The use of a spatial distribution model in labeling sulci

While accurate sulcal identification can be a challenge even for expert neuroanatomists, there are sulci that are to some degree more consistent, and for which anatomical correspondence can be established across subjects. These are the larger primary sulci. The localization of these sulci allows us to generate a spatial distribution or probabilistic map which can be used to label candidate sulci. A graph that maps the structural relationships between sulci can also be constructed and unlabeled sulci (or the more variable secondary and tertiary sulci) can be identified against this reference.

These two ideas, the use of the probabilistic atlas and the graph, have been incorporated into automated and semi-automated labeling methods in various ways. In this post I will present the basic idea behind the use of the spatial distribution model.

The use of a probabilistic atlas
Probabilistic maps compute the probability for each tissue class at every voxel location using a large database of segmented and labeled anatomical structures. Evans et al. [3] coined the name Statistical Probabilistic Anatomical Maps or SPAM for these models. Paul Thompson has a nice description of these SPAM models and the Brainvisa website has a nice visualization of a sulcal atlas which is reproduced below:

A straightforward implementation of the probabilistic atlas paradigm can be seen in Le Goualher et al. [1] [2]. SPAM models give the probability for each sulcal class so that at any given location, unlabeled sulci are assigned the most probable label for that location. In other words, to label a new sulcus :

Let:           be a sulcal label

Compute:     where p is the probability from a SPAM atlas
Assign:      


The use of a point distribution model
A different spatial distribution model is used by Lohmann et al. [4]. A point distribution model introduced by Cootes et al. [5] computes the shape of sulcal basins across a training set. Any unlabeled sulcus can be expressed as a linear combination of the eigenvalues generated from the PCA of this shape covariance matrix; an optimization over the linear function gives the best label.

Spatial distribution models give spatial bounds but this is not adequate to discriminate between the sulci in a local region. They are usually combined with graphs which model connections between sulci thus giving local structural context. In the combined strategy, the spatial information is used to supply spatial priors [6], localization constraints or to narrow the search space in an optimization or graph matching process [7].

I will write about the use of graph models in my next post.

References
1) Georges Le Goualher, D. Louis Collins and Christian Barillot, Alan C. Evans, "Automatic Identification of Cortical Sulci Using a 3D Probabilistic Atlas," In MICCAI, 1998, pp. 509-518.
2) Georges Le Goualher, E. Procyk, D.L. Collins, R. Venugopal, Christian Barillot, "Automated Extraction and Variability Analysis of Sulcal Neuroanatomy," IEEE Trans. Med. Imag., 18(3), 1999, pp. 206-217.
3) A. C. Evans, D. L. Collins, P. Neelin, M. Kamber, S. Marrett, "Three-dimensional correlative imaging: Applications in human brain mapping," Advances in Functional NeuroImaging: Technical Foundations,(ed. R. Thatcher and M. Hallett and T. Zeffiro and E. John and M. Huerta) Academic Press, 1994, pp. 145-162.
4) Gabrielle Lohmann and Y. von Cramon, "Automatic labeling of the human cortical surface using sulcal basins," IEEE Trans. Med. Imag., 4, 2000, pp. 179-188.

5) Timothy F. Cootes, Christopher J. Taylor, David H. Cooper, Jim Graham, "Active Shape Models-Their Training and Application," Computer Vision and Image Understanding, 61(1), 1995, pp. 38-59.
6) M. Perrot, D. Rivière, J.-F. Mangin, "Identifying cortical sulci from localizations, shape and local organization," ISBI, 2008, pp. 420-423.
7) Yang, F & Kruggel, F., "A graph matching approach for labeling brain sulci using location, orientation, and shape," Neurocomputing, 2009, pp. 179-190.

Posts on Sulcal Labeling
1) Why we label sulci
2) Why is sulcal labeling difficult ?
3) The use of a spatial distribution model in labeling sulci

Why is sulcal labeling difficult?

This is a follow-up to an earlier post Why we label sulci. There will be two or three more posts; taken altogether, they will describe the sulcal labeling problem.

The labeling of sulci is a challenging problem. This is because, cortical sulci are highly variable. Sulci vary not just across individuals but even between the hemispheres of a single brain [1]. It might be useful when looking for ways to address this variability to classify this variation as follows:

Variation in physical features
Sulci vary in shape, in scale and in their placement (i.e. position and orientation) The figure below illustrates how the variability can make feature selection difficult.

The boxplot shows the length distribution for 18 subjects. The 10 types or classes of sulci shown cannot be identified solely on a length measurement. This poses a problem for feature selection and classification.
Figure credit: Meena Mani




Variation in branching
19th century illustrations such as those from Horsley [2], trace the wide variations along a sulcal fold. A whole nomenclature has developed since then to account for the branch variations possible along a single sulcus. (An example from the Ono atlas is illustrative--see figure below). For this reason, there is no gold standard in sulcal labeling; one neuroanatomist may disagree with another.

The figure to the left shows the pattern variations for a single sulcus (the posterior end of the superior frontal sulcus). Types A, B, C, D, are possible variations for this sulcus (for the 25 postmortem brains examined, 4 variations were found). The pattern in the two hemispheres of a single subject may differ; the left may be Type B and the right may be Type C. The lengths of the small segments and the connections they make to other sulci may also vary. Reproduced from Ono et al. [1].

Variation in number
Sulci may be continuous (present as one uninterrupted segment) in some individuals, fragmented (exist as multiple segments) in others and altogether absent in yet others. The larger primary sulci which start forming early in fetal development are the most consistent; the secondary and tertiary sulci are not always expressed.

References
1) Ono, M., Kubic, S. & Abernathy, C. (1892) "Atlas of the Cerebral Sulci", (Thieme, New York).
2) Horsley, V. (1892) "On the topographical relations of the cranium and surface of the cerebrum", In "Contribution to the surface anatomy of the cerebral hemispheres", pp.306-355, (Royal Irish Academy).


Posts on Sulcal Labeling
1) Why we label sulci
2) Why is sulcal labeling difficult ?
3) The use of a spatial distribution model in labeling sulci

Medical visualization frontier application

The goal of medical imaging is to present the data in a useful format and in a very interesting TEDx talk Anders Ynnerman demonstrates cool new applications in medical visualization that will be possible in the near future.

Graphics processors have become substantially faster in the last ten years. We can now put together** the gigabytes (terabytes if extended to the time domain) of MRI and CT data generated when scanning a single subject and create 3D (or 4D) images from which relevant information can be selectively extracted. This opens up new and very interesting possibilities. One such application is the virtual autopsy where with ipad-style interactions one can look at cadavers in hard-to-maneuver angles or selectively view metal to, for instance, identify the extent of knife stab injuries or locate bullet shards. Ynnerman also suggests touch-sensitive haptic applications: a surgeon can literally touch the data--a beating heart for example--pre-surgery.

It's really a great 17 minute talk--here's the link.

**(Aside from fast GPUs, there are other ways in which people are hoping to handle the explosion of data from these medical scans. The use of oompressive sensing algorithms is one but the more general idea is to reduce the data before, during or after the scan.)