Research: Medial Axis Extraction

Obtaining the medial axis of a cell (and associated diameters) produces a model which can be imported into morphometric software and compartment modeling programs such as NEURON and GENESIS.

Quantization errors arise in standard skeletonization algorithms from the integer nature of digital images. Iterative thinning skeletonization methods can provide a distance in voxels from each tree node to the surface of the object. This distance is the D⁶ metric, obtained by counting the number of voxels as they are removed in the minimal 6-connected path from the surface to the medial axis. In existing skeletonization or vectorization algorithms for dendriticvmorphometry, the branch cross-section at any node is approximated as circular, with the D⁶ metric providing the single diameter estimate. The precision of this diameter estimate is limited to the physical size of the voxels. For small structures such as thin dendrites and spines, comprising only a few voxels even at maximal imaging resolution, the error can be significant if this measure is used directly.

Medial Axis Extraction by NeuronStudio

Figure 1: The workflow for NeuronStudio. The acquired data is fed into the program which consists of 3 main phases: image processing, model creation, and spine detection and analysis. Thses phases can be done in cyclical fashion until the desired accuracy is acheived.

We have a developed an application named NeuronStudio that can obtain the medial axis from images generated by laser scanning (CLSM) or multi-photon microscopy without using skeletonization. Using custom built algorithms, the model can be iteratively built and refined to the desired level of detail using a point and click interface. The user simply defines a seed location from which the automated tracing begins. The medial axis is generated in real-time until a resolution or intensity level in the object structure is reached which cannot be traced.

In addition to the automated medial axis extraction features, a powerful manual and semi-manual extraction system is built into the program. Using point and click tools, sections of a model can be created from scratch, or spliced into any existing model.

A full range of editing operations is also available which allow for manual corrections to the extracted model including translation, rotation, and deletion.

Section Labeling

Figure 2: Closeup view of the section labeling procedure. The branch points (or soma) delimit the start of the sections.

Figure 3: Complete section labeling of a cell.

A section of a model can be defined as an unbranching set of medial axis points. Using NeuronStudio these can be color coded for easy visualization. In addition, these sections are given an integer index value that is used in the output of detected spines so that statistics such as spine density, etc., can be more easily calculated.

These sections also correspond to the definition of a section in compartmental modeling packages such as NEURON, and associated HOC files. The model can be exported into this format using NeuronStudio. In the outputted file a an array of sections is created, connected, and filled with 3D points. Figure 2 shows the color-coded sections of some dendrites of a model. Note how each unbranching section is labeled in a different color.

Branch Order Labeling

Figure 4: Closeup view of the centripetal labeling scheme. Highest orders are near the soma. Order increases when 2 or more branches of the same order intersect at a branching point.	Figure 5: Complete centripetal labeling of a cell.
Figure 6: Closeup view of the centrifugal labeling scheme. Lowest orders near the soma. Order increases by 1 at each branchpoint.	Figure 7: Complete centrifugal labeling of a cell.

In addition to labeling sections, NeuronStudio also provides the ability to classify the medial axis into branch orders. Orders are similar to sections in that they represent an (unbranching) sequence of points, but our definition allows it to cross through a junction point.

The first is a centripetal labeling scheme where the lowest order is at the tips of the dendritic structure, with order increasing inwards towards the soma. In the figures it can be seen that the order is increased only when 2 (or more) child branches with the same order intersect at a junction point.

The second is a centfrifugal labeling scheme where the lowest order is at the branches starting at the soma, with order increasing outwards. Whenever a branching point is encountered, the order is increased.