Constrained stochastic state estimation of deformable 1D objects: Application to single-view 3D reconstruction of catheters with radio-opaque markers.

Minimally invasive fluoroscopy-based procedures are the gold standard for diagnosis and treatment of various pathologies of the cardiovascular system. This kind of procedures imply for the clinicians to infer the 3D shape of the device from 2D images, which is known to be an ill-posed problem. In this paper we present a method to reconstruct the 3D shape of the interventional device, with the aim of improving the navigation. The method combines a physics-based simulation with non-linear Bayesian filter. Whereas the physics-based model provides a prediction of the shape of the device navigating within the blood vessels (taking into account non-linear interactions between the catheter and the surrounding anatomy), an Unscented Kalman Filter is used to correct the navigation model using 2D image features as external observations. The proposed framework has been evaluated on both synthetic and real data, under different model parameterizations, filter parameters tuning and external observations data-sets. Comparing the reconstructed 3D shape with a known ground truth, for the synthetic data-set, we obtained average values for 3D Hausdorff Distance of 0.81±0.53mm, for the 3D mean distance at the segment of 0.37±0.17mm and an average 3D tip error of 0.24±0.13mm. For the real data-set,we obtained an average 3D Hausdorff distance of 1.74±0.77mm, a average 3D mean distance at the distal segment of 0.91±0.14mm, an average 3D error on the tip of 0.53±0.09mm. These results show the ability of our method to retrieve the 3D shape of the device, under a variety of filter parameterizations and challenging conditions: uncertainties on model parameterization, ambiguous views and non-linear complex phenomena such as stick and slip motions.

3D Physics-Based Registration of 2D Dynamic MRI Data.

We present a method allowing for intra-operative targeting of a specific anatomical feature. The method is based on a registration of 3D pre-operative data to 2D intra-operative images. Such registration is performed using an elastic model reconstructed from the 3D images, in combination with sliding constraints imposed via Lagrange multipliers. We register the pre-operative data, where the feature is clearly detectable, to intra-operative dynamic images where such feature is no more visible. Despite the lack of visibility on the 2D MRI images, we are able both to determine the location of the target as well as follow its displacement due to respiratory motion.

Constraint-based simulation for non-rigid real-time registration.

In this paper we propose a method to address the problem of non-rigid registration in real-time. We use Lagrange multipliers and soft sliding constraints to combine data acquired from dynamic image sequence and a biomechanical model of the structure of interest. The biomechanical model plays a role of regularization to improve the robustness and the flexibility of the registration. We apply our method to a pre-operative 3D CT scan of a porcine liver that is registered to a sequence of 2D dynamic MRI slices during the respiratory motion. The finite element simulation provides a full 3D representation (including heterogeneities such as vessels, tumor,...) of the anatomical structure in real-time.

Atlas-based transfer of boundary conditions for biomechanical simulation.

An environment composed of different types of living tissues (such as the abdominal cavity) reveals a high complexity of boundary conditions, which are the attachments (e.g. connective tissues, ligaments) connecting different anatomical structures. Together with the material properties, the boundary conditions have a significant influence on the mechanical response of the organs, however corresponding correct mechanical modeling remains a challenging task, as the connective structures are difficult to identify in certain standard imaging modalities. In this paper, we present a method for automatic modeling of boundary conditions in deformable anatomical structures, which is an important step in patient-specific biomechanical simulations. The method is based on a statistical atlas which gathers data defining the connective structures attached to the organ of interest. In order to transfer the information stored in the atlas to a specific patient, the atlas is registered to the patient data using a physics-based technique and the resulting boundary conditions are defined according to the mean position and variance available in the atlas. The method is evaluated using abdominal scans of ten patients. The results show that the atlas provides a sufficient information about the boundary conditions which can be reliably transferred to a specific patient. The boundary conditions obtained by the atlas-based transfer show a good match both with actual segmented boundary conditions and in terms of mechanical response of deformable organs.