A New Dissipation Function to Model the Rate-Dependent Mechanical Behavior of Semilunar Valve Leaflets.

A new dissipation function Wv is devised and presented to capture the rate-dependent mechanical behavior of the semilunar heart valves. Following the experimentally-guided framework introduced in our previous work (Anssari-Benam et al., 2022 "Modelling the Rate-Dependency of the Mechanical Behaviour of the Aortic Heart Valve: An Experimentally Guided Theoretical Framework," J. Mech. Behav. Biomed. Mater., 134, p. 105341), we derive our proposed Wv function from the experimental data pertaining to the biaxial deformation of the aortic and pulmonary valve specimens across a 10,000-fold range of deformation rate, exhibiting two distinct rate-dependent features: (i) the stiffening effect in σ-λ curves with increase in rate; and (ii) the asymptotic effect of rate on stress levels at higher rates. The devised Wv function is then used in conjunction with a hyperelastic strain energy function We to model the rate-dependent behavior of the valves, incorporating the rate of deformation as an explicit variable. It is shown that the devised function favorably captures the observed rate-dependent features, and the model provides excellent fits to the experimentally obtained σ-λ curves. The proposed function is thereby recommended for application to the rate-dependent mechanical behavior of heart valves, as well as other soft tissues that exhibit a similar rate-dependent behavior.

Microfluidic Manufacture of Lipid-Based Nanomedicines.

Nanoparticulate technologies have revolutionized drug delivery allowing for passive and active targeting, altered biodistribution, controlled drug release (temporospatial or triggered), enhanced stability, improved solubilization capacity, and a reduction in dose and adverse effects. However, their manufacture remains immature, and challenges exist on an industrial scale due to high batch-to-batch variability hindering their clinical translation. Lipid-based nanomedicines remain the most widely approved nanomedicines, and their current manufacturing methods remain discontinuous and face several problems such as high batch-to-batch variability affecting the critical quality attributes (CQAs) of the product, laborious multistep processes, need for an expert workforce, and not being easily amenable to industrial scale-up involving typically a complex process control. Several techniques have emerged in recent years for nanomedicine manufacture, but a paradigm shift occurred when microfluidic strategies able to mix fluids in channels with dimensions of tens of micrometers and small volumes of liquid reagents in a highly controlled manner to form nanoparticles with tunable and reproducible structure were employed. In this review, we summarize the recent advancements in the manufacturing of lipid-based nanomedicines using microfluidics with particular emphasis on the parameters that govern the control of CQAs of final nanomedicines. The impact of microfluidic environments on formation dynamics of nanomaterials, and the application of microdevices as platforms for nanomaterial screening are also discussed.

Modelling the rate-dependency of the mechanical behaviour of the aortic heart valve: An experimentally guided theoretical framework.

A theoretical framework, based on extant experimental findings, is presented to devise a novel viscous dissipation function Wv in order to model the rate-dependent mechanical behaviour of the aortic heart valve. The experimental data encompasses Cauchy stress-stretch (σ-λ) curves obtained across a 10,000-fold range of stretch rates (λ˙), from quasi-static (λ˙= 0.001 s-1) to upper-range of physiological (λ˙= 12.4 s-1) deformation rates. The analysis of the data elicits two important trends: (i) the mechanical behaviour of the aortic valve across the tested rates is rate-dependent, with specimens becoming stiffer by increasing rate; and (ii) there appears to be a plateau in the rate-effects on the σ-λ curves; i.e. the rate-effects approach an asymptote with increase in the stretch rate λ˙. Guided by these empirical observations, we devise our new Wv function and demonstrate that the well-known form of the dissipation function commonly used in the literature is a special case of our proposed Wv. The ensuing model is then compared against the experimental σ-λ curves and is shown to provide favourable predictions. An important advantage of the employed modelling framework is that it allows the incorporation of the rate of deformation, which is a direct experimental control parameter, as an explicit modelling variable. The application of the proposed model is thereby recommended for heart valves and other soft tissues that exhibit similar rate-dependent features.

