Eulerian formulation of elastic rods

Multibody dynamic modeling of the behavior of flexible instruments used in cervical cancer brachytherapy

BACKGROUND

The steep radiation dose gradients in cervical cancer brachytherapy (BT) necessitate a thorough understanding of the behavior of afterloader source cables or needles in the curved channels of (patient-tailored) applicators.

PURPOSE

The purpose of this study is to develop and validate computer models to simulate: (1) BT source positions, and (2) insertion forces of needles in curved applicator channels. The methodology presented can be used to improve the knowledge of instrument behavior in current applicators and aid the development of novel (3D-printed) BT applicators.

METHODS

For the computer models, BT instruments were discretized in finite elements. Simulations were performed in SPACAR by formulating nodal contact force and motion input models and specifying the instruments' kinematic and dynamic properties. To evaluate the source cable model, simulated source paths in ring applicators were compared with manufacturer-measured source paths. The impact of discrepancies on the dosimetry was estimated for standard plans. To validate needle models, simulated needle insertion forces in curved channels with varying curvature, torsion, and clearance, were compared with force measurements in dedicated 3D-printed templates.

RESULTS

Comparison of simulated with manufacturer-measured source positions showed 0.5-1.2 mm median and <2.0 mm maximum differences, in all but one applicator geometry. The resulting maximum relative dose differences at the lateral surface and at 5 mm depth were 5.5% and 4.7%, respectively. Simulated insertion forces for BT needles in curved channels accurately resembled the forces experimentally obtained by including experimental uncertainties in the simulation.

CONCLUSION

The models developed can accurately predict source positions and insertion forces in BT applicators. Insights from these models can aid novel applicator design with improved motion and force transmission of BT instruments, and contribute to the estimation of overall treatment precision. The methodology presented can be extended to study other applicator geometries, flexible instruments, and afterloading systems.

Deformations of a 2D Elastica under a random distribution of normal loads

We describe the deformations of a 2D elastic structure (beam, rod or filament) subjected to randomly distributed local orthogonal forces. The fiber is in quasistatic equilibrium condition when a given force distribution is acting on it. To analyze the effects of force fluctuations on the observed configurations, we study the behavior of the bending moment at the origin and the filament curvature, as a function of nominal values of the local mean forces and small, moderate and large fluctuations around them.

Steady state motion of a shear deformable beam in contact with a traveling surface

A shear deformable beam moving along a straight path is considered as an idealization of the problem of stationary operation of a belt drive. The partial contact with a traveling surface results in the shear deformation of the beam. The tangential contact force grows near the end of the contact zone. Assuming perfect adhesion of the lower fiber of the beam to the traveling surface (no slip), we analytically demonstrate the necessity of accounting for concentrated contact forces and jump conditions, which is important for modeling the belt-pulley interaction. Along with dynamic effects, we further consider a frictional model with zones of stick and slip contact and demonstrate its convergence to the results with perfect adhesion at growing maximal friction force.