Stress-Swelling Finite Element Modeling of Cervical Response With Homeostatic Collagen Fiber Distributions

During pregnancy, the cervix experiences significant mechanical property change due to tissue swelling, and to ongoing changes in the collagen content. In this paper, we model how these two effects contribute to cervical deformation as the pressure load on top of the cervix increases. The cervix and its surrounding supporting ligaments are taken into consideration in the resulting mechanical analysis. The cervix itself is treated as a multilayered tube-like structure, with layer-specific collagen orientation. The cervical tissue in each layer is treated in terms of a collagen constituent that remodels with time within a ground substance matrix that experiences swelling. The load and swelling are taken to change sufficiently slowly so that the collagen properties at any instant can be regarded as being in a state of homeostasis. Among other things, the simulations show how the luminal cross-sectional area varies along its length as a function of pressure and swelling. In general, an increase in pressure causes an overall shortening of the lumen while an increase in swelling has the opposite effect.

Development of a computational model for acute ischemic stroke recanalization through cyclic aspiration

Acute ischemic stroke (AIS), the result of embolic occlusion of a cerebral artery, is responsible for 87% of the 6.5 million stroke-related deaths each year. Despite improvements from first-generation thrombectomy devices for treating AIS, 80% of eligible stroke patients will either die or suffer a major disability. In order to maximize the number of patients with good outcomes, new AIS therapies need to be developed to achieve complete reperfusion on the first pass. One such therapy that has shown promise experimentally is the application of cyclic aspiration pressure, which led to higher recanalization rates at lower pressure magnitudes. In order to investigate AIS and cyclic aspiration recanalization, an improved computational modeling framework was developed, combining a viscoelastic thromboembolus model with a cohesive zone (CZ) model for the thromboembolus-artery interface. The model was first validated against experimental displacement data of a cyclically aspirated thromboembolus analog. The CZ model parameters, including the addition of a damage accumulation model, were then investigated computationally to determine their individual effects on the thromboembolus and CZ behavior. The relaxation time and the damage model critical opening length were shown to have the greatest effect on the CZ opening and led to increased displacement that accumulated with repeated loading. Additional simulations were performed with parameters relevant to AIS including internal carotid artery dimensions and thromboemboli mechanical properties. In these AIS cases, more upstream CZ opening was observed compared to the thromboembolus analog cases and greater displacement was achieved with the lower-frequency aspiration (0.5 vs 1 Hz).

Numerical Study of the Blood Flow in a Deformable Human Aorta

In this work, we present a numerical investigation of blood flow in a portion of the human vascular system. More precisely, the present work analyzed the blood flow in the upper portion of the aorta. The aorta and its ramified blood vessels are surrounded by the cardiac muscle. The blood flow generates pressure on the internal surfaces of the artery and its ramifications, thereby causing deformation of the cardiac muscle. The numerical analysis used the Navier–Stokes equations as the governing equations of blood flow for the calculation of the velocity field and pressure distribution in the blood. The neo-Hookean hyperelastic model was used for the description of the behavior of the vessel walls. The velocity and pressure distributions were analyzed. The deformation of the vessel was also investigated. The numerical results could be used to better understand and predict the factors that trigger cardiovascular diseases and distortions of the aorta and as a diagnostic tool in clinical applications.

Phase-contrast MRI versus numerical simulation to quantify hemodynamical changes in cerebral aneurysms after flow diverter treatment

Cerebral aneurysms are a major risk factor for intracranial bleeding with devastating consequences for the patient. One recently established treatment is the implantation of flow-diverters (FD). Methods to predict their treatment success before or directly after implantation are not well investigated yet. The aim of this work was to quantitatively study hemodynamic parameters in patient-specific models of treated cerebral aneurysms and its correlation with the clinical outcome. Hemodynamics were evaluated using both computational fluid dynamics (CFD) and phase contrast (PC) MRI. CFD simulations and in vitro MRI measurements were done under similar flow conditions and results of both methods were comparatively analyzed. For preoperative and postoperative distribution of hemodynamic parameters, CFD simulations and PC-MRI velocity measurements showed similar results. In both cases where no occlusion of the aneurysm was observed after six months, a flow reduction of about 30-50% was found, while in the clinically successful case with complete occlusion of the aneurysm after 6 months, the flow reduction was about 80%. No vortex was observed in any of the three models after treatment. The results are in agreement with recent studies suggesting that CFD simulations can predict post-treatment aneurysm flow alteration already before implantation of a FD and PC-MRI could validate the predicted hemodynamic changes right after implantation of a FD.