A review of brachytherapy physical phantoms developed over the last 20 years: clinical purpose and future requirements.

Within the brachytherapy community, many phantoms are constructed in-house, and less commercial development is observed as compared to the field of external beam. Computational or virtual phantom design has seen considerable growth; however, physical phantoms are beneficial for brachytherapy, in which quality is dependent on physical processes, such as accuracy of source placement. Focusing on the design of physical phantoms, this review paper presents a summary of brachytherapy specific phantoms in published journal articles over the last twenty years (January 1, 2000 - December 31, 2019). The papers were analyzed and tabulated by their primary clinical purpose, which was deduced from their associated publications. A substantial body of work has been published on phantom designs from the brachytherapy community, but a standardized method of reporting technical aspects of the phantoms is lacking. In-house phantom development demonstrates an increasing interest in magnetic resonance (MR) tissue mimicking materials, which is not yet reflected in commercial phantoms available for brachytherapy. The evaluation of phantom design provides insight into the way, in which brachytherapy practice has changed over time, and demonstrates the customised and broad nature of treatments offered.

Helically arranged cross struts in azhdarchid pterosaur cervical vertebrae and their biomechanical implications.

Azhdarchid pterosaurs, the largest flying vertebrates, remain poorly understood, with fundamental aspects of their palaeobiology unknown. X-ray computed tomography reveals a complex internal micro-architecture for three-dimensionally preserved, hyper-elongate cervical vertebrae of the Cretaceous azhdarchid pterosaur, Alanqa sp. Incorporation of the neural canal within the body of the vertebra and elongation of the centrum result in a "tube within a tube" supported by helically distributed trabeculae. Linear elastic static analysis and linearized buckling analysis, accompanied with a finite element model, reveal that as few as 50 trabeculae increase the buckling load by up to 90%, implying that a vertebra without the trabeculae is more prone to elastic instability due to axial loads. Subsuming the neural tube into the centrum tube adds considerable stiffness to the cervical series, permitting the uptake of heavy prey items without risking damage to the cervical series, while at the same time allowing considerable skeletal mass reduction.

Rate-dependent mechanical behaviour of semilunar valves under biaxial deformation: From quasi-static to physiological loading rates.

In this study we investigate the rate-dependency of the mechanical behaviour of semilunar heart valves under biaxial deformation, from quasi-static to physiological loading rates. This work extends and complements our previous undertaking, where the rate-dependency in the mechanical behaviour of semilunar valve specimens was documented in sub-physiological rate domains (Acta Biomater. 2019; https://doi.org/10.1016/j.actbio.2019.02.008). For the first time we demonstrate herein that the stress-stretch curves obtained from specimens under physiological rates too are markedly different to those at sufficiently lower rates and at quasi-static conditions. The results importantly underline that the mechanical behaviour of semilunar heart valves is rate dependent, and the physiological mechanical behaviour of the valves may not be correctly obtained via material characterisation tests at arbitrary low deformation rates. Presented results in this work provide an inclusive dataset for material characterisation and modelling of semilunar heart valves across a 10,000 fold deformation rate, both under equi-biaxial and 1:3 ratio deformation rates. The important application of these results is to inform the development of appropriate mechanical testing protocols, as well as devising new models, for suitable determination of the rate-dependent constitutive mechanical behaviour of the semilunar valves.

Comparative finite element modelling of aneurysm formation and physiologic inflation in the descending aorta.

Despite the general interest in aneurysm rupture prediction, the aneurysm formation has received limited attention. The goal of this study is to assess whether an aneurysm may be instigated in a healthy model of an aorta inflated by a supra-physiological pressure. The effect of two main aspects on numerical predictions has been explored: i) the geometric design and ii) the constitutive law adopted to represent the material properties. Firstly, higher values of wall stress and displacement magnitude were generated in the physiologic model compared to the cylindrical one when assigning the same material properties. Secondly, greater deformations are observed in the anisotropic model compared to the isotropic one.

