Abstract
There is an increasing need for shape statistics in medical imaging to provide quantitative measures to aid in diagnosis, prognosis and therapy planning. In view of this, we describe methods for computing such statistics by utilizing a well-posed framework for representing the shape of surfaces as currents. Given this representation we can compute an atlas as a mean representation of the population and the main modes of variation around this mean. The modes are computed using principal component analysis (PCA) and applying standard correlation analysis to these allows to correlate shape features with clinical indices. Beyond this, we can compute a generative model of growth using partial least squares regression (PLS) and canonical correlation analysis (CCA). In this chapter, we investigate a clinical application of these statistical techniques on the shape of the heart for patients with repaired Tetralogy of Fallot (rToF), a severe congenital heard defect that requires surgical repair early in infancy. We relate the shape to the severity of the pathology and we build a bi-ventricular growth model of the rToF heart from cross-sectional data which gives insights about the evolution of the disease. Relation between this chapter and our class: This chapter is describing an extension of the mathematical techniques that are described in the course “computational anatomy and physiology” for the analysis of the shape of anatomical organs. It is showing how the analysis of organ deformation across patients can be used to model the impact of remodeling with the hope to get more insight on the pathophysiology.
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Notes
- 1.
In this paper, atlas is always taken in the sense of template and not in the sense of the atlas of differential geometry.
- 2.
We use the term “geodesic shooting” to define the integration of the Euler-Lagrange equations, which plays the role of the exponential map in Riemannian geometry.
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Acknowledgements
The computational tools used in this chapter were originally developed within the context of the European FP6 project Health-e-Child (http://www.health-e-child.org/). The software was made available to the community in collaboration with the EU network of Excellence Virtual Physiological Human (http://www.vph-noe.eu/). The extension to the analysis of the bi-ventricular shape of the heart in rToF was performed in the context of the European ITEA2 Care4Me project (www.care4me.eu/).
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McLeod, K., Mansi, T., Sermesant, M., Pongiglione, G., Pennec, X. (2013). Statistical Shape Analysis of Surfaces in Medical Images Applied to the Tetralogy of Fallot Heart. In: Cazals, F., Kornprobst, P. (eds) Modeling in Computational Biology and Biomedicine. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31208-3_5
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