Image-driven Stochastic Identification of Boundary Conditions for Predictive Simulation

International audienceIn computer-aided interventions, biomechanical models reconstructed from the pre-operative data are used via augmented reality to facilitate the intra-operative navigation. The predictive power of such models highly depends on the knowledge of boundary conditions. However , in the context of patient-specific modeling, neither the pre-operative nor the intra-operative modalities provide a reliable information about the location and mechanical properties of the organ attachments. We present a novel image-driven method for fast identification of boundary conditions which are modelled as stochastic parameters. The method employs the reduced-order unscented Kalman filter to transform in real-time the probability distributions of the parameters, given observations extracted from intra-operative images. The method is evaluated using synthetic, phantom and real data acquired in vivo on a porcine liver. A quantitative assessment is presented and it is shown that the method significantly increases the predictive power of the biomechanical model

The effect of discretization on parameter identification. Application to patient-specific simulations

International audienceIdentifying the elastic parameters of a finite element model from a dynamically acquired set of observations is a fundamental challenge in many data-driven medical applications going from soft surgical robotics to image-guided per-operative simulations. While various strategies exist to tackle the parameter-identification inverse problem [Aster et al., 2013], the effect of sub-optimal discretization, as often required in real-time applications, is largely overlooked. Indeed, the need to tune the parameter values in order to account for discretization-induced stiffening in specific models is reported in different works (e.g. [Chen et al., 2015, Anna et al., 2018]). However, to the best of our knowledge, no systematic study of this phenomenon exists to date, nor has any strategy to select optimal effective values been developed. Our work addresses the issue of parameter identification in coarsened meshes with special attention to the dynamical nature of the identification. We focus on the estimation of Young's moduli in simplified systems and show that the estimated stiffnesses are underestimated in a systematic manner when reducing the number of degrees of freedom. We also show that the effective stiffness of a given coarse mesh, when associated with an undersampled mesh discretization, is not constant but strongly depends on the prescribed deformations. These results show that the estimated parameters should not be considered as the true parameter value of the organ or tissue but instead are model-dependent values. We argue that Bayesian methods present a clear advantage w.r.t. classical minimization methods by their ability to efficiently adapt the local parameter values

Image-guided Simulation of Heterogeneous Tissue Deformation For Augmented Reality during Hepatic Surgery

International audienceThis paper presents a method for real-time augmentation of vas- cular network and tumors during minimally invasive liver surgery. Internal structures computed from pre-operative CT scans can be overlaid onto the laparoscopic view for surgery guidance. Com- pared to state-of-the-art methods, our method uses a real-time biomechanical model to compute a volumetric displacement field from partial three-dimensional liver surface motion. This permits to properly handle the motion of internal structures even in the case of anisotropic or heterogeneous tissues, as it is the case for the liver and many anatomical structures. Real-time augmentation results are presented on in vivo and ex vivo data and illustrate the benefits of such an approach for minimally invasive surgery

Multifidelity-CMA: a multifidelity approach for efficient personalisation of 3D cardiac electromechanical models

International audiencePersonalised computational models of theheart are of increasing interest for clinical applica-tions due to their discriminative and predictive abili-ties. However, the simulation of a single heartbeat witha 3D cardiac electromechanical model can be long andcomputationally expensive, which makes some practicalapplications, such as the estimation of model parame-ters from clinical data (the personalisation), very slow.Here we introduce an original multidelity approachbetween a 3D cardiac model and a simplied "0D" ver-sion of this model, which enables to get reliable (andextremely fast) approximations of the global behaviorof the 3D model using 0D simulations. We then usethis multidelity approximation to speed-up an ecientparameter estimation algorithm, leading to a fast andcomputationally ecient personalisation method of the3D model. In particular, we show results on a cohort of121 dierent heart geometries and measurements. Fi-nally, an exploitable code of the 0D model with scriptsto perform parameter estimation will be released to thecommunity

Finite element method-based kinematics and closed-loop control of soft, continuum manipulators

