Further evidence for the dynamic stability of intracranial saccular aneurysms

Understanding intracranial aneurysm sounds via high-fidelity fluid-structure-interaction modelling

BACKGROUND

Since the 1960s, the origins of intracranial aneurysm bruits and musical murmurs have been debated, with proposed mechanisms ranging from self-excitation (i.e., resonance) by stable pulsatile flow, to vibration caused by unstable (laminar vortex shedding or turbulent) flow. This knowledge gap has impeded the use of intracranial sounds a marker of aneurysm remodelling or rupture risk. New computational techniques now allow us to model these phenomena.

METHODS

We performed high-fidelity fluid-structure interaction simulations capable of understanding the magnitude and mechanisms of such flow-induced vibrations, under pulsatile flow conditions. Six cases from a previous cohort were used.

RESULTS

In five cases, underlying flow instabilities present as broad-band, random vibrations, consistent with previously-described bruits, while the sac also exhibits resonance, rocking back and forth in different planes of motion, consistent with previously described musical murmurs. Both types of vibration have amplitudes in the range of 0.1 to 1 μm. The murmurs extend into diastole, after the underlying flow instability has dissipated, and do not exhibit the characteristic repeating frequency harmonics of previously hypothesized vortex-shedding mechanisms. The remaining case with stable pulsatile flow does not vibrate. Spectrograms of the simulated vibrations are consistent with previously reported microphone and Doppler ultrasound recordings.

CONCLUSIONS

Our results provide a plausible explanation for distinct intracranial aneurysm sounds and characterize the mechanical environment of a vibrating aneurysm wall. Future work should aim to quantify the deleterious effects of these overlooked stimuli on the vascular wall, to determine which changes to the wall makeup are associated with vibration.

Vascular Mechanobiology: Homeostasis, Adaptation, and Disease

Cells of the vascular wall are exquisitely sensitive to changes in their mechanical environment. In healthy vessels, mechanical forces regulate signaling and gene expression to direct the remodeling needed for the vessel wall to maintain optimal function. Major diseases of arteries involve maladaptive remodeling with compromised or lost homeostatic mechanisms. Whereas homeostasis invokes negative feedback loops at multiple scales to mediate mechanobiological stability, disease progression often occurs via positive feedback that generates mechanobiological instabilities. In this review, we focus on the cell biology, wall mechanics, and regulatory pathways associated with arterial health and how changes in these processes lead to disease. We discuss how positive feedback loops arise via biomechanical and biochemical means. We conclude that inflammation plays a central role in overriding homeostatic pathways and suggest future directions for addressing therapeutic needs.

Constitutive interpretation of arterial stiffness in clinical studies: a methodological review

Clinical assessment of arterial stiffness relies on noninvasive measurements of regional pulse wave velocity or local distensibility. However, arterial stiffness measures do not discriminate underlying changes in arterial wall constituent properties (e.g., in collagen, elastin, or smooth muscle), which is highly relevant for development and monitoring of treatment. In arterial stiffness in recent clinical-epidemiological studies, we systematically review clinical-epidemiological studies (2012–) that interpreted arterial stiffness changes in terms of changes in arterial wall constituent properties (63 studies included of 514 studies found). Most studies that did so were association studies (52 of 63 studies) providing limited causal evidence. Intervention studies (11 of 63 studies) addressed changes in arterial stiffness through the modulation of extracellular matrix integrity (5 of 11 studies) or smooth muscle tone (6 of 11 studies). A handful of studies (3 of 63 studies) used mathematical modeling to discriminate between extracellular matrix components. Overall, there exists a notable gap in the mechanistic interpretation of stiffness findings. In constitutive model-based interpretation, we first introduce constitutive-based modeling and use it to illustrate the relationship between constituent properties and stiffness measurements (“forward” approach). We then review all literature on modeling approaches for the constitutive interpretation of clinical arterial stiffness data (“inverse” approach), which are aimed at estimation of constitutive properties from arterial stiffness measurements to benefit treatment development and monitoring. Importantly, any modeling approach requires a tradeoff between model complexity and measurable data. Therefore, the feasibility of changing in vivo the biaxial mechanics and/or vascular smooth muscle tone should be explored. The effectiveness of modeling approaches should be confirmed using uncertainty quantification and sensitivity analysis. Taken together, constitutive modeling can significantly improve clinical interpretation of arterial stiffness findings.

