The feasibility of vibration analysis as a technique to detect osseointegration of transfemoral implants

One of the main causes of above knee or transfemoral amputation (TFA) in the developed world is trauma to the limb. The number of people undergoing TFA due to limb trauma, particularly due to war injuries, has been increasing. Typically the trauma amputee population, including war-related amputees, are otherwise healthy, active and desire to return to employment and their usual lifestyle. Consequently there is a growing need to restore long-term mobility and limb function to this population. Traditionally transfemoral amputees are provided with an artificial or prosthetic leg that consists of a fabricated socket, knee joint mechanism and a prosthetic foot. Amputees have reported several problems related to the socket of their prosthetic limb. These include pain in the residual limb, poor socket fit, discomfort and poor mobility. Removing the socket from the prosthetic limb could eliminate or reduce these problems. A solution to this is the direct attachment of the prosthesis to the residual bone (femur) inside the residual limb. This technique has been used on a small population of transfemoral amputees since 1990. A threaded titanium implant is screwed in to the shaft of the femur and a second component connects between the implant and the prosthesis. A period of time is required to allow the implant to become fully attached to the bone, called osseointegration (OI), and be able to withstand applied load; then the prosthesis can be attached. The advantages of transfemoral osseointegration (TFOI) over conventional prosthetic sockets include better hip mobility, sitting comfort and prosthetic retention and fewer skin problems on the residual limb. However, due to the length of time required for OI to progress and to complete the rehabilitation exercises, it can take up to twelve months after implant insertion for an amputee to be able to load bear and to walk unaided. The long rehabilitation time is a significant disadvantage of TFOI and may be impeding the wider adoption of the technique. There is a need for a non-invasive method of assessing the degree of osseointegration between the bone and the implant. If such a method was capable of determining the progression of TFOI and assessing when the implant was able to withstand physiological load it could reduce the overall rehabilitation time. Vibration analysis has been suggested as a potential technique: it is a non destructive method of assessing the dynamic properties of a structure. Changes in the physical properties of a structure can be identified from changes in its dynamic properties. Consequently vibration analysis, both experimental and computational, has been used to assess bone fracture healing, prosthetic hip loosening and dental implant OI with varying degrees of success. More recently experimental vibration analysis has been used in TFOI. However further work is needed to assess the potential of the technique and fully characterise the femur-implant system. The overall aim of this study was to develop physical and computational models of the TFOI femur-implant system and use these models to investigate the feasibility of vibration analysis to detect the process of OI. Femur-implant physical models were developed and manufactured using synthetic materials to represent four key stages of OI development (identified from a physiological model), simulated using different interface conditions between the implant and femur. Experimental vibration analysis (modal analysis) was then conducted using the physical models. The femur-implant models, representing stage one to stage four of OI development, were excited and the modal parameters obtained over the range 0-5kHz. The results indicated the technique had limited capability in distinguishing between different interface conditions. The fundamental bending mode did not alter with interfacial changes. However higher modes were able to track chronological changes in interface condition by the change in natural frequency, although no one modal parameter could uniquely distinguish between each interface condition. The importance of the model boundary condition (how the model is constrained) was the key finding; variations in the boundary condition altered the modal parameters obtained. Therefore the boundary conditions need to be held constant between tests in order for the detected modal parameter changes to be attributed to interface condition changes. A three dimensional Finite Element (FE) model of the femur-implant model was then developed and used to explore the sensitivity of the modal parameters to more subtle interfacial and boundary condition changes. The FE model was created using the synthetic femur geometry and an approximation of the implant geometry. The natural frequencies of the FE model were found to match the experimental frequencies within 20% and the FE and experimental mode shapes were similar. Therefore the FE model was shown to successfully capture the dynamic response of the physical system. As was found with the experimental modal analysis, the fundamental bending mode of the FE model did not alter due to changes in interface elastic modulus. Axial and torsional modes were identified by the FE model that were not detected experimentally; the torsional mode exhibited the largest frequency change due to interfacial changes (103% between the lower and upper limits of the interface modulus range). Therefore the FE model provided additional information on the dynamic response of the system and was complementary to the experimental model. The small changes in natural frequency over a large range of interface region elastic moduli indicated the method may only be able to distinguish between early and late OI progression. The boundary conditions applied to the FE model influenced the modal parameters to a far greater extent than the interface condition variations. Therefore the FE model, as well as the experimental modal analysis, indicated that the boundary conditions need to be held constant between tests in order for the detected changes in modal parameters to be attributed to interface condition changes alone. The results of this study suggest that in a clinical setting it is unlikely that the in vivo boundary conditions of the amputated femur could be adequately controlled or replicated over time and consequently it is unlikely that any longitudinal change in frequency detected by the modal analysis technique could be attributed exclusively to changes at the femur-implant interface. Therefore further development of the modal analysis technique would require significant consideration of the clinical boundary conditions and investigation of modes other than the bending modes.

