How suture networks improve the protective function of natural structures: A multiscale investigation.

Myriad natural protective structures consist of bone plates joined by convoluted unmineralized (soft) collagenous sutures. Examples of such protective structures include: shells of turtles, craniums of almost all animals (including humans), alligator armour, armadillo armour, and others. The function of sutures has been well researched. However, whether, and if so how, sutures improve protective performance during a predator attack has received limited attention. Sutures are ubiquitous in protective structures, and this motivates the question as to whether sutures optimize the protective function of the structure. Hence, in this work the behaviour of structures that contain sutures during predator attacks is investigated. We show that sutures decrease the maximum strain energy density that turtle shells experience during predator attacks by more than an order of magnitude. Hence, sutures make turtle shells far more resilient to material failure, such as, fracture, damage, and plastic deformations. Additionally, sutures increase the viscous behaviour of the shell causing increased dissipation of energy during predator attacks. Further investigations into the influence of sutures on behaviour during locomotion and breathing are also presented. The results presented in this work motivate the inclusion of sutures in biomimetically designed protective structures, such as helmets and protective clothing. STATEMENT OF SIGNIFICANCE: Myriad bony protective structures contain networks of sutures, that is con- voluted soft collagenous tissue. Their ubiquity motivates the question, whether, and if so how, sutures improve protective performance. Hence, this work inves- tigates how sutures affect protective performance using computational experi- ments. Due to the length scale of sutures being far smaller than the structures in which they reside, classical modelling approaches are prohibitively expensive. Hence, in this work, a multiscale approach is taken. To our knowledge, this is the first multiscale investigation of structures that contain sutures. Among other insights, we show that sutures decrease the maximum strain energy density in structures during predator attacks by over an order of mag- nitude. Hence, sutures make structures far more resilient to failure.

Computationally modelling the mechanical behaviour of turtle shell sutures-A natural interlocking structure.

Sutures, the soft collagenous tissue joining interdigitating bony protrusions on the edges of bone plates, play a significant mechanical role in allowing a turtle shell to respond optimally to a range of loading regimes. In this contribution, qualitative and quantitative aspects of the mechanical behaviour of turtle shell suture regions are investigated by means of mathematical modelling. Notable features of the model include: (i) a geometrically realistic three dimensional model for the suture geometry; (ii) taking the hyperelastic, anisotropic and incompressible nature of the suture material into account; and (iii) a novel method for defining the collagen fibre directions within the suture. The model is validated against a physical three point bending test and replicates many of the qualitative and quantitative aspects of the mechanical behaviour. The model is then used to elucidate the effect that sutures have on the shell's mechanical behaviour during a predator attack. It is found that the sutures increase the energy required from a predator during an attack whilst cushioning the brittle bone, and so protecting it from fracture. Additionally, longer bony protrusions increase strain energy absorption but also increase the likelihood of fracture.

Microstructurally-based constitutive modelling of the skin - Linking intrinsic ageing to microstructural parameters.

A multiphasic constitutive model of the skin that implicitly accounts for the process of intrinsic (i.e. chronological) ageing via variation of the constitutive parameters is proposed. The structurally-motivated constitutive formulation features distinct mechanical contributions from collagen and elastin fibres. The central hypothesis underpinning this study is that the effects of ageing on the mechanical properties of the tissue are directly linked to alterations in the microstructural characteristics of the collagen and elastin networks. Constitutive parameters in the model, corresponding to different ages, are identified from published experimental data on bulge tests of human skin. The numerical results demonstrate that degradation of the elastin meshwork and variations in anisotropy of the collagen network are plausible mechanisms to explain ageing in terms of macroscopic tissue stiffening. Whereas alterations in elastin affect the low-modulus region of the skin stress-strain curve, those related to collagen have an impact on the linear region.

A validated patient-specific FSI model for vascular access in haemodialysis.

The flow rate inside arteriovenous fistulas is many times higher than physiological flow and is accompanied by high wall shear stress resulting in low patency rates. A fluid-structure interaction finite element model is developed to analyse the blood flow and vessel mechanics to elucidate the mechanisms that can lead to failure. The simulations are validated against flow measurements obtained from magnetic resonance imaging data.

Computational analysis of the radial mechanical performance of PLLA coronary artery stents.

Stents have been an effective tool to restore and maintain the patency of narrowed blood vessels, but they must have sufficient radial strength. Biodegradable stent materials have substantially lower mechanical properties than permanent stents. The stent geometry and material properties must be considered simultaneously when assessing stent performance. Material tests were performed to determine the mechanical characteristics of high-molecular-weight poly-l-lactic acid (PLLA). The results were used to calibrate an anisotropic elastic-plastic material model. Three distinct geometries were analysed with a range of material stiffness values in a finite element analysis to investigate their comparative effect on the radial strength, recoil, and radial stiffness. The performance of the different geometries varies substantially, with one particular geometry, with the highest material stiffness of 9 GPa, exceeding the desired radial strength of 300 mmHg.