The Effect of Strain Hardening on the Dynamic Response of Human Artery Segments

Background:

When subjected to time-dependent blood pressure, human arteries undergo large deformations, exhibiting mainly nonlinear hyperelastic type of response. The mechanical response of arteries depends on the health of tissues that comprise the artery walls. Typically, healthy arteries exhibit convex strain hardening under tensile loads, atherosclerotic parts exhibit stiffer response, and aneurysmatic parts exhibit softening response. In reality, arterial dynamics is the dynamics of a propagating pulse, originating in heart ventricle, propagating along aorta, bifurcating, etc. Artery as a whole cannot be simulated as a lump ring, however its cross section can be simulated as a vibrating ring having a phase lag with respect to the other sections, creating a running pressure wave. A full mathematical model would require fluid-solid interaction modeling continuity of blood flow in a compliant vessel and a momentum equation. On the other hand, laboratory testing often uses small-length arteries, the response of which is covered by the present work. In this way, material properties that change along the artery length can be investigated.

Objective:

The effect of strain hardening on the local dynamic response of human arteries (excluding the full fluid-structure interaction) is examined through appropriate hyperelastic models related to the health condition of the blood vessel. Furthermore, this work aims at constituting a basis for further investigation of the dynamic response of arteries accounting for viscosity.

Method:

The governing equation of motion is formulated for three different hyperelastic material behaviors, based on the constitutive law proposed by Skalak et al., Hariton, and Mooney-Rivlin, associated with the hardening behavior of healthy, atherosclerotic, and aneurysmatic arteries, respectively. The differences between these modelling implementations are caused by physiology, since aneurysmatic arteries are softer and often sclerotic arteries are stiffer than healthy arteries. The response is investigated by proper normalization of the involved material parameters of the arterial walls, geometry of the arteries, load histories, time effects, and pre-stressing. The effect of each problem parameter on the arterial response has been studied. The peak response of the artery segment is calculated in terms of radial displacements, principal elongations, principal stresses, and strain-energy density. The validity of the proposed analytical models is demonstrated through comparison with previous studies that investigate the dynamic response of arterial models.

Results:

Important metrics that can be useful to vascular surgery are the radial deformation and the maximum strain-energy density along with the radial resonance frequencies. These metrics are found to be influenced heavily by the nonlinear strain-hardening characteristics of the model and the longitudinal pre-stressing.

Conclusion:

The proposed formulation permits a systematic and generalizable investigation, which, together with the low computational cost of analysis, makes it a valuable tool for calculating the response of healthy, atherosclerotic, and aneurysmatic arteries. The radial resonance frequencies can explain certain murmures developed in stenotic arteries.

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.

Mechanobiological stability: a new paradigm to understand the enlargement of aneurysms?

Static and dynamic mechanical instabilities were previously suggested, and then rejected, as mediators of aneurysmal development, which leaves open the question of the underlying mechanism. In this paper, we suggest as a new paradigm the interpretation of aneurysms as mechanobiological instabilities. For illustrative purposes, we compare analytical calculations with computational simulations of the growth and remodelling of idealized fusiform abdominal aortic aneurysms and experimental and clinical findings. We show that the concept of mechanobiological stability is consistent with the impact of risk factors such as age, smoking or diabetes on the initiation and enlargement of these lesions as well as adaptive processes in the healthy abdominal aorta such as dilatation during ageing or in hypertension. In general, high stiffness, an increased capacity for stress-mediated matrix production, and slow matrix turnover all improve the mechanobiological stability of blood vessels. This theoretical understanding may help guide prognosis and the development of future therapies for aneurysms as it enables systematic ways to attenuate enlargement.

