I. Alfaro

Real-time deformable models of non-linear tissues by model reduction techniques

In this paper we introduce a new technique for the real-time simulation of non-linear tissue behavior based on a model reduction technique known as proper orthogonal (POD) or Karhunen-Loève decompositions. The technique is based upon the construction of a complete model (using finite element modelling or other numerical technique, for instance, but possibly from experimental data) and the extraction and storage of the relevant information in order to construct a model with very few degrees of freedom, but that takes into account the highly non-linear response of most living tissues. We present its application to the simulation of palpation a human cornea and study the limitations and future needs of the proposed technique.

Accounting for large deformations in real-time simulations of soft tissues based on reduced-order models

Model reduction techniques have shown to constitute a valuable tool for real-time simulation in surgical environments and other fields. However, some limitations, imposed by real-time constraints, have not yet been overcome. One of such limitations is the severe limitation in time (established in 500Hz of frequency for the resolution) that precludes the employ of Newton-like schemes for solving non-linear models as the ones usually employed for modeling biological tissues. In this work we present a technique able to deal with geometrically non-linear models, based on the employ of model reduction techniques, together with an efficient non-linear solver. Examples of the performance of the technique over some examples will be given.

Real Time Simulation of Biological Soft Tissues: A PGD Approach

We introduce here a novel approach for the numerical simulation of nonlinear, hyperelastic soft tissues at kilohertz feedback rates necessary for haptic rendering. This approach is based upon the use of proper generalized decomposition techniques, a generalization of PODs. Proper generalized decomposition techniques can be considered as a means of a priori model order reduction and provides a physics-based meta-model without the need for prior computer experiments. The suggested strategy is thus composed of an offline phase, in which a general meta-model is computed, and an online evaluation phase in which the results are obtained at real time. Results are provided that show the potential of the proposed technique, together with some benchmark test that shows the accuracy of the method.

Real‐time simulation of surgery by reduced‐order modeling and X‐FEM techniques

This paper describes a novel approach for the simulation of surgery by a combined technique of model order reduction and extended finite element method (X-FEM) methods. Whereas model order reduction techniques employ globally supported (Ritz) shape functions, a combination with X-FEM methods on a locally superimposed patch is developed for cutting simulation without remeshing. This enables to obtain models with very few degrees of freedom that run under real-time constrains even for highly non-linear tissue constitutive equations. To show the performance of the technique, we studied an application to refractive surgery in the cornea.

Simulation of axisymmetric discharging in metallic silos. Analysis of the induced pressure distribution and comparison with different standards

The main objective of this paper is to present a new contribution to the problem of dynamic continuum simulation of discharge of cylindrical silos by the Finite Element Method where many attempts have been made in the past by other researchers. We start with a study of the bulk solid constitutive behaviour, the analysis of the stored-solid to silo-wall contact interaction and with a discussion of the remeshing and rezoning algorithms needed to appropriately take into account the large displacements and the associated mesh distortions that appear in this type of problems. Some restrictions of the simulation are due to the axisymmetry of the model and the constitutive assumptions. First of all, a static analysis is accomplished using the usual hypotheses included in different standards to check the ability of the method to reproduce standard available solutions. After this calibration stage, a dynamic analysis is carried out to take into account the effects induced by the silo quaking phenomena, computing the overpressure factor and comparing the obtained results with the pressure estimations established by different standards like the European standard Eurocode ENV 1991-4, the French AFNOR P22 630, the German DIN 1055 or the American ACI 313-97 and R313-97.

Real-time in silico experiments on gene regulatory networks and surgery simulation on handheld devices

AbstractSimulation of all phenomena taking place in a surgical procedure is a formidable task that involves, when possible, the use of supercomputing facilities over long time periods. However, decision taking in the operating room needs for fast methods that provide an accurate response in real time. To this end, Model Order Reduction (MOR) techniques have emerged recently in the field of Computational Surgery to help alleviate this burden. In this paper, we review the basics of classical MOR and explain how a technique recently developed by the authors and coined as Proper Generalized Decomposition could make real-time feedback available with the use of simple devices like smartphones or tablets. Examples are given on the performance of the technique for problems at different scales of the surgical procedure, form gene regulatory networks to macroscopic soft tissue deformation and cutting.

Recent advances in the meshless simulation of aluminium extrusion and other related forming processes

SummaryIn this paper we review some recent results in the field of numerical simulation of extrusion and other forming processes obtained by the authors by using a meshless approach, together with a wide review of the existing bibliography on the topic. Three main alternatives exist in the literature, namely (updated) Lagrangian, Eulerian and arbitrary Lagrangian-Eulerian (ALE) methods. A review of the most important characteristics of each of these three approaches is here presented and their possible advantages are pointed out. Finally, an updated Lagrangian approach over a meshless approximation, based on a class of methods globally coined as natural element methods (also as natural neighbour Galerkin methods) is analysed and its relative advantages studied. Some numerical examples are included that clearly show the potential capabilities of the proposed method.

Towards a pancreatic surgery simulator based on model order reduction

In this work a pancreatic surgery simulator is developed that provides the user with haptic feedback. The simulator is based on the use of model order reduction techniques, particularly Proper Generalized Decomposition methods. The just developed simulator presents some notable advancements with respect to existing works in the literature, such as the consideration of non-linear hyperelasticity for the constitutive modeling of soft tissues, an accurate description of contact between organs and momentum and energy conserving time integration schemes. Pancreas, liver, gall bladder, and duodenum are modeled in the simulator, thus providing with a very realistic and immersive perception to the user.

Real-Time Simulation for Virtual Surgery in a PGD Framework

We analyze here the use of proper generalized decompositions (PGD) for real-time simulation of living soft tissues in virtual surgery environments. These tissues are usually modeled as hyperelastic solids, and therefore present important difficulties for their simulation under real-time constraints (i.e., feedback rates on the order of1 kHz).PGD techniques provide with physics-based meta-models without any prior computer experiment, that can be used on-line for the simulation under such severe constraints. These metemodels are constructed on the assumption of the problem to be multi-dimensional, with parameters as additional space dimensions. These parameters, in this case, are taken as the position of contact of surgical tool and organ, modulus of the contact force and orientation (a 9D problem). PGD techniques allow to solve efficiently these high-dimensional problems without the burden associated to the application of mesh-based techniques to these problems.Copyright

Meshless Simulation of Friction Stir Welding

This paper encompasses our first efforts towards the numerical simulation of friction stir welding by employing a Lagrangian approach. To this end, we have employed a meshless method, namely the Natural Element Method (NEM). Friction Stir welding is a welding process where the union between the work pieces is achieved through the extremely high deformation imposed by a rotating pin, which moves between the two pieces. This extremely high strain is the main responsible of the difficulties associated with the numerical simulation of this forming process. Eulerian and Arbitrary Lagrangian‐Eulerian (ALE) frameworks encounter difficulties in some aspects of the simulation. For instance, these approaches need additional techniques for the description of the boundary between materials, such as level sets, boundary markers or similar. In this paper we address the issue of employing a Lagrangian framework, which adequately describes the evolution in time of the interphase. The meshless character of the technique a...