A coordinate system describing the interior of organs is a powerful tool for a systematic localization of injured tissue. If the same coordinate values are assigned to specific anatomical landmarks, the coordinate system allows integration of data across different medical image modalities. Harmonic mappings have been used to produce parametric coordinate systems over the surface of anatomical shapes, given their flexibility to set values at specific locations through boundary conditions. However, most of the existing implementations in medical imaging restrict to either anatomical surfaces, or the depth coordinate with boundary conditions is given at sites of limited geometric diversity. In this paper we present a method for anatomical volumetric parameterization that extends current harmonic parameterizations to the interior anatomy using information provided by the volume medial surface. We have applied the methodology to define a common reference system for the liver shape and functional anatomy. This reference system sets a solid base for creating anatomical models of the patient's liver, and allows comparing livers from several patients in a common framework of reference.
Distortion of Left Ventricle (LV) external anatomy is related to some dysfunctions, such as hypertrophy. The
architecture of myocardial fibers determines LV electromechanical activation patterns as well as mechanics. Thus,
their joined modelling would allow the design of specific interventions (such as peacemaker implantation and LV
remodelling) and therapies (such as resynchronization).
On one hand, accurate modelling of external anatomy requires either a dense sampling or a continuous infinite
dimensional approach, which requires non-Euclidean statistics. On the other hand, computation of fiber models
requires statistics on Riemannian spaces. Most approaches compute separate statistical models for external
anatomy and fibers architecture.
In this work we propose a general mathematical framework based on differential geometry concepts for
computing a statistical model including, both, external and fiber anatomy. Our framework provides a continuous
approach to external anatomy supporting standard statistics. We also provide a straightforward formula for the
computation of the Riemannian fiber statistics. We have applied our methodology to the computation of complete
anatomical atlas of canine hearts from diffusion tensor studies. The orientation of fibers over the average external
geometry agrees with the segmental description of orientations reported in the literature.