International audienceThis paper presents a modeling methodology and experimental validation for soft 1 manipulators to obtain forward and inverse kinematic models under quasistatic conditions. It offers a way to obtain the kinematic characteristics of this type of soft robots that is suitable for offline path planning and position control. The modeling methodology presented relies on continuum mechanics which does not provide analytic solutions in the general case. Our approach proposes a real-time numerical integration strategy based on Finite Element Method (FEM) with a numerical optimization based on Lagrangian Multipliers to obtain forward and inverse models. To reduce the dimension of the problem, at each step, a projection of the model to the constraint space (gathering actuators, sensors and end-effector) is performed to obtain the smallest number possible of mathematical equations to be solved. This methodology is applied to obtain the kinematics of two different manipulators with complex structural geometry. An experimental comparison is also performed in one of the robots, between two other geometric approaches and the approach that is showcased in this paper. A closed-loop controller based on a state estimator is proposed. The controller is experimentally validated and its robustness is evaluated using Lypunov stability method

Data-driven simulation for augmented surgery

International audienceTo build an augmented view of an organ during surgery, it is essential to have a biomechanical model with appropriate material parameters and boundary conditions , able to match patient specific properties. Adaptation to the patient's anatomy is obtained by exploiting the image-rich context specific to our application domain. While information about the organ shape, for instance, can be obtained preoper-atively, other patient-specific parameters can only be determined intraoperatively. To this end, we are developing data-driven simulations, which exploit information extracted from a stream of medical images. Such simulations need to run in real-time. To this end we have developed dedicated numerical methods, which allow for real-time computation of finite element simulations. The general principle consists in combining finite element approaches with Bayesian methods or deep learning techniques, that allow to keep control over the underlying computational model while allowing for inputs from the real world. Based on a priori knowledge of the mechanical behavior of the considered organ, we select a constitutive law to model its deformations. The predictive power of such constitutive law highly depends on the knowledge of the material parameters and A. Mendizaba

Multiplicative Jacobian Energy Decomposition Method for Fast Porous Visco-Hyperelastic Soft Tissue Model

Abstract. Simulating soft tissues in real time is a significant challenge since a compromise between biomechanical accuracy and computational efficiency must be found. In this paper, we propose a new discretization method, the Multiplicative Jacobian Energy Decomposition (MJED) which is an alternative to the classical Galerkin FEM (Finite Element Method) formulation. This method for discretizing non-linear hyperelastic materials on linear tetrahedral meshes leads to faster stiffness matrix assembly for a large variety of isotropic and anisotropic materials. We show that our new approach, implemented within an implicit time integration scheme, can lead to fast and realistic liver deformations including hyperelasticity, porosity and viscosity.

Population-based priors in cardiac model personalisation for consistent parameter estimation in heterogeneous databases

International audiencePersonalised cardiac models are a virtual representation of the patient heart, with parameter values for which the simulation fits the available clinical measurements. Models usually have a large number of parameters while the available data for a given patient is typically limited to a small set of measurements, thus the parameters cannot be estimated uniquely. This is a practical obstacle for clinical applications, where accurate parameter values can be important. Here we explore an original approach based on an algorithm called Iteratively Updated Priors (IUP), in which we perform successive personalisations of a full database through Maximum A Posteriori (MAP) estimation, where the prior probability at an iteration is set from the distribution of personalised parameters in the database at the previous iteration. At the convergence of the algorithm, estimated parameters of the population lie on a linear subspace of reduced (and possibly sufficient) dimension in which for each case of the database, there is a (possibly unique) parameter value for which the simulation fits the measurements. We first show how this property can help the modeler select a relevant parameter subspace for personalisation. In addition, since the resulting priors in this subspace represent the population statistics in this subspace, they can be used to perform consistent parameter estimation for cases where measurements are possibly different or missing in the database, which we illustrate with the personalisation of a heterogeneous database of 811 cases

Meshless Mechanics and Point-Based Visualization Methods for Surgical Simulations