Effects of Variations of Flow and Heart Rate on Intra-Aneurysmal Hemodynamics in a Ruptured Internal Carotid Artery Aneurysm During Exercise

BACKGROUND

Hemodynamics is thought to play an important role in the mechanisms responsible for initiation, growth, and rupture of intracranial aneurysms. Computational fluid dynamic (CFD) analysis is used to assess intra-aneurysmal hemodynamics.

OBJECTIVES

This study aimed to investigate the effects of variations in heart rate and internal carotid artery (ICA) flow rate on intra-aneurysmal hemodynamics, in an ICA aneurysm, by using computational fluid dynamics.

PATIENTS AND METHODS

Computed tomography angiography (CTA) was performed in a 55 years old female case, with a saccular ICA aneurysm, to create a patient-specific geometrical anatomic model of the aneurysm. The intra-aneurysmal hemodynamic environments for three states with different flow and heart rates were analyzed using patient-specific image-based CFD modeling.

RESULTS

Results showed significant changes for the three simulated states. For a proportion of the states examined, results were counterintuitive. Systolic and time-averaged wall shear stress and pressure on the aneurysm wall showed a proportional evolution with the mainstream flow rate.

CONCLUSION

Results reinforced the pivotal role of vascular geometry, with respect to hemodynamics, together with the importance of performing patient-specific CFD analyses, through which the effect of different blood flow conditions on the aneurysm hemodynamics could be evaluated.

A 3D MODEL FOR MURAL-CELL-MEDIATED DESTRUCTIVE REMODELING DURING EARLY DEVELOPMENT OF A CEREBRAL ANEURYSM

Development of a diagnostic tool for predicting the behavior of cerebral aneurysms was the inspiration of many research groups in recent years. In the present study a fluid–solid-growth (FSG) model for the early development of a cerebral aneurysm was presented in a 3D model of the internal carotid artery (ICA). This model is the result of two parallel mechanisms: first, defining arterial wall as a living tissue with the ability of degradation, growth and remodeling and second, full coupling of the wall and the blood flow. Taking into account the shear dependent nature of elastin degradation and mural-cell-mediated destructive activities, here, the degradation process has been linked to high effective stress of the vascular wall. The evolving properties of the elastinous and collagenous constituents have been predicted during the early development of the aneurysm and the code is applicable to more complicated aneurismal growth models.

RUPTURE MODEL OF INTRACRANIAL SACCULAR ANEURYSMS DUE TO HYPERTENSION

The risk of rupture of intracranial saccular aneurysms is one of the leading dilemmas for patients and neurologists. Although the probability of rupture is small, the consequences of rupture are usually fatal or crippling, and a concern for the patient is whether or not to treat an existing aneurysm. In this paper, an idealized model of saccular aneurysms with assumed Fung material behavior was investigated for rupture potential when the stresses exceeded the maximum wall strength of the aneurysm wall. Numerical simulations used various levels of blood pressure, from normal to hypertensive, in order to determine correlations of aneurysm size and risk of rupture. Results showed that hypertensive individuals harboring cerebral aneurysms with a size of at least 6 mm are at risk.

Modeling rupture of growing aneurysms

Growth and rupture of aneurysms are driven by micro-structural alterations of the arterial wall yet precise mechanisms underlying the process remain to be uncovered. In the present work we examine a scenario when the aneurysm evolution is dominated by turnover of collagen fibers. In the latter case it is natural to hypothesize that rupture of individual fibers (or their bonds) causes the overall aneurysm rupture. We examine this hypothesis in computer simulations of growing aneurysms in which constitutive equations describe both collagen evolution and failure. Failure is enforced in constitutive equations by limiting strain energy that can be accumulated in a fiber. Within the proposed theoretical framework we find a range of parameters that lead to the aneurysm rupture. We conclude in a qualitative agreement with clinical observations that some aneurysms will rupture while others will not.

Computational fluid dynamics in brain aneurysms

Because of its ability to deal with any geometry, image-based computational fluid dynamics (CFD) has been progressively used to investigate the role of hemodynamics in the underlying mechanisms governing the natural history of cerebral aneurysms. Despite great progress in methodological developments and many studies using patient-specific data, there are still significant controversies about the precise governing processes and divergent conclusions from apparently contradictory results. Sorting out these issues requires a global vision of the state of the art and a unified approach to solving this important scientific problem. Towards this end, this paper reviews the contributions made using patient-specific CFD models to further the understanding of these mechanisms, and highlights the great potential of patient-specific computational models for clinical use in the assessment of aneurysm rupture risk and patient management.

Wall shear stress distribution inside growing cerebral aneurysm

BACKGROUND AND PURPOSE

Hemodynamic stimulation has been suggested to affect the growth of cerebral aneurysms. The present study examined the effects of intra-aneurysmal hemodynamics on aneurysm growth.

