Surgical simulation as a practice has gained popularity owing to the dexterity
it can impart to the surgical interventions and planning. It is also extremely
challenging since it requires an accurate correlation to reality. The objective of
this study is to develop computational tools that can simulate cutting in soft
biological tissues and suggest a stress based criterion for predicting the onset of
failure.
The cutting algorithm proposed in this study is based on the total Lagrangian
explicit dynamics approach and gives due consideration to the nonlinearities
associated with tissue-like materials, both geometric and material. The
constitutive response of the tissue is modeled using a hyperelastic Neo-Hookean
material and the dynamic equations of equilibrium are derived based on the
total Lagrangian formulation. The equations of equilibrium are integrated using
the central difference operator. The algorithm uses node snapping and edge
relocation procedures to align the edge of the element with the direction of cut.
The second part of the thesis focuses on determining a stress-based cutting
criterion to mark the beginning of failure in the tissue. For a given set of
force-displacement data from experimental results reported in the literature on
porcine liver, we construct finite element models using a commercially available
finite element code to simulate the deformation field in the tissue. The aim is to
find the stress state in the tissue corresponding to that rupture displacement.
A number of studies are performed to analyze the effect of parameters like the
tool velocity, radius of the tool, on the reaction force and stress state in the
tissue.