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.

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