Research: Applications of Rayburst

The Rayburst Algorithm is a generic shape analysis algorithm, implemented within the CNIC lab as a C software library, and freely available for download.

Volume, Surface-Area, and Local Diameters

Accurate estimation of diameters, volumes and surface areas of complex 3D structures imaged with LSM requires versatile and efficient techniques. Such morphological parameters are of general interest in many domains of biology and in the study of pathological states. These analyses depend on the ability to digitize complex biological structures in 3D with sufficient accuracy and automation for objective and reliable statistics.

The Rayburst sampling algorithm is one such technique that can be used to compute local diameters, surface areas and volumes of 3D structures, with specific applications to neuronal dendritic branches, spine morphometry and spatially complex histopathologic lesions.

Figure 1: Dendritic branch diameter estimation by 2D Rayburst, irrespective of orientation of a branch. The rays cast from the sampling core are shown in gold with the one chosen as the diameter shown in blue. The subvoxel accuracy of the threshold is overlaid as a green line intersecting the ends of the rays.

Analysis of Tubes Using 2D Rayburst

Neurons are composed of axonal and dendritic trees, whose basic element is a tubular branch section. Standard software packages for neuronal morphometry represent neuronal branches as generalized cylinders, that is, as a chain of nodes with a diameter specified at each node. To represent the 3D shape, the diameter at each node must be estimated.

In earlier implementations, we used the 3D Rayburst core to estimate node diameters. For data acquired by LSM, the point spread function of the microscope can distort the apparent thickness of branches significantly along the direction of the optic axis. In such cases, and whenever radial measures are presumed approximately symmetric in the X, Y, and Z directions, a 2D Rayburst in the XY plane at each node is insensitive to residual Z axis smear, yielding a reliable estimate of branch diameter regardless of the orientation of the branch within the image stack.

Analysis of Complex Volumetric Shapes Using 3D Rayburst

An example of application of the 3D Rayburst core is estimation of the volume and surface area of a star-convex globular structure such as a dendritic spine or a more complex structure such as an amyloid plaque in a mouse model of Alzheimer disease, or other pathological processes such as tumors or vascular abnormalities.

Figure 2: The figure above shows the estimation of volume and surface area of a dendritic spine using Rayburst (top row), as well as additional applications of the algorithm including dendritic diameters (middle row), and surface area and volume calculations of complex shapes such as plaques (bottom row).

Before casting the rays, the sampling core can be visualized as a geosphere of unit radius. As the vectors are cast through the voxels of the object, the geosphere is conceptually stretched and fitted to match the true exterior manifold of the structure. Each triangle on the geodesic sphere can be considered to be the base of a three-sided pyramid with the apex at the origin of the sampling core. The total volume of the structure can be computed as the sum of the volumes of these pyramids. Similarly, the surface area is computed as the sum of the areas of the bases.

Adaptive Selection of Number of Rays

In applications of either 2D or 3D Rayburst, the optimum number of rays may be automatically selected at run time to achieve a specified accuracy or critical tolerance. For 2D Rayburst, this tolerance refers to the relative change with successive iterations in the cross-sectional area of cylindrical sections. For 3D Rayburst, the tolerance refers to the relative change in computed volume with successive mesh refinements. Rather than compute volume or cross-sectional area at each successive iteration, we have devised a test for detecting convergence to the optimal number of rays, based on midpoint displacement. When the estimated tolerance computed from the data is less than the predetermined critical tolerance, we can assume that the number of rays is optimal for the specified accuracy level. As each iteration shares a proportion of its rays with the previous iteration, these earlier rays need not be recast, resulting in a measurable speedup of the adaptive procedure.

Future Applications

Other potential applications of the Rayburst technique include different imaging modalities such as serial section electron microscopy, widefield imaging, live two-photon images or magnetic resonance angiography. The only constraint on potential applications is that the images can be adequately segmented.