Cardiac Fiber Extraction & Tracing

Project Summary

Orientation extraction and tracing of tubular structures in medical images are important quantitative tools for
developing models of the heart both at the histological and cytological levels. For instance, the configuration
of the myocardial fibers and the Purkinje network are crucial for modeling the mechanical and electrical properties
of the heart and understanding structural changes with myocardial infarction or arrhythmias. Likewise, the cytological
mechanical properties are related to the spatial orientation of the cytoskeletal filaments. In addition, detection
and enhancement of human vasculature is important for giving insight before interventional procedures.

The problems of detecting orientation and tracing tubular structures are closely related to a primal problem in image processing and computer vision: edge detection. Existing approaches to solve those problems are based on the image Hessian H(x) or the structure tensor S(x) at the point of interest x. Consider a grayscale image I:&upsih &rarr &real, &upsih being the image domain. While H(x) possesses 2^{nd} order derivative information, i.e. H(x) = [I_{xx} I_{xy}; I_{yx}
I_{yy}], the structure tensor S(x) has 1^{st} order derivative information, S(x) = [I_{x}^{2}
I_{x}I_{y}; I_{y}I_{x} I_{y}^{2}].
The eigendecomposition of the matrix H (or S) gives the orientation information: the eigenvector associated with the leading
eigenvalue is in the direction of the maximum gradient (perpendicular to the structure) and the remaining eigenvector shows the
tangential direction (along the structure). However, in case of intersections or bifurcations, it has the drawback of
"averaging" the orientation information built in the true structure. In our problem we have to deal with not only the image noise
but also the complexity such as intersection of fibers and bifurcation of the structure, which make the aforementioned approaches
useless.

In this project, we consider the problem of extracting spatial orientation and tracing 2-D and 3-D tubular structures in medical images.The problems we try to solve are:

The problems of detecting orientation and tracing tubular structures are closely related to a primal problem in image processing and computer vision: edge detection. Existing approaches to solve those problems are based on the image Hessian H(x) or the structure tensor S(x) at the point of interest x. Consider a grayscale image I:&upsih &rarr &real, &upsih being the image domain. While H(x) possesses 2

In this project, we consider the problem of extracting spatial orientation and tracing 2-D and 3-D tubular structures in medical images.The problems we try to solve are:

- Local orientation extraction in myofiber arrays.
- Tracing tubular structures such as fibers, vessels, Purkinje network, etc. in medical images.

Local Orientation Extraction

In [1], we propose a nonlinear template to extract the local orientation at a point of interest using both a directional
and an appearance profile. The directional profile is extracted by computing several intensity differences dictated by
the template, whereas the appearance profile is formed by examining the intensity coherence along the template. The local
orientation of the structure is then detected by locating the mode of the combined profiles. Figure 1 shows the preliminary
results of our algorithm.

Figure 1: (a) Template response on a synthetic 2-D image with a bifurcating fiber. Extraction of local
orientation in (b) microtubules, and (c) cardiac myofibers.

Tracing Tubular Structures

The same nonlinear template can be used to track tubular structures. In [1], we present an interactive tracing algorithm
that locates points on a tubular structure by maximizing a cost function. More specifically, starting from a
user-specified seed point, we find the next point in the curve by maximizing a cost function that favors both
smoothness of the curve as well as alignment with the locally estimated orientation. Figure 2 shows the preliminary
results of our tracing algorithm.

Figure 2: Preliminary results on fiber tracing in 3-D Purkinje network.

Publications

[1]

Nonlinear Filtering for Extracting Orientation and Tracing Tubular Structures in 2-D Medical Images.

IEEE International Symposium on Biomedical Imaging (ISBI'08), Paris, France, May 2008.