LMap: Shape-Preserving Local Mappings for Biomedical Visualization

Adaptive area-preserving parameterization of open and closed anatomical surfaces

The parameterization of open and closed anatomical surfaces is of fundamental importance in many biomedical applications. Spherical harmonics, a set of basis functions defined on the unit sphere, are widely used for anatomical shape description. However, establishing a one-to-one correspondence between the object surface and the entire unit sphere may induce a large geometric distortion in case the shape of the surface is too different from a perfect sphere. In this work, we propose adaptive area-preserving parameterization methods for simply-connected open and closed surfaces with the target of the parameterization being a spherical cap. Our methods optimize the shape of the parameter domain along with the mapping from the object surface to the parameter domain. The object surface will be globally mapped to an optimal spherical cap region of the unit sphere in an area-preserving manner while also exhibiting low conformal distortion. We further develop a set of spherical harmonics-like basis functions defined over the adaptive spherical cap domain, which we call the adaptive harmonics. Experimental results show that the proposed parameterization methods outperform the existing methods for both open and closed anatomical surfaces in terms of area and angle distortion. Surface description of the object surfaces can be effectively achieved using a novel combination of the adaptive parameterization and the adaptive harmonics. Our work provides a novel way of mapping anatomical surfaces with improved accuracy and greater flexibility. More broadly, the idea of using an adaptive parameter domain allows easy handling of a wide range of biomedical shapes.

LDeform: Longitudinal deformation analysis for adaptive radiotherapy of lung cancer

PURPOSE

Conventional radiotherapy for large lung tumors is given over several weeks, during which the tumor typically regresses in a highly nonuniform and variable manner. Adaptive radiotherapy would ideally follow these shape changes, but we need an accurate method to extrapolate tumor shape changes. We propose a computationally efficient algorithm to quantitate tumor surface shape changes that makes minimal assumptions, identifies fixed points, and can be used to predict future tumor geometrical response.

METHODS

A novel combination of nonrigid iterative closest point (ICP) and local shape-preserving map algorithms, LDeform, is developed to enable visualization, prediction, and categorization of both diffeomorphic and nondiffeomorphic tumor deformations during an extended course of radiotherapy.

RESULTS

We tested and validated our technique on 31 longitudinal CT/MRI subjects, with five to nine time points each. Based on this tumor deformation analysis, regions of local growth, shrinkage, and anchoring are identified and tracked across multiple time points. This categorization in turn represents a rational biomarker of local response. Results demonstrate useful predictive power, with an averaged Dice coefficient and surface mean-squared error of 0.85 and 2.8 mm, respectively, over all images.

CONCLUSIONS

We conclude that the LDeform algorithm can facilitate the adaptive decision-making process during lung cancer radiotherapy.