Studying the influence of hydrogel injections into the infarcted left ventricle using the element-free Galerkin method.

Myocardial infarction is an increasing health problem worldwide. Because of an under-supply of blood, the cardiomyocytes in the affected region permanently lose their ability to contract. This in turn gradually weakens the overall heart function. A new therapeutic approach based on the injection of a gel into the infarcted area aims to support the healing and to inhibit adverse remodelling that can lead to heart failure. A computational model is the basis for obtaining a better understanding of the heart mechanics, in particular, how myocardial infarction and gel injections affect its pumping performance. A strain invariant-based stored energy function is proposed to account for the passive mechanical behaviour of the model, which also makes provision for active contraction. To incorporate injections an additive homogenization approach is introduced. The numerical framework is developed using an in-house code based on the element-free Galerkin method. The main focus of this contribution is to investigate the influence of gel injections on the mechanics of the left ventricle during the diastolic filling and systolic isovolumetric (isochoric) contraction phases. It is found that gel injections are able to reduce the elevated fibre stresses caused by an infarct.

The biomechanics of the human tongue.

The human tongue is composed mainly of skeletal muscle tissue and has a complex architecture. Its anatomy is characterised by interweaving yet distinct muscle groups. It is a significant contributor to the phenomenon of obstructive sleep apnoea syndrome. A realistic model of the tongue and computational simulations are important in areas such as linguistics and speech therapy. The aim of this work is to report on the construction of a geometric and constitutive model of the human tongue and to demonstrate its use in computational simulations for obstructive sleep apnoea syndrome research. The geometry of the tongue and each muscle group of the tongue, including muscle fibre orientations, are captured from the Visible Human Project dataset. The fully linear muscle model is based on the Hill three-element model that represents the constituent parts of muscle fibres. The mechanics of the model are limited to quasi-static, small-strain, linear-elastic behaviour. The main focus of this work is on the material directionality and muscle activation. The transversely isotropic behaviour of the muscle tissue is accounted for, as well as the influence of muscle activation. The behaviour of the model is illustrated in a number of benchmark tests and for the case of a subject in the supine position.

Mechanics of cranial sutures during simulated cyclic loading.

Previous computational and experimental analyses revealed that cranial sutures, fibrous joints between the bones, can reduce the strain experienced by the surrounding skull bones during mastication. This damping effect reflects the importance of including sutures in finite element (FE) analyses of the skull. Using the FE method, the behaviour of three suture morphologies of increasing complexity (butt-ended, moderate interdigitated, and complex interdigitated) during static loading was recently investigated, and the sutures were assumed to have linear elastic properties. In the current study, viscoelastic properties, derived from published experimental results of the nasofrontal suture of young pigs (Sus scrofa), are applied to the three idealised bone-suture models. The effects of suture viscoelasticity on the stress, strain, and strain energy in the models were computed for three different frequencies (corresponding to periods of 1, 10, and 100s) and compared to the results of a static, linear elastic analysis. The range of applied frequencies broadly represents different physiological activities, with the highest frequency simulating mastication and the lowest frequency simulating growth and pressure of the surrounding tissues. Comparing across all three suture morphologies, strain energy and strain in the suture decreased with the increase in suture complexity. For each suture model, the magnitude of strain decreased with an increase in frequency, and the magnitudes were similar for both the elastic and 1s frequency analyses. In addition, a viscous response is less apparent in the higher frequency analyses, indicating that viscous properties are less important to the behaviour of the suture during those analyses. The FE results suggest that implementation of viscoelastic properties may not be necessary for computational studies of skull behaviour during masticatory loading but instead might be more relevant for studies examining lower frequency physiological activities.

Computational model of soft tissues in the human upper airway.

This paper presents a three-dimensional finite element model of the tongue and surrounding soft tissues with potential application to the study of sleep apnoea and of linguistics and speech therapy. The anatomical data was obtained from the Visible Human Project, and the underlying histological data was also extracted and incorporated into the model. Hyperelastic constitutive models were used to describe the material behaviour, and material incompressibility was accounted for. An active Hill three-element muscle model was used to represent the muscular tissue of the tongue. The neural stimulus for each muscle group was determined through the use of a genetic algorithm-based neural control model. The fundamental behaviour of the tongue under gravitational and breathing-induced loading is investigated. It is demonstrated that, when a time-dependent loading is applied to the tongue, the neural model is able to control the position of the tongue and produce a physiologically realistic response for the genioglossus.

A simple fluid-structure coupling algorithm for the study of the anastomotic mechanics of vascular grafts.

