Computational Bone Mechanics Modeling with Frequency Dependent Rheological Properties and Crosslinking

Bone is a largely bipartite viscoelastic composite. Its mechanical behavior is determined by strain rate and the relative proportions of its principal constituent elements, hydroxyapatite and collagen, but is also largely dictated by their geometry and topology. Collagen fibrils include many segments of tropocollagen in staggered, parallel sequences. The physical staggering of this tropocollagen allows for gaps known as hole-zones, which serve as nucleation points for apatite mineral. The distance between adjacent repeat units of tropocollagen is known as D-Spacing and can be measured by Atomic Force Microscopy (AFM). This D-Spacing can vary in length slightly within a bundle, but by an additional order of magnitude within the same specimen, and can significantly alter the proportion of hydroxyapatite. Previous researchers have built and refined a Finite Element Analysis “Complex Model” to capture the consequences of adjusting D-Spacing and the viscoelastic parameters. This will ultimately serve to elucidate and perhaps predict the mechanical consequences of biological events that alter these parameters. This study aims to further refine the model’s precision by accounting for crosslinking between fibrils, the presence of which serves to add mechanical strength. This study also looks to refine the currently used rheological models by way of frequency dependent parameters in the hopes of improving model accuracy over a wider frequency range. Hormonal factors such as estrogen can significantly determine the composition of bone. Menopause marks a significant reduction in circulating estrogen and has been shown to factor heavily in the development of conditions like osteoporosis. Because sheep feature a hormonal cycle and skeletal structure similar to humans, three of six mature Columbia-Rambouillet ewes were randomly selected to undergo an ovariectomy, the remainder serving as sham-operated controls. Twelve months later twenty-five beam samples were harvested from their radius bones for mechanical analysis and other testing, including atomic force microscopy (AFM) and dynamic mechanical analysis (DMA). The data gleaned from these tests provide an experimental basis of comparison with The Complex Model. A 2-D Finite Element Analysis model in Abaqus was first created by Miguel Mendoza, which enforced viscoelasticity and a realistic proportion and placement of hydroxyapatite and collagen. The viscoelasticity was modeled using a Standard Linear Solid involving springs and a dashpot element. Crosslinks of varying number and location were arranged within the former model configuration as node to surface tie-constraints to explore the treatment of the FEA Model as a more realistic assembly of parts. Frequencies utilized for this model included 1, 3, 9 and 12 Hz. This approach is referred to in this research as the Intermolecular Forces (IMF) Scheme. The model was subsequently refined by Christopher Ha and Austin Cummings. The model was characterized by 2x100 unit half-cells, the lengths of which were randomly generated by a Python script. This script ingested the mean and standard deviation D-Spacing length to generate a model geometrically similar to a real specimen bearing those dimensions. A frequency dependent value for the dashpot element in the rheological model used for tropocollagen was developed using this latter FEA model, named the Complex Model. Dashpot values explored for this variable dashpot included 0.0125, 0.125, 0.3125, 0.45, 0.5875, 0.725, 0.8625 and 1.25 GPa-s, some values chosen for their high performance in past studies and others to further narrow the search for the best performing dashpot. All dashpot values were investigated over the previously stated frequencies in addition to 2, 5, 7 and 12 Hz. The best fit dashpot values were plotted against the frequencies in which they best performed and a polynomial trend line was fitted to establish an equation, and that equation was used to modify an existing user material subroutine for tropocollagen to provide an automatic frequency dependent dashpot value to Abaqus. This approach is referred to in this research as the Variable Dashpot (VD) Scheme. Results for the IMF scheme generally performed poorly, with the fully tie-constrained model performing best with 0.77 and 0.024 for R2 and RMSE respectively. Of the randomized crosslink models, that with the lowest number (N=20) of randomly placed non-enzymatic crosslinks performed best with 0.81 and 0.051 for R2 and RMSE respectively. Increasing the number of randomized crosslinks reduced model fit, and the remaining three variants exhibited mean R2 and RMSE values of 0.66-0.67 and 0.052 respectively. For the VD scheme, models running custom modified variable dashpot UMATs yielded R2 and RMSE values of 0.87 and 0.012 for C2207, and 0.89 and 0.008 for C1809. This is a notable fit considering all other material property parameters are held constant throughout each frequency. In the rheological model, this research also found a striking difference between the frequency dependent viscous element values that made each model perform best. This indicates that differences in D-Spacing standard deviations between OVX and control may be associated with distinct strain-rate dependent mechanical responses

