finite-element-modelling-of-a-cellular-electric-microenvironment

Finite Element Modelling of a Cellular Electric Microenvironment

Clinical studies show electrical stimulation (ES) to be a potential therapy for the healing and regeneration of various tissues. Understanding the ...

surrogate-model-development-for-digital-experiments-in-welding

Surrogate Model Development for Digital Experiments in Welding

The manufacturing industry heavily relies on welding processes to join materials, forming integral components across various sectors. Many aspects will ...

automatic-laser-based-geometry-capture-for-finite-element-analysis

Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads

Fusion welding for high-value manufacturing requires strict process controls on component distortion and ascertaining levels of residual stress imparted ...

The University of Manchester

University of Manchester

Being able to predict bone fracture or implant stability needs a proper constitutive model of trabecular bone at the macroscale in multiaxial, non-monotonic loading modes. Its macroscopic damage behaviour has been investigated experimentally in the past, mostly with the restriction of uniaxial cyclic loading experiments for different samples, which does not allow for the investigation of several load cases in the same sample as damage in one direction may affect the behaviour in other directions. Homogenised finite element models of whole bones have the potential to assess complicated scenarios and thus improve clinical predictions. The aim of this study is to use a homogenisation-based multiscale procedure to upscale the damage behaviour of bone from an assumed solid phase constitutive law and investigate its multiaxial behaviour for the first time. Twelve cubic specimens were each submitted to nine proportional strain histories by using a parallel code developed in-house. Evolution of post-elastic properties for trabecular bone was assessed for a small range of macroscopic plastic strains in these nine load cases. Damage evolution was found to be non-isotropic, and both damage and hardening were found to depend on the loading mode (tensile, compression or shear); both were characterised by linear laws with relatively high coefficients of determination. It is expected that the knowledge of the macroscopic behaviour of trabecular bone gained in this study will help in creating more precise continuum FE models of whole bones that improve clinical predictions.

Effect of including damage at the tissue level in the nonlinear homogenisation of trabecular bone.

The purpose of this paper is to provide a high level, holistic overview of the work being undertaken in the wind energy industry. It summarises the main techniques used to simulate both aerodynamic and structural issues associated with wind turbines and farms. The motivation behind this paper is to provide new researchers with an outlook of the modelling and simulation landscape, whilst highlighting the trends and direction research is taking. Each section summarises an individual area of simulation and modelling, covering the important historical research findings and a comprehensive analysis of recent work. This segregated approach emphasises the key components of wind energy. Topics range in geometric scales and detail, ranging from atmospheric boundary layer modelling, to fatigue and fracture in the turbine blades. More recent studies have begun to combine a range of scales and physics to better approximate real systems and provide higher fidelity and accurate analyses to manufacturers and companies. This paper shows a clear trend towards coupling both scales and physics into singular models utilising high performance computing system.

Building a Digital Wind Farm.

This paper uses X-ray computed tomography to track the mechanical response of a vertebrate (Barnacle goose) long bone subjected to an axial compressive load, which is increased gradually until failure. A loading rig was mounted in an X-ray computed tomography system so that a time-lapse sequence of three-dimensional (3D) images of the bone's internal (cancellous or trabecular) structure could be recorded during loading. Five distinct types of deformation mechanism were observed in the cancellous part of the bone. These were (i) cracking, (ii) thinning (iii) tearing of cell walls and struts, (iv) notch formation, (v) necking and (vi) buckling. The results highlight that bone experiences brittle (notch formation and cracking), ductile (thinning, tearing and necking) and elastic (buckling) modes of deformation. Progressive deformation, leading to cracking was studied in detail using digital image correlation. The resulting strain maps were consistent with mechanisms occurring at a finer-length scale. This paper is the first to capture time-lapse 3D images of a whole long bone subject to loading until failure. The results serve as a unique reference for researchers interested in how bone responds to loading. For those using computer modelling, the study not only provides qualitative information for verification and validation of their simulations but also highlights that constitutive models for bone need to take into account a number of different deformation mechanisms.