Physical factors effecting cerebral aneurysm pathophysiology

Many factors that are either blood-, wall-, or hemodynamics-borne have been associated with the initiation, growth, and rupture of intracranial aneurysms. The distribution of cerebral aneurysms around the bifurcations of the circle of Willis has provided the impetus for numerous studies trying to link hemodynamic factors (flow impingement, pressure, and/or wall shear stress) to aneurysm pathophysiology. The focus of this review is to provide a broad overview of such hemodynamic associations as well as the subsumed aspects of vascular anatomy and wall structure. Hemodynamic factors seem to be correlated to the distribution of aneurysms on the intracranial arterial tree and complex, slow flow patterns seem to be associated with aneurysm growth and rupture. However, both the prevalence of aneurysms in the general population and the incidence of ruptures in the aneurysm population are extremely low. This suggests that hemodynamic factors and purely mechanical explanations by themselves may serve as necessary, but never as necessary and sufficient conditions of this disease's causation. The ultimate cause is not yet known, but it is likely an additive or multiplicative effect of a handful of biochemical and biomechanical factors.

A shell-based inverse approach of stress analysis in intracranial aneurysms

Predicting pressure induced wall stress in intracranial aneurysms continues to be of interest for aneurysm safety assessment. In quasi-static analysis, there are two distinct approaches that one may take, the forward approach and the inverse approach. The inverse approach starts from a deformed configuration and thus is naturally suited to image-based, patient-specific analysis. Early studies by the authors' team suggested that the inverse approach, in the context of estimating the wall stress in cerebral aneurysms, depends weakly on the material description. In this article, we present a population study to further demonstrate the inverse method, in particular, the remarkable feature of insensitivity to material properties. Twenty-six aneurysm models derived from patient-specific images were employed in the study. Wall stresses were predicted in both the inverse and forward approaches using three material models. Results showed that, while forward computation yielded up to ~100% stress difference between some materials, the inverse solutions stayed close across materials. The inverse method, in addition to being methodologically accurate in dealing with pre-deformations, has the added convenience of insensitivity to uncertainties in wall tissue properties. New insight into the stress-geometry relation was also discussed.

On the Stability of Lung Parenchymal Lesions with Applications to Early Pneumothorax Diagnosis

Spontaneous pneumothorax, a prevalent medical challenge in most trauma cases, is a form of sudden lung collapse closely associated with risk factors such as lung cancer and emphysema. Our work seeks to explore and quantify the currently unknown pathological factors underlying lesion rupture in pneumothorax through biomechanical modeling. We hypothesized that lesion instability is closely associated with elastodynamic strain of the pleural membrane from pulsatile air flow and collagen-elastin dynamics. Based on the principles of continuum mechanics and fluid-structure interaction, our proposed model coupled isotropic tissue deformation with pressure from pulsatile air motion and the pleural fluid. Next, we derived mathematical instability criteria for our ordinary differential equation system and then translated these mathematical instabilities to physically relevant structural instabilities via the incorporation of a finite energy limiter. The introduction of novel biomechanical descriptions for collagen-elastin dynamics allowed us to demonstrate that changes in the protein structure can lead to a transition from stable to unstable domains in the material parameter space for a general lesion. This result allowed us to create a novel streamlined algorithm for detecting material instabilities in transient lung CT scan data via analyzing deformations in a local tissue boundary.

A MATHEMATICAL MODEL OF BLOOD FLOW IN AN INTRACRANIAL ANEURYSM: ANALYTICAL AND NUMERICAL STUDY

An aneurysm is a local enlargement of the vessel lumen due to the weakening of the wall material. We propose a mathematical model of the pulsatile blood flow through the system consisting of the cerebral artery and an aneurysm. The mathematical model is based on mass and energy conservation laws. It comprises non-linear rheological properties of the aneurysm and artery, and inertial and resistant properties of the blood flow. The model equations are analyzed by the methods of non-linear dynamics and they are solved numerically. Special attention is paid to the flow stability as a function of the aneurysmal and arterial material properties, the mean and oscillating arterial pressure, and the frequency of heart pulsations. The results of the work can be summarized as follows: (i) the model equations are stable at normal physiological conditions and developed aneurysms, (ii) with decreasing of the aneurysmal compliance, the aneurysmal volume pulsations increase and a limit point of flow stability is approached, (iii) the increased amplitude of the pulsatile pressure and the heart frequency cannot lead to flow instabilities.

