Numerical modelling of corneal biomechanical behaviour

Numerical modelling based on finite element analysis is used to represent the biomechanical behaviour of the cornea. The construction details of the model including the discretisation method, the mesh density, the thickness distribution, the topography idealisation, the boundary conditions and the material properties, are optimised to improve efficiency. Factors which are found to have a considerable effect on model accuracy are considered and those with effect below a certain low threshold are ignored to reduce cost of analysis. The model is validated against laboratory tests involving pressure inflation of corneal trephinates while monitoring their behaviour. To illustrate the potential of the validated model in studying corneal biomechanics, its use in modelling Goldmann applanation tonometry (GAT) is briefly described. In studying GAT, the model is able to accurately trace the behaviour of the cornea under tonometric pressure and monitor the gap closure and the progress of deformation to the point of applanation.     

Mathematical modelling of corneal swelling

This paper presents a differential model of the corneal transport system capable of modelling thickness changes in response to osmotic perturbations applied to either limiting membrane. The work is directed towards understanding corneal behaviour in vivo. The model considers the coupled viscous flows within the corneal stroma and across the epithelial and endothelial membranes. The flows within the stroma are established based on transport theory in porous media, while the flows across the membranes are described using the phenomenological equations of irreversible thermodynamics. The ability of the numerical model to reproduce corneal thickness changes in response to endothelial perturbations was tested against available experimental data. The sensitivity of the model to changes in stromal and membrane transport coefficients was examined.     

Grasp modelling with a biomechanical model of the hand

The use of a biomechanical model for human grasp modelling is presented. A previously validated biomechanical model of the hand has been used. The equilibrium of the grasped object was added to the model through the consideration of a soft contact model. A grasping posture generation algorithm was also incorporated into the model. All the geometry was represented using a spherical extension of polytopes (s-topes) for efficient collision detection. The model was used to simulate an experiment in which a subject was asked to grasp two cylinders of different diameters and weights. Different objective functions were checked to solve the indeterminate problem. The normal finger forces estimated by the model were compared to those experimentally measured. The popular objective function sum of the squared muscle stresses was shown not suitable for the grasping simulation, requiring at least being complemented by task-dependent grasp quality measures.     

Mechanical behaviour modelling of balloon-expandable stents

Endoprostheses are small struts placed by intravascular way to restore the vascular lumen and flow conditions. The purpose of this work is to provide models for evaluation and characterisation of some mechanical properties of a balloon-expandable stent by using the finite element method. Here we present the results for a metallic tubular peripheral prosthesis: the P308 Palmaz stent. We focus on the mechanisms linked to the structure expansion and its long-term behaviour. Several models are constructed in order to determine the stent shape after dilation and to assess the stress and strain fields in its wall due to this transformation. They inform us about the shortening percentage on expansion, degrees of radial and longitudinal recoil, and weaknesses of the structure. Various methods, differing in their levels of complexity, are then attempted to exhibit the predominant factors responsible for the crushing of a stent under external pressure. Moreover, the sensitivity of this critical pressure to geometric imperfections is studied. Lastly, since this kind of material is implanted for a lifetime, we test the stent with regard to fatigue life. Beyond safety considerations, this type of characterisation provides mechanical properties that are often difficult to obtain by experiments. If it was available for various stents, such information could be used to choose the appropriate prosthesis for specific applications. Moreover, confronted with observations from practitioners, they might lead to a better understanding of the failure or success of a particular design and to work on the product optimisation.     

Locomotor behaviour in Plio-Pleistocene sabre-tooth cats: a biomechanical analysis

The locomotor behaviour of some large extinct carnivores, including several species of Plio-Pleistocene sabre-tooth cats, is here reconstructed, based on a comparison of the cross-sectional geometric properties and linear dimensions of their femora and humeri with those of large modern carnivores. The long bones are modelled as simple beams, thereby allowing the use of basic beam theory in assessing relevant functional parameters such as second moments of area of the diaphyses when subjected to compressive and bending stresses. Three Pleistocene carnivores, Smilodon fatalis, Homotherium serum , and Panthera atrox seem to have had ecological and functional equivalents among the late Miocene-Early Pliocene genera, Barbourofelis, Machairodus , and Nimravides , respectively. Barbourofelis and Smilodon were 'cat-like'in dental morphology but some structural characteristics of their limb bones had 'bear-like'affinities. Machairodus and Homotherium were cursorial, whereas Nimravides and P. atrox display the limb morphology of true ambush predators. Various aspects of the postcranial skeleton of some of these extinct carnivores suggest that they may have employed locomotory gaits that lack modern analogs.     