A study of the progression of damage in an axially loaded  femur using X-ray computed tomography and digital image correlation.

Dromaeosaurid theropod dinosaurs, such as Velociraptor, possess strongly recurved, hypertrophied and hyperextensible ungual claws on the pes (digit II) and manus. The morphology of these unguals has been linked to the capture and despatching of prey. However, the mechanical properties or, more importantly, the mechanical potential of these structures have not been explored. Generation of a 3D finite element (FE) stress/strain contour map of a Velociraptor manual ungual has allowed us to evaluate quantitatively the mechanical behavior of a dromaeosaurid claw for the first time. An X-ray microtomography scan allowed construction of an accurate 3D FE mesh. Analogue material from an extant avian theropod, the pedal digit and claw of an eagle owl (Bubo bubo), was analyzed to provide input data for the Velociraptor claw FE model (FEM). The resultant FEM confirms that dromaeosaurid claws were well-adapted for climbing as they would have been resistant to forces acting in a single (longitudinal) plane, in this case due to gravity. However, the strength of the unguals was limited with respect to forces acting tangential to the long-axis of the claw. The tip of the claw functioned as the puncturing and gripping element of the structure, whereas the expanded proximal portion transferred the load stress through the trabeculae and cortical bone. Enhanced climbing abilities of dromaeosaurid dinosaurs supports a scansorial phase in the evolution of flight.

Biomechanics of dromaeosaurid dinosaur claws: application of X-ray microtomography, nanoindentation, and finite element analysis.

Tendons are composed of longitudinally aligned collagen fibrils arranged in bundles with an undulating pattern, called crimp. The crimp structure is established during embryonic development and plays a vital role in the mechanical behaviour of tendon, acting as a shock-absorber during loading. However, the mechanism of crimp formation is unknown, partly because of the difficulties of studying tendon development in vivo. Here, we used a 3D cell culture system in which embryonic tendon fibroblasts synthesise a tendon-like construct comprised of collagen fibrils arranged in parallel bundles. Investigations using polarised light microscopy, scanning electron microscopy and fluorescence microscopy showed that tendon constructs contained a regular pattern of wavy collagen fibrils. Tensile testing indicated that this superstructure was a form of embryonic crimp producing a characteristic toe region in the stress-strain curves. Furthermore, contraction of tendon fibroblasts was the critical factor in the buckling of collagen fibrils during the formation of the crimp structure. Using these biological data, a finite element model was built that mimics the contraction of the tendon fibroblasts and monitors the response of the Extracellular matrix. The results show that the contraction of the fibroblasts is a sufficient mechanical impulse to build a planar wavy pattern. Furthermore, the value of crimp wavelength was determined by the mechanical properties of the collagen fibrils and inter-fibrillar matrix. Increasing fibril stiffness combined with constant matrix stiffness led to an increase in crimp wavelength. The data suggest a novel mechanism of crimp formation, and the finite element model indicates the minimum requirements to generate a crimp structure in embryonic tendon.

Tenocyte contraction induces crimp formation in tendon-like tissue.

Classic beam theory is frequently used in biomechanics to model the stress behaviour of vertebrate long bones, particularly when creating intraspecific scaling models. Although methodologically straightforward, classic beam theory requires complex irregular bones to be approximated as slender beams, and the errors associated with simplifying complex organic structures to such an extent are unknown. Alternative approaches, such as finite element analysis (FEA), while much more time-consuming to perform, require no such assumptions. This study compares the results obtained using classic beam theory with those from FEA to quantify the beam theory errors and to provide recommendations about when a full FEA is essential for reasonable biomechanical predictions. High-resolution computed tomographic scans of eight vertebrate long bones were used to calculate diaphyseal stress owing to various loading regimes. Under compression, FEA values of minimum principal stress (σ(min)) were on average 142 per cent (±28% s.e.) larger than those predicted by beam theory, with deviation between the two models correlated to shaft curvature (two-tailed p = 0.03, r(2) = 0.56). Under bending, FEA values of maximum principal stress (σ(max)) and beam theory values differed on average by 12 per cent (±4% s.e.), with deviation between the models significantly correlated to cross-sectional asymmetry at midshaft (two-tailed p = 0.02, r(2) = 0.62). In torsion, assuming maximum stress values occurred at the location of minimum cortical thickness brought beam theory and FEA values closest in line, and in this case FEA values of τ(torsion) were on average 14 per cent (±5% s.e.) higher than beam theory. Therefore, FEA is the preferred modelling solution when estimates of absolute diaphyseal stress are required, although values calculated by beam theory for bending may be acceptable in some situations.