Modulation of depth-dependent properties in tissue-engineered cartilage with a semi-permeable membrane and perfusion : a continuum model of matrix metabolism and transport

The functional properties of cartilaginous tissues are determined predominantly by the content, distribution, and organization of proteoglycan and collagen in the extracellular matrix. Extracellular matrix accumulates in tissue-engineered cartilage constructs by metabolism and transport of matrix molecules, processes that are modulated by physical and chemical factors. Constructs incubated under free-swelling conditions with freely permeable or highly permeable membranes exhibit symmetric surface regions of soft tissue. The variation in tissue properties with depth from the surfaces suggests the hypothesis that the transport processes mediated by the boundary conditions govern the distribution of proteoglycan in such constructs. A continuum model (DiMicco and Sah in Transport Porus Med 50:57-73, 2003) was extended to test the effects of membrane permeability and perfusion on proteoglycan accumulation in tissue-engineered cartilage. The concentrations of soluble, bound, and degraded proteoglycan were analyzed as functions of time, space, and non-dimensional parameters for several experimental configurations. The results of the model suggest that the boundary condition at the membrane surface and the rate of perfusion, described by non-dimensional parameters, are important determinants of the pattern of proteoglycan accumulation. With perfusion, the proteoglycan profile is skewed, and decreases or increases in magnitude depending on the level of flow-based stimulation. Utilization of a semi-permeable membrane with or without unidirectional flow may lead to tissues with depth-increasing proteoglycan content, resembling native articular cartilage.

Natural convection boundary-layer adjacent to an inclined flat plate subject to sudden and ramp heating

The natural convection thermal boundary layer adjacent to an inclined flat plate subject to sudden heating and a temperature boundary condition which follows a ramp function up until a specified time and then remains constant is investigated. The development of the flow from start-up to a steady-state has been described based on scaling analyses and verified by numerical simulations. Different flow regimes based on the Rayleigh number are discussed with numerical results for both boundary conditions. For ramp heating, the boundary layer flow depends on the comparison of the time at which the ramp heating is completed and the time at which the boundary layer completes its growth. If the ramp time is long compared with the steady state time, the layer reaches a quasi steady mode in which the growth of the layer is governed solely by the thermal balance between convection and conduction. On the other hand, if the ramp is completed before the layer becomes steady; the subsequent growth is governed by the balance between buoyancy and inertia, as for the case of instantaneous heating.

Natural convection from a plane vertical porous surface in non-isothermal surroundings

In this paper, laminar natural convection flow from a permeable and isothermal vertical surface placed in non-isothermal surroundings is considered. Introducing appropriate transformations into the boundary layer equations governing the flow derives non-similar boundary layer equations. Results of both the analytical and numerical solutions are then presented in the form of skin-friction and Nusselt number. Numerical solutions of the transformed non-similar boundary layer equations are obtained by three distinct solution methods, (i) the perturbation solutions for small � (ii) the asymptotic solution for large � (iii) the implicit finite difference method for all � where � is the transpiration parameter. Perturbation solutions for small and large values of � are compared with the finite difference solutions for different values of pertinent parameters, namely, the Prandtl number Pr, and the ambient temperature gradient n.

Ability of modal analysis to detect osseointegration of implants in transfemoral amputees : a physical model study

Owing to the successful use of non-invasive vibration analysis to monitor the progression of dental implant healing and stabilization, it is now being considered as a method to monitor femoral implants in transfemoral amputees. This study uses composite femur-implant physical models to investigate the ability of modal analysis to detect changes at the interface between the implant and bone simulating those that occur during osseointegration. Using electromagnetic shaker excitation, differences were detected in the resonant frequencies and mode shapes of the model when the implant fit in the bone was altered to simulate the two interface cases considered: firm and loose fixation. The study showed that it is beneficial to examine higher resonant frequencies and their mode shapes (rather than the fundamental frequency only) when assessing fixation. The influence of the model boundary conditions on the modal parameters was also demonstrated. Further work is required to more accurately model the mechanical changes occurring at the bone-implant interface in vivo, as well as further refinement of the model boundary conditions to appropriately represent the in vivo conditions. Nevertheless, the ability to detect changes in the model dynamic properties demonstrates the potential of modal analysis in this application and warrants further investigation.

