Section: New Results

Handling non-rigid deformations

Participants : Marie-Odile Berger, Jaime Garcia Guevara, Erwan Kerrien, Daryna Panicheva, Raffaella Trivisonne, Pierre-Frédéric Villard.

Compliance-based non rigid registration

Within J. Guevara's PhD thesis, we are investigating non rigid registration methods which exploit the matching of the vascular trees and are able to cope with large deformations of the organ. This year, we have developed a matching method which is entirely based on the mechanical properties of the organ. We thus avoid tedious parameter tuning which is required by many methods and instead use parameters whose values are known or can be measured. Our method makes use of an advanced biomechanical model which handles heterogeneities and anisotropy due to vasculature. The main originality of the method lies in the definition of a better and novel metric for generating improved graph-matching hypotheses, based on the notion of compliance, the inverse of stiffness. This method reduces the computation time by predicting first the most plausible matching hypotheses on a mechanical basis and reduces the sensitivity on the search space parameters. These contributions improve the registration quality and meet intra-operative timing constraints. Experiments have been conducted on ten realistic synthetic datasets and two real porcine datasets which where automatically segmented. This work was recently accepted in the journal Annals of Biomedical Engineering [9], [11].

Individual-specific heart valve modeling

Recent works on computer-based models of mitral valve behavior rely on manual extraction of the complex valve geometry, which is tedious and requires a high level of expertise. On the contrary, in the context of D. Panicheva's PhD thesis, we are investigating methods to segment the chordae with little human supervision which produce mechanically-coherent simulations of the mitral valve.

Valve chordae are generalized cylinders: Instead of being limited to a line, the central axis is a continuous curve; instead of a constant radius, the radius varies along the axis. Most of the time, chordae sections are flattened ellipses and classical model-based methods commonly used for vessel enhancement or vessel segmentation fail. We have exploited the fact that there are no other generalized cylinders than the chordae in the CT scan and we have proposed a topology-based method for chordae extraction. This approach is flexible and only requires the knowledge of an upper bound of the maximum radius of the chordae. The method has been tested on three CT scans. Overall, non-chordae structures are correctly identified and detected chordae ending points match up with actual chordae attachment points [21].

We then worked on evaluating the effectiveness of our approach. The valve behavior was simulated with a biomechanical framework based on the Finite Element Method. A structural model with no fluid-structure interaction was used. Physiological behavior was simulated by mechanical forces such as blood pressure, contact forces and tension forces applied from chordae tensions. The chordae segmentation was validated by comparing the simulation results to those obtained with manually segmented chordae [22].

Image-based biomechanical simulation of the diaphragm during mechanical ventilation

When intensive care patients are subjected to mechanical ventilation, the ventilator causes damage to the muscles that govern the normal breathing, leading to Ventilator Induced Diaphragmatic Dysfunction (VIDD). The INVIVE project aims to study the mechanics of respiration through numerical simulation in order to learn more about the onset of VIDD. We have worked during this year on how to compute solutions of the static linear elasticity equation using last year's work on the diaphragm geometry [26]. Since obtaining an analytical formulation of the boundary conditions in 3D is complex, we have worked on adapting our method to implicit geometries built from 2D data of the diaphragm. The idea is to have an analytical formulation of both the geometry and the boundary conditions to validate our radial basis framework. It is based on points belonging to a cross-section that has been chosen in the middle of the diaphragm. Points are gathered in groups inside rectangles based on a K-means classification. Rectangle dimensions are set so as to ensure cross-coverage. Curve patches are then computed for each rectangle using radial basis functions. A list of local curves is obtained from both the thoracic and abdomen zones and by combining them it is possible to evaluate the global implicit curve of the diaphragm.

3D catheter navigation from monocular images

In interventional radiology, the 3D shape of the micro-tool (guidewire, micro-catheter or micro-coil) can be very difficult, if not impossible to infer from fluoroscopy images. We consider this question as a single view 3D curve reconstruction problem. Our aim is to assess whether, and under which conditions, a sophisticated physics-based model can be effective to compensate for the incomplete data in this ill-posed problem.

Raffaella Trivisonne started her PhD thesis in November 2015 (co-supervised by Stéphane Cotin, from MIMESIS team in Strasbourg) to address this research topic. An unscented Kalman filter is used as a fusion mechanism, in a non-rigid shape-from-motion approach: the observations are image data (opaque markers placed along the device), and the model is implemented through interactive physics-based simulation. Our contribution is to handle contacts, which introduce discontinuities in the first and second order derivatives of motion (resp. velocity and forces). Extensive validation on both synthetic and phantom-based data has been carried out this year [30], and various state vector parametrizations have been investigated, in particular in a view to achieve data assimilation of mechanical parameters to improve the predictability of simulation.

In this context, validation is made very complex by the need to acquire ground truth 3D curve shapes that are subjected to contacts and demonstrate highly transient dynamic deformations (e.g. stick and slip transitions after contact). Thomas Mangin was hired on a 1-year engineer contract (started in March 2019) to design and develop an experimental platform to acquire such ground truth data. The catheter is inserted in a translucent, silicon vascular phantom to generate contacts with no visual occlusion of the catheter shape. It is reconstructed from images acquired by a stereo rig made of two orthogonal high speed cameras. The motion is fully controlled by an original 3D-printed active device that induces accurate translation and rotation motions to the micro-tool. Monte-Carlo simulations are currently being carried out to certify the accuracy of the ground truth data produced by this system.