T.C. Gasser

A new Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models

In this paper we develop a new constitutive law for the description of the (passive) mechanical response of arterial tissue. The artery is modeled as a thick-walled nonlinearly elastic circular cylindrical tube consisting of two layers corresponding to the media and adventitia (the solid mechanically relevant layers in healthy tissue). Each layer is treated as a fiber-reinforced material with the fibers corresponding to the collagenous component of the material and symmetrically disposed with respect to the cylinder axis. The resulting constitutive law is orthotropic in each layer. Fiber orientations obtained from a statistical analysis of histological sections from each arterial layer are used. A specific form of the law, which requires only three material parameters for each layer, is used to study the response of an artery under combined axial extension, inflation and torsion. The characteristic and very important residual stress in an artery in vitro is accounted for by assuming that the natural (unstressed and unstrained) configuration of the material corresponds to an open sector of a tube, which is then closed by an initial bending to form a load-free, but stressed, circular cylindrical configuration prior to application of the extension, inflation and torsion. The effect of residual stress on the stress distribution through the deformed arterial wall in the physiological state is examined.The model is fitted to available data on arteries and its predictions are assessed for the considered combined loadings. It is explained how the new model is designed to avoid certain mechanical, mathematical and computational deficiencies evident in currently available phenomenological models. A critical review of these models is provided by way of background to the development of the new model.

A structural model for the viscoelastic behavior of arterial walls : Continuum formulation and finite element analysis

In this paper we present a two-layer structural model suitable for predicting reliably the passive (unstimulated) time-dependent three-dimensional stress and deformation states of healthy young arterial walls under various loading conditions. It extends to the viscoelastic regime a recently developed constitutive framework for the elastic strain response of arterial walls (see Holzapfel et al. (2001)). The structural model is formulated within the framework of nonlinear continuum mechanics and is well-suited for a finite element implementation. It has the special merit that it is based partly on histological information, thus allowing the material parameters to be associated with the constituents of each mechanically-relevant arterial layer. As one essential ingredient from the histological information the constitutive model requires details of the directional organization of collagen fibers as commonly observed under a microscope. We postulate a fully automatic technique for identifying the orientations of cellular nuclei, these coinciding with the preferred orientations in the tissue. The biological material is assumed to behave incompressibly so that the constitutive function is decomposed locally into volumetric and isochoric parts. This separation turns out to be advantageous in avoiding numerical complications within the finite element analysis of incompressible materials. For the description of the viscoelastic behavior of arterial walls we employ the concept of internal variables. The proposed viscoelastic model admits hysteresis loops that are known to be relatively insensitive to strain rate, an essential mechanical feature of arteries of the muscular type. To enforce incompressibility without numerical difficulties, the finite element treatment adopted is based on a three-field Hu-Washizu variational approach in conjunction with an augmented Lagrangian optimization technique. Two numerical examples are used to demonstrate the reliability and efficiency of the proposed structural model for arterial wall mechanics as a basis for large scale numerical simulations.

Comparison of a Multi-Layer Structural Model for Arterial Walls With a Fung-Type Model, and Issues of Material Stability

The goals of this paper are (i) to re-examine the constitutive law for the description of the (passive) highly nonlinear and anisotropic response of healthy elastic arteries introduced recently by the authors, (ii) to show how the mechanical response of a carotid artery under inflation and extension predicted by the structural model compares with that for a three-dimensional form of Fung-type strain-energy function, (iii) to provide a new set of material parameters that can be used in a finite element program, and (iv) to show that the model has certain mathematical features that are important from the point of view of material and numerical stability.

Biomechanical Rupture Risk Assessment of Abdominal Aortic Aneurysms : Model Complexity versus Predictability of Finite Element Simulations

OBJECTIVE Investigation of the predictability of finite element (FE) models regarding rupture risk assessment of abdominal aortic aneurysms (AAAs). MATERIALS AND MATERIALS Peak wall stress (PWS) and peak wall rupture risk (PWRR) of ruptured (n = 20) and non-ruptured (n = 30) AAAs were predicted by four FE models of different complexities derived from computed tomography (CT) data. Two matching sub-groups of ruptured and non-ruptured aneurysms were used to investigate the usability of different FE models to discriminate amongst them. RESULTS All FE models exhibited a strong positive correlation between PWS and PWRR with the maximum diameter. FE models, which excluded the intra-luminal thrombus (ILT) failed to discriminate between ruptured and non-ruptured aneurysms. The predictability of all applied FE models was strengthened by including wall strength data, that is, computing the PWRR. The most sophisticated FE model applied in this study predicted PWS and PWRR 1.17 (p = 0.021) and 1.43 (p = 0.016) times higher in ruptured than diameter-matched non-ruptured aneurysms, respectively. CONCLUSIONS PWRR reinforces PWS as a biomechanical rupture risk index. The ILT has a major impact on AAA biomechanics and rupture risk, and hence, needs to be considered in meaningful FE simulations. The applied FE models, however, could not explain rupture in all analysed aneurysms.

