![]() They operate by casting the problem in a parametric way, by considering every possible parameter of the problem (the position of application of the load, material parameters, etc.) as a new dimension in the phase space, end then solving the resulting high-dimensional problem off-line, once for life. Proper Generalized Decomposition (PGD) techniques, however, operate in a slightly different way. ![]() Methods as the empirical interpolation method or the coupling with Asymptotic Numerical Methods aim at solving these deficiencies. In particular, projection-based (a posteriori) model order reduction techniques very often lack of efficiency in non-linear problems, where the complete system of equations needs to be rebuilt in order to perform consistent linearization, thus loosing all the pretended gain. However, they are not free of limitations. These techniques that, essentially, develop models with a minimal number of degrees of freedom, seem to be very well suited for the purpose of developing a real-time simulator. Recently, model order reduction techniques have opened a different way of looking at real-time simulation. However, these explicit algorithms are not unconditionally stable, and often lack of an appropriate energy conservation. In general, they are based on the employ of explicit finite element simulations, that allow for a fast resolution, element by element, of the equations of motion. It has not been until very recently that truly non-linear constitutive models have been developed. Indeed, the problem is highly non-linear, due to both the constitutive modeling of soft living tissues, frequently considered as hyperelastic, and the non-linear phenomena taking place at the operating room: contact, friction, cutting, etc.Īll these limitations make the development of surgery simulators a delicate task that has faced important difficulties in the last decades. ![]() This is due to the complexity of the problem and the need for a feedback response at some 500 Hz to 1 kHz. And this is despite the well-known limitations that nowadays surgical simulators have. It is now well known and scientifically demonstrated that the use of surgery simulators provides the practitioner with a fast method to developed the necessary skills.
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