A Numerical Method to Enhance the Accuracy of Mass-Spring Systems for Modeling Soft Tissue Deformations

This technical note presents a numerical corrective technique that allows control of nonlinearity in a mass-spring system (MSS) independent of its spring constants or system topology. The governing equations of MSS in the form of ordinary differential equations or a regular function accompanied by any boundary or initial condition as known constraints, are employed to modify the results. A least-squares algorithm coupled with the finite difference method is used to discretize the basic residual function implemented in this corrective technique. This numerical solution is applicable to both static and dynamic MSS. This technique is easy to implement and has accuracy similar to that of the equivalent finite element method (FEM) solution to the same system whereas solutions are obtained in a fraction of the CPU time. The proposed technique can also be used to smooth solutions from other methods such as FEM or boundary element method (BEM).