Modeling rupture of growing aneurysms

High-frequency wall vibrations in a cerebral patient-specific aneurysm model

The presence of high-frequency velocity fluctuations in aneurysms have been confirmed by in-vivo measurements and by several numerical simulation studies. Only a few studies have located and recorded wall vibrations in in-vitro experiments using physiological patient models. In this study, we investigated the wall fluctuations produced by a flowing perfusion fluid in a true-to-scale elastic model of a cerebral fusiform aneurysm using a laser Doppler vibrometer (LDV). The model was obtained from patient data. The experimental setup reproduced physiologically relevant conditions using a compliant perfusion system, physiological flow parameters, unsteady flow and a non-Newtonian fluid. Three geometrically identical models with different wall elasticities were used for measurements. The influence of five different flow rates was considered. Wall vibrations were predominantly found at frequencies in the range 40-60 Hz and 255-265 Hz. Their amplitude increased with increasing elasticity of the model, but the spectral peaks remained at about the same frequency. Varying the flow rate produced almost no changes in the frequency domain of the models. The frequency of the spectral peaks varied slightly between points at the lateral wall and at the bottom of the aneurysm. Indeed, embedding the model in a fluid during measurements produced higher and smoother amplitude fluctuations.

Isotropic Failure Criteria Are Not Appropriate for Anisotropic Fibrous Biological Tissues

The von Mises (VM) stress is a common stress measure for finite element models of tissue mechanics. The VM failure criterion, however, is inherently isotropic, and therefore may yield incorrect results for anisotropic tissues, and the relevance of the VM stress to anisotropic materials is not clear. We explored the application of a well-studied anisotropic failure criterion, the Tsai–Hill (TH) theory, to the mechanically anisotropic porcine aorta. Uniaxial dogbones were cut at different angles and stretched to failure. The tissue was anisotropic, with the circumferential failure stress nearly twice the axial (2.67 ± 0.67 MPa compared to 1.46 ± 0.59 MPa). The VM failure criterion did not capture the anisotropic tissue response, but the TH criterion fit the data well (R2 = 0.986). Shear lap samples were also tested to study the efficacy of each criterion in predicting tissue failure. Two-dimensional failure propagation simulations showed that the VM failure criterion did not capture the failure type, location, or propagation direction nearly as well as the TH criterion. Over the range of loading conditions and tissue geometries studied, we found that problematic results that arise when applying the VM failure criterion to an anisotropic tissue. In contrast, the TH failure criterion, though simplistic and clearly unable to capture all aspects of tissue failure, performed much better. Ultimately, isotropic failure criteria are not appropriate for anisotropic tissues, and the use of the VM stress as a metric of mechanical state should be reconsidered when dealing with anisotropic tissues.

A novel chemo-mechano-biological model of arterial tissue growth and remodelling

Arterial growth and remodelling (G&R) is mediated by vascular cells in response to their chemical and mechanical environment. To date, mechanical and biochemical stimuli tend to be modelled separately, however this ignores their complex interplay. Here, we present a novel mathematical model of arterial chemo-mechano-biology. We illustrate its application to the development of an inflammatory aneurysm in the descending human aorta. The arterial wall is modelled as a bilayer cylindrical non-linear elastic membrane, which is internally pressurised and axially stretched. The medial degradation that accompanies aneurysm development is driven by an inflammatory response. Collagen remodelling is simulated by adaption of the natural reference configuration of constituents; growth is simulated by changes in normalised mass-densities. We account for the distribution of attachment stretches that collagen fibres are configured to the matrix and, innovatively, allow this distribution to remodel. This enables the changing functional role of the adventitia to be simulated. Fibroblast-mediated collagen growth is represented using a biochemical pathway model: a system of coupled non-linear ODEs governs the evolution of fibroblast properties and levels of key biomolecules under the regulation of Transforming Growth Factor (TGF)-β, a key promoter of matrix deposition. Given physiologically realistic targets, different modes of aneurysm development can be captured, while the predicted evolution of biochemical variables is qualitatively consistent with trends observed experimentally. Interestingly, we observe that increasing the levels of collagen-promoting TGF-β results in arrest of aneurysm growth, which seems to be consistent with experimental evidence. We conclude that this novel Chemo-Mechano-Biological (CMB) mathematical model has the potential to provide new mechanobiological insight into vascular disease progression and therapy.