Experimental investigation of wheel/rail rolling contact at railhead edge

Wheel-rail rolling contact at railhead edge, such as a gap in an insulated rail joint, is a complex problem; there are only limited analytical, numerical and experimental studies available on this problem in the academic literature. This paper describes experimental and numerical investigations of railhead strains in the vicinity of the edge under the contact of a loaded wheel. A full-scale test rig was developed to cyclically apply wheel/rail rolling contact load to the edge zone of the railhead. An image analysis technique was employed to determine the railhead vertical, lateral and shear strain components. The vertical strains determined using the image analysis method have been validated with the strain gauge measurements and used for the calibration of a 3D nonlinear Finite Element Model (FEM) that simulates the wheel/rail contact at the railhead edge and use suitable boundary conditions commensurate to the experimental setup. The FEM was then used to determine other states of strains.

Adaption and use of a compressible flow code for turbomachinery design

The present paper presents and discusses the use of dierent codes regarding the numerical simulation of a radial-in ow turbine. A radial-in ow turbine test case was selected from published literature [1] and commercial codes (Fluent and CFX) were used to perform the steady-state numerical simulations. An in-house compressible- ow simulation code, Eilmer3 [2] was also adapted in order to make it suitable to perform turbomachinery simulations and preliminary results are presented and discussed. The code itself as well as its adaptation, comprising the addition of terms for the rotating frame of reference, programmable boundary conditions for periodic boundaries and a mixing plane interface between the rotating and non-rotating blocks are also discussed. Several cases with dierent orders of complexity in terms of geometry were considered and the results were compared across the dierent codes. The agreement between these results and published data is also discussed.

Stability and convergence of a finite volume method for the space fractional advection-dispersion equation

We consider the space fractional advection–dispersion equation, which is obtained from the classical advection–diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis.

A preconditioned Lanczos method for space-fractional reaction-diffusion equations on two-dimensional unstructured meshes

We consider a two-dimensional space-fractional reaction diffusion equation with a fractional Laplacian operator and homogeneous Neumann boundary conditions. The finite volume method is used with the matrix transfer technique of Ilić et al. (2006) to discretise in space, yielding a system of equations that requires the action of a matrix function to solve at each timestep. Rather than form this matrix function explicitly, we use Krylov subspace techniques to approximate the action of this matrix function. Specifically, we apply the Lanczos method, after a suitable transformation of the problem to recover symmetry. To improve the convergence of this method, we utilise a preconditioner that deflates the smallest eigenvalues from the spectrum. We demonstrate the efficiency of our approach for a fractional Fisher’s equation on the unit disk.

An accurate numerical scheme for the contraction of a bubble in a Hele-Shaw cell

We report on an accurate numerical scheme for the evolution of an inviscid bubble in radial Hele-Shaw flow, where the nonlinear boundary effects of surface tension and kinetic undercooling are included on the bubble-fluid interface. As well as demonstrating the onset of the Saffman-Taylor instability for growing bubbles, the numerical method is used to show the effect of the boundary conditions on the separation (pinch-off) of a contracting bubble into multiple bubbles, and the existence of multiple possible asymptotic bubble shapes in the extinction limit. The numerical scheme also allows for the accurate computation of bubbles which pinch off very close to the theoretical extinction time, raising the possibility of computing solutions for the evolution of bubbles with non-generic extinction behaviour.

Automatic segmentation of choroidal thickness in optical coherence tomography

The assessment of choroidal thickness from optical coherence tomography (OCT) images of the human choroid is an important clinical and research task, since it provides valuable information regarding the eye’s normal anatomy and physiology, and changes associated with various eye diseases and the development of refractive error. Due to the time consuming and subjective nature of manual image analysis, there is a need for the development of reliable objective automated methods of image segmentation to derive choroidal thickness measures. However, the detection of the two boundaries which delineate the choroid is a complicated and challenging task, in particular the detection of the outer choroidal boundary, due to a number of issues including: (i) the vascular ocular tissue is non-uniform and rich in non-homogeneous features, and (ii) the boundary can have a low contrast. In this paper, an automatic segmentation technique based on graph-search theory is presented to segment the inner choroidal boundary (ICB) and the outer choroidal boundary (OCB) to obtain the choroid thickness profile from OCT images. Before the segmentation, the B-scan is pre-processed to enhance the two boundaries of interest and to minimize the artifacts produced by surrounding features. The algorithm to detect the ICB is based on a simple edge filter and a directional weighted map penalty, while the algorithm to detect the OCB is based on OCT image enhancement and a dual brightness probability gradient. The method was tested on a large data set of images from a pediatric (1083 B-scans) and an adult (90 B-scans) population, which were previously manually segmented by an experienced observer. The results demonstrate the proposed method provides robust detection of the boundaries of interest and is a useful tool to extract clinical data.