Penetration-Enhanced Ultrasharp Microneedles and Prediction on Skin Interaction for Efficient Transdermal Drug Delivery

This paper presents penetration-enhanced hollow microneedles and an analysis on the biomechanical interaction between microneedles and skin tissue. The aim of this paper is to fabricate microneedles that reliably penetrate the skin tissue without using penetration enhancers or special insertion tools that were used in the previous studies. The microneedles are made of silicon and feature ultrasharp tips and side openings. The microneedle chips were experimentally tested in vivo by injection of dye markers. To further investigate the penetration, the insertion progression and the insertion force were monitored by measuring the electrical impedance between microneedles and a counter electrode on the skin. The microneedle design was also tested using a novel simulation approach and compared to other previously published microneedle designs. The purpose of this specific part of the paper was to investigate the interaction mechanisms between a microneedle and the skin tissue. This investigation is used to predict how the skin deforms upon insertion and how microneedles can be used to create a leak-free liquid delivery into the skin. The fabricated microneedles successfully penetrated dry living human skin at all the tested sites. The insertion characteristic of the microneedle was superior to an earlier presented type, and the insertion force of a single microneedle was estimated to be below 10 mN. This low insertion force represents a significant improvement to earlier reported results and potentially allows a microneedle array with hundreds of needles to be inserted into tissue by hand.

A Three-dimensional Finite Element Model for Arterial Clamping

Clamp induced injuries of the arterial wall may determine the outcome of surgical procedures. Thus, it is important to investigate the underlying mechanical effects. We present a three-dimensional finite element model, which allows the study of the mechanical response of an artery-treated as a two-layer tube-during arterial clamping. The important residual stresses, which are associated with the load-free configuration of the artery, are also considered. In particular, the finite element analysis of the deformation process of a clamped artery and the associated stress distribution is presented. Within the clamping area a zone of axial tensile peak-stresses was identified, which (may) cause intimal and medial injury. This is an additional injury mechanism, which clearly differs from the commonly assumed wall damage occurring due to compression between the jaws of the clamp. The proposed numerical model provides essential insights into the mechanics of the clamping procedure and the associated injury mechanisms. It allows detailed parameter studies on a virtual clamped artery, which can not be performed with other methodologies. This approach has the potential to identify the most appropriate clamps for certain types of arteries and to guide optimal clamp design.

A novel strategy to translate the biomechanical rupture risk of abdominal aortic aneurysms to their equivalent diameter risk : Method and retrospective validation

OBJECTIVE To translate the individual abdominal aortic aneurysm (AAA) patients biomechanical rupture risk profile to risk-equivalent diameters, and to retrospectively test their predictability in ruptured and non-ruptured aneurysms. METHODS Biomechanical parameters of ruptured and non-ruptured AAAs were retrospectively evaluated in a multicenter study. General patient data and high resolution computer tomography angiography (CTA) images from 203 non-ruptured and 40 ruptured aneurysmal infrarenal aortas. Three-dimensional AAA geometries were semi-automatically derived from CTA images. Finite element (FE) models were used to predict peak wall stress (PWS) and peak wall rupture index (PWRI) according to the individual anatomy, gender, blood pressure, intra-luminal thrombus (ILT) morphology, and relative aneurysm expansion. Average PWS diameter and PWRI diameter responses were evaluated, which allowed for the PWS equivalent and PWRI equivalent diameters for any individual aneurysm to be defined. RESULTS PWS increased linearly and PWRI exponentially with respect to maximum AAA diameter. A size-adjusted analysis showed that PWS equivalent and PWRI equivalent diameters were increased by 7.5 mm (p = .013) and 14.0 mm (p < .001) in ruptured cases when compared to non-ruptured controls, respectively. In non-ruptured cases the PWRI equivalent diameters were increased by 13.2 mm (p < .001) in females when compared with males. CONCLUSIONS Biomechanical parameters like PWS and PWRI allow for a highly individualized analysis by integrating factors that influence the risk of AAA rupture like geometry (degree of asymmetry, ILT morphology, etc.) and patient characteristics (gender, family history, blood pressure, etc.). PWRI and the reported annual risk of rupture increase similarly with the diameter. PWRI equivalent diameter expresses the PWRI through the diameter of the average AAA that has the same PWRI, i.e. is at the same biomechanical risk of rupture. Consequently, PWRI equivalent diameter facilitates a straightforward interpretation of biomechanical analysis and connects to diameter-based guidelines for AAA repair indication. PWRI equivalent diameter reflects an additional diagnostic parameter that may provide more accurate clinical data for AAA repair indication.