MATERIALS AND METHODS

Velocity profiles were measured for 2 cases of AcomA aneurysms. Realistically shaped models of these aneurysms were constructed, based on CT angiograms. Flow fields and WSS in the models were measured by using particle image velocimetry and LDV. In 1 case, hemodynamic changes were observed in 4 stages of growth over a 27-month period, whereas no development was observed in the other case.

RESULTS

The growing model had a smaller and more stagnant recirculation area than that in the nongrowth model. The WSS was markedly reduced in the enlarging region in the growing models, whereas extremely low WSS was not found in the nongrowth model. In addition, a higher WSSG was consistently observed adjacent to the enlarging region during aneurysm growth.

CONCLUSIONS

The results indicated that the flow structure of recirculation itself does not necessarily lead to high likelihood of cerebral aneurysm. However, WSSG and WSS were distinctly different between the 2 cases. Higher WSSG was found surrounding the growing region, and extremely low WSS was found at the growing region of the growing cerebral aneurysm.

Perspectives on biological growth and remodeling

The continuum mechanical treatment of biological growth and remodeling has attracted considerable attention over the past fifteen years. Many aspects of these problems are now well-understood, yet there remain areas in need of significant development from the standpoint of experiments, theory, and computation. In this perspective paper we review the state of the field and highlight open questions, challenges, and avenues for further development.

Modeling of fibroblast-controlled strengthening and remodeling of uniaxially constrained collagen gels

A theoretical model for the remodeling of collagen gels is proposed. The collagen fabric is modeled as a network of collagen fibers, which in turn are composed of collagen fibrils. In the model, the strengthening of collagen fabric is accomplished by fibroblasts, which continuously recruit and attach more collagen fibrils to existing collagen fibers. The fibroblasts also accomplish a reorientation of collagen fibers. Fibroblasts are assumed to reorient collagen fibers toward the direction of maximum material stiffness. The proposed model is applied to experiments in which fibroblasts were inserted into a collagen gel. The model is able to predict the force-strain curves for the experimental collagen gels, and the final distribution of collagen fibers also agrees qualitatively with the experiments.

Modelling evolution and the evolving mechanical environment of saccular cerebral aneurysms

A fluid-solid-growth (FSG) model of saccular cerebral aneurysm evolution is developed. It utilises a realistic two-layered structural model of the internal carotid artery and explicitly accounts for the degradation of the elastinous constituents and growth and remodelling (G&R) of the collagen fabric. Aneurysm inception is prescribed: a localised degradation of elastin results in a perturbation in the arterial geometry; the collagen fabric adapts, and the artery achieves a new homeostatic configuration. The perturbation to the geometry creates an altered haemodynamic environment. Subsequent degradation of elastin is explicitly linked to low wall shear stress (WSS) in a confined region of the arterial domain. A sidewall saccular aneurysm develops, the collagen fabric adapts and the aneurysm stabilises in size. A quasi-static analysis is performed to determine the geometry at diastolic pressure. This enables the cyclic stretching of the tissue to be quantified, and we propose a novel index to quantify the degree of biaxial stretching of the tissue. Whilst growth is linked to low WSS from a steady (systolic) flow analysis, a pulsatile flow analysis is performed to compare steady and pulsatile flow parameters during evolution. This model illustrates the evolving mechanical environment for an idealised saccular cerebral aneurysm developing on a cylindrical parent artery and provides the guidance to more sophisticated FSG models of aneurysm evolution which link G&R to the local mechanical stimuli of vascular cells.

Constitutive modelling of arteries

This review article is concerned with the mathematical modelling of the mechanical properties of the soft biological tissues that constitute the walls of arteries. Many important aspects of the mechanical behaviour of arterial tissue can be treated on the basis of elasticity theory, and the focus of the article is therefore on the constitutive modelling of the anisotropic and highly nonlinear elastic properties of the artery wall. The discussion focuses primarily on developments over the last decade based on the theory of deformation invariants, in particular invariants that in part capture structural aspects of the tissue, specifically the orientation of collagen fibres, the dispersion in the orientation, and the associated anisotropy of the material properties. The main features of the relevant theory are summarized briefly and particular forms of the elastic strain-energy function are discussed and then applied to an artery considered as a thick-walled circular cylindrical tube in order to illustrate its extension–inflation behaviour. The wide range of applications of the constitutive modelling framework to artery walls in both health and disease and to the other fibrous soft tissues is discussed in detail. Since the main modelling effort in the literature has been on the passive response of arteries, this is also the concern of the major part of this article. A section is nevertheless devoted to reviewing the limited literature within the continuum mechanics framework on the active response of artery walls, i.e. the mechanical behaviour associated with the activation of smooth muscle, a very important but also very challenging topic that requires substantial further development. A final section provides a brief summary of the current state of arterial wall mechanical modelling and points to key areas that need further modelling effort in order to improve understanding of the biomechanics and mechanobiology of arteries and other soft tissues, from the molecular, to the cellular, tissue and organ levels.