Estimation of aneurysm wall stresses created by treatment with a shape memory polymer foam device

In this study, compliant latex thin-walled aneurysm models are fabricated to investigate the effects of expansion of shape memory polymer foam. A simplified cylindrical model is selected for the in-vitro aneurysm, which is a simplification of a real, saccular aneurysm. The studies are performed by crimping shape memory polymer foams, originally 6 and 8 mm in diameter, and monitoring the resulting deformation when deployed into 4-mm-diameter thin-walled latex tubes. The deformations of the latex tubes are used as inputs to physical, analytical, and computational models to estimate the circumferential stresses. Using the results of the stress analysis in the latex aneurysm model, a computational model of the human aneurysm is developed by changing the geometry and material properties. The model is then used to predict the stresses that would develop in a human aneurysm. The experimental, simulation, and analytical results suggest that shape memory polymer foams have potential of being a safe treatment for intracranial saccular aneurysms. In particular, this work suggests oversized shape memory foams may be used to better fill the entire aneurysm cavity while generating stresses below the aneurysm wall breaking stresses.

Modelling carotid artery adaptations to dynamic alterations in pressure and flow over the cardiac cycle

Motivated by recent clinical and laboratory findings of important effects of pulsatile pressure and flow on arterial adaptations, we employ and extend an established constrained mixture framework of growth (change in mass) and remodelling (change in structure) to include such dynamical effects. New descriptors of cell and tissue behavior (constitutive relations) are postulated and refined based on new experimental data from a transverse aortic arch banding model in the mouse that increases pulsatile pressure and flow in one carotid artery. In particular, it is shown that there was a need to refine constitutive relations for the active stress generated by smooth muscle, to include both stress- and stress rate-mediated control of the turnover of cells and matrix and to account for a cyclic stress-mediated loss of elastic fibre integrity and decrease in collagen stiffness in order to capture the reported evolution, over 8 weeks, of luminal radius, wall thickness, axial force and in vivo axial stretch of the hypertensive mouse carotid artery. We submit, therefore, that complex aspects of adaptation by elastic arteries can be predicted by constrained mixture models wherein individual constituents are produced or removed at individual rates and to individual extents depending on changes in both stress and stress rate from normal values.

Patient-specific wall stress analysis in cerebral aneurysms using inverse shell model

Stress analyses of patient-specific vascular structures commonly assume that the reconstructed in vivo configuration is stress free although it is in a pre-deformed state. We submit that this assumption can be obviated using an inverse approach, thus increasing accuracy of stress estimates. In this paper, we introduce an inverse approach of stress analysis for cerebral aneurysms modeled as nonlinear thin shell structures, and demonstrate the method using a patient-specific aneurysm. A lesion surface derived from medical images, which corresponds to the deformed configuration under the arterial pressure, is taken as the input. The wall stress in the given deformed configuration, together with the unstressed initial configuration, are predicted by solving the equilibrium equations as opposed to traditional approach where the deformed geometry is assumed stress free. This inverse approach also possesses a unique advantage, that is, for some lesions it enables us to predict the wall stress without accurate knowledge of the wall elastic property. In this study, we also investigate the sensitivity of the wall stress to material parameters. It is found that the in-plane component of the wall stress is indeed insensitive to the material model.

Intraneural ganglia: a clinical problem deserving a mechanistic explanation and model

Intraneural ganglion cysts have been considered a curiosity for 2 centuries. Based on a unifying articular (synovial) theory, recent evidence has provided a logical explanation for their formation and propagation. The fundamental principle is that of a joint origin and a capsular defect through which synovial fluid escapes following the articular branch, typically into the parent nerve. A stereotypical, reproducible appearance has been characterized that suggests a shared pathogenesis. In the present report the authors will provide a mechanistic explanation that can then be mathematically tested using a preliminary model created by finite element analysis.

