Viscoelastic and Nonlinear Organ Model for Control of Needle Insertion Manipulator

This paper shows the viscoelastic and nonlinear organ deformation model for organ model-based control of needle insertion, in which the deformation of an organ is calculated intraoperatively and the needle is manipulated with organ deformation taken into consideration. An organ model including such detailed material characteristics is important to achieve the control method in question. Firstly, the material properties of the liver are modeled from the measured data and its viscoelastic characteristics are represented by differential equations, including the term of the fractional derivative. Nonlinearity in terms of the fractional derivative was measured, and modeled using the quadratic function of strain. Next, a solution of an FE model using such material properties is shown. We use sampling time scaling property as the solution for the viscoelastic system. The solution for a nonlinear system using the Modified Newton-Raphson method is also shown. Finally, the organ deformation, assuming the needle is inserted, is simulated using an organ model and the overall deformation and distribution of the strain at each element is computed in these simulations.