A novel musculoskeletal joint modelling for orthopaedic applications

This thesis was submitted for the degree of Docter of Philosophy and awarded by Brunel University.The objective of the work carried out in this thesis was to develop analytical and computational tools to model and investigate musculoskeletal human joints. It was recognised that the FEA was used by many researchers in modelling human musculoskeletal motion, loading and stresses. However the continuum mechanics played only a minor role in determining the articular joint motion, and its value was questionable. This is firstly due to the computational cost and secondly due to its impracticality for this application. On the other hand, there isn’t any suitable software for precise articular joint motion analysis to deal with the local joint stresses or non standard joints. The main requirement in orthopaedics field is to develop a modeller software (and its associated theories) to model anatomic joint as it is, without any simplification with respect to joint surface morphology and material properties of surrounding tissues. So that the proposed modeller can be used for evaluating and diagnosing different joint abnormalities but furthermore form the basis for performing implant insertion and analysis of the artificial joints. The work which is presented in this thesis is a new frame work and has been developed for human anatomic joint analysis which describes the joint in terms of its surface geometry and surrounding musculoskeletal tissues. In achieving such a framework several contributions were made to the 6DOF linear and nonlinear joint modelling, the mathematical definition of joint stiffness, tissue path finding and wrapping and the contact with collision analysis. In 6DOF linear joint modelling, the contribution is the development of joint stiffness and damping matrices. This modelling approach is suitable for the linear range of tissue stiffness and damping properties. This is the first of its kind and it gives a firm analytical basis for investigating joints with surrounding tissue and the cartilage. The 6DOF nonlinear joint modelling is a new scheme which is described for modelling the motion of multi bodies joined by non-linear stiffness and contact elements. The proposed method requires no matrix assembly for the stiffness and damping elements or mass elements. The novelty in the nonlinear modelling, relates to the overall algorithmic approach and handling local non-linearity by procedural means. The mathematical definition of joint stiffness is also a new proposal which is based on the mathematical definition of stiffness between two bodies. Based on the joint stiffness matrix properties, number of joint stiffness invariants was obtained analytically such as the centre of stiffness, the principal translational stiffnesses, and the principal rotational stiffnesses. In corresponding to these principal stiffnesses, their principal axes have been also obtained. Altogether, a joint is assessed by six principal axes and six principal stiffnesses and its centre of stiffness. These formulations are new and show that a joint can be described in terms of inherent stiffness properties. It is expected that these will be better in characterising a joint in comparison to laxity based characterisation. The development of tissue path finding and wrapping algorithms are also introduced as new approaches. The musculoskeletal tissue wrapping involves calculating the shortest distance between two points on a meshed surface. A new heuristic algorithm was proposed. The heuristic is based on minimising the accumulative divergence from the straight line between two points on the surface and the direction of travel on the surface (i.e. bone). In contact and collision based development, the novel algorithm has been proposed that detects possible colliding points on the motion trajectory by redefining the distance as a two dimensional measure along the velocity approach vector and perpendicular to this vector. The perpendicular distance determines if there are potentially colliding points, and the distance along the velocity determines how close they are. The closest pair among the potentially colliding points gives the “time to collision”. The algorithm can eliminate the “fly pass” situation where very close points may not collide because of the direction of their relative velocity. All these developed algorithms and modelling theories, have been encompassed in the developed prototype software in order to simulate the anatomic joint articulations through modelling formulations developed. The software platform provides a capability for analysing joints as 6DOF joints based on anatomic joint surfaces. The software is highly interactive and driven by well structured database, designed to be highly flexible for the future developments. Particularly, two case studies are carried out in this thesis in order to generate results relating to all the proposed elements of the study. The results obtained from the case studies show good agreement with previously published results or model based results obtained from Lifemod software, whenever comparison was possible. In some cases the comparison was not possible because there were no equivalent results; the results were supported by other indicators. The modelling based results were also supported by experiments performed in the Brunel Orthopaedic Research and Learning Centre

