Felipe Bordeu

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 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.

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

New routes to advanced simulation of material forming

We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD), based on the assumption of a separated form of the unknown field. It has demonstrated its capabilities in dealing with highdimensional problems overcoming the strong limitations of classical approaches. Many challenging problems can be efficiently cast into a multidimensional framework. For instance, parameters in a model (loads, initial conditions, boundary conditions, material parameters, geometrical parameters,...) can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort virtual chart. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, in highly complex scenarios and on deployed platforms.

Real Time Simulation of Non-Linear Solids by PGD Techniques

We analyse here how Dynamic Data Driven Application Systems (DDDAS) can constitute a valuable tool in the field of forming processes. Simulation tools in the field of DDDAS are required to provide a response in real-time, a requisite that is often too severe for complex problems. Here, we consider that of hyperelasticity, commonly used in different fields such as rubber manufacturing or surgery, for instance. We analyse here how model reduction techniques, and particularly Proper Generalized Decompositions (PGD) methods can provide a suitable response to the strong requirements posed by DDDAS. We will consider two different approaches to the problem. The first one is an explicit approach that nevertheless provides with good results. The second one is based on the use of Asymptotic Numerical Method.