Aneurysm strength can decrease under calcification

Aneurysms are abnormal dilatations of vessels in the vascular system that are prone to rupture. Prediction of the aneurysm rupture is a challenging and unsolved problem. Various factors can lead to the aneurysm rupture and, in the present study, we examine the effect of calcification on the aneurysm strength by using micromechanical modeling. The calcified tissue is considered as a composite material in which hard calcium particles are embedded in a hyperelastic soft matrix. Three experimentally calibrated constitutive models incorporating a failure description are used for the matrix representation. Two constitutive models describe the aneurysmal arterial wall and the third one - the intraluminal thrombus. The stiffness and strength of the calcified tissue are simulated in uniaxial tension under the varying amount of calcification, i.e. the relative volume of the hard inclusion within the periodic unit cell. In addition, the triaxiality of the stress state, which can be a trigger for the cavitation instability, is tracked. Results of the micromechanical simulation show an increase of the stiffness and a possible decrease of the strength of the calcified tissue as compared to the non-calcified one. The obtained results suggest that calcification (i.e. the presence of hard particles) can significantly affect the stiffness and strength of soft tissue. The development of refined experimental techniques that will allow for the accurate quantitative assessment of calcification is desirable.

Cavitation instability as a trigger of aneurysm rupture

Aneurysm formation and growth is accompanied by microstructural alterations in the arterial wall. Particularly, the loss of elastin may lead to tissue disintegration and appearance of voids or cavities at the micron scale. Unstable growth and coalescence of voids may be a predecessor and trigger for the onset of macroscopic cracks. In the present work, we analyze the instability of membrane (2D) and bulk (3D) voids under hydrostatic tension by using two experimentally calibrated constitutive models of abdominal aortic aneurysm enhanced with energy limiters. The limiters provide the saturation value for the strain energy, which indicates the maximum energy that can be stored and dissipated by an infinitesimal material volume. We find that the unstable growth of voids can start when the critical stress is considerably less than the aneurysm strength. Moreover, this critical stress may even approach the arterial wall stress in the physiological range. This finding suggests that cavitation instability can be a rational indicator of the aneurysm rupture.

Human thoracic and abdominal aortic aneurysmal tissues: Damage experiments, statistical analysis and constitutive modeling

Development of aortic aneurysms includes significant morphological changes within the tissue: collagen content increases, elastin content reduces and smooth muscle cells degenerate. We seek to quantify the impact of these changes on the passive mechanical response of aneurysms in the supra-physiological loading range via mechanical testing and constitutive modeling. We perform uniaxial extension tests on circumferentially and axially oriented strips from five thoracic (65.6 years ± 13.4, mean ± SD) and eight abdominal (63.9 years ± 11.4) aortic fusiform aneurysms to investigate both continuous and discontinuous softening during supra-physiological loading. We determine the significance of the differences between the fitted model parameters: diseased thoracic versus abdominal tissues, and healthy (Weisbecker et al., J. Mech. Behav. Biomed. Mater. 12, 93-106, 2012) versus diseased tissues. We also test correlations among these parameters and age, Body Mass Index (BMI) and preoperative aneurysm diameter, and investigate histological cuts. Tissue response is anisotropic for all tests and the anisotropic pseudo-elastic damage model fits the data well for both primary loading and discontinuous softening which we interpret as damage. We found statistically relevant differences between model parameters fitted to diseased thoracic versus abdominal tissues, as well as between those fitted to healthy versus diseased tissues. Only BMI correlated with fitted model parameters in abdominal aortic aneurysmal tissues.

Age of collagen in intracranial saccular aneurysms

BACKGROUND AND PURPOSE

The chronological development and natural history of cerebral aneurysms (CAs) remain incompletely understood. We used (14)C birth dating of a main constituent of CAs, that is, collagen type I, as an indicator for biosynthesis and turnover of collagen in CAs in relation to human cerebral arteries to investigate this further.

METHODS

Forty-six ruptured and unruptured CA samples from 43 patients and 10 cadaveric human cerebral arteries were obtained. The age of collagen, extracted and purified from excised CAs, was estimated using (14)C birth dating and correlated with CA and patient characteristics, including the history of risk factors associated with atherosclerosis and potentially aneurysm growth and rupture.

RESULTS

Nearly all CA samples contained collagen type I, which was <5 years old, irrespective of patient age, aneurysm size, morphology, or rupture status. However, CAs from patients with a history of risk factors (smoking or hypertension) contained significantly younger collagen than CAs from patients with no risk factors (mean, 1.6±1.2 versus 3.9±3.3 years, respectively; P=0.012). CAs and cerebral arteries did not share a dominant structural protein, such as collagen type I, which would allow comparison of their collagen turnover.

CONCLUSIONS

The abundant amount of relatively young collagen type I in CAs suggests that there is an ongoing collagen remodeling in aneurysms, which is significantly more rapid in patients with risk factors. These findings challenge the concept that CAs are present for decades and that they undergo only sporadic episodes of structural change.