Mathematical modelling of the degradation behaviour of biodegradable metals

A mathematical model for the biodegradation of magnesium is developed in this study to inspect the corrosion behaviour of biodegradable implants. The aim of this study was to provide a suitable framework for the assessment of the corrosion rate of magnesium which includes the process of formation/dissolution of the protective film. The model is intended to aid the design of implants with suitable geometries. The level-set method is used to follow the changing geometry of the implants during the corrosion process. A system of partial differential equations is formulated based on the physical and chemical processes that occur at the implant-medium boundary in order to simulate the effect of the formation of a protective film on the degradation rate. The experimental data from the literature on the corrosion of a high-purity magnesium sample immersed in simulated body fluid is used to calibrate the model. The model is then used to predict the degradation behaviour of a porous orthopaedic implant. The model successfully reproduces the precipitation of the corrosion products on the magnesium surface and the effect on the degradation rate. It can be used to simulate the implant degradation and the formation of the corrosion products on the surface of biodegradable magnesium implants with complex geometries.     

The mathematical modelling of cell kinetics in corneal epithelial wound healing

This paper considers the comparison of experimental spatial and temporal data of mitotic rates measured during corneal epithelial wound healing (CEWH) of a rat model with the predictions of a computer modelling framework. We begin by briefly showing that previous models, used in the study of corneal epithelial wound healing speeds, are inadequate for the study of cell kinetics. We proceed to formulate a new modelling framework more suited to such a study. This framework is simulated in its simplest form, and the results from this motivate a new realisation of the modelling framework, including a caricature of age structuring. Finally, a model with a simple representation of juxtacrine signalling is considered. The final model captures many, though not all, of the trends of the experimental data. This paper thus lays a foundation for the modelling of the cell kinetics of corneal epithelial wound healing, and yields valuable insight regarding the important mechanisms a model should consider in order to reproduce the observed experimental trends.     

Ultrasonic model and system for measurement of corneal biomechanical properties and validation on phantoms

Non-invasive measurement of biomechanical properties of corneas may provide important information for ocular disease management and therapeutic procedures. An ultrasonic non-destructive evaluation method with a wave propagation model was developed to determine corneal biomechanical properties in vivo. In this study, we tested the feasibility of the approach in differentiating the mechanical properties of soft contact lenses as corneal phantoms. Three material types of soft contact lenses (six samples in each group) were measured using a broadband ultrasound transducer. The ultrasonic reflections from the contact lenses were recorded by a 500MHz/8-bit digitizer, and displayed and processed by a PC. A reference signal was recorded to compute the normalized power spectra using Fast Fourier Transformation. An inverse algorithm based on least-squares minimization was used to reconstruct three parameters of the contact lenses: density, thickness, and elastic constants lambda+2micro. The thickness of each sample was verified using an electronic thickness gauge, and the averaged density for each type of lenses was verified using Archimedes' principle and manufacturer's report. Our results demonstrated that the ultrasonic system was able to differentiate the elastic properties of the three types of the soft contact lenses with statistical significance (P-value<0.001). The reconstructed thicknesses and densities agreed well with the independent measurements. Our studies on corneal phantoms indicated that the ultrasonic system was sensitive and accurate in measuring the material properties of cornea-like structures. It is important to optimize the system for in vivo measurements.     

