry com-munity.

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Online Submission ID: 1096

(a) (total: 263; manual: 128; automated: 139)

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(b) (total: 60; manual: 35; automated: 33)

#25

(c) (total: 95; manual: 25; automated: 30)

#9

(d) (total: 42; manual: 9; automated: 8)

Fig. 11. Classification results: Left: Stained Images showing manualclassification by domain experts; Right: Gray images showing classifi-cation using our automated method. The caption in each image denotethe total number of cells in the image, the number of OR-axons clas-sified manually and automatically respectively. Note that the domainexperts nor the automated algorithm were aware of each others classi-fication results.

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