A computational model of in vitro angiogenesis based on extracellular matrix fibre orientation

Recent interest in the process of vascularisation within the biomedical community has motivated numerous new research efforts focusing on the process of angiogenesis. Although the role of chemical factors during angiogenesis has been well documented, the role of mechanical factors, such as the interaction between angiogenic vessels and the extracellular matrix, remains poorly understood. In vitro methods for studying angiogenesis exist; however, measurements available using such techniques often suffer from limited spatial and temporal resolutions. For this reason, computational models have been extensively employed to investigate various aspects of angiogenesis. This paper outlines the formulation and validation of a simple and robust computational model developed to accurately simulate angiogenesis based on length, branching and orientation morphometrics collected from vascularised tissue constructs. Microvessels were represented as a series of connected line segments. The morphology of the vessels was determined by a linear combination of the collagen fibre orientation, the vessel density gradient and a random walk component. Excellent agreement was observed between computational and experimental morphometric data over time. Computational predictions of microvessel orientation within an anisotropic matrix correlated well with experimental data. The accuracy of this modelling approach makes it a valuable platform for investigating the role of mechanical interactions during angiogenesis.     

Comparison of an EMG-based and a stress-based method to predict shoulder muscle forces

The estimation of muscle forces in musculoskeletal shoulder models is still controversial. Two different methods are widely used to solve the indeterminacy of the system: electromyography (EMG)-based methods and stress-based methods. The goal of this work was to evaluate the influence of these two methods on the prediction of muscle forces, glenohumeral load and joint stability after total shoulder arthroplasty. An EMG-based and a stress-based method were implemented into the same musculoskeletal shoulder model. The model replicated the glenohumeral joint after total shoulder arthroplasty. It contained the scapula, the humerus, the joint prosthesis, the rotator cuff muscles supraspinatus, subscapularis and infraspinatus and the middle, anterior and posterior deltoid muscles. A movement of abduction was simulated in the plane of the scapula. The EMG-based method replicated muscular activity of experimentally measured EMG. The stress-based method minimised a cost function based on muscle stresses. We compared muscle forces, joint reaction force, articular contact pressure and translation of the humeral head. The stress-based method predicted a lower force of the rotator cuff muscles. This was partly counter-balanced by a higher force of the middle part of the deltoid muscle. As a consequence, the stress-based method predicted a lower joint load (16% reduced) and a higher superior–inferior translation of the humeral head (increased by 1.2 mm). The EMG-based method has the advantage of replicating the observed cocontraction of stabilising muscles of the rotator cuff. This method is, however, limited to available EMG measurements. The stress-based method has thus an advantage of flexibility, but may overestimate glenohumeral subluxation.     

Accuracy of specimen-specific nonlinear finite element analysis for evaluation of radial diaphysis strength in cadaver material

The feasibility of a user-specific finite element model for predicting the in situ strength of the radius after implantation of bone plates for open fracture reduction was established. The effect of metal artifact in CT imaging was characterized. The results were verified against biomechanical test data. Fourteen cadaveric radii were divided into two groups: (1) intact radii for evaluating the accuracy of radial diaphysis strength predictions with finite element analysis and (2) radii with a locking plate affixed for evaluating metal artifact. All bones were imaged with CT. In the plated group, radii were first imaged with the plates affixed (for simulating digital plate removal). They were then subsequently imaged with the locking plates and screws removed (actual plate removal). Fracture strength of the radius diaphysis under axial compression was predicted with a three-dimensional, specimen-specific, nonlinear finite element analysis for both the intact and plated bones (bones with and without the plate captured in the scan). Specimens were then loaded to failure using a universal testing machine to verify the actual fracture load. In the intact group, the physical and predicted fracture loads were strongly correlated. For radii with plates affixed, the physical and predicted (simulated plate removal and actual plate removal) fracture loads were strongly correlated. This study demonstrates that our specimen-specific finite element analysis can accurately predict the strength of the radial diaphysis. The metal artifact from CT imaging was shown to produce an overestimate of strength.     

Modelling drug elution from stents: effects of reversible binding in the vascular wall and degradable polymeric matrix

Today the most popular approach for the prevention of the restenosis consists in the use of the drug eluting stents. The stent acts as a source of drug, from a coating or from a reservoir, which is transported into and through the artery wall. In this study, the behaviour of a model of a hydrophilic drug (heparin) released from a coronary stent into the arterial wall is investigated. The presence of the specific binding site action is modelled using a reversible chemical reaction that explains the prolonged presence of drug in the vascular tissue. An axi-symmetric model of a single stent strut is considered. First an advection–diffusion problem is solved using the finite element method. Then a simplified model with diffusion only in the arterial wall is compared with: (i) a model including the presence of reversible binding sites in the vascular wall and (ii) a model featuring a drug reservoir made of a degradable polymeric matrix. The results show that the inclusion of a reversible binding for the drug leads to delayed release curves and that the polymer erosion affects the drug release showing a quicker elution of the drug from the stent.     