Lecture notes in Medical and Biological Physics

Matter most commonly exists as a solid, liquid, or gas; these states are known as the three common phases of matter. Solids have a de nite shape and a speci c volume, liquids have a de nite volume but their shape changes depending on the container in which they are held, and gases have neither a de nite shape nor a speci c volume as their molecules move to ll the container in which they are held. Liquids and gases are considered to be uids because they yield to shearing forces, whereas solids resist them. Note that the extent to which uids yield to shearing forces (and hence ow easily and quickly) depends on a quantity called the viscosity. Liquids deform easily when stressed and do not spring back to their original shape once the force is removed because the atoms are free to slide about and change neighbors that is, they ow (so they are a type of uid) with the molecules held together by their mutual attraction. Because the atoms are closely packed, liquids, like solids, resist compression

Lecture notes in Medical and Biological Physics

Matter most commonly exists as a solid, liquid, or gas; these states are known as the three common phases of matter. Solids have a de nite shape and a speci c volume, liquids have a de nite volume but their shape changes depending on the container in which they are held, and gases have neither a de nite shape nor a speci c volume as their molecules move to ll the container in which they are held. Liquids and gases are considered to be uids because they yield to shearing forces, whereas solids resist them. Note that the extent to which uids yield to shearing forces (and hence ow easily and quickly) depends on a quantity called the viscosity. Liquids deform easily when stressed and do not spring back to their original shape once the force is removed because the atoms are free to slide about and change neighbors that is, they ow (so they are a type of uid) with the molecules held together by their mutual attraction. Because the atoms are closely packed, liquids, like solids, resist compression

Fractional order models of the human respiratory system

The fractional calculus is a generalization of classical integer-order integration and derivation to fractional (non-integer) order operators. Fractional order (FO) models are those models which contain such fractional order operators. A common representation of these models is in frequency domain, due to its simplicity. The dynamical systems whose model can be approximated in a natural way using FO terms, exhibit specific features, such as viscoelasticity, diffusion and a fractal structure; hence the respiratory system is an ideal application for FO models. Although viscoelastic and diffusive properties were intensively investigated in the respiratory system, the fractal structure was ignored. Probably one of the reasons is that the respiratory system does not pose a perfect symmetry, hence failing to satisfy one of the conditions for being a typical fractal structure. In the 70s, the respiratory impedance determined by the ratio of air-pressure and air-flow, has been introduced in a model structure containing a FO term. It has also been shown that the fractional order models outperform integer-order models on input impedance measurements. However, there was a lack of underpinning theory to clarify the appearance of the fractional order in the FO model structure. The thesis describes a physiologically consistent approach to reach twofold objectives: 1. to provide a physiologically-based mathematical explanation for the necessity of fractional order models for the input impedance, and 2. to determine the capability of the best fractional order model to classify between healthy and pathological cases. Rather than dealing with a specific case study, the modelling approach presents a general method which can be used not only in the respiratory system application, but also in other similar systems (e.g. leaves, circulatory system, liver, intestines). Furthermore, we consider also the case when symmetry is not present (e.g. deformations in the thorax - kyphoscoliose) as well as various pathologies. We provide a proof-of-concept for the appearance of the FO model from the intrinsic structure of the respiratory tree. Several clinical studies are then conducted to validate the sensitivity and specificity of the FO model in healthy groups and in various pathological groups