Computer-based modeling and simulation practices have become an integral part of the medical education field. For surgical simulation applications, realistic constitutive modeling of soft tissue is considered to be one of the most challenging aspects of the problem, because biomechanical soft-tissue models need to reflect the correct elastic response, have to be efficient in order to run at interactive simulation rates, and be able to support operations such as cuts and sutures. Mesh-based solutions, where the connections between the individual degrees of freedom (DoF) are defined explicitly, have been the traditional choice to approach these problems. However, when the problem under investigation contains a discontinuity that disrupts the connectivity between the DoFs, the underlying mesh structure has to be reconfigured in order to handle the newly introduced discontinuity correctly. This reconfiguration for mesh-based techniques is typically called dynamic remeshing, and most of the time it causes the performance bottleneck in the simulation. In this dissertation, the efficiency of point-based meshless methods is investigated for both constitutive modeling of elastic soft tissues and visualization of simulation objects, where arbitrary discontinuities/cuts are applied to the objects in the context of surgical simulation. The point-based deformable object modeling problem is examined in three functional aspects: modeling continuous elastic deformations with, handling discontinuities in, and visualizing a point-based object. Algorithmic and implementation details of the presented techniques are discussed in the dissertation. The presented point-based techniques are implemented as separate components and integrated into the open-source software framework SOFA. The presented meshless continuum mechanics model of elastic tissue were verified by comparing it to the Hertzian non-adhesive frictionless contact theory. Virtual experiments were setup with a point-based deformable block and a rigid indenter, and force-displacement curves obtained from the virtual experiments were compared to the theoretical solutions. The meshless mechanics model of soft tissue and the integrated novel discontinuity treatment technique discussed in this dissertation allows handling cuts of arbitrary shape. The implemented enrichment technique not only modifies the internal mechanics of the soft tissue model, but also updates the point-based visual representation in an efficient way preventing the use of costly dynamic remeshing operations

A computational study of post-infarct mechanical effects of injected biomaterial into ischaemic myocardium

Includes abstract.Includes bibliographical references.Cardiovascular diseases account for one third of all deaths worldwide, more than 33% of which are related to ischaemic heart disease, involving a myocardial infarction (MI). Emerging MI therapies involving biomaterial injections have shown some benefits; the underlying mechanisms of which remain unclear. Computational models offer considerable potential to study the biomechanics of a myocardial infarction and novel therapies. Geometrical data of a healthy human left ventricle (LV) obtained from magnetic resonance images (MRI) was used to create a finite element (FE) mesh of the LV at the end-systolic time point using Continuity® 6.3 (University of California in San Diego, US). A mesh of 96 hexahedral elements with high order basis functions was employed to adequately describe the geometry of the LV. Simulations of diastolic filling and systolic contraction were performed using a transversely isotropic exponential strain energy function and a model for active stress based on contraction at the cellular level. An anterior apical, transmural MI was modelled in the LV encompassing 16% of the LV wall volume. The infarct was modelled at acute and fibrotic stages of post-infarct LV remodelling by altering the constitutive and active stress models to best describe passive and active behaviour of the ischaemic myocardium at each time point. The geometry of the LV with the fibrotic infarct was adjusted to represent the wall thinning that occurs during LV post-MI remodelling. Hydrogel injection was modelled as layers with material properties differing from those of the surrounding myocardium while accounting for thickening of the LV wall at the injection site. The study design comprised a healthy case and two infarcted cases with and without hydrogel injection. The end-diastolic volume (EDV) increased in the acute infarct model compared to the healthy case due to the reduced stiffness in the infarct wall. An EDV increase was not observed in the fibrotic infarct model compared to the healthy case. This was partially attributed to the increase in infarct stiffness and partially due to the fact that remodelling-related dilation of the LV was not implemented in the model. Inclusion of hydrogel lowered EDV in both the acute and fibrotic models. The predicted ejection fraction (EF) decreased from 41.2% for the healthy case to 28.5% and 33.0% for the acute and fibrotic infarct models, respectively. Inclusion of hydrogel layers caused an improvement in EF in the acute model only