General methodology for quantifying collagen alignment and the structural organization of the tissue.

<p>First row: one optical slice of a 3D second harmonic generation multiphoton confocal image (Scale bar 20m). Corresponding confocal images of the cell nuclei were segmented using the Otsu Thresholding algorithm. Connected pixels were found in this segmented image and each connected component was labeled as an individual cell nuclei. Using these segmented confocal images of nuclei, we reconstructed and visualized the tissue on top of the collagen in 3D (Second row). For each nucleus, the center of mass was found and assigned as the x,y,z coordinates of that nucleus. Using the nuclei locations, cell-graphs that capture the spatial relationship between the nuclei were constructed and visualized (Third row). The collagen alignment around every edge of the graph was quantified and the Collagen Alignment Index that measures the quality of the alignment is assigned to each edge. Cell-graph edges that have an alignment greater than a given threshold (in this case 0.6) were drawn thicker to highlight areas of enhanced remodeling in 3D (Fourth row).</p

Edge-based and Node-based Voronoi partitioning.

<p>Two different Voronoi construction techniques were used in this work, done both from a cell-graph node perspective and from a cell-graph edge perspective. In <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0012783#pone-0012783-g003" target="_blank">Figure 3(a)</a>, a sample Voronoi diagram using the cell coordinates as the seed points is shown where blue (node with edges) and red (node without edges) circles are the cell nodes. Blue lines correspond to cell graph edges while dashed red lines correspond to the Voronoi compartments. In this original state of the Voronoi diagram, each cell-graph edge was shared by two separate Voronoi compartments. In <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0012783#pone-0012783-g003" target="_blank">Figure 3(b)</a>, to capture the information between cells the method was altered to set the center of the edges as the seed points. This construction ensures that each cell-graph edge is encapsulated in only one Voronoi compartment. To capture the information between cells the method was altered to set the center of the edge as the seed point. This construction ensures that each cell-graph edge is encapsulated in only one Voronoi compartment. These compartments were projected onto the corresponding SHG image to assign each pixel of type I collagen signal to a given graph node (A) or edge (B).</p

Outline of the algorithm to compute Collagen Alignment Index (CAI).

<p>After segmenting the nuclei, cell-graph are built capturing the spatial distribution. Voronoi diagrams are built and the gradient vectors in each Voronoi compartment are calculated. A distribution of the angles between the cell-graph edges and the gradient vectors is calculated to find the CAI metric.</p

Clustering of treated and untreated samples.

<p>Singular value decomposition (SVD) and k-means statistical tests demonstrated that MSC in type I collagen gels progress through three stages during early compaction events I, II and III.</p

This schematic describes a conceptual model for MSC mediated collagen alignment during early phases of hydrogel compaction in 3D culture developed from results presented here.

<p>MSC interact and engage their type I collagen microenvironment to organize it over time. This process occurs via three distinct and phases, I, II and III. Untreated gels progress through these phases as cells first begin to interact with their surrounding collagen independently and then engage with cells in their immediate environment to cooperatively pull, and align the collagen matrix. They peak here at Collagen Alignment Index CAI approaching to 1. As the cells continue to interact they loose this directionality and begin to cooperate in more complex ways with cells surrounding them resulting in a reentry into early clusters of collagen organization (IIb and Ib). Intermediate phases can be indicative of different interactions as depicted above. When induced to differentiate through treatment with the MEK inhibitor PD98059 (treated), MSC accelerate through these early phases of remodeling to efficiently direct their cooperativity and slowly reorganize. Plots are indicative of the cooperativity metric Collagen Alignment Index, solid line (untreated) and dashed line (treated). Inset images represent second harmonic generation images of the type I collagen matrix indicative of each stage of remodeling and schematics are given to represent the hypothesized cooperation occurring between cells.</p

Quantification of MSC cooperativity during type I collagen fibrillogenesis.

<p>The distribution of the angles between the gradient vectors and cell-graph edges are plotted for untreated and treated (shown as PD) samples at each time point imaged. Histograms plot the frequency of each angle found within the corresponding set of images weighted according to the gradient magnitudes. The area under the curve between 60 and 120 degrees (red shaded area) is assigned as the Collagen Alignment Index for that sample and shown in the middle of the curve. This metric attains its maximum value at day 2 in the untreated tissue sample whereas in the treated tissue samples this value takes its maximum value as early as hour 12. Using these distributions, the samples were clustered into three groups by k-means algorithm. The first and the last tissue samples of both the untreated and treated tissues grouped in one cluster, day 2 of untreated and hour 12 of treated example were grouped in the second cluster and all the other samples clustered as a third. This analysis was performed on distinct biological samples, n = 3.</p

Gradient vector analysis for quantification of type I collagen structure.

<p>Given a segmented image and voronoi construction we can quantify type I collagen alignment with respect to either the graph edge or node. Two cells, A, B are depicted in 3D space. The coordinates of these cells are given as , . The cell-graph edge was therefore represented as the vector . The red line gives the boundaries of the edge-based Voronoi diagram. For each pixel in this compartment the gradient vector that measures the direction of the maximum intensity change is calculated and the angle between the gradient vector and the cell-graph edge was calculated. Using the distribution of these angles, or the sum of all the gradient vectors we assessed direction and magnitude of collagen organization in 3D space.</p

MSC in treated type I collagen gels exhibit accelerated satisfaction.

<p>Node-based Voronoi diagrams were constructed as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0012783#pone-0012783-g003" target="_blank">Figure 3(a)</a> and gradient vectors calculated for each pixel within the compartment. Using node-based voronoi construction, collagen alignment around an individual cell was captured. The gradient vectors were summed and assigned as the net force to the nucleus in the respective Voronoi compartment. To find the magnitude of these individual forces, the net gradient vector was projected onto the cell-graph edges using the minimum norm projection method. The magnitudes of these projections on each cell-graph edge were assigned as the weight of that edge. Using these weights the overall tissue structure and collagen formation in the tissue were represented by a weighted graph, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0012783#pone-0012783-g002" target="_blank">Figure 2</a>. The weights of each edge are summed and the resulting sum is the Global Dissatisfaction Level (GDL) of the sample, normalized to image size. The global dissatisfaction of the treated samples decreases more rapidly when compared to untreated controls.</p