Influence of medial collagen organization and axial in situ stretch on saccular cerebral aneurysm growth

A model for saccular cerebral aneurysm growth, proposed by Kroon and Holzapfel (2007, "A Model for Saccular Cerebral Aneurysm Growth in a Human Middle Cerebral Artery," J. Theor. Biol., 247, pp. 775-787; 2008, "Modeling of Saccular Aneurysm Growth in a Human Middle Cerebral Artery," ASME J. Biomech. Eng., 130, p. 051012), is further investigated. A human middle cerebral artery is modeled as a two-layer cylinder where the layers correspond to the media and the adventitia. The immediate loss of media in the location of the aneurysm is taken to be responsible for the initiation of the aneurysm growth. The aneurysm is regarded as a development of the adventitia, which is composed of several distinct layers of collagen fibers perfectly aligned in specified directions. The collagen fibers are the only load-bearing constituent in the aneurysm wall; their production and degradation depend on the stretch of the wall and are responsible for the aneurysm growth. The anisotropy of the surrounding media was modeled using the strain-energy function proposed by Holzapfel et al. (2000, "A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models," J. Elast., 61, pp. 1-48), which is valid for an elastic material with two families of fibers. It was shown that the inclusion of fibers in the media reduced the maximum principal Cauchy stress and the maximum shear stress in the aneurysm wall. The thickness increase in the aneurysm wall due to material growth was also decreased. Varying the fiber angle in the media from a circumferential direction to a deviation of 10 deg from the circumferential direction did, however, only show a little effect. Altering the axial in situ stretch of the artery had a much larger effect in terms of the steady-state shape of the aneurysm and the resulting stresses in the aneurysm wall. The peak values of the maximum principal stress and the thickness increase both became significantly higher for larger axial stretches.

Coupling hemodynamics with vascular wall mechanics and mechanobiology to understand intracranial aneurysms

Arteries exhibit a remarkable ability to adapt in response to sustained alterations in hemodynamic loading, to heal in response to injuries, and to compensate in response to diverse disease conditions. Nevertheless, such compensatory adaptations are limited and many vascular disorders, if untreated, lead to significant morbidity or mortality. Parallel advances in vascular biology, medical imaging, biomechanics, and computational methods promise to provide increased insight into many arterial diseases, including intracranial aneurysms. In particular, although it may be possible to identify useful clinical correlations between either the blood flow patterns within or the shape of aneurysms and their rupture-potential, our ultimate goal should be to couple studies of hemodynamics with those of wall mechanics and the underlying mechanobiology so that we can understand better the mechanisms by which aneurysms arise, enlarge, and rupture and thereby identify better methods of treatment. This paper presents one such approach to fluid-solid-growth (FSG) modeling of intracranial aneurysms.

VASCULAR MECHANICS, MECHANOBIOLOGY, AND REMODELING

Arteries exhibit a remarkable ability to adapt in response to sustained alterations in hemodynamic loading as well as in response to disease, injury, and clinical treatment. A better understanding of such adaptations will be aided greatly by formulating, testing, and refining appropriate theoretical frameworks for modeling the biomechanics and associated mechanobiology. The goal of this brief review is to highlight some recent developments in the use of a constrained mixture theory of arterial growth and remodeling, with particular attention to the requisite constitutive relations, and to highlight future directions of needed research.

A new constitutive model for multi-layered collagenous tissues

Collagenous tissues such as the aneurysmal wall or the aorta are multi-layered structures with the mean fibre alignments distinguishing one layer from another. A constitutive representation of the multiple collagen layers is not yet developed, and hence the aim of the present study. The proposed model is based on the constitutive theory of finite elasticity and is characterized by an anisotropic strain-energy function which takes the material structure into account. The passive tissue behaviour is modelled and the related mechanical response is assumed to be dominated by elastin and collagen. While elastin is modelled by the neo-Hookean material the constitutive response of collagen is assumed to be transversely isotropic for each individual layer and based on an exponential function. The proposed constitutive function is polyconvex which ensures material stability. The model has five independent material parameters, each of which has a clear physical interpretation: the initial stiffnesses of the collagen fabric in the two principal directions, the shear modulus pertaining to the non-collagenous matrix material, a parameter describing the level of nonlinearity of the collagen fabric, and the angle between the principal directions of the collagen fabric and the reference coordinate system. An extension-inflation test of the adventitia of a human femoral artery is simulated by means of the finite element method and an error function is minimized by adjusting the material parameters yielding a good agreement between the model and the experimental data.