Modeling the dynamics of filaments for medical applications

• Equations of motion of rod-like filaments are solved by a finite difference scheme.
• Cantilever type filaments with genuine suture thread properties are modeled.
• Numerical simulations show buckling due to application of axial load and a twist.
• Transverse motion due to impulse input, tested with analytical solutions, is shown.
• The adopted numerical scheme is fast and can be used for real-time simulations.

We present a theoretical formulation based on the Cosserat theory of rods to describe the motion of rod-like filaments (e.g., surgical threads) used in surgical suturing. The equations of motion are simplified using certain approximations and the resulting equations are solved using the finite difference (centered difference) scheme in time and space. The boundary conditions involve the specification of the force and moment at the free end of the thread and symmetry conditions commonly encountered during surgeries. Numerical simulations of suture threads with genuine material parameters and geometries specific to surgical scenarios are presented.