Summary: Increasing detection of unruptured intracranial aneurysms, catastrophic outcomes from subarachnoid hemorrhage, and risks and cost of treatment necessitate defining objective predictive parameters of aneurysm rupture risk. Image-based computational fluid dynamics models have suggested associations between hemodynamics and intracranial aneurysm rupture, albeit with conflicting findings regarding wall shear stress. We propose that the “high-versus-low wall shear stress” controversy is a manifestation of the complexity of aneurysm pathophysiology, and both high and low wall shear stress can drive intracranial aneurysm growth and rupture. Low wall shear stress and high oscillatory shear index trigger an inflammatory-cell-mediated pathway, which could be associated with the growth and rupture of large, atherosclerotic aneurysm phenotypes, while high wall shear stress combined with a positive wall shear stress gradient trigger a mural-cell-mediated pathway, which could be associated with the growth and rupture of small or secondary bleb aneurysm phenotypes. This hypothesis correlates disparate intracranial aneurysm pathophysiology with the results of computational fluid dynamics in search of more reliable risk predictors.

http://www.ajnr.org/content/ajnr/35/7/1254.full.pdf

High WSS or Low WSS? Complex Interactions of Hemodynamics with Intracranial Aneurysm Initiation, Growth, and Rupture: Toward a Unifying Hypothesis

The past 20 years have witnessed ever-growing evidence that the mechanical properties of biological tissues, from nanoscale to macroscale dimensions, are fundamental for cellular behaviour and consequent tissue functionality. This knowledge, combined with previously known biochemical cues, has greatly advanced the field of biomaterial development, tissue engineering and regenerative medicine. It is now established that approaches to engineer biological tissues must integrate and approximate the mechanics, both static and dynamic, of native tissues. Nevertheless, the literature on the mechanical properties of biological tissues differs greatly in methodology, and the available data are widely dispersed. This Review gathers together the most important data on the stiffness of living tissues and discusses the intricacies of tissue stiffness from a materials perspective, highlighting the main challenges associated with engineering lifelike tissues and proposing a unified view of this as yet unreported topic. Emerging advances that might pave the way for the next decade’s take on bioengineered tissue stiffness are also presented, and differences and similarities between tissues in health and disease are discussed, along with various techniques for characterizing tissue stiffness at various dimensions from individual cells to organs. The complexity of biological tissue presents a challenge for engineering of mechanically compatible materials. In this Review, the stiffness of tissue components — from extracellular matrix and single cells to bulk tissue — is outlined, and how this understanding facilitates the engineering of materials with lifelike properties is discussed.

/pdf/the-stiffness-of-living-tissues-and-its-implications-for-49xikp5kk1.pdf

The stiffness of living tissues and its implications for tissue engineering

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.

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2010.0058

Constitutive modelling of arteries

Advances in numerical methods and three-dimensional imaging techniques have enabled the quantification of cardiovascular mechanics in subject-specific anatomic and physiologic models. Patient-specific models are being used to guide cell culture and animal experiments and test hypotheses related to the role of biomechanical factors in vascular diseases. Furthermore, biomechanical models based on noninvasive medical imaging could provide invaluable data on the in vivo service environment where cardiovascular devices are employed and on the effect of the devices on physiologic function. Finally, patient-specific modeling has enabled an entirely new application of cardiovascular mechanics, namely predicting outcomes of alternate therapeutic interventions for individual patients. We review methods to create anatomic and physiologic models, obtain properties, assign boundary conditions, and solve the equations governing blood flow and vessel wall dynamics. Applications of patient-specific models of cardiovascul...

/pdf/patient-specific-modeling-of-cardiovascular-mechanics-3c2lb3fqwt.pdf

Patient-specific modeling of cardiovascular mechanics.

The article surveys the current state of our understanding of turbidity currents, with an emphasis on their fluid mechanics. It highlights the significant role these currents play within the global sediment cycle, and their importance in environmental processes and in the formation of hydrocarbon reservoirs. Events and mechanisms governing the initiation of turbidity currents are reviewed, along with experimental observations and findings from field studies regarding their internal velocity and density structure. As turbidity currents propagate over the seafloor, they can trigger the evolution of a host of topographical features through the processes of deposition and erosion, such as channels, levees, and sediment waves. Potential linear instability mechanisms are discussed that may determine the spatial scales of these features. Finally, the hierarchy of available theoretical models for analyzing the dynamics of turbidity currents is outlined, ranging from dimensional analysis and integral models to both depth-averaged and depth-resolving simulation approaches.

