Suleiman Banihani

A comparison of some model order reduction methods for fast simulation of soft tissue response using the point collocation-based method of finite spheres

In this paper we develop the point collocation-based method of finite spheres (PCMFS) to simulate the viscoelastic response of soft biological tissues and evaluate the effectiveness of model order reduction methods such as modal truncation (MT), Hankel optimal model and truncated balanced realization (TBR) techniques for PCMFS. The PCMFS is a physics-based meshfree numerical technique for real time simulation of surgical procedures. Since computational speed has a significant role in simulation of surgical procedures, model order reduction methods have been compared for relative gains in efficiency and computational accuracy. Of these methods, TBR results in the highest accuracy with an average error which is within 3.37% of the full model while MT results in the highest efficiency with a computational cost reduction of 54.2% compared to the full model.

POD for Real-Time Simulation of Hyperelastic Soft Biological Tissue Using the Point Collocation Method of Finite Spheres

The point collocation method of finite spheres (PCMFS) is used to model the hyperelastic response of soft biological tissue in real time within the framework of virtual surgery simulation. The proper orthogonal decomposition (POD) model order reduction (MOR) technique was used to achieve reduced-order model of the problem, minimizing computational cost. The PCMFS is a physics-based meshfree numerical technique for real-time simulation of surgical procedures where the approximation functions are applied directly on the strong form of the boundary value problem without the need for integration, increasing computational efficiency. Since computational speed has a significant role in simulation of surgical procedures, the proposed technique was able to model realistic nonlinear behavior of organs in real time. Numerical results are shown to demonstrate the effectiveness of the new methodology through a comparison between full and reduced analyses for several nonlinear problems. It is shown that the proposed technique was able to achieve good agreement with the full model; moreover, the computational and data storage costs were significantly reduced.

COMPUTATIONALLY EFFICIENT TECHNIQUE FOR THE SOLUTION OF TIMOSHENKO BEAM AND MINDLIN-REISSNER PLATE PROBLEMS USING THE METHOD OF FINITE SPHERES

In this paper we discuss the application of the method of finite spheres (MFS) to the solution of shear deformable beam and plate problems. A computationally efficient technique is presented in which the integration points and weights are generated using a genetic algorithm and stored in a lookup table using normalized coordinates much like a table of Gauss integration points and weights. This technique offers a significant reduction of computational time while maintaining accuracy.

Robust Backstepping Control for a Four-Bar Linkage Mechanism Driven by a DC Motor

Four-bar linkage mechanisms have dragged the attention of many specialists due to its importance in the academic and industrial sectors. Hence, a lot of research work has been conducted to understand their complex behavior and explore various control techniques. In fact, such mechanisms possess highly nonlinear dynamics that require advanced nonlinear control methods. In addition, the four-bar linkage mechanism is exposed to significant dynamic fluctuations at high speeds due to the system inertias. In this paper, a backstepping control algorithm with a robust scheme is designed and applied on the four-bar linkage mechanism to investigate and explore its dynamical performance under various operating conditions and without a priori knowledge of the model parameters. Five operating conditions are introduced and tested in numerical simulations to show that the proposed nonlinear controller successfully regulates and tracks the speed of the driving link of the mechanism and shows a satisfactory performance.