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Abstract

This thesis introduces the physical simulation of surgical thread for usage in a microsurgical training simulator for the education of medical students. To allow interactive simulation the thread must be real time capable. Importantly, in the simulation, the thread must behave in a way that it looks like a real thread to the user. The user can then "dive into" the simulation, because for the user, the simulation of the thread appears real. We refer to this "diving into" the simulation as "immersion". The physical model of the thread is a mass-spring model based on the Kirchhoff theory for elastic rods. One challenge is the stiffness constraint of the thread. A real world thread does not change it's length signiffcantly even under high stress. In a mass-spring model this property can be obtained by using high spring constants. But if an explicit integration method is applied the so called "overshooting" effect presents a problem. It causes the system to diverge when the spring constants are too high. In this thesis the problem is addressed by applying an implicit integration method. A key property of implicit integration methods is that it is unconditionally stable and thereby allows a large time step in the numerical integration. But it also requires that a linear system of size equal to the number of degrees of freedom in the system is solved. If the number of degrees of freedom is high this conflicts with the real-time requirement of the simulation. In this work it is shown that for the case of the thread the matrix in the linear system is banded and can therefore be solved in linear time. Another advantage of the implicit integration is that forces are propagated along the complete thread within one time step. For the simulation of microsurgical sutures knots have to be modeled. A knot causes numerous contacts of the thread with itself. The contact forces are modeled and calculated using a physical model. Because all forces propagate along the whole thread within one time step all contacts interact with each other. A force applied at one contact affects all other contacts. Because of this all contact forces have to be solved for simultaneously. The interaction of the contacts due to the implicit integration are calculated resulting in a linear system which describes the relation between the contact forces and the relative movement of the thread at the contacts. Physically correct contact forces have to be found with this linear system. Similar to the simulation of rigid bodies, a linear complementary problem or a nonlinear complementary problem results depending on the model that is used for the contact forces. In case of rigid body simulation the "projected Gauss-Seidel" is a proven method for solving the problem. In this thesis the nonlinear conjugate gradient (NNCG) method from Silcowitz-Hansen et al. is applied. This method was originally developed for rigid body simulations. The thread has been integrated into the microsurgical training simulator "MicroSim". Which is to say, interactions between the thread and tissue and forceps have been modeled and incorporated into "MicroSim". These interactions have to be compatible with the implicit integration of the thread. In a joint work with Sismanidis and Schuppe a training module for MicroSim has been developed. This training module allows for training of a microsurgical anastomosis of blood vessels.