Computational optimization methods for modeling the effect of muscle forces on bone strength adaptation

An improved understanding of the mechanical influences that alter the strength of a bone can aid in the refinement of the wide array of currently available techniques to counteract the losses of bone strength that occur due to age or disuse both on Earth and in Space. To address this need, computational modeling methods to quantitatively analyze and compare the effects of mechanical factors on the strength of a targeted bone within a multibone, multimuscle system are developed and implemented in this work. Through a more detailed representation of the system in which the bone acts and the creation of a model that does not require experimentally based parameters, the developed techniques eliminate many of the difficulties that have often hindered these musculoskeletal phenomena from being studied with the tools and methods readily employed in the investigation of their inert mechanical counterparts. The computational techniques developed couple the determination of the muscle forces acting within the system studied, the stresses they induce within the bones of the system, and the ensuing adaptations of the shape of one of these bones, altering its strength. This is accomplished through the use of gradient based optimization methods, finite element methods, and gradientless optimization methods, respectively. The developed gradientless optimization methods in this work progress the bone shape design toward one with a more uniform state of stress through the relative effects of measures of the local stress state, the global stress state, and the variation of the local stress state over the region being optimized. Quantitative measures of the progression towards a uniformity of the stress state during the optimization process are defined so that relative changes can be directly compared between the various mechanical factors studied. Similarly, methods are developed to independently assess the ability of the conditions studied to induce bone shape alterations that improve the strength of the bone under a standard set of loading conditions. The implementation of the model in a parametric study of methods to improve the resistance of the tibia bone to stress fractures demonstrates its ability to evaluate the effects of various loading conditions, with forces and stresses studied ranging three orders of magnitude. From this investigation, loading modes are identified that improve the bone\u27s strength in the fracture prone region by up to 20%. The developed computational modeling techniques eliminate the difficulties inherent in the experimental investigation of mechanically based alterations to bone strength and provide a means for the improved understanding and, ultimately, better control of these adaptive phenomena

CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions

We introduce a general framework for active learning in regression problems. Our framework extends the standard setup by allowing for general types of data, rather than merely pointwise samples of the target function. This generalization covers many cases of practical interest, such as data acquired in transform domains (e.g., Fourier data), vector-valued data (e.g., gradient-augmented data), data acquired along continuous curves, and, multimodal data (i.e., combinations of different types of measurements). Our framework considers random sampling according to a finite number of sampling measures and arbitrary nonlinear approximation spaces (model classes). We introduce the concept of generalized Christoffel functions and show how these can be used to optimize the sampling measures. We prove that this leads to near-optimal sample complexity in various important cases. This paper focuses on applications in scientific computing, where active learning is often desirable, since it is usually expensive to generate data. We demonstrate the efficacy of our framework for gradient-augmented learning with polynomials, Magnetic Resonance Imaging (MRI) using generative models and adaptive sampling for solving PDEs using Physics-Informed Neural Networks (PINNs)

On the Statics, Dynamics, and Stability of Continuum Robots: Model Formulations and Efficient Computational Schemes

This dissertation presents advances in continuum-robotic mathematical-modeling techniques. Specifically, problems of statics, dynamics, and stability are studied for robots with slender elastic links. The general procedure within each topic is to develop a continuous theory describing robot behavior, develop a discretization strategy to enable simulation and control, and to validate simulation predictions against experimental results.Chapter 1 introduces the basic concept of continuum robotics and reviews progress in the field. It also introduces the mathematical modeling used to describe continuum robots and explains some notation used throughout the dissertation.The derivation of Cosserat rod statics, the coupling of rods to form a parallel continuum robot (PCR), and solution of the kinematics problem are reviewed in Chapter 2. With this foundation, soft real-time teleoperation of a PCR is demonstrated and a miniature prototype robot with a grasper is controlled.Chapter 3 reviews the derivation of Cosserat rod dynamics and presents a discretization strategy having several desirable features, such as generality, accuracy, and potential for good computational efficiency. The discretized rod model is validated experimentally using high speed camera footage of a cantilevered rod. The discretization strategy is then applied to simulate continuum robot dynamics for several classes of robot, including PCRs, tendon-driven robots, fluidic actuators, and concentric tube robots.In Chapter 4, the stability of a PCR is analyzed using optimal control theory. Conditions of stability are gradually developed starting from a single planar rod and finally arriving at a stability test for parallel continuum robots. The approach is experimentally validated using a camera tracking system.Chapter 5 provides closing discussion and proposes potential future work

Multi-objective particle swarm optimization for the structural design of concentric tube continuum robots for medical applications

