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Human aging results in a progressive decline in the active force generation capability of skeletal muscle. While many factors related to the changes of morphological and structural properties in muscle fibers and the extracellular matrix (ECM) have been considered as possible reasons for causing age-related force reduction, it is still not fully understood why the decrease in force generation under eccentric contraction (lengthening) is much less than that under concentric contraction (shortening). Biomechanically, it was observed that connective tissues (endomysium) stiffen as ages, and the volume ratio of connective tissues exhibits an age-related increase. However, limited skeletal muscle models take into account the microstructural characteristics as well as the volume fraction of tissue material. This study aims to provide a numerical investigation in which the muscle fibers and the ECM are explicitly represented to allow quantitative assessment of the age-related force reduction mechanism. To this end, a fiber-level honeycomb-like microstructure is constructed and modeled by a pixel-based Reproducing Kernel Particle Method (RKPM), which allows modeling of smooth transition in biomaterial properties across material interfaces. The numerical investigation reveals that the increased stiffness of the passive materials of muscle tissue reduces the force generation capability under concentric contraction while maintains the force generation capability under eccentric contraction. The proposed RKPM microscopic model provides effective means for the cellular-scale numerical investigation of skeletal muscle physiology. NOVELTY STATEMENT: A cellular-scale honeycomb-like microstructural muscle model constructed from a histological cross-sectional image of muscle is employed to study the causal relations between age-associated microstructural changes and age-related force loss using Reproducing Kernel Particle Method (RKPM). The employed RKPM offers an effective means for modeling biological materials based on pixel points in the medical images and allow modeling of smooth transition in the material properties across interfaces. The proposed microstructure-informed muscle model enables quantitative evaluation on how cellular-scale compositions contribute to muscle functionality and explain differences in age-related force changes during concentric, isometric and eccentric contractions.

Computational mechanics is a growing discipline that is commonly used to provide invaluable insight for engineering analyses, particularly when theoretical or empirical analyses are impractical. Computer simulations can handle complex problems more readily than analytical methods and are often much less expensive and less time consuming than performing experiments. However, developing simulation models for moderate to complex geometries is still a time consuming task. The upfront cost of developing models is an impediment that reduces the effectiveness of simulation in engineering design and analysis.Meshfree methods provide flexible means of creating approximation functions using only a collection of points with corresponding window functions. This flexibility makes meshfree methods attractive for problems involving large deformation and failure, where mesh-based methods, such as the finite element method, experience complications due to mesh entanglement. Without the need of generating a quality mesh, meshfree methods also have a greatly simplified simulation development process. However, for problems with complicated geometries such as non-convex or multi-body domains, poor solution accuracy and reduced convergence rates are observed due to inaccurate representation of complex geometry unless the extents of the window functions, and thus approximation functions, are carefully controlled. The required control is not available with the Euclidean metrics that are commonly used to construct the window functions.In this dissertation, methods of providing more control in window function design are presented. ``Conforming'' window functions are constructed using local triangulations in two and three dimensions, allowing efficient and systematic handling of complex geometries. Graph distances are used in conjunction with Euclidean metrics to provide adequate information for shaping the window functions. The conforming window functions are demonstrated using the Reproducing Kernel Particle Method showing improved accuracy and convergence rates for problems with challenging geometries. Additional attention is given to addressing the challenges of simulating nearly incompressible material response and to maintaining a higher stable time increment for dynamic problems that are solved using explicit time integration.Addressing the boundary-related challenges of meshfree methods both opens the methods to a broader class of problems and enables an agile simulation development process.

The computational accuracy of the traditional reproducing kernel particle method (RKPM) is susceptible to different kernel functions. To eliminate the adverse effects of the different kernel functions on the computational accuracy of the RKPM, the radial basis function (RBF) is introduced and the radial basis reproducing kernel particle method (RRKPM) is proposed. Compared with the RKPM, the proposed method has the advantages of greater computational accuracy and faster convergence speed. Furthermore, the proposed method is applied to analyze the elastic deformation process of materials with various defects. Utilizing the Galerkin weak form of elastic mechanical problem, the RRKPM of elastic mechanics is established and the corresponding formulae are derived. Combined with the numerical examples, the shaped parameter of the RBF, the scaling parameter and the penalty factor are discussed. Finally, several different examples are adopted to demonstrate the applicability and correctness of the RRKPM.

