Meshless deformable models for LV motion analysis

We propose a novel meshless deformable model for in vivo cardiac left ventricle (LV) 3D motion estimation. As a relatively new technology, tagged MRI (tMRI) provides a direct and noninvasive way to reveal local deformation of the myocardium, which creates a large amount of heart motion data which requiring quantitative analysis. In our study, we sample the heart motion sparsely at intersections of three sets of orthogonal tagging planes and then use a new meshless deformable model to recover the dense 3D motion of the myocardium temporally during the cardiac cycle. We compute external forces at tag intersections based on tracked local motion and redistribute the force to meshless particles throughout the myocardium. Internal constraint forces at particles are derived from local strain energy using a Moving Least Squares (MLS) method. The dense 3D motion field is then computed and updated using the Lagrange equation. The new model avoids the singularity problem of mesh-based models and is capable of tracking large deformation with high efficiency and accuracy. In particular, the model performs well even when the control points (tag intersections) are relatively sparse. We tested the performance of the meshless model on a numerical phantom, as well as in vivo heart data of healthy subjects and patients. The experimental results show that the meshless deformable model can fully recover the myocardium motion in 3D. 1

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

Non-rigid registration of 2-D/3-D dynamic data with feature alignment

In this work, we are computing the matching between 2D manifolds and 3D manifolds with temporal constraints, that is we are computing the matching among a time sequence of 2D/3D manifolds. It is solved by mapping all the manifolds to a common domain, then build their matching by composing the forward mapping and the inverse mapping. At first, we solve the matching problem between 2D manifolds with temporal constraints by using mesh-based registration method. We propose a surface parameterization method to compute the mapping between the 2D manifold and the common 2D planar domain. We can compute the matching among the time sequence of deforming geometry data through this common domain. Compared with previous work, our method is independent of the quality of mesh elements and more efficient for the time sequence data. Then we develop a global intensity-based registration method to solve the matching problem between 3D manifolds with temporal constraints. Our method is based on a 4D(3D+T) free-from B-spline deformation model which has both spatial and temporal smoothness. Compared with previous 4D image registration techniques, our method avoids some local minimum. Thus it can be solved faster and achieve better accuracy of landmark point predication. We demonstrate the efficiency of these works on the real applications. The first one is applied to the dynamic face registering and texture mapping. The second one is applied to lung tumor motion tracking in the medical image analysis. In our future work, we are developing more efficient mesh-based 4D registration method. It can be applied to tumor motion estimation and tracking, which can be used to calculate the read dose delivered to the lung and surrounding tissues. Thus this can support the online treatment of lung cancer radiotherapy

A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes

In this paper we show and discuss the use of a versatile interaction potential approach coupled with an immersed boundary method to simulate a variety of flows involving deformable bodies. In particular, we focus on two kinds of problems, namely (i) deformation of liquid-liquid interfaces and (ii) flow in the left ventricle of the heart with either a mechanical or a natural valve. Both examples have in common the two-way interaction of the flow with a deformable interface or a membrane. The interaction potential approach (de Tullio & Pascazio, Jou. Comp. Phys., 2016; Tanaka, Wada and Nakamura, Computational Biomechanics, 2016) with minor modifications can be used to capture the deformation dynamics in both classes of problems. We show that the approach can be used to replicate the deformation dynamics of liquid-liquid interfaces through the use of ad-hoc elastic constants. The results from our simulations agree very well with previous studies on the deformation of drops in standard flow configurations such as deforming drop in a shear flow or a cross flow. We show that the same potential approach can also be used to study the flow in the left ventricle of the heart. The flow imposed into the ventricle interacts dynamically with the mitral valve (mechanical or natural) and the ventricle which are simulated using the same model. Results from these simulations are compared with ad- hoc in-house experimental measurements. Finally, a parallelisation scheme is presented, as parallelisation is unavoidable when studying large scale problems involving several thousands of simultaneously deforming bodies on hundreds of distributed memory computing processors

Overview of the numerical methods for the modelling of rock mechanics problems

Počeci numeričkih metoda sežu u rane 1960-e. Već tada je bilo jasno da numeričke metode mogu biti uspješno upotrijebljene za različita inženjerska i znanstvena područja, uključujući i primjenu u mehanici stijena. Ubrzan razvoj računala je omogućavao razvoj numeričkih metoda i rješavanje računalno zahtjevnijih sustava. Takav razvoj doveo je do velikog broja različitih metoda i pristupa koji se mogu svrstati u dvije skupine: metode kontinuuma i metode diskontinuuma. Određene zadaće zahtijevaju prednosti oba pristupa, što je dovelo do razvoja kombiniranih konačno-diskretnih metoda. Prvi cilj ovog rada je predstavljanje numeričkih metoda i pristupa koji se koriste za rješavanje zadaća u mehanici stijena, kao i kratko objašnjenje osnovnih teorijskih postavki svake od metoda. Drugi cilj je osvrt na primjenjivost pojedine metode u mehanici stijena.The numerical methods have their origin in the early 1960s and even at that time it was noted that numerical methods can be successfully applied in various engineering and scientific fields, including the rock mechanics. Moreover, the rapid development of computers was a necessary background for solving computationally more demanding problems and the development process of the methods in general. Thus, we have many different methods presently, which can be separated into two main branches: continuum and discontinuum-based numerical methods. Some problems require the strengths of both main approaches which brought the hybrid continuum/discontinuum methods. The first goal of this paper is to present the state of the art numerical methods and approaches for solving the rock mechanics problems, as well as to give the brief explanation about the theoretical background of each method. The second goal is to emphasise the area of applicability of the methods in rock mechanics

Modeling of Free Surface Flows with Elastic Bodies Interactions

In this paper, a series of new fluid and structure interactions test cases with strong free surface effects are presented and computations of such flows with the Particle Finite Element Method (PFEM) (Idelsohn, Oiiate, Del Pin and Calvo, 2006) are documented. The structures object of study are elastic cantilever bars clamped inside sloshing tanks subjected ro roll motion. The possibilities of PFEM for the coupled simulation of moderately violent free surface flows interacting with elastic bodies are investigated. The problem can be described as the coupling of a sloshing flow with an easily deformable elastic body. A series of experiments designed and executed specifically for these tests are also described. The experiments comprise cases with different liquid height and liquids of different viscosity. The aim is to identify canonical benchmark problems in FSI (Fluid and Structure Interactions), including free surfaces, for future comparisons between different numerical approaches