A novel musculoskeletal joint modelling for orthopaedic applications

The objective of the work carried out in this thesis was to develop analytical and computational tools to model and investigate musculoskeletal human joints. It was recognised that the FEA was used by many researchers in modelling human musculoskeletal motion, loading and stresses. However the continuum mechanics played only a minor role in determining the articular joint motion, and its value was questionable. This is firstly due to the computational cost and secondly due to its impracticality for this application. On the other hand, there isn’t any suitable software for precise articular joint motion analysis to deal with the local joint stresses or non standard joints. The main requirement in orthopaedics field is to develop a modeller software (and its associated theories) to model anatomic joint as it is, without any simplification with respect to joint surface morphology and material properties of surrounding tissues. So that the proposed modeller can be used for evaluating and diagnosing different joint abnormalities but furthermore form the basis for performing implant insertion and analysis of the artificial joints. The work which is presented in this thesis is a new frame work and has been developed for human anatomic joint analysis which describes the joint in terms of its surface geometry and surrounding musculoskeletal tissues. In achieving such a framework several contributions were made to the 6DOF linear and nonlinear joint modelling, the mathematical definition of joint stiffness, tissue path finding and wrapping and the contact with collision analysis. In 6DOF linear joint modelling, the contribution is the development of joint stiffness and damping matrices. This modelling approach is suitable for the linear range of tissue stiffness and damping properties. This is the first of its kind and it gives a firm analytical basis for investigating joints with surrounding tissue and the cartilage. The 6DOF nonlinear joint modelling is a new scheme which is described for modelling the motion of multi bodies joined by non-linear stiffness and contact elements. The proposed method requires no matrix assembly for the stiffness and damping elements or mass elements. The novelty in the nonlinear modelling, relates to the overall algorithmic approach and handling local non-linearity by procedural means. The mathematical definition of joint stiffness is also a new proposal which is based on the mathematical definition of stiffness between two bodies. Based on the joint stiffness matrix properties, number of joint stiffness invariants was obtained analytically such as the centre of stiffness, the principal translational stiffnesses, and the principal rotational stiffnesses. In corresponding to these principal stiffnesses, their principal axes have been also obtained. Altogether, a joint is assessed by six principal axes and six principal stiffnesses and its centre of stiffness. These formulations are new and show that a joint can be described in terms of inherent stiffness properties. It is expected that these will be better in characterising a joint in comparison to laxity based characterisation. The development of tissue path finding and wrapping algorithms are also introduced as new approaches. The musculoskeletal tissue wrapping involves calculating the shortest distance between two points on a meshed surface. A new heuristic algorithm was proposed. The heuristic is based on minimising the accumulative divergence from the straight line between two points on the surface and the direction of travel on the surface (i.e. bone). In contact and collision based development, the novel algorithm has been proposed that detects possible colliding points on the motion trajectory by redefining the distance as a two dimensional measure along the velocity approach vector and perpendicular to this vector. The perpendicular distance determines if there are potentially colliding points, and the distance along the velocity determines how close they are. The closest pair among the potentially colliding points gives the “time to collision”. The algorithm can eliminate the “fly pass” situation where very close points may not collide because of the direction of their relative velocity. All these developed algorithms and modelling theories, have been encompassed in the developed prototype software in order to simulate the anatomic joint articulations through modelling formulations developed. The software platform provides a capability for analysing joints as 6DOF joints based on anatomic joint surfaces. The software is highly interactive and driven by well structured database, designed to be highly flexible for the future developments. Particularly, two case studies are carried out in this thesis in order to generate results relating to all the proposed elements of the study. The results obtained from the case studies show good agreement with previously published results or model based results obtained from Lifemod software, whenever comparison was possible. In some cases the comparison was not possible because there were no equivalent results; the results were supported by other indicators. The modelling based results were also supported by experiments performed in the Brunel Orthopaedic Research and Learning Centre.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: ● Formulations and Numerical Methods ● Efficient Methods and Real-Time Applications ● Flexible Multibody Dynamics ● Contact Dynamics and Constraints ● Multiphysics and Coupled Problems ● Control and Optimization ● Software Development and Computer Technology ● Aerospace and Maritime Applications ● Biomechanics ● Railroad Vehicle Dynamics ● Road Vehicle Dynamics ● Robotics ● Benchmark ProblemsPostprint (published version