Determination of Wall Tension in Cerebral Artery Aneurysms by Numerical Simulation

Background and Purpose— Cerebral artery aneurysms rupture when wall tension exceeds the strength of the wall tissue. At present, risk-assessment of unruptured aneurysms does not include evaluation of the lesions shape, yet clinical experience suggests that this is of importance. We aimed to develop a computational model for simulation of fluid-structure interaction in cerebral aneurysms based on patient specific lesion geometry, with special emphasis on wall tension.

Methods— An advanced isogeometric fluid-structure analysis model incorporating flexible aneurysm wall based on patient specific computed tomography angiogram images was developed. Variables used in the simulation model were retrieved from a literature review.

Results— The simulation results exposed areas of high wall tension and wall displacement located where aneurysms usually rupture.

Conclusion— We suggest that analyzing wall tension and wall displacement in cerebral aneurysms by numeric simulation could be developed into a novel method for individualized prediction of rupture risk.

Growth rates of intracranial aneurysms: exploring constancy

OBJECT

The annual rate of rupture of intracranial aneurysms is often assumed to be constant, but it is unknown whether this assumption is true. Recent case reports have suggested that aneurysms grow fast in a short period of time. The authors of the present report investigated the plausibility of a constant growth rate for intracranial aneurysms.

METHODS

Assuming a constant aneurysm growth rate within an individual and varying rates between individuals, a hypothetical cohort was simulated. Individuals with high growth rates will display aneurysm formation and rupture at a young age; such persons disappear early from the hypothetical cohort. As a result the mean lesion growth rate varies over time. In hypothetical cohorts with different initial mean growth rates, the authors calculated age-specific incidence rates (per 100,000 person-years) of subarachnoid hemorrhage and compared these rates with population-based data on the incidence of subarachnoid hemorrhage (per 100,000 person-years).

RESULTS

A hypothetical cohort with a mean initial growth rate of 0.18 mm/year reproduced most closely the incidence rates observed in the population. However, even for this most plausible hypothetical cohort, age-specific incidence rates in the model differed substantially and statistically significantly from those observed in the population.

CONCLUSIONS

Based on the results of this study, it is unlikely that intracranial aneurysms in general grow at a constant time-independent rate. The authors hypothesized that the actual growth process is irregular and discontinuous, which results in periods with and without aneurysm growth and with high and low risks of rupture.

Intracranial and abdominal aortic aneurysms: similarities, differences, and need for a new class of computational models

Intracranial saccular and abdominal aortic aneurysms (ISAs and AAAs, respectively) result from different underlying disease processes and exhibit different rupture potentials, yet they share many histopathological and biomechanical characteristics. Moreover, as in other vascular diseases, hemodynamics and wall mechanics play important roles in the natural history and possible treatment of these two types of lesions. The goals of this review are twofold: first, to contrast the biology and mechanics of intracranial and abdominal aortic aneurysms to emphasize that separate advances in our understanding of each disease can aid in our understanding of the other disease, and second, to suggest that research on the biomechanics of aneurysms must embrace a new paradigm for analysis. That is, past biomechanical studies have provided tremendous insight but have progressed along separate lines, focusing on either the hemodynamics or the wall mechanics. We submit that there is a pressing need to couple in a new way the separate advances in vascular biology, medical imaging, and computational biofluid and biosolid mechanics to understand better the mechanobiology, pathophysiology, and treatment of these lesions, which continue to be responsible for significant morbidity and mortality. We refer to this needed new class of computational tools as fluid-solid-growth (FSG) models.

