Arterial Tissue in Health and Disease: Experimental Data, Collagen-Based Modeling and Simulation, Including Aortic Dissection. In: Holzapfel GA, Ogden RW, editors. Biomechanical Modelling at the Molecular, Cellular and Tissue Levels. Vienna: Springer; 2009. pp. 259-344. [DOI: 10.1007/978-3-211-95875-9_4]

Sensitivity of Arterial Hyperelastic Models to Uncertainties in Stress-Free Measurements

Despite major advances made in modeling vascular tissue biomechanics, the predictive power of constitutive models is still limited by uncertainty of the input data. Specifically, key measurements, like the geometry of the stress-free (SF) state, involve a definite, sometimes non-negligible, degree of uncertainty. Here, we introduce a new approach for sensitivity analysis of vascular hyperelastic constitutive models to uncertainty in SF measurements. We have considered two vascular hyperelastic models: the phenomenological Fung model and the structure-motivated Holzapfel-Gasser-Ogden (HGO) model. Our results indicate up to 160% errors in the identified constitutive parameters for a 5% measurement uncertainty in the SF data. Relative margins of errors of up to 30% in the luminal pressure, 36% in the axial force, and over 200% in the stress predictions were recorded for 10% uncertainties. These findings are relevant to the large body of studies involving experimentally based modeling and analysis of vascular tissues. The impact of uncertainties on calibrated constitutive parameters is significant in context of studies that use constitutive parameters to draw conclusions about the underlying microstructure of vascular tissues, their growth and remodeling processes, and aging and disease states. The propagation of uncertainties into the predictions of biophysical parameters, e.g., force, luminal pressure, and wall stresses, is of practical importance in the design and execution of clinical devices and interventions. Furthermore, insights provided by the present findings may lead to more robust parameters identification techniques, and serve as selection criteria in the trade-off between model complexity and sensitivity.

An incremental deformation model of arterial dissection

We develop a mathematical model for a small axisymmetric tear in a residually stressed and axially pre-stretched cylindrical tube. The residual stress is modelled by an opening angle when the load-free tube is sliced along a generator. This has application to the study of an aortic dissection, in which a tear develops in the wall of the artery. The artery is idealised as a single-layer thick-walled axisymmetric hyperelastic tube with collagen fibres using a Holzapfel-Gasser-Ogden strain-energy function, and the tear is treated as an incremental deformation of this tube. The lumen of the cylinder and the interior of the dissection are subject to the same constant (blood) pressure. The equilibrium equations for the incremental deformation are derived from the strain energy function. We develop numerical methods to study the opening of the tear for a range of material parameters and boundary conditions. We find that decreasing the fibre angle, decreasing the axial pre-stretch and increasing the opening angle all tend to widen the dissection, as does an incremental increase in lumen and dissection pressure.

Rupture limit evaluation of human cerebral aneurysms wall: Experimental study

BACKGROUND AND PURPOSE

Rupture risk of intracranial aneurysms is a major issue for public healthcare. A way to obtain an individual rupture risk assessment is a main objective of many research teams in the world. For many years, we have investigated the relationship between the mechanical properties of aneurysm wall tissues and the rupture risk. In this work, we try to go further and investigate rupture limit values.

METHODS

Following surgical clipping, a specific conservation protocol was applied to aneurysmal tissues in order to preserve their mechanical properties. Thirty-nine intracranial aneurysms (27 females, 12 males) were tested using a uniaxial tensile test machine under physiological conditions, temperature, and saline isotonic solution. These represented 24 unruptured and 15 ruptured aneurysms. Stress/strain curves were then obtained for each sample, and a fitting algorithm was applied following a Yeoh hyperelastic model with 2 parameters. Moreover, uniaxial tensile tests were conducted until rupture of samples to obtain values of stress and strain rupture limit.

RESULTS

The significant parameter a C₂ of the hyperelastic Yeoh model, allowed us to classify samples' rigidity following the terminology we adopted in previous papers (Costalat et al., 2011; Sanchez et al., 2013): Soft, Stiff and Intermediate. Moreover, strain/stress rupture limit values were gathered and analyzed thanks to the tissue rigidity, the status of the aneurysm (initially ruptured or unruptured) and the gender of the patient.

CONCLUSION

Strain rupture limit was found quite stable around 20% and seems not to be correlated with the status of the aneurysm (initially ruptured or unruptured), neither with the gender of the patient. However, stretch and stress rupture limit seems not to be independent on the rigidity. The study confirms that ruptured aneurysms mainly present a soft tissue and unruptured aneurysms present a stiff material.

A novel computational remodelling algorithm for the probabilistic evolution of collagen fibre dispersion in biaxially strained vascular tissue

In this work, we constructed a novel collagen fibre remodelling algorithm that incorporates the complex nature of random evolution acting on single fibres causing macroscopic fibre dispersion. The proposed framework is different from the existing remodelling algorithms, in that the microscopic random force on cellular scales causing a rotational-type Brownian motion alone is considered as an aspect of vascular tissue remodelling. A continuum mechanical framework for the evolution of local dispersion and how it could be used for modeling the evolution of internal radius of biaxially strained artery structures under constant internal blood pressure are presented. A linear evolution form for the statistical fibre dispersion is employed in the model. The random force component of the evolution, which depends on the mechanical stress stimuli, is described by a single parameter. Although the mathematical form of the proposed model is simple, there is a strong link between the microscopic evolution of collagen dispersion on the cellular level and its effects on the macroscopic visible world through mechanical variables. We believe that the proposed algorithm utilizes a better understanding of the relationship between the evolution rates of mean fibre direction and fibre dispersion. The predictive capability of the algorithm is presented using experimental data. The model has been simulated by solving a single-layered axisymmetric artery (adventitia) deformation problem. The algorithm performed well for estimating the quantitative features of experimental anisotropy, the mean fibre direction vector and the dispersion (κ) measurements under strain-dependent evolution assumptions.

Determination of the layer-specific distributed collagen fibre orientations in human thoracic and abdominal aortas and common iliac arteries

The established method of polarized microscopy in combination with a universal stage is used to determine the layer-specific distributed collagen fibre orientations in 11 human non-atherosclerotic thoracic and abdominal aortas and common iliac arteries (63 ± 15.3 years, mean ± s.d.). A dispersion model is used to quantify over 37 000 recorded fibre angles from tissue samples. The study resulted in distinct fibre families, fibre directions, dispersion and thickness data for each layer and all vessels investigated. Two fibre families were present for the intima, media and adventitia in the aortas, with often a third and sometimes a fourth family in the intima in the respective axial and circumferential directions. In all aortas, the two families were almost symmetrically arranged with respect to the cylinder axis, closer to the axial direction in the adventitia, closer to the circumferential direction in the media and in between in the intima. The same trend was found for the intima and adventitia of the common iliac arteries; however, there was only one preferred fibre alignment present in the media. In all locations and layers, the observed fibre orientations were always in the tangential plane of the walls, with no radial components and very small dispersion through the wall thickness. A wider range of in-plane fibre orientations was present in the intima than in the media and adventitia. The mean total wall thickness for the aortas and the common iliac artery was 1.39 and 1.05 mm, respectively. For the aortas, a slight thickening of the intima and a thinning of the media in increasingly distal regions were observed. A clear intimal thickening was present distal to the branching of the celiac arteries. All data, except for the media of the common iliac arteries, showed two prominent collagen fibre families for all layers so that two-fibre family models seem most appropriate.