Concentric tube robots belong to the class of continuum robotic systems whose morphology is described by continuous tangent curvature vectors. They are composed of multiple, interacting tubes nested inside one another and are characterized by their inherent flexibility. Concentric tube continuum robots equipped with tools at their distal end have high potential in minimally invasive surgery. Their morphology enables them to reach sites within the body that are inaccessible with commercial tools or that require large incisions. Further, they can be deployed through a tight lumen or follow a nonlinear path. Fundamental research has been the focus during the last years bringing them closer to the operating room. However, there remain challenges that require attention. The structural synthesis of concentric tube continuum robots is one of these challenges, as these types of robots are characterized by their large parameter space. On the one hand, this is advantageous, as they can be deployed in different patients, anatomies, or medical applications. On the other hand, the composition of the tubes and their design is not a straightforward task but one that requires intensive knowledge of anatomy and structural behavior. Prior to the utilization of such robots, the composition of tubes (i.e. the selection of design parameters and application-specific constraints) must be solved to determine a robotic design that is specifically targeted towards an application or patient. Kinematic models that describe the change in morphology and complex motion increase the complexity of this synthesis, as their mathematical description is highly nonlinear. Thus, the state of the art is concerned with the structural design of these types of robots and proposes optimization algorithms to solve for a composition of tubes for a specific patient case or application. However, existing approaches do not consider the overall parameter space, cannot handle the nonlinearity of the model, or multiple objectives that describe most medical applications and tasks. This work aims to solve these fundamental challenges by solving the parameter optimization problem by utilizing a multi-objective optimization algorithm. The main concern of this thesis is the general methodology to solve for patient- and application-specific design of concentric tube continuum robots and presents key parameters, objectives, and constraints. The proposed optimization method is based on evolutionary concepts that can handle multiple objectives, where the set of parameters is represented by a decision vector that can be of variable dimension in multidimensional space. Global optimization algorithms specifically target the constrained search space of concentric tube continuum robots and nonlinear optimization enables to handle the highly nonlinear elasticity modeling. The proposed methodology is then evaluated based on three examples that include cooperative task deployment of two robotic arms, structural stiffness optimization under the consideration of workspace constraints and external forces, and laser-induced thermal therapy in the brain using a concentric tube continuum robot. In summary, the main contributions are 1) the development of an optimization methodology that describes the key parameters, objectives, and constraints of the parameter optimization problem of concentric tube continuum robots, 2) the selection of an appropriate optimization algorithm that can handle the multidimensional search space and diversity of the optimization problem with multiple objectives, and 3) the evaluation of the proposed optimization methodology and structural synthesis based on three real applications

An MBO scheme for clustering and semi-supervised clustering of signed networks

We introduce a principled method for the signed clustering problem, where the goal is to partition a weighted undirected graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges spanning across clusters are mostly negative. Our method relies on a graph-based diffuse interface model formulation utilizing the Ginzburg–Landau functional, based on an adaptation of the classic numerical Merriman–Bence–Osher (MBO) scheme for minimizing such graph-based functionals. The proposed objective function aims to minimize the total weight of inter-cluster positively-weighted edges, while maximizing the total weight of the inter-cluster negatively-weighted edges. Our method scales to large sparse networks, and can be easily adjusted to incorporate labelled data information, as is often the case in the context of semisupervised learning. We tested our method on a number of both synthetic stochastic block models and real-world data sets (including financial correlation matrices), and obtained promising results that compare favourably against a number of state-of-the-art approaches from the recent literature

Deep Reinforcement Learning for Inverse Kinematics and Path Following for Concentric Tube Robots

Concentric tube robots (CTRs) are continuum robots that allow for bending and twisting motions unattainable by traditional rigid link robots. The curvilinear backbones can benefit surgical applications by improving dexterity, enlarging the workspace, and reducing trauma at the entry point of the instrument. The curvilinear backbone that is attributed is the result of pre-curved, super-elastic tubes arranged concentrically. Each tube has a straight and pre-curved section and is actuated in rotation and translation from the tube base with the neighboring tube interactions producing the curvilinear backbone. The modeling of the neighboring tube interactions is non-trivial, and an explored topic in CTR literature. However, model-based kinematics and control can be inaccurate due to inherent manufacturing errors of the tubes, permanent deformation over time, and unmodelled physical interactions. This thesis proposes a model-free control method using deep reinforcement learning (DRL). The DRL framework aims to control the end-effector of the CTR with limited modeling information by leveraging simulation data, which is much less costly than hardware data. To develop a DRL framework, a Markov Decision Process (MDP) with states, actions, and rewards needs to be defined for the inverse kinematics task. First, action exploration was investigated with this MDP in a simpler simulation as CTRs have a unique extension degree of freedom per tube. Next, state representation, curriculum reward, and adaptation methods over multiple CTR systems were developed in a more accurate simulation. To validate the work in simulation, a noise-induced simulation environment was utilized to demonstrate the initial robustness of the learned policy. Finally, a hardware system was developed where a workspace characterization was performed to determine simulation to hardware differences. By using Sim2Real domain transfer, a simulation policy was successfully transferred to hardware for inverse kinematics and path following, validating the approach

The optimisation of brass instruments to include wall vibration effects

This thesis focuses on the design optimisation of a brass instrument. The bore profile of such an instrument is known to be the primary influence on the sound of the instrument as it directly controls the shape of the air-column contained within the instruments' walls. It has long been claimed, however, that other factors, such as the wall material and wall vibrations, are also significant, although to a lesser degree. In recent years, it has been proven that wall vibrations do indeed have an audible effect on the sound (Moore et al 2005, Kausel et al 2007, Nachtmann et al 2007, Kausel, Zietlow and Moore 2010). This effect corresponds to a relative increase in the power of upper harmonics of the sound spectrum when vibrations are greatest, and relative increase in the power of the lower harmonics, in particular the fundamental, when vibrations are at their least. The result is a timbral difference where a greater relative power in the upper harmonics results in a 'brighter' sound, and where the opposite results in a 'darker' sound. Studies have also found that the degree of the wall vibration is increased when the resonant frequencies of the air-column and those of the instruments' structure align. It is this principle that this work is based on. The primary objective of this work was to devise a suitable approach for incorporating the wall vibration effect into an optimisation method to investigate the optimum designs for two scenarios: maximum wall vibration and minimum wall vibration. It was also of interest to investigate if there were any design characteristics for each scenario. Two analysis methods were investigated for their suitability, namely free and forced vibration using finite element analysis (FEA). Different approaches to defining the design variables were explored and the suitability of different optimisation algorithms was investigated. The free vibration approach was found to be inadequate for this application due to the inherent omission of valuable magnitude information. The forced vibration approach was found to be more successful, although it was not possible to align a resonance with each frequency of interest