A First-Order Mechanical Device to Model Traumatized Craniovascular Biodynamics

Mathematical models currently exist that explore the physiology of normal and traumatized intracranial function. Mechanical models are used to assess harsh environments that may potentially cause head injuries. However, few mechanical models are designed to study the adaptive physiologic response to traumatic brain injury. We describe a first-order physical model designed and fabricated to elucidate the complex biomechanical factors associated with dynamic intracranial physiology. The unidirectional flow device can be used to study interactions between the cranium, brain tissue, cerebrospinal fluid, vasculature, blood, and the heart. Solid and fluid materials were selected to simulate key properties of the cranial system. Total constituent volumes (solid and fluid) and volumetric flow (650 ml/min) represent adult human physiology, and the lengths of the individual segments along the flow-path are in accord with Poiseuille's equation. The physical model includes a mechanism to simulate autoregulatory vessel dynamics. Intracranial pressures were measured at multiple locations throughout the model during simulations with and without post-injury brain tissue swelling. Two scenarios were modeled for both cases: Applications of vasodilation/constriction and changes in the head of bed position. Statistical results indicate that all independent variables had significant influence over fluid pressures measured throughout the model (p < 0.0001) including the vasoconstriction mechanism (p = 0.0255). The physical model represents a first-order design realization that helps to establish a link between mathematical and mechanical models. Future designs will provide further insight into traumatic head injury and provide a framework for unifying the knowledge gained from mathematical models, injury mechanics, clinical observations, and the response to therapies.

Nonlinear Anisotropic Stress Analysis of Anatomically Realistic Cerebral Aneurysms

Background. Static deformation analysis and estimation of wall stress distribution of patient-specific cerebral aneurysms can provide useful insights into the disease process and rupture. Method of Approach. The three-dimensional geometry of saccular cerebral aneurysms from 27 patients (18 unruptured and nine ruptured) was reconstructed based on computer tomography angiography images. The aneurysm wall tissue was modeled using a nonlinear, anisotropic, hyperelastic material model (Fung-type) which was incorporated in a user subroutine in ABAQUS. Effective material fiber orientations were assumed to align with principal surface curvatures. Static deformation of the aneurysm models were simulated assuming uniform wall thickness and internal pressure load of 100mmHg. Results. The numerical analysis technique was validated by quantitative comparisons to results in the literature. For the patient-specific models, in-plane stresses in the aneurysm wall along both the stiff and weak fiber directions showed significant regional variations with the former being higher. The spatial maximum of stress ranged from as low as 0.30MPa in a small aneurysm to as high as 1.06MPa in a giant aneurysm. The patterns of distribution of stress, strain, and surface curvature were found to be similar. Sensitivity analyses showed that the computed stress is mesh independent and not very sensitive to reasonable perturbations in model parameters, and the curvature-based criteria for fiber orientations tend to minimize the total elastic strain energy in the aneurysms wall. Within this small study population, there were no statistically significant differences in the spatial means and maximums of stress and strain values between the ruptured and unruptured groups. However, the ratios between the stress components in the stiff and weak fiber directions were significantly higher in the ruptured group than those in the unruptured group. Conclusions. A methodology for nonlinear, anisotropic static deformation analysis of geometrically realistic aneurysms was developed, which can be used for a more accurate estimation of the stresses and strains than previous methods and to facilitate prospective studies on the role of stress in aneurysm rupture.

Parameterization of the shape of intracranial saccular aneurysms using Legendre polynomials

Our recent studies of the nonlinear mechanics of saccular aneurysms suggest that it is unlikely that these lesions enlarge or rupture via material (limit point) or dynamic (resonance) instabilities. Rather, there is a growing body of evidence from both vascular biology and biomechanical analyses that implicate mechanosensitive growth and remodeling processes. There is, therefore, a pressing need to quantify regional multiaxial wall stresses which, because of the membrane-like behavior of many aneurysms, necessitates better information on the applied loads and regional surface curvatures. Herein, we present and illustrate a method whereby regional curvatures can be estimated easily for sub-classes of human aneurysms based on clinically available data from magnetic resonance angiography (MRA). Whereas Legendre polynomials are used to illustrate this approach, different functions may prove useful for different sub-classes of lesions.