Finite element modelling versus classic beam theory: comparing methods for stress estimation in a morphologically diverse sample of vertebrate long bones.

March of the titans: the locomotor capabilities of sauropod dinosaurs.

Following rupture, tendons are sutured to reapproximate the severed ends and permit healing. Several repair techniques are employed clinically, with recent focus towards high-strength sutures, permitting early active mobilisation thus improving resultant joint mobility. However, the arrangement of suture repairs locally alters the loading environment experienced by the tendon. The extent of the augmented stress distribution and its effect on the tissue is unknown. Stress distribution cannot be established using traditional tensile testing, in vivo, or ex vivo study of suture repairs. We have developed a 3D finite element model of a Kessler suture repair employing multiscale modelling to represent tendon microstructure and incorporate its highly orthotropic behaviour into the tissue description. This was informed by ex vivo tensile testing of porcine flexor digitorum profundus tendon. The transverse modulus of the tendon was 0.2551 ± 0.0818 MPa and 0.1035 ± 0.0454 MPa in proximal and distal tendon samples, respectively, and the interfibrillar tissue modulus ranged from 0.1021 to 0.0416 MPa. We observed an elliptically shaped region of high stress around the suture anchor, consistent with a known region of acellularity which develop 72 h post-operatively and remain for at least a year. We also observed a stress shielded region close to the severed tendon ends, which may impair collagen fibre realignment during the remodelling stage of repair due to the lack of tensile stress.

Sutured tendon repair; a multi-scale finite element model.

Computational homogenisation approaches using high resolution images and finite element (FE) modelling have been extensively employed to evaluate the anisotropic elastic properties of trabecular bone. The aim of this study was to extend its application to characterise the macroscopic yield behaviour of trabecular bone. Twenty trabecular bone samples were scanned using a micro-computed tomography device, converted to voxelised FE meshes and subjected to 160 load cases each (to define a homogenised multiaxial yield surface which represents several possible strain combinations). Simulations were carried out using a parallel code developed in-house. The nonlinear algorithms included both geometrical and material nonlinearities. The study found that for tension-tension and compression-compression regimes in normal strain space, the yield strains have an isotropic behaviour. However, in the tension-compression quadrants, pure shear and combined normal-shear planes, the macroscopic strain norms at yield have a relatively large variation. Also, our treatment of clockwise and counter-clockwise shears as separate loading cases showed that the differences in these two directions cannot be ignored. A quadric yield surface, used to evaluate the goodness of fit, showed that an isotropic criterion adequately represents yield in strain space though errors with orthotropic and anisotropic criteria are slightly smaller. Consequently, although the isotropic yield surface presents itself as the most suitable assumption, it may not work well for all load cases. This work provides a comprehensive assessment of material symmetries of trabecular bone at the macroscale and describes in detail its macroscopic yield and its underlying microscopic mechanics.

Evaluating the macroscopic yield behaviour of trabecular bone using a nonlinear homogenisation approach.

