Differential models for the simulation of the muscle mechanics are based on iteratively updating a mesh grid and deducing its new state through a finite element model. Models usually assume that the mesh grid is almost regular, and this makes a degradation of the simulation accuracy in long simulation sequences, since the mesh tends to be less regular when the number of iterations increases. We present a model that has the aim of reducing this accuracy degradation. It is based on recomputing the mesh grid returned by the model in each iteration through the concept of graph matching. The new model is currently in use to analyse the dynamics of the human heart when some pressure is applied to it. The final goal of the project (which is not shown in this paper) is to deduce the optimal position and strength pressure applied to the heart that increases the chance of reviving it with the minimum tissue damage. Experimental validation shows our model returns a higher accuracy of the muscle position through some iterations than classical differential models with an insignificant increase of runtime. Thus, it is worth recomputing the mesh grid since the simulation accuracy drastically increases at the expense of a low runtime increase.

Attributed graphs are structures that are useful to represent objects through the information of their local parts and their relations. Each characteristic in the local parts is represented by different attributes on the nodes. In this context, the comparison between structured objects is performed through a distance between attributed graphs. If we want to correctly tune the distance and the node correspondence between graphs, we have to add some weights on the node attributes to gauge the importance of each local characteristic. In this paper, we present a method to learn the weights on each node attribute. It is based on building an embedded space and imposing the weights we want to learn to be the constants of the hyperplane deduced by a linear regression applied on a cloud of points. These points represent the node-to-node mappings.