Structures involving multiple materials are difficult for meshfree methods to model accurately due to the strain discontinuity introduced at the material interface. An immersed Reproducing Kernel Particle Method (RKPM) approach is proposed to model inhomogeneous materials using an immersed domain approach to allow independent approximations and discretizations for the background matrix and the foreground inclusion. In this approach, Nitsche’s method is introduced to enforce the interface compatibility conditions in a variationally consistent manner. The proposed method simplifies the spatial discretization procedures for multi-material problems involving complex geometries because the conforming requirements in discretization at the interface are avoided. Efficient and stable domain integration methods for the immersed RKPM discretization are investigated, and the performance of several approaches are compared. Specifically, conforming and non-conforming domain integration between the foreground and background domains are discussed. Optimal convergence is achieved without tedious procedures such as enrichment functions or boundary singular kernels commonly employed in other meshfree methods for solving multi-material problems. Several numerical examples are presented to examine the effectiveness of the proposed method. A non-linear formulation of the immersed RKPM method is also presented and its effectiveness in modeling brittle materials using an elastic-damage model is investigated.

This paper introduces the meshfree Reproducing Kernel Particle Method (RKPM) in conjunction with a stabilized conforming nodal integration for 3D image-based modeling of skeletal muscles. This approach allows for construction of simulation model based on pixel data obtained from medical images. The model consists of different materials and muscle fiber direction obtained from Diffusion Tensor Imaging (DTI) is input at each pixel point. The reproducing kernel (RK) approximation also allows a representation of material heterogeneity with smooth transition. A multiphase multichannel level set based segmentation using Magnetic Resonance Images (MRI) and DTI formulated under a modified functional has been integrated into RKPM framework. The use of proposed methods for modeling the human lower leg is demonstrated.

Reproducing kernel method (RKM) has its origins in wavelets and it is based on convolution theory. Being their continuous version, RKM is often referred as the general framework for meshless methods. In fact, since in real computation discretization is inevitable, these integrals need to be evaluated numerically, leading to the creation of reproducing kernel particle method RKPM and moving least squares MLS approximation. Nevertheless, in this paper the integrals in RKM are explicitly evaluated for polynomials basis function and simple geometries in one, two and three dimensions even with conforming holes. Moreover, a general formula is provided for complicated shapes also for multiple connected domains. This is possible through a boundary formulation where domain integrals involved in RKM are transformed by Gauss theorem in circular or flux integrals. Parallelization is readily enabled since no preliminary arrangements of nodes is needed for the moments matrix. Furthermore, using symbolic inversion, computation of shape functions in RKM is considerably speeded up.

This thesis presents a computational model of the surgical stitching tasks and a path planning algorithm for robotic assisted stitching. The overall goal of the research is to enable surgical robots to perform automatic suturing. Suturing comprises several distinct steps, one of them is the stitching. During stitching, reaching the desired exit point is difficult because it must be accomplished without direct visual feedback. Moreover, the stitching is a time consuming procedure repeated multiple times during suturing. Therefore, it would be desirable to enhance the surgical robots with the ability of performing automatic suturing. The focus of this work is on the automation of the stitching task. The thesis presents a model based path planning algorithm for the autonomous stitching. The method uses a nonlinear model for the curved needle - soft tissue interaction. The tissue is modeled as a deformable object using continuum mechanics tools. This thesis uses a mesh free deformable tissue model namely, Reproducing Kernel Particle Method (RKPM). RKPM was chosen as it has been proven to accurately handle large deformation and requires no re-meshing algorithms. This method has the potential to be more realistic in modeling various material characteristics by using appropriate strain energy functions. The stitching task is simulated using a constrained deformable model; the deformable tissue is constrained by the interaction with the curved needle. The stitching model was used for needle trajectory path planning during stitching. This new path planning algorithm for the robotic stitching was developed, implemented, and evaluated. Several simulations and experiments were conducted. The first group of simulations comprised random insertions from different insertion points without planning to assess the modeling method and the trajectory of the needle inside the tissue. Then the parameters of the simulations were set according to the measured experimental parameters. The proposed path planning method was tested using a surgical ETHICON needle of type SH 1=2 Circle with the radius of 8:88mm attached to a robotic manipulator. The needle was held by a grasper which is attached to the robotic arm. The experimental results illustrate that the path planned curved needle insertions are fifty percent more accurate than the unplanned ones. The results also show that this open loop approach is sensitive to model parameters. Master of Applied Science (MASc)

International audience; In this paper we propose a new approximation technique within the context of meshless methods able to reproduce functions with discontinuous derivatives. This approach involves some concepts of the reproducing kernel particle method (RKPM), which have been extended in order to reproduce functions with discon-tinuous derivatives. This strategy will be referred as Enriched Reproducing Kernel Particle Approximation (E-RKPA). The accuracy of the proposed technique will be compared with standard RKP approximations (which only reproduces polynomials).

International audience; In this paper we propose a new approximation technique within the context of meshless methods able to reproduce functions with discontinuous derivatives. This approach involves some concepts of the reproducing kernel particle method (RKPM), which have been extended in order to reproduce functions with discon-tinuous derivatives. This strategy will be referred as Enriched Reproducing Kernel Particle Approximation (E-RKPA). The accuracy of the proposed technique will be compared with standard RKP approximations (which only reproduces polynomials).