Capturing the Multiscale Anatomical Shape Variability with Polyaffine Transformation Trees

International audienceMandible fractures are classified depending on their location. In clinical practice, locations are grouped into regions at different scales according to anatomical, functional and esthetic considerations. Implant design aims at defining the optimal implant for each patient. Emerging population-based techniques analyze the anatomical variability across a population and perform statistical analysis to identify an optimal set of implants. Current efforts are focused on finding clusters of patients with similar characteristics and designing one implant for each cluster. Ideally, the description of anatomical variability is directly connected to the clinical regions. This connection is what we present here, by introducing a new registration method that builds upon a tree of locally affine transformations that describes variability at different scales. We assess the accuracy of our method on 146 CT images of femurs. Two medical experts provide the ground truth by manually measuring six landmarks. We illustrate the clinical importance of our method by clustering 43 CT images of mandibles for implant design. The presented method does not require any application-specific input, which makes it attractive for the analysis of other multiscale anatomical structures. At the core of our new method lays the introduction of a new basis for stationary velocity fields. This basis has very close links to anatomical substructures. In the future, this method has the potential to discover the hidden and possibly sparse structure of the anatomy

Improving Understanding of Long-Term Cardiac Functional Remodelling via Cross-Sectional Analysis of Polyaffine Motion Parameters

International audienceChanges in cardiac motion dynamics occur as a direct result of alterations in structure, hemodynamics, and electrical activation. Abnormal ventricular motion compromises long-term sustainability of heart function. While motion abnormalities are reasonably well documented and have been identified for many conditions, the remodelling process that occurs as a condition progresses is not well understood. Thanks to the recent development of a method to quantify full ventricular motion (as opposed to 1D abstractions of the motion) with few comparable parameters, population-based statistical analysis is possible. A method for describing functional remodelling is proposed by performing statistical cross-sectional analysis of spatio-temporally aligned subject-specific polyaffine motion parameters. The proposed method is applied to pathological and control datasets to compare functional remodelling occurring as a process of disease as opposed to a process of ageing

Statistical analysis of organs' shapes and deformations: the Riemannian and the affine settings in computational anatomy

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and medicine that aims at analyzing and modeling the biological variability of organs' shapes at the population level. Shapes are equivalence classes of images, surfaces or deformations of a template under rigid body (or more general) transformations. Thus, they belong to non-linear manifolds. In order to deal with multiple samples in non-linear spaces, a consistent statistical framework on Riemannian manifolds has been designed over the last decade. We detail in this chapter the extension of this framework to Lie groups endowed with the affine symmetric connection, a more invariant (and thus more consistent) but non-metric structure on transformation groups. This theory provides strong theoretical bases for the use of one-parameter subgroups and diffeomorphisms parametrized by stationary velocity fields (SVF), for which efficient image registration methods like log-Demons have been developed with a great success from the practical point of view. One can further reduce the complexity with locally affine transformations , leading to parametric diffeomorphisms of low dimension encoding the major shape variability. We illustrate the methodology with the modeling of the evolution of the brain with Alzheimer's disease and the analysis of the cardiac motion from MRI sequences of images

Highly Reduced Model of the Cardiac Function for Fast Simulation

International audienceIn this article we present a drastic dimension reduction method to link the biophysical parameters of an electromechanical model of the heart with a compact representation of cardiac motion. Our approach relies on a projection of the displacement fields along the whole cardiac motion to the space of reduced-polyaffine transformations. Using these transformations, not only we describe the motion using a very small number of parameters but we show that each of these parameters has a physiological meaning. Moreover, using a PLS regression on a learning set made of a large number of simulations, we are able to find which of the input parameters of the model most impact the motion and what are the main relations mapping the polyaffine representation to the parameters of the model. We illustrate the potential of this method for building a direct and very fast model characterized by a highly reduced number of parameters

Spatio-Temporal Tensor Decomposition of a Polyaffine Motion Model for a Better Analysis of Pathological Left Ventricular Dynamics

International audienceGiven that heart disease can cause abnormal motion dynamics over the cardiac cycle, which can then affect cardiac function, understanding and quantifying cardiac motion can provide insight for clinicians to aid in diagnosis, therapy planning, as well as to determine the prognosis for a given patient. The goal of this paper is to extract population-specific cardiac motion patterns from 3D displacements in order to firstly identify the mean motion behaviour in a population and secondly to describe pathology-specific motion patterns in terms of the spatial and temporal aspects of the motion. Since there are common motion patterns observed in patients suffering from the same condition, extracting these patterns can lead towards a better understanding of a disease. Quantifying cardiac motion at a population level is not a simple task since images can vary widely in terms of image quality, size, resolution and pose. To overcome this, we analyse the parameters obtained from a cardiac-specific Polyaffine motion tracking algorithm, which are aligned both spatially and temporally to a common reference space. Once all parameters are aligned, different subjects and different populations can be compared and analysed in the space of Polyaffine transformations by projecting the transformations to a reduced-order subspace in which dominant motion patterns in each population can be extracted and analysed. Using tensor decomposition allows the spatial and temporal aspects to be decoupled in order to study the different components individually. The proposed method was validated on healthy volunteers and Tetralogy of Fallot patients according to known spatial andtemporal behaviour for each population. A key advantage of the proposed method is the ability to regenerate motion sequences from the respective models, thus the models can be visualised in terms of the full motion, which allows for better understanding of the motion dynamics of different populations

Visual analytics methods for shape analysis of biomedical images exemplified on rodent skull morphology

In morphometrics and its application fields like medicine and biology experts are interested in causal relations of variation in organismic shape to phylogenetic, ecological, geographical, epidemiological or disease factors - or put more succinctly by Fred L. Bookstein, morphometrics is "the study of covariances of biological form". In order to reveal causes for shape variability, targeted statistical analysis correlating shape features against external and internal factors is necessary but due to the complexity of the problem often not feasible in an automated way. Therefore, a visual analytics approach is proposed in this thesis that couples interactive visualizations with automated statistical analyses in order to stimulate generation and qualitative assessment of hypotheses on relevant shape features and their potentially affecting factors. To this end long established morphometric techniques are combined with recent shape modeling approaches from geometry processing and medical imaging, leading to novel visual analytics methods for shape analysis. When used in concert these methods facilitate targeted analysis of characteristic shape differences between groups, co-variation between different structures on the same anatomy and correlation of shape to extrinsic attributes. Here a special focus is put on accurate modeling and interactive rendering of image deformations at high spatial resolution, because that allows for faithful representation and communication of diminutive shape features, large shape differences and volumetric structures. The utility of the presented methods is demonstrated in case studies conducted together with a collaborating morphometrics expert. As exemplary model structure serves the rodent skull and its mandible that are assessed via computed tomography scans

Incorporation of a deformation prior in image reconstruction

International audienceThis article presents a method to incorporate a deformation prior in image reconstruction via the formalism of deformation modules. The framework of deformation modules allows to build diffeomorphic deformations that satisfy a given structure. The idea is to register a template image against the indirectly observed data via a modular deformation, incorporating this way the deformation prior in the reconstruction method. We show that this is a well-defined regularization method (proving existence, stability and convergence) and present numerical examples of reconstruction from 2-D tomographic simulations and partially-observed images