Insights into the micromechanics of stress-relaxation and creep behaviours in the aortic valve.

Viscoelastic attributes of the aortic valve (AV) tissue are, in part, reflected in stress-relaxation and creep behaviours observed in vitro. While the extent of AV time-dependent behaviour under physiological conditions is not yet fully understood, in vitro the tissue exhibits clear stress-relaxation but minimal creep under equi-biaxial loading, in contrast to uniaxial loading where creep is evidently exhibited. Tissue-level stress-relaxation behaviour follows the form of (single and double) Maxwell-type exponential decay relaxation modes, and creep occurs in the form of exponential primary followed by linear secondary creep modes. This paper aims to provide an explanation for these behaviours based on the AV microstructural (i.e. fibre-level) mechanics. The kinematics of AV microstructural reorganisation is investigated experimentally using confocal microscopy to track the interstitial cell nuclei as markers of AV microstructural reorganisation under uniaxial loading. A theoretical framework is then applied to describe the experimentally observed kinematics in mathematical terms. Using this framework it is shown that at the microstructural level, AV stress-relaxation and creep behaviours both stem from the same dissipative kinematics of fibre-fibre and fibre-matrix interactions, that occur as a consequence of microstructural reorganisation due to the applied tissue-level loads. It is additionally shown that the proposed dissipative kinematics correctly predict the nature of relaxation and creep behaviours, i.e. the type and the number of modes involved. Further analysis is presented to demonstrate that the origin of the minimal creep behaviour under equi-biaxial loading can be explained to stem from tissue-level loading boundary conditions. These key findings help to better understand the underlying causes of AV stress-relaxation and creep behaviours in vivo, and why these may differ from the behaviours observed under non-physiological in vitro loading.

Rate-dependency of the mechanical behaviour of semilunar heart valves under biaxial deformation.

This paper presents an experimental investigation and evidence of rate-dependency in the planar mechanical behaviour of semilunar heart valves. Samples of porcine aortic and pulmonary valves were subjected to biaxial deformations across 1000-fold stretch rate, ranging from λ̇=0.001 to 1 s-1. The experimental campaign encompassed protocols covering (i) tests on samples without preconditioning, (ii) preconditioning immediately followed by tensile tests; and (iii) tensile tests at different rates performed on the same preconditioned specimen. Our results indicate that under all employed loading protocols, heart valve samples exhibit a marked rate-dependency in their deformation behaviour. This rate-dependency is reflected in stress-stretch curves and the calculated ensuing gradients, where samples typically show stiffening with increased rate. These results underpin one conclusive outcome: the in-plane mechanical behaviour of semilunar valves is rate-dependent (p<0.05 for Cauchy stress levels ≥50 kPa). This outcome implies that the rate of deformation for characterising the mechanical behaviour of semilunar heart valves may not be chosen arbitrarily low, and models that incorporate rate-effects may be more appropriate for better capturing the mechanical behaviour of heart valves. STATEMENT OF SIGNIFICANCE: This study presents for the first time a comprehensive set of results and evidence of rate-dependency in the mechanical behaviour of semilunar heart valves under biaxial deformation. Our results challenge the widely-applied assumption in the bulk of the existing literature, where an implicit rate-independency is assumed in both experimental and modelling propositions related to the biomechanics of the aortic and pulmonary valves. This study therefore creates a solid platform for future research in heart valve biomechanics with two important implications. First, experimental campaigns have to be carried out at high stretch rates; ideally as close to the physiological rate as possible. Second, new continuum/computational models are required to address the rate-dependent mechanical behaviour of the semilunar valves.

A transverse isotropic constitutive model for the aortic valve tissue incorporating rate-dependency and fibre dispersion: Application to biaxial deformation.

