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International audience; Foot ulcers are usually the consequence of a trauma associated to diabetes that could lead to amputation and shorten life expectancy. In this chapter some technologies that could prevent pressure foot ulcers for diabetic persons are presented. There are three essential components: 1) a smart sock to monitor the pressure applied to the foot, 2) a patient-specific finite element model of the foot that includes the soft tissues and bony prominences to compute the required indicators like stress and strain in the foot and 3) a reduced order model that is able to compute the results of the finite element model in real-time and with a small error. To create the reduced order model Proper Orthogonal Decomposition with Interpolation (PODI) was employed. The displacements in the foot based on the reduced order model were computed in 0.1s; although the relative error norm was 2.6% which seems acceptable from a clinical point of view

A novel meshless deformation model of biological soft tissue, which is mainly based on the radial basis function point interpolation, is presented for interactive simulation applications such as virtual surgery simulators. Compared with conventional mesh models, the proposed model is particularly suitable for simulating large deformation, sucking and cutting tasks since there is no need to maintain grid information. Kelvin viscoelasticity, which represents relaxation, creep, and hysteresis of soft tissue, is integrated into the proposed model, making the simulation much more realistic than many existing meshless models. To verify the validity of the proposed model, a biomechanical test was performed on real-life biological tissue and the results show that the maximum relative error between the forces from the biomechanical test and those obtained from the model is less than 5.8%. The proposed model was also implemented on a neurosurgery simulator, which showed that the deformation of the brain tumor can be simulated in a high degree of accuracy with real-time performance. In particular, the error and distortion from the remeshing process inherited in conventional mesh models when deformation is large are avoided.

A posteriori error estimation for the nodeless variable finite element method is presented. A nodeless variable finite element method using flux-based formulation is developed and combined with an adaptive meshing technique to analyze two-dimensional thermal-structural problems. The continuous flux and stresses are determined by using the flux-based formulation while the standard linear element interpolation functions are used to determine the discontinuous flux and stresses. To measure the global error, the L2 norm error is selected to find the root-mean-square error over the entire domain. The finite element formulation and its detailed finite element matrices are presented. Accuracy of the estimated error is measured by the percentage relative error. An adaptive meshing technique, that can generate meshes corresponding to solution behaviors automatically, is implemented to further improve the solution accuracy. Several examples are presented to evaluate the performance and accuracy of the combined method.