Turbidity Currents and Their Deposits

We present the first mathematical model to account for the evolution of the abdominal aortic aneu- rysm The artery is modelled as a two-layered, cylindrical membrane using nonlinear elasticity and a physiologically realistic constitutive model It is subject to a constant systolic pressure and a physiological axial prestretch The development of the aneurysm is assumed to be a conse- quence of the remodelling of its material constituents Microstructural 'recruitment' and fibre density variables for the collagen are introduced into the strain energy density functions This enables the remodelling of colla- gen to be addressed as the aneurysm enlarges An axi- symmetric aneurysm, with axisymmetric degradation of elastin and linear differential equations for the remodel- ling of the fibre variables, is simulated numerically Using physiologically determined parameters to model the abdominal aorta and realistic remodelling rates for its constituents, the predicted dilations of the aneurysm are consistent with those observed in vivo An asymmetric aneurysm with spinal contact is also modelled, and the stress distributions are consistent with previous studies

https://www.maths.gla.ac.uk/~nah/reprints/WHH04journal.pdf

A mathematical model for the growth of the abdominal aortic aneurysm

The novel three-dimensional (3D) mathematical model for the development of abdominal aortic aneurysm (AAA) of Watton et al. Biomech Model Mechanobiol 3(2): 98-113, (2004) describes how changes in the micro-structure of the arterial wall lead to the development of AAA, during which collagen remodels to compensate for loss of elastin. In this paper, we examine the influence of several of the model's material and remodelling parameters on growth rates of the AAA and compare with clinical data. Furthermore, we calculate the dynamic properties of the AAA at different stages in its development and examine the evolution of clinically measurable mechanical properties. The model predicts that the maximum diameter of the aneurysm increases exponentially and that the ratio of systolic to diastolic diameter decreases from 1.13 to 1.02 as the aneurysm develops; these predictions are consistent with physiological observations of Vardulaki et al. Br J Surg 85:1674-1680 (1998) and Lanne et al. Eur J Vasc Surg 6:178-184 (1992), respectively. We conclude that mathematical models of aneurysm growth have the potential to be useful, noninvasive diagnostic tools and thus merit further development.

https://www.maths.gla.ac.uk/~nah/reprints/WattonHill-BMMB2007.pdf

Evolving mechanical properties of a model of abdominal aortic aneurysm.

Modelling the mechanical response of elastin for arterial tissue

The physiological mechanisms that give rise to the inception and development of a cerebral aneurysm are accepted to involve the interplay between the local mechanical forces acting on the arterial wall and the biological processes occurring at the cellular level. In fact, the wall shear stresses (WSSs) that act on the endothelial cells are thought to play a pivotal role. A computational framework is proposed to explore the link between the evolution of a cerebral aneurysm and the influence of hemodynamic stimuli that act on the endothelial cells. An aneurysm evolution model, which utilizes a realistic microstructural model of the arterial wall, is combined with detailed 3D hemodynamic solutions. The evolution of the blood flow within the developing aneurysm determines the distributions of the WSS and the spatial WSS gradient (WSSG) that act on the endothelial cell layer of the tissue. Two illustrative examples are considered: Degradation of the elastinous constituents is driven by deviations of WSS or the WSSG from normotensive values. This model provides the basis to further explore the etiology of aneurysmal disease.

Coupling the Hemodynamic Environment to the Evolution of Cerebral Aneurysms: Computational Framework and Numerical Examples

Experimental and theoretical guidance is needed to understand how the collagen fabric evolves during the development of aneurysms. In this paper, we model the development of an aneurysm as a cylindrical/spherical membrane subject to 1D enlargement; these conceptual models reflect the development of fusiform and saccular cerebral aneurysms. The mechanical response is attributed to the elastin and collagen. We introduce variables which define the elastin and collagen fibre concentration; these evolve to simulate growth/atrophy of the constituents. A hypothetical aneurysm model is analysed: collagen stretch is constant, elastin degrades and collagen fibre concentration can adapt to maintain mechanical equilibrium. An analytic expression for the rate of evolution of the fibre concentration is derived. The functional form is dependent on (i) the current collagen fibre concentration, (ii) the deviations in the collagen fibre stretch from the attachment stretch, (iii) the rate of change of fibre stretch, (iv) the rate of loss of elastin and (v) the ratio of load borne by elastinous and collagenous constituents. Finally, numerical examples of aneurysm development are considered. Suitable candidates for the fibre concentration evolution equations are identified that yield stabilization of the aneurysm even when there is complete loss of elastin. This theoretical analysis provides the basis for the development of physiologically realistic models of aneurysm development.

Paul N. Watton

Papers

A mathematical model for the growth of the abdominal aortic aneurysm

Evolving mechanical properties of a model of abdominal aortic aneurysm.

Modelling the mechanical response of elastin for arterial tissue

Coupling the Hemodynamic Environment to the Evolution of Cerebral Aneurysms: Computational Framework and Numerical Examples

Modelling the growth and stabilization of cerebral aneurysms.