Assessment of a fictitious domain method for patient-specific biomechanical modelling of press-fit orthopaedic implantation

In this article, we discuss an application of a fictitious domain method to the numerical simulation of the mechanical process induced by press-fitting cementless femoral implants in total hip replacement surgeries. Here, the primary goal is to demonstrate the feasibility of the method and its advantages over competing numerical methods for a wide range of applications for which the primary input originates from computed tomography-, magnetic resonance imaging- or other regular-grid medical imaging data. For this class of problems, the fictitious domain method is a natural choice, because it avoids the segmentation, surface reconstruction and meshing phases required by unstructured geometry-conforming simulation methods. We consider the implantation of a press-fit femoral artificial prosthesis as a prototype problem for sketching the application path of the methodology. Of concern is the assessment of the robustness and speed of the methodology, for both factors are critical if one were to consider patient-specific modelling. To this end, we report numerical results that exhibit optimal convergence rates and thus shed a favourable light on the approach.     

Critical analysis of musculoskeletal modelling complexity in multibody biomechanical models of the upper limb

The inverse dynamics technique applied to musculoskeletal models, and supported by optimisation techniques, is used extensively to estimate muscle and joint reaction forces. However, the solutions of the redundant muscle force sharing problem are sensitive to the detail and modelling assumptions of the models used. This study presents four alternative biomechanical models of the upper limb with different levels of discretisation of muscles by bundles and muscle paths, and their consequences on the estimation of the muscle and joint reaction forces. The muscle force sharing problem is solved for the motions of abduction and anterior flexion, acquired using video imaging, through the minimisation of an objective function describing muscle metabolic energy consumption. While looking for the optimal solution, not only the equations of motion are satisfied but also the stability of the glenohumeral and scapulothoracic joints is preserved. The results show that a lower level of muscle discretisation provides worse estimations regarding the muscle forces. Moreover, the poor discretisation of muscles relevant to the joint in analysis limits the applicability of the biomechanical model. In this study, the biomechanical model of the upper limb describing the infraspinatus by a single bundle could not solve the complete motion of anterior flexion. Despite the small differences in the magnitude of the forces predicted by the biomechanical models with more complex muscular systems, in general, there are no significant variations in the muscular activity of equivalent muscles.     

Sensitivity of corneal biomechanical and optical behavior to material parameters using design of experiments method

The optical performance of the human cornea under intraocular pressure (IOP) is the result of complex material properties and their interactions. The measurement of the numerous material parameters that define this material behavior may be key in the refinement of patient-specific models. The goal of this study was to investigate the relative contribution of these parameters to the biomechanical and optical responses of human cornea predicted by a widely accepted anisotropic hyperelastic finite element model, with regional variations in the alignment of fibers. Design of experiments methods were used to quantify the relative importance of material properties including matrix stiffness, fiber stiffness, fiber nonlinearity and fiber dispersion under physiological IOP. Our sensitivity results showed that corneal apical displacement was influenced nearly evenly by matrix stiffness, fiber stiffness and nonlinearity. However, the variations in corneal optical aberrations (refractive power and spherical aberration) were primarily dependent on the value of the matrix stiffness. The optical aberrations predicted by variations in this material parameter were sufficiently large to predict clinically important changes in retinal image quality. Therefore, well-characterized individual variations in matrix stiffness could be critical in cornea modeling in order to reliably predict optical behavior under different IOPs or after corneal surgery.     

Quantification of biomechanical properties of human corneal scar using acoustic radiation force optical coherence elastography

Biomechanical properties of corneal scar are strongly correlated with many corneal diseases and some types of corneal surgery, however, there is no elasticity information available about corneal scar to date. Here, we proposed an acoustic radiation force optical coherence elastography system to evaluate corneal scar elasticity. Elasticity quantification was first conducted on ex vivo rabbit corneas, and the results validate the efficacy of our system. Then, experiments were performed on an ex vivo human scarred cornea, where the structural features, the elastic wave propagations, and the corresponding Young’s modulus of both the scarred region and the normal region were achieved and based on this, 2D spatial distribution of Young’s modulus of the scarred cornea was depicted. Up to our knowledge, we realized the first elasticity quantification of corneal scar, which may provide a potent tool to promote clinical research on the disorders and surgery of the cornea.     

