p 0: lowest- DTS voxel on a detached spine p 1: closest point to surface of the dendritic model: m: maximum point on an attached spine within the bell-shaped domain shown in transparent red p m: projection of m onto line segment D max :: limit of the bell-shaped domain that encloses the spine stem. F) Schematic showing parameters of the spine stem reattachment routine. White line between yellow detached and red attached spines represents an approximate scale of 0.8 µm. Because the tip of the attached spine falls within the bell-shaped region, the algorithm merges these two clusters into a single spine. The voxels of the attached (red) and detached (yellow) spines are represented as cubes within a volume rendering of the dataset. E) Bell-shaped region (transparent red) used to detect the stem of a spine whose neck cannot be adequately resolved. Because of poor resolution of the spine neck, this thin spine is detected as two separate spines. D) Volumetric data showing an apparently detached spine head, and its spine stem attached to the dendrite. At the valley marked by the white arrow, the gradients reverse direction: red gradients point leftward, toward the center of mass of the red spine blue gradients point rightward, toward the center of mass of the blue spine. Vector heads are colored red or blue black tails point in direction of increasing intensity. C) Local 3D gradient vectors used to declump two merged spines. The merged spines have been properly detected as separate clusters indicated by differently colored voxels. B) Result of clustering algorithm using the cluster declumping routine described in the text. D) Schematic of cluster layer-building, showing exterior maximum (red cube at maximum point) floor of layer 6 (proximal end of purple layer) and depth of layer 6 (distance from exterior maximum to floor).Ĭluster Declumping and Spine Stem Reattachment.Ī) Volumetric data showing cluster of three spines that appear merged due to limited image resolution. Scale bar shown as red horizontal edge of lower left corner of AABB represents 0.45 µm. Hence, the layer immediately preceding this becomes the spine base (orange layer, orange arrow). The yellow layer is the first to exhibit a spread ratio exceeding SR (crit) (yellow arrow). C) In the last iteration, the diagonal of the bounding box exceeds the user-provided maximum spine width ( MSW), as the green layer floods into the dendrite (green arrow). B) Fourth iteration of the cluster-building algorithm produces the green layer, and correspondingly larger bounding box. White frame shows each corner of the layer's AABB. Individual voxels are rendered as wireframe cubes in successive layers of different colors, superimposed on a volume-rendered dendritic spine. The number of exterior maxima is usually much greater than the number of spines, since multiple maxima may occur on a single spine (white arrow), or along the surface of the dendrites (red arrow).Ĭluster-Building by Iterative Addition of Layers. D) Volume-rendered spiny dendrite with voxels representing exterior maxima drawn as red cubes (voxel size exaggerated to enhance visibility). The inset on the right illustrates bulk rejection of voxels in a single leaf (red shaded cube) that does not intersect the MSH zone (grey envelope surrounding model) created by a small dendritic section. Recursive subdivision of the 3D space results in increasingly smaller cubes surrounding the model. C) Octree calculated for the top fork of the dendritic section shown in (A). The dark grey envelope around the dendrite represents the MSH, measured from the surface of the 3D model, as indicated by the white dashed line. Spine candidate voxels V 1 and V 2 are shown with their corresponding distance to surface ( DTS) values (red arrows). A single capsule formed by a cylindrical dendritic segment capped by two hemispheres at consecutive nodes is outlined in blue. B) Close-up view of a spiny dendritic section, volume rendered in grayscale, with superimposed 3D model formed by sequential green frustra. Four corners of the axis-aligned bounding box (AABB) are shown, with the length of each axis segment representing 10 µm to depict the scale in 3D. Processing of Candidate Voxels for Spine Detection.Ī) Dendritic model rendered as green balls superimposed on volume-rendered data (light grey voxels), augmented by the maximum spine height ( MSH, dark grey envelope surrounding dendrites that contains all spine candidate voxels).
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