Neurological Disease Diagnosis and Treatment via Precise Robotic Intervention

This work focuses on the development and application of mechatronic systems for measurement, diagnosis and treatment of acute and chronic neurological conditions. The development of an automated tendon reflex stimulation device, as well as analysis and classification methods for both automated and manual stimulus delivery will provide the groundwork for improvements to both diagnosis and treatment of neurological injuries. In a similar vein, development of a variable resonance actuator for Magnetic Resonance Elastography imaging enables tissue property measurement of the intervertebral discs, hopefully providing an early marker and better understanding of degeneration. In addition to MRI based spinal tissue property measurements, an MRI guided high precision robot is developed for direct injection into the spinal cord, along with an accompanying image guided control scheme. The novel parallel plane mechanism enables control of 4 degrees of freedom, while the linear piezoelectric actuators in a direct drive configuration enables superior accuracy. Taken together, these robotic device developments constitute contributions to the field of precision medical robotics with applications to physiological understanding of the human body.Ph.D

Viscoelasticity

This book contains a wealth of useful information on current research on viscoelasticity. By covering a broad variety of rheology, non-Newtonian fluid mechanics and viscoelasticity-related topics, this book is addressed to a wide spectrum of academic and applied researchers and scientists but it could also prove useful to industry specialists. The subject areas include, theory, simulations, biological materials and food products among others

An integrated approach to whole-body vibration

Obiettivo di questa tesi è la determinazione e quantificazione degli effetti della whole-body vibration al corpo umano, in termini di consumo energetico, tramite un approccio globale e integrato. L’obiettivo è ottenuto considerando il corpo umano come una struttura organica complessa. Allo scopo di comprendere come questo risponda alle vibrazioni verticali, il consumo energetico del corpo umano è stato misurato per mezzo della variazione della temperatura superficiale con tecniche di misurazione a termografia infrarossa. Lo spostamento dei muscoli invece con il sistema di analisi di movimento Vicon MX. Infine, per quanto riguarda il consumo di ossigeno con il sistema telemetrico Cosmed K4. Il primo passo è stato l’istituzione di un protocollo appropriato che soddisfi l’obiettivo di questo studio. Infatti, la mancanza di coerenza nei protocollo di whole-body vibration che si trovano allo stato dell’arte, ha reso essenziale l’istituzione di un apposito protocollo, ed a questo scopo è stata definita la struttura dell’esperimento. Di conseguenza, è stata avviata una serie di prove per esaminare la risposta del corpo umano alle vibrazioni verticali, cambiando la durata e la frequenza della vibrazione, nonché la durata del periodo di riposo. In totale, quattro persone in piedi sono state sottoposte a vibrazioni verticali, in una pedana vibrante, a frequenze da 20 a 50 Hz. Dopo l’instaurazione del protocollo finale, sono stati avviate una serie di prove di laboratorio. In particolare, sono state scelte tre frequenze per le vibrazioni: 20, 30 e 45 Hz. I risultati ottenuti più interessanti di questo studio, riguardano il consumo di ossigeno, la temperatura superficiale e i coefficienti di trasmissibilità dell’accelerazione.The objective of this thesis is to determine and quantify the effects of whole-body vibration to the human body in terms of energy expenditure, by means of a global and integrated approach. This objective is attained by considering the human body as a complex organic structure. In order to understand how it responds to vertical vibrations, the energy expenditure of the human body was measured by means of the variation in superficial temperature with the aid of infrared thermography, the displacement of the muscles with the aid of the Vicon MX motion analysis system and the oxygen uptake with the aid of the Cosmed K4 telemetric system. The establishment of an appropriate protocol which satisfies the aim of this study was the first goal. The lack of consistency in whole-body vibration protocols in the current published studies makes the establishment of an appropriate protocol essential, and in this sense, an experiment setup was implemented. Therefore, a series of experiments was conducted to examine the response of the human body to vertical vibrations, changing the duration and the frequency of vertical vibration, and the duration of rest period. A number of four persons were subjected to vertical vibrations on a vibrating table in a standing position at a frequency ranging from 20 to 50 Hz. After the establishment of the final protocol, a series of laboratory experiments took place. Three different vibration frequencies were chosen: 20, 30 and 45 Hz corresponding to three different tests. The most interesting findings regard the oxygen consumption, the superficial temperature evolution, and the transmissibility coefficients for the acceleration