Ratchetting of railhead in the vicinity of the gap of the insulated rail joints

Insulated Rail Joints (IRJs) are designed to electrically isolate two rails in rail tracks to control the signalling system for safer train operations. Unfortunately the gapped section of the IRJs is structurally weak and often fails prematurely especially in heavy haul tracks, which adversely affects service reliability and efficiency. The IRJs suffer from a number of failure modes; the railhead ratchetting at the gap is, however, regarded as the root cause and attended to in this thesis. Ratchetting increases with the increase in wheel loads; in the absence of a life prediction model, effective management of the IRJs for increased wagon wheel loads has become very challenging. Therefore, the main aim of this thesis is to determine method to predict IRJs' service life. The distinct discontinuity of the railhead at the gap makes the Hertzian theory and the rolling contact shakedown map, commonly used in the continuously welded rails, not applicable to examine the metal ratchetting of the IRJs. Finite Element (FE) technique is, therefore, used to explore the railhead metal ratchetting characteristics in this thesis, the boundary conditions of which has been determined from a full scale study of the IRJ specimens under rolling contact of the loaded wheels. A special purpose test set up containing full-scale wagon wheel was used to apply rolling wheel loads on the railhead edges of the test specimens. The state of the rail end face strains was determined using a non-contact digital imaging technique and used for calibrating the FE model. The basic material parameters for this FE model were obtained through independent uniaxial, monotonic tensile tests on specimens cut from the head hardened virgin rails. The monotonic tensile test data have been used to establish a cyclic load simulation model of the railhead steel specimen; the simulated cyclic load test has provided the necessary data for the three decomposed kinematic hardening plastic strain accumulation model of Chaboche. A performance based service life prediction algorithm for the IRJs was established using the plastic strain accumulation obtained from the Chaboche model. The predicted service lives of IRJs using this algorithm have agreed well with the published data. The finite element model has been used to carry out a sensitivity study on the effects of wheel diameter to the railhead metal plasticity. This study revealed that the depth of the plastic zone at the railhead edges is independent of the wheel diameter; however, large wheel diameter is shown to increase the IRJs' service life.

Development of empirical equations for irradiance profile of a standard parabolic trough collector using Monte Carlo ray tracing technique

Irradiance profile around the receiver tube (RT) of a parabolic trough collector (PTC) is a key effect of optical performance that affects the overall energy performance of the collector. Thermal performance evaluation of the RT relies on the appropriate determination of the irradiance profile. This article explains a technique in which empirical equations were developed to calculate the local irradiance as a function of angular location of the RT of a standard PTC using a vigorously verified Monte Carlo ray tracing model. A large range of test conditions including daily normal insolation, spectral selective coatings and glass envelop conditions were selected from the published data by Dudley et al. [1] for the job. The R2 values of the equations are excellent that vary in between 0.9857 and 0.9999. Therefore, these equations can be used confidently to produce realistic non-uniform boundary heat flux profile around the RT at normal incidence for conjugate heat transfer analyses of the collector. Required values in the equations are daily normal insolation, and the spectral selective properties of the collector components. Since the equations are polynomial functions, data processing software can be employed to calculate the flux profile very easily and quickly. The ultimate goal of this research is to make the concentrating solar power technology cost competitive with conventional energy technology facilitating its ongoing research.

Beyond tasks and gateways: discovering BPMN models with subprocesses, boundary events and activity markers

Existing techniques for automated discovery of process models from event logs largely focus on extracting flat process models. In other words, they fail to exploit the notion of subprocess, as well as structured error handling and repetition constructs provided by contemporary process modeling notations, such as the Business Process Model and Notation (BPMN). This paper presents a technique for automated discovery of BPMN models containing subprocesses, interrupting and non-interrupting boundary events, and loop and multi-instance markers. The technique analyzes dependencies between data attributes associated with events, in order to identify subprocesses and to extract their associated logs. Parent process and subprocess models are then discovered separately using existing techniques for flat process model discovery. Finally, the resulting models and logs are heuristically analyzed in order to identify boundary events and markers. A validation with one synthetic and two real-life logs shows that process models derived using the proposed technique are more accurate and less complex than those derived with flat process model discovery techniques.

Fractional models in space for diffusive processes in heterogeneous media with applications in cell motility and electrical signal propagation

This work addresses fundamental issues in the mathematical modelling of the diffusive motion of particles in biological and physiological settings. New mathematical results are proved and implemented in computer models for the colonisation of the embryonic gut by neural cells and the propagation of electrical waves in the heart, offering new insights into the relationships between structure and function. In particular, the thesis focuses on the use of non-local differential operators of non-integer order to capture the main features of diffusion processes occurring in complex spatial structures characterised by high levels of heterogeneity.