A microstructurally informed model for the mechanical response of three-dimensional actin networks

We propose a class of microstructurally informed models for the linear elastic mechanical behaviour of cross-linked polymer networks such as the actin cytoskeleton. Salient features of the models include the possibility to represent anisotropic mechanical behaviour resulting from anisotropic filament distributions, and a power law scaling of the mechanical properties with the filament density. Mechanical models within the class are parameterized by seven different constants. We demonstrate a procedure for determining these constants using finite element models of three-dimensional actin networks. Actin filaments and cross-links were modelled as elastic rods, and the networks were constructed at physiological volume fractions and at the scale of an image voxel. We show the performance of the model in estimating the mechanical behaviour of the networks over a wide range of filament densities and degrees of anisotropy.     

A mixed finite element formulation for a non-linear,transversely isotropic material model for the cardiac tissue

In this paper we present a mixed finite element method for modeling the passive properties of the myocardium. The passive properties are described by a non-linear, transversely isotropic, hyperelastic material model, and the myocardium is assumed to be almost incompressible. Single-field, pure displacement-based formulations are known to cause numerical difficulties when applied to incompressible or slightly compressible material cases. This paper presents an alternative approach in the form of a mixed formulation, where a separately interpolated pressure field is introduced as a primary unknown in addition to the displacement field. Moreover, a constraint term is included in the formulation to enforce (almost) incompressibility. Numerical results presented in the paper demonstrate the difficulties related to employing a pure displacement-based method, applying a set of physically relevant material parameter values for the cardiac tissue. The same problems are not experienced for the proposed mixed method. We show that the mixed formulation provides reasonable numerical results for compressible as well as nearly incompressible cases, also in situations of large fiber stretches. There is good agreement between the numerical results and the underlying analytical models.     

Mathematica numerical simulation of peristaltic biophysical transport of a fractional viscoelastic fluid through an inclined cylindrical tube

This paper studies the peristaltic transport of a viscoelastic fluid (with the fractional second-grade model) through an inclined cylindrical tube. The wall of the tube is modelled as a sinusoidal wave. The flow analysis is presented under the assumptions of long wave length and low Reynolds number. Caputo's definition of fractional derivative is used to formulate the fractional differentiation. Analytical solutions are developed for the normalized momentum equations. Expressions are also derived for the pressure, frictional force, and the relationship between the flow rate and pressure gradient. Mathematica numerical computations are then performed. The results are plotted and analysed for different values of fractional parameter, material constant, inclination angle, Reynolds number, Froude number and peristaltic wave amplitude. It is found that fractional parameter and Froude number resist the flow pattern while material constant, Reynolds number, inclination of angle and amplitude aid the peristaltic flow. Furthermore, frictional force and pressure demonstrate the opposite behaviour under the influence of the relevant parameters emerging in the equations of motion. The study has applications in uretral biophysics, and also potential use in peristaltic pumping of petroleum viscoelastic bio-surfactants in chemical engineering and astronautical applications involving conveyance of non-Newtonian fluids (e.g. lubricants) against gravity and in conduits with deformable walls.     

Development of software for human muscle force estimation

Muscle force estimation (MFE) has become more and more important in exploring principles of pathological movement, studying functions of artificial muscles, making surgery plan for artificial joint replacement, improving the biomechanical effects of treatments and so on. At present, existing software are complex for professionals, so we have developed a new software named as concise MFE (CMFE). CMFE which provides us a platform to analyse muscle force in various actions includes two MFE methods (static optimisation method and electromyographic-based method). Common features between these two methods have been found and used to improve CMFE. A case studying the major muscles of lower limb of a healthy subject walking at normal speed has been presented. The results are well explained from the effect of the motion produced by muscles during movement. The development of this software can improve the accuracy of the motion simulations and can provide a more extensive and deeper insight in to muscle study.     

Towards a patient-specific estimation of intra-operative femoral fracture risk

Abstract

Total Hip Arthroplasty requires pre-surgical evaluation between un-cemented and cemented prostheses. A Patient with intra-operative periprosthetic fracture and another with a successful outcome were recruited, and their finite element models were constructed by processing CT data, assuming elastic-plastic behavior of the bone as function of the local density. To resemble the insertion of the prosthesis into the femur, a fictitious thermal dilatation is applied to the broach volume. Strain-based fracture risk factor is estimated, depicting results in terms of the total mechanical strain expressed using a simple “traffic lights” color code to provide immediate, concise, and intelligible pre-operative information to surgeons.