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Many researchers have proposed the use of biomechanical models for high accuracy soft
organ non-rigid image registration, but one main problem in using comprehensive models
is the long computation time required to obtain the solution. In this paper we propose
to use the Total Lagrangian formulation of the Finite Element method together with
Dynamic Relaxation for computing intra-operative organ deformations. We study the
best ways of estimating the parameters involved and we propose a termination criteria
that can be used in order to obtain fast results with prescribed accuracy. The simulation
results prove the accuracy and computational efficiency of the method, even in cases
involving large deformations, nonlinear materials and contacts.