On the inference of function from structure using biomechanical modelling and simulation of extinct organisms

Biomechanical modelling and simulation techniques offer some hope for unravelling the complex inter-relationships of structure and function perhaps even for extinct organisms, but have their limitations owing to this complexity and the many unknown parameters for fossil taxa. Validation and sensitivity analysis are two indispensable approaches for quantifying the accuracy and reliability of such models or simulations. But there are other subtleties in biomechanical modelling that include investigator judgements about the level of simplicity versus complexity in model design or how uncertainty and subjectivity are dealt with. Furthermore, investigator attitudes toward models encompass a broad spectrum between extreme credulity and nihilism, influencing how modelling is conducted and perceived. Fundamentally, more data and more testing of methodology are required for the field to mature and build confidence in its inferences.     

Numerical modelling of pollen dispersion on the regional scale

New parameterisations were developed to calculate the emission and resuspension flux of pollen grains. These new parameterisations were included in the comprehensive mesoscale model system KAMM/DRAIS. Two types of simulations were performed. In the first case, horizontally homogeneous meteorology was assumed. In this case, pollen concentration rapidly decreased with the distance from the source. In the second case, where the fully three-dimensional model was applied, atmospheric lifetime of the pollen grains increased remarkably. This was mainly caused by the vertical wind speeds induced by topographic effects. Consequently, the pollen grains could travel much larger distances until they were deposited and finally removed from the atmosphere. This is an important finding with respect to the problem of cross pollination. Due to the lack of measurements, a number of parameters had to be assumed. However, the parameterisation proposed may well serve as a starting point of a daily pollen forecast with numerical models.     

Numerical modelling of the angiogenesis process in wound contraction

Angiogenesis consists of the growth of new blood vessels from the pre-existing vasculature. This phenomenon takes place in several biological processes, including wound healing. In this work, we present a mathematical model of angiogenesis applied to skin wound healing. The developed model includes biological (capillaries and fibroblasts), chemical (oxygen and angiogenic growth factor concentrations) and mechanical factors (cell traction forces and extracellular matrix deformation) that influence the evolution of the healing process. A novelty from previous works, apart from the coupling of angiogenesis and wound contraction, is the more realistic modelling of skin as a hyperelastic material. Large deformations are addressed using an updated Lagrangian approach. The coupled non-linear model is solved with the finite element method, and the process is studied over two wound geometries (circular and elliptical) of the same area. The results indicate that the elliptical wound vascularizes two days earlier than the circular wound but that they experience a similar contraction level, reducing its size by 25 %.     

Numerical modelling of plasticity induced by transcranial magnetic stimulation

We use neural field theory and spike-timing dependent plasticity to make a simple but biophysically reasonable model of long-term plasticity changes in the cortex due to transcranial magnetic stimulation (TMS). We show how common TMS protocols can be captured and studied within existing neural field theory. Specifically, we look at repetitive TMS protocols such as theta burst stimulation and paired-pulse protocols. Continuous repetitive protocols result mostly in depression, but intermittent repetitive protocols in potentiation. A paired pulse protocol results in depression at short ( < ～ 10 ms) and long ( > ～ 100 ms) interstimulus intervals, but potentiation for mid-range intervals. The model is sensitive to the choice of neural populations that are driven by the TMS pulses, and to the parameters that describe plasticity, which may aid interpretation of the high variability in existing experimental results. Driving excitatory populations results in greater plasticity changes than driving inhibitory populations. Modelling also shows the merit in optimizing a TMS protocol based on an individual’s electroencephalogram. Moreover, the model can be used to make predictions about protocols that may lead to improvements in repetitive TMS outcomes.     

The epitheliome: agent-based modelling of the social behaviour of cells

We have developed a new computational modelling paradigm for predicting the emergent behaviour resulting from the interaction of cells in epithelial tissue. As proof-of-concept, an agent-based model, in which there is a one-to-one correspondence between biological cells and software agents, has been coupled to a simple physical model. Behaviour of the computational model is compared with the growth characteristics of epithelial cells in monolayer culture, using growth media with low and physiological calcium concentrations. Results show a qualitative fit between the growth characteristics produced by the simulation and the in vitro cell models.