Micro-finite element models have been extensively employed to evaluate the elastic properties of trabecular bone and, to a limited extent, its yield behaviour. The macroscopic stiffness tensor and yield surface are of special interest since they are essential in the prediction of bone strength and stability of implants at the whole bone level. While macroscopic elastic properties are now well understood, yield and post-yield properties are not. The aim of this study is to shed some light on what the effect of the solid phase yield criterion is on the macroscopic yield of trabecular bone for samples with different microstructure. Three samples with very different density were subjected to a large set of apparent load cases (which is important since physiological loading is complex and can have multiple components in stress or strain space) with two different solid phase yield criteria: Drucker-Prager and eccentric-ellipsoid. The study found that these two criteria led to small differences in the macroscopic yield strains for most load cases except for those that were compression-dominated; in these load cases, the yield strains for the Drucker-Prager criterion were significantly higher. Higher density samples resulted in higher differences between the two criteria. This work provides a comprehensive assessment of the effect of two different solid phase yield criteria on the macroscopic yield strains of trabecular bone, for a wide range of load cases, and for samples with different morphology.

Nonlinear homogenisation of trabecular bone: Effect of solid phase constitutive model.

Brain is an actuator for control and coordination. When a pathology arises in cranium, it may leave a degenerative, disfiguring and destabilizing impact on brain physiology. However, the leading consequences of the same may vary from case to case. Tumour, in this context, is a special type of pathology which deforms brain parenchyma permanently. From translational perspective, deformation mechanics and pressures, specifically the intracranial cerebral pressure (ICP) in a tumour-housed brain, have not been addressed holistically in literature. This is an important area to investigate in neuropathy prognosis. To address this, we aim to solve the pressure mystery in a tumour-based brain in this study and present a fairly workable methodology. Using image-based finite-element modelling, we reconstruct a tumour-based brain and probe resulting deformations and pressures (ICP). Tumour is grown by dilating the voxel region by 16 and 30 mm uniformly. Cumulatively three cases are studied including an existing stage of the tumour. Pressures of cerebrospinal fluid due to its flow inside the ventricle region are also provided to make the model anatomically realistic. Comparison of obtained results unequivocally shows that as the tumour region increases its area and size, deformation pattern changes extensively and spreads throughout the brain volume with a greater concentration in tumour vicinity. Second, we conclude that ICP pressures inside the cranium do increase substantially; however, they still remain under the normal values (15 mmHg). In the end, a correlation relationship of ICP mechanics and tumour is addressed. From a diagnostic purpose, this result also explains why generally a tumour in its initial stage does not show symptoms because the required ICP threshold has not been crossed. We finally conclude that even at low ICP values, substantial deformation progression inside the cranium is possible. This may result in plastic deformation, midline shift etc. in the brain.

How growing tumour impacts intracranial pressure and deformation mechanics of brain.

Non-healing wounds have led to a soaring clinical and socioeconomical need for advanced wound-care techniques. Electrical stimulation is an emerging therapy inspired by the wound's endogenous electric field. Promising results of clinical trials have encouraged efforts to create wearable stimulation devices, uncover multiple cellular targets, and optimize stimulation regimes. However, the field faces a translational bottleneck. This review aims to highlight the gaps between in vivo treatments and in vitro associated experiments by discussing the current knowledge of the generation, characterization, and targets of electrical stimuli. It becomes clear that enabling the translation of this technology will require increasing the complexity of the current models for skin endogenous and controlled ion transport, and investigating which stimulus has an optimum effect on cells derived from chronic wound-prone patients.

Status and challenges of electrical stimulation use in chronic wound healing.

This manuscript provides optical microscopy, scanning electron microscopy, and transmission electron microscopy micrographs that show the microstructure of three superfine nuclear graphite grades IG-110, 2114 and ETU-10. This collection of microstructural data showcases the microstructure of these materials and helps to differentiate the most important features or phases of these graphite grades. In particular, the microstructural data illustrate the filler and binder morphology of these grades. Moreover, samples of as-received and oxidized IG-110 were characterized via optical microscopy and x-ray computed tomography. The microstructural data of oxidized IG-110 shows the porosity generated by oxidation experiments. These micrographs and data provide a unique insight into the microstructural features and oxidation effects in nuclear graphite and can be used to perform quantitative porosity analysis. This collection of microstructural data complements the modeling and characterization described in the associated manuscript, "Using porous random fields to predict the elastic modulus of unoxidized and oxidized superfine graphite (Arregui-Mena et al., 2022)."