This paper presents a continuum-based transverse isotropic model incorporating rate-dependency and fibre dispersion, applied to the planar biaxial deformation of aortic valve (AV) specimens under various stretch rates. The rate dependency of the mechanical behaviour of the AV tissue under biaxial deformation, the (pseudo-) invariants of the right Cauchy-Green deformation-rate tensor C associated with fibre dispersion, and a new fibre orientation density function motivated by fibre kinematics are presented for the first time. It is shown that the model captures the experimentally observed deformation of the specimens, and characterises a shear-thinning behaviour associated with the dissipative (viscous) kinematics of the matrix and the fibres. The application of the model for predicting the deformation behaviour of the AV under physiological rates is illustrated and an example of the predicted σ-λ curves is presented. While the development of the model was principally motivated by the AV biomechanics requisites, the comprehensive theoretical approach employed in the study renders the model suitable for application to other fibrous soft tissues that possess similar rate-dependent and structural attributes.

Modeling the Deformation of the Elastin Network in the Aortic Valve.

This paper is concerned with proposing a suitable structurally motivated strain energy function, denoted by Weelastin network, for modeling the deformation of the elastin network within the aortic valve (AV) tissue. The AV elastin network is the main noncollagenous load-bearing component of the valve matrix, and therefore, in the context of continuum-based modeling of the AV, the Weelastin network strain energy function would essentially serve to model the contribution of the "isotropic matrix." To date, such a function has mainly been considered as either a generic neo-Hookean term or a general exponential function. In this paper, we take advantage of the established structural analogy between the network of elastin chains and the freely jointed molecular chain networks to customize a structurally motivated Weelastin network function on this basis. The ensuing stress-strain (force-stretch) relationships are thus derived and fitted to the experimental data points reported by (Vesely, 1998, "The Role of Elastin in Aortic Valve Mechanics," J. Biomech., 31, pp. 115-123) for intact AV elastin network specimens under uniaxial tension. The fitting results are then compared with those of the neo-Hookean and the general exponential models, as the frequently used models in the literature, as well as the "Arruda-Boyce" model as the gold standard of the network chain models. It is shown that our proposed Weelastin network function, together with the general exponential and the Arruda-Boyce models provide excellent fits to the data, with R2 values in excess of 0.98, while the neo-Hookean function is entirely inadequate for modeling the AV elastin network. However, the general exponential function may not be amenable to rigorous interpretation, as there is no structural meaning attached to the model. It is also shown that the parameters estimated by the Arruda-Boyce model are not mathematically and structurally valid, despite providing very good fits. We thus conclude that our proposed strain energy function Weelastin network is the preferred choice for modeling the behavior of the AV elastin network and thereby the isotropic matrix. This function may therefore be superimposed onto that of the anisotropic collagen fibers family in order to develop a structurally motivated continuum-based model for the AV.

The effect of thickness measurement on numerical arterial models.

Several optical-based techniques for measuring the sample thickness (ST) of soft tissues have been proposed in the literature to overcome the limits of hand-operated procedures. However, ST measurement still remains arbitrary. The stress calculated during an experimental procedure, usually based on a constant thickness value for all samples, cannot be considered representative of the actual stress experienced by the tissue. Therefore, a new optical methodology to measure ST is proposed and compared to four different thickness estimations. A simplified aortic geometry, under physiologic pulsatile conditions, is used to assess the impact of ST measurement on stress predictions. An additional computational model investigates the effect of such thickness values on critical pressure levels that may instigate aneurysm formation in a homogeneous or artificially modified geometry. Comparing the results obtained for the application of a pulsatile load, wall stress values associated to minimum ST are at least 24kPa inferior to maximum ST. Critical pressure values appear to be inversely proportional to ST estimation: simulations, associated to maximum ST, predict aneurysm formation for pressure levels at least 7kPa inferior to minimum ST outcomes. Finally, the role of the strain-energy function used to fit the experimental data is demonstrated to be fundamental for predictions of aneurysm formation.

A transverse isotropic viscoelastic constitutive model for aortic valve tissue.