Vascular anastomoses constitute a main factor in poor graft performance due to mismatches in distensibility between the host artery and the graft. This work aims at computational fluid-structure investigations of proximal and distal anastomoses of vein grafts and synthetic grafts. Finite element and finite volume models were developed and coupled with a user-defined algorithm. Emphasis was placed on the simplicity of the coupling algorithm. An artery and vein graft showed a larger dilation mismatch than an artery and synthetic graft. The vein graft distended nearly twice as much as the artery while the synthetic graft displayed only approximately half the arterial dilation. For the vein graft, luminal mismatching was aggravated by development of an anastomotic pseudo-stenosis. While this study focused on end-to-end anastomoses as a vehicle for developing the coupling algorithm, it may serve as useful point of departure for further investigations such as other anastomotic configurations, refined modelling of sutures and fully transient behaviour.

Mechanics of cranial sutures using the finite element method.

To investigate how cranial suture morphology and the arrangement of sutural collagen fibres respond to compressive and tensile loads, an idealised bone-suture-bone complex was analysed using a two-dimensional finite element model. Three suture morphologies were simulated with an increasing interdigitation index (I.I.): butt-ended, moderate interdigitated, and complex interdigitated. The collagen matrix within all sutures was modelled as an isotropic material, and as an orthotropic material in the interdigitated sutures with fibre alignment as reported in studies of miniature pigs. Static uniform compressive or tensile loading was applied to the complex. In interdigitated sutures with isotropic material properties, the orientation of the maximum (tensile) principal stresses within the suture matched the collagen fibre orientation observed in compressed and tensed sutures of miniature pigs. This suggests that randomly arranged sutural collagen fibres could optimise to an orientation most appropriate to withstand the predominant type of loading. A compression-resistant fibre arrangement imparted the highest suture strain energy relative to the isotropic and tension-resistant arrangements, indicating that this configuration maximises energy storage. A comparison across the different suture morphologies indicated that bone strain energy generally decreased with a decrease in I.I., irrespective of the sutural fibre arrangement. However, high bone stress at the interdigitation apices shifted to the limbs of the suture with an increase in I.I. These combined findings highlight the importance of suture morphology and anisotropy as properties having a significant influence on sutural mechanics.

Aortic valve leaflet mechanical properties facilitate diastolic valve function.

This work was concerned with the numerical simulation of the behaviour of aortic valves whose material can be modelled as non-linear elastic anisotropic. Linear elastic models for the valve leaflets with parameters used in previous studies were compared with hyperelastic models, incorporating leaflet anisotropy with pronounced stiffness in the circumferential direction through a transverse isotropic model. The parameters for the hyperelastic models were obtained from fits to results of orthogonal uniaxial tensile tests on porcine aortic valve leaflets. The computational results indicated the significant impact of transverse isotropy and hyperelastic effects on leaflet mechanics; in particular, increased coaptation with peak values of stress and strain in the elastic limit. The alignment of maximum principal stresses in all models follows approximately the coarse collagen fibre distribution found in aortic valve leaflets. The non-linear elastic leaflets also demonstrated more evenly distributed stress and strain which appears relevant to long-term scaffold stability and mechanotransduction.

The use of finite element methods and genetic algorithms in search of an optimal fabric reinforced porous graft system.

The mechanics of arteries result from the properties of the soft tissue constituents and the interaction of the wall layers, predominantly media and adventitia. This concept was adopted in this study for the design of a tissue regenerative vascular graft. To achieve the desired structural properties of the graft, most importantly a diametric compliance of 6%/100 mmHg, finite element methods and genetic algorithms were used in an integrated approach to identify the mechanical properties of an adventitial fabric layer that were required to optimally complement an intimal/medial polyurethane layer with interconnected porosity of three different size classes. The models predicted a compliance of 16.0, 19.2, and 31.5%/100 mmHg for the non-reinforced grafts and 5.3, 5.5, and 6.0%/100 mmHg for the fabric-reinforced grafts. The latter, featuring fabrics manufactured according to the required non-linear mechanical characteristics numerically predicted, exhibited an in vitro compliance of 2.1 +/- 0.8, 3.0 +/- 2.4, and 4.0 +/- 0.7% /100 mmHg. The combination of finite element methods and genetic algorithms was shown to be able to successfully optimize the mechanical design of the composite graft. The method offers potential for the application to alternative concepts of modular vascular grafts and the incorporation of tissue ingrowth and biodegradation.

A three-dimensional finite analysis of adaptive remodelling in the proximal femur.

A finite element analysis of adaptive bone remodelling in the proximal femur is presented. The use of a three-dimensional model permits a realistic representation of femur geometry, and also allows the possibility of examining the effects of fully three-dimensional loading situations. The long-term pattern of remodelling shows a realistic evolution of density distribution, with a tendency towards a steady state, though the simplified load cases used to model gait are not sufficient to predict the formation of the cortical shell.