The impact of intraluminal thrombus failure on the mechanical stress in the wall of abdominal aortic aneurysms.

OBJECTIVES The role of the intraluminal thrombus (ILT) in abdominal aortic aneurysm (AAA) rupture is controversial, and it is still not clear if an ILT increases or decreases AAA rupture risk. Specifically, signs of bleeding in the ILT are considered to increase AAA rupture risk. To further explore this hypothesis, intact AAAs (n = 4) with clear signs of fissures in the ILT, identified by computed tomography angiography (CTA) were investigated. METHODS Two different cases of ILT fissuring were investigated, where (1) ILT fissures were extracted directly from the CTA data and (2) a hypothetical fissure was introduced in the otherwise-intact ILT tissue. Wall stress distributions were predicted based on detailed Finite Element (FE) models. RESULTS ILT fissures extracted from CTA data locally increase the mechanical stress in the underlying wall by up to 30%. The largest impact on wall stress was observed if the ILT crack reaches the aneurysm wall, or if it involves large parts of the ILT. By contrast, a concentric failure in the medial ILT, which does not reach the aneurysm wall, has almost no impact on wall stress distribution. Hypothetical ILT fissures that connect the lumen with the wall cause a twofold increase of the stress in the underlying wall. CONCLUSIONS ILT fissures increase the stress in the underlying wall, whereas regions other than that remain unaffected. If ILT fissures reach the wall or involve large parts of the ILT, the resulting increase in wall stress could possibly cause AAA rupture.

An Integrated Fluid-Chemical Model Toward Modeling the Formation of Intra-Luminal Thrombus in Abdominal Aortic Aneurysms

Abdominal Aortic Aneurysms (AAAs) are frequently characterized by the presence of an Intra-Luminal Thrombus (ILT) known to influence their evolution biochemically and biomechanically. The ILT progression mechanism is still unclear and little is known regarding the impact of the chemical species transported by blood flow on this mechanism. Chemical agonists and antagonists of platelets activation, aggregation, and adhesion and the proteins involved in the coagulation cascade (CC) may play an important role in ILT development. Starting from this assumption, the evolution of chemical species involved in the CC, their relation to coherent vortical structures (VSs) and their possible effect on ILT evolution have been studied. To this end a fluid-chemical model that simulates the CC through a series of convection-diffusion-reaction (CDR) equations has been developed. The model involves plasma-phase and surface-bound enzymes and zymogens, and includes both plasma-phase and membrane-phase reactions. Blood is modeled as a non-Newtonian incompressible fluid. VSs convect thrombin in the domain and lead to the high concentration observed in the distal portion of the AAA. This finding is in line with the clinical observations showing that the thickest ILT is usually seen in the distal AAA region. The proposed model, due to its ability to couple the fluid and chemical domains, provides an integrated mechanochemical picture that potentially could help unveil mechanisms of ILT formation and development.

Mechano-biology in the thoracic aortic aneurysm: a review and case study

An aortic aneurysm is a permanent and localized dilatation of the aorta resulting from an irreversible loss of structural integrity of the aortic wall. The infrarenal segment of the abdominal aorta is the most common site of aneurysms; however, they are also common in the ascending and descending thoracic aorta. Many cases remain undetected because thoracic aortic aneurysms (TAAs) are usually asymptomatic until complications such as aortic dissection or rupture occurs. Clinical estimates of rupture potential and dissection risk, and thus interventional planning for TAAs, are currently based primarily on the maximum diameter and growth rate. The growth rate is calculated from maximum diameter measurements at two subsequent time points; however, this measure cannot reflect the complex changes of vessel wall morphology and local areas of weakening that underline the strong regional heterogeneity of TAA. Due to the high risks associated with both open and endovascular repair, an intervention is only justified if the risk for aortic rupture or dissection exceeds the interventional risks. Consequently, TAAs clinical management remains a challenge, and new methods are needed to better identify patients for elective repair. We reviewed the pathophysiology of TAAs and the role of mechanical stresses and mathematical growth models in TAA management; as a proof of concept, we applied a multiscale biomechanical analysis to a case study of TAA.