Microstructural characterization data of as received IG-110, 2114 and ETU-10 nuclear graphite grades and oxidation characterization data of IG-110.

Pterosaurs were the largest animals to have achieved powered flight in the history of life on Earth, possessing wingspans akin to some modern light aircraft. Vertebrate fossils have shown their potential to retain information on the chemical, physical, and mechanical properties of precursor bone. However, the fossil record is not a traditional source of inspiration for engineers to create palaeo-bioinspired designs. To explore its potential, this study has imaged the three-dimensional porosity of pterosaur bone intending to inspire and improve the mechanical properties of aerospace materials. Historically, two-dimensional histological analysis has resolved fine-scale structures in fossilised bone, which damages the sample. By applying advanced X-ray imaging techniques in this study (using Image Quality Indicators) we show it is possible to non-destructively resolve/verify the microarchitecture of pterosaur bone not previously seen in three dimensions. Pterosaur bone porosity has helped map the macroscopic stresses of this biomaterial but ultimately presents an opportunity to inspire advanced manufactured materials. This microarchitecture of bone offers a unique geometry where self-healing materials with internal monitoring systems can be developed. The iterative process of Darwinian natural selection has evolved multiple engineering solutions that can be reverse engineered to solve challenges facing industry in the 21st Century.

ArticleTotal : 3	Year
Publication title Cited by 2	2021
Publication title Cited by 2	2025
Publication title	2025

Article	Year
Effect of including damage at the tissue level in the nonlinear homogenisation of trabecular bone. Biomechanics and modeling in mechanobiology\| PubMed ID: 28500359	2017
Building a Digital Wind Farm. Archives of computational methods in engineering : state of the art reviews\| PubMed ID: 30443152	2018
A study of the progression of damage in an axially loaded femur using X-ray computed tomography and digital image correlation. PeerJ\| PubMed ID: 28652932	2017
Biomechanics of dromaeosaurid dinosaur claws: application of X-ray microtomography, nanoindentation, and finite element analysis. Anatomical record (Hoboken, N.J. : 2007)\| PubMed ID: 19711472	2009
Tenocyte contraction induces crimp formation in tendon-like tissue. Biomechanics and modeling in mechanobiology\| PubMed ID: 21735243	2012
Finite element modelling versus classic beam theory: comparing methods for stress estimation in a morphologically diverse sample of vertebrate long bones. Journal of the Royal Society, Interface\| PubMed ID: 23173199	2013
March of the titans: the locomotor capabilities of sauropod dinosaurs. PloS one\| PubMed ID: 24348896	2013
Sutured tendon repair; a multi-scale finite element model. Biomechanics and modeling in mechanobiology\| PubMed ID: 24840732	2015
Evaluating the macroscopic yield behaviour of trabecular bone using a nonlinear homogenisation approach. Journal of the mechanical behavior of biomedical materials\| PubMed ID: 27108348	2016
Nonlinear homogenisation of trabecular bone: Effect of solid phase constitutive model. Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine\| PubMed ID: 28427317	2017
How growing tumour impacts intracranial pressure and deformation mechanics of brain. Royal Society open science\| PubMed ID: 34631118	2021
Status and challenges of electrical stimulation use in chronic wound healing. Current opinion in biotechnology\| PubMed ID: 35398709	2022
Microstructural characterization data of as received IG-110, 2114 and ETU-10 nuclear graphite grades and oxidation characterization data of IG-110. Data in brief\| PubMed ID: 36045641	2022
Harnessing 3D microarchitecture of pterosaur bone using multi-scale X-ray CT for aerospace material design. Scientific reports\| PubMed ID: 39962103	2025

Lee Margetts

Biography

JoVE Journal Publications

Other Publications