A new anisotropic viscoelastic model is developed for application to the aortic valve (AV). The directional dependency in the mechanical properties of the valve, arising from the predominantly circumferential alignment of collagen fibres, is accounted for in the form of transverse isotropy. The rate dependency of the valve's mechanical behaviour is considered to stem from the viscous (η) dissipative effects of the AV matrix, and is incorporated as an explicit function of the deformation rate ([Formula: see text]). Model (material) parameters were determined from uniaxial tensile deformation tests of porcine AV specimens at various deformation rates, by fitting the model to each experimental dataset. It is shown that the model provides an excellent fit to the experimental data across all different rates and satisfies the condition of strict local convexity. Based on the fitting results, a nonlinear relationship between η and [Formula: see text] is established, highlighting a 'shear-thinning' behaviour for the AV with increase in the deformation rate. Using the model and these outcomes, the stress-deformation curves of the AV tissue under physiological deformation rates in both the circumferential and radial directions are predicted and presented. To verify the predictive capabilities of the model, the stress-deformation curves of AV specimens at an intermediate deformation rate were estimated and validated against the experimental data at that rate, showing an excellent agreement. While the model is primarily developed for application to the AV, it may be applied without the loss of generality to other collagenous soft tissues possessing a similar structure, with a single preferred direction of embedded collagen fibres.

Evaluation of bioprosthetic heart valve failure using a matrix-fibril shear stress transfer approach.

A matrix-fibril shear stress transfer approach is devised and developed in this paper to analyse the primary biomechanical factors which initiate the structural degeneration of the bioprosthetic heart valves (BHVs). Using this approach, the critical length of the collagen fibrils l c and the interface shear acting on the fibrils in both BHV and natural aortic valve (AV) tissues under physiological loading conditions are calculated and presented. It is shown that the required critical fibril length to provide effective reinforcement to the natural AV and the BHV tissue is l c  = 25.36 µm and l c  = 66.81 µm, respectively. Furthermore, the magnitude of the required shear force acting on fibril interface to break a cross-linked fibril in the BHV tissue is shown to be 38 µN, while the required interfacial force to break the bonds between the fibril and the surrounding extracellular matrix is 31 µN. Direct correlations are underpinned between these values and the ultimate failure strength and the failure mode of the BHV tissue compared with the natural AV, and are verified against the existing experimental data. The analyses presented in this paper explain the role of fibril interface shear and critical length in regulating the biomechanics of the structural failure of the BHVs, for the first time. This insight facilitates further understanding into the underlying causes of the structural degeneration of the BHVs in vivo.

Unified viscoelasticity: Applying discrete element models to soft tissues with two characteristic times.

Discrete element models have often been the primary tool in investigating and characterising the viscoelastic behaviour of soft tissues. However, studies have employed varied configurations of these models, based on the choice of the number of elements and the utilised formation, for different subject tissues. This approach has yielded a diverse array of viscoelastic models in the literature, each seemingly resulting in different descriptions of viscoelastic constitutive behaviour and/or stress-relaxation and creep functions. Moreover, most studies do not apply a single discrete element model to characterise both stress-relaxation and creep behaviours of tissues. The underlying assumption for this disparity is the implicit perception that the viscoelasticity of soft tissues cannot be described by a universal behaviour or law, resulting in the lack of a unified approach in the literature based on discrete element representations. This paper derives the constitutive equation for different viscoelastic models applicable to soft tissues with two characteristic times. It demonstrates that all possible configurations exhibit a unified and universal behaviour, captured by a single constitutive relationship between stress, strain and time as: σ+Aσ̇+Bσ¨=Pε̇+Qε¨. The ensuing stress-relaxation G(t) and creep J(t) functions are also unified and universal, derived as [Formula: see text] and J(t)=c2+(ε0-c2)e(-PQt)+σ0Pt, respectively. Application of these relationships to experimental data is illustrated for various tissues including the aortic valve, ligament and cerebral artery. The unified model presented in this paper may be applied to all tissues with two characteristic times, obviating the need for employing varied configurations of discrete element models in preliminary investigation of the viscoelastic behaviour of soft tissues.