Afshin Anssari-Benam

Anisotropic time-dependant behaviour of the aortic valve

The complex tri-layered structure of the aortic valve (AV) results in anisotropic quasi-static mechanical behaviour. However, its influence on AV viscoelasticity remains poorly understood. Viscoelasticity may strongly influence AV dynamic mechanical behaviour, making it essential to characterise the time-dependent response for designing successful substitutes. This study attempts to characterise the time-dependent behaviour of the AV at different strain and load increments, and to gain insight into the contribution of the microstructure to this behaviour. Uniaxial incremental stress-relaxation and creep experiments were undertaken, and the experimental data analysed with a generalised Maxwell model, to determine the characteristic time-dependent parameters. Results showed that the time dependent response of the tissue differed with the loading direction, and also with the level of applied load or strain, in both stress-relaxation and creep phenomena. Both phenomena were consistently more pronounced in the radial loading direction. Fitting of the Maxwell model highlighted that the time dependent modes required to model the data also varied in different increments, and additionally with the loading direction. These results suggest that different micro-structural mechanisms may be activated in stress-relaxation and creep, determined by the microstructural organisation of the valve matrix in each loading direction, at each strain or load increment.

Strain Transfer Through the Aortic Valve

The complex structural organization of the aortic valve (AV) extracellular matrix (ECM) enables large and highly nonlinear tissue level deformations. The collagen and elastin (elastic) fibers within the ECM form an interconnected fibrous network (FN) and are known to be the main load-bearing elements of the AV matrix. The role of the FN in enabling deformation has been investigated and documented. However, there is little data on the correlation between tissue level and FN-level strains. Investigating this correlation will help establish the mode of strain transfer (affine or nonaffine) through the AV tissue as a key feature in microstructural modeling and will also help characterize the local FN deformation across the AV sample in response to applied tissue level strains. In this study, the correlation between applied strains at tissue level, macrostrains across the tissue surface, and local FN strains were investigated. Results showed that the FN strain distribution across AV samples was inhomogeneous and nonuniform, as well as anisotropic. There was no direct transfer of the deformation applied at tissue level to the fibrous network. Loading modes induced in the FN are different than those applied at the tissue as a result of different local strains in the valve layers. This nonuniformity of local strains induced internal shearing within the FN of the AV, possibly exposing the aortic valve interstitial cells (AVICs) to shear strains and stresses.

On the specimen length dependency of tensile mechanical properties in soft tissues: gripping effects and the characteristic decay length.

Uniaxial tensile tests to failure have regularly been employed to characterise the material properties of various biological tissues, ranging from heart valves (Anssari-Benam et al., 2011) and arteries (Teng et al., 2009; Lillie et al., 2010) to tendons (Legerlotz et al., 2010), intervertebral discs (Nerurkar et al., 2010) and liver (Brunon et al., 2010), providing valuable quantitative data on important mechanical properties such as ultimate stress, strain and modulus. These properties, by definition, are intrinsic material properties and thus should not depend on the geometry of the specimen

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 valves 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 (λ˙). 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 λ˙ 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.

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.

Atherosclerotic plaques: is endothelial shear stress the only factor?

Initiation and development of atherosclerosis has largely been attributed to irregular shear stress patterns and values, in the current literature. Abnormalities such as low shear stress, reversing and oscillatory shear force patterns, as well as temporal variations of shear stress are the most cited factors. However, clinical findings have further indicated that plaques have still been formed and developed in arterial sites that possess relatively more steady and higher shear stresses than those observed in studies correlating low or oscillatory shear stresses with atherosclerosis. These data imply that deviations in shear stress from its normal physiological pattern alone may not be the only factor inducing atherosclerosis, and additional haemodynamics parameter other then shear stress may also contribute to the initiation and development of plaques. In this paper, we hypothesise that the combined effect of wall shear stress and circumferential stress waves, in the form of angular phase difference between the two waves at each cardiac cycle, may be a more accurate determinant of plaque formation and growth. Furthermore, arterial sites that possess more positive values of this angular phase difference may be more prone to plaque formation or development. If proved correct, this theory can transform our understanding of endothelial cell mechanotransduction and mechanobiology, and may lead to design and utilisation of new diagnostic procedures and equipment as predictive and preventive clinical tools for patients with abnormal arterial blood pressure.

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 Ċ 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.

Response to letter to the editor: “End effects in mechanical testing of biomaterials”

We appreciate the detailed response from Professor Horgan, discussing our letter to the editor concerned with end effects when mechanical testing soft tissues (Anssari-Benam et al., 2012a), and providing further insightful analysis. The concepts of end effects and characteristic decay length have indeed been well established for a long time in the context of solid mechanics, with substantial contributions from Professor Horgan, towards establishing theoretical and analytical criteria for their characterisation, as referenced in our previous publication (Anssari-Benam et al., 2012b; from Horgan (1972), Choi and Horgan (1977).