Stability Analysis of Arteries Under Torsion.

Vascular tortuosity may impede blood flow, occlude the lumen, and ultimately lead to ischemia or even infarction. Mechanical loads like blood pressure, axial force, and also torsion are key factors participating in this complex mechanobiological process. The available studies on arterial torsion instability followed computational or experimental approaches, yet single available theoretical study had modeled the artery as isotropic linear elastic. This paper aim is to validate a theoretical model of arterial torsion instability against experimental data. The artery is modeled as a single-layered, nonlinear, hyperelastic, anisotropic solid, with parameters calibrated from experiment. Linear bifurcation analysis is then performed to predict experimentally measured stability margins. Uncertainties in geometrical parameters and in measured mechanical response were considered. Also, the type of rate (incremental) boundary conditions (RBCs) impact on the results was examined (e.g., dead load, fluid pressure). The predicted critical torque and twist angle followed the experimentally measured trends. The closest prediction errors in the critical torque and twist rate were 22% and 67%, respectively. Using the different RBCs incurred differences of up to 50% difference within the model predictions. The present results suggest that the model may require further improvements. However, it offers an approach that can be used to predict allowable twist levels in surgical procedures (like anastomosis and grafting) and in the design of stents for arteries subjected to high torsion levels (like the femoropopliteal arteries). It may also be instructive in understanding biomechanical processes like arterial tortuosity, kinking, and coiling.

Instability of Incompatible Bilayered Soft Tissues and the Role of Interface Conditions.

Mechanical stability analysis is instructive in explaining biological processes like morphogenesis, organogenesis, and pathogenesis of soft tissues. Consideration of the layered, residually stressed structure of tissues, requires accounting for the joint effects of interface conditions and layer incompatibility. This paper is concerned with the influence of imposed rate (incremental) interface conditions (RICs) on critical loads in soft tissues, within the context of linear bifurcation analysis. Aiming at simplicity, we analyze a model of bilayered isotropic hyperelastic (neo-Hookean) spherical shells with residual stresses generated by "shrink-fitting" two perfectly bonded layers with radial interfacial incompatibility. This setting allows a comparison between available, seemingly equivalent, interface conditions commonly used in the literature of layered media stability. We analytically determine the circumstances under which the interface conditions are equivalent or not, and numerically demonstrate significant differences between interface conditions with increasing level of layer incompatibility. Differences of more than tenfold in buckling and 30% in inflation instability critical loads are recorded using the different RICs. Contrasting instability characteristics are also revealed using the different RICs in the presence of incompatibility: inflation instability can occur before pressure maximum, and spontaneous instability may be excluded for thin shells. These findings are relevant to the growing body of stability studies of layered and residually stressed tissues. The impact of interface conditions on critical thresholds is significant in studies that use concepts of instability to draw conclusions about the normal development and the pathologies of tissues like arteries, esophagus, airways, and the brain.

On Rate Boundary Conditions for Soft Tissue Bifurcation Analysis.

Mechanical instability of soft tissues can either risk their normal function or alternatively trigger patterning mechanisms during growth and morphogenesis processes. Unlike standard stability analysis of linear elastic bodies, for soft tissues undergoing large deformations it is imperative to account for the nonlinearities induced by the coupling between load and surface changes at onset of instability. The related issue of boundary conditions, in context of soft tissues, has hardly been addressed in the literature, with most of available research employing dead-load conditions. This paper is concerned with the influence of imposed homogeneous rate (incremental) surface data on critical loads and associated modes in soft tissues, within the context of linear bifurcation analysis. Material behavior is modeled by compressible isotropic hyperelastic strain energy functions (SEFs), with experimentally validated material parameters for the Fung-Demiray SEF, over a range of constitutive response (including brain and liver tissues). For simplicity, we examine benchmark problems of basic spherical patterns: full sphere, spherical cavity, and thick spherical shell. Limiting the analysis to primary hydrostatic states we arrive at universal closed-form solutions, thus providing insight on the role of imposed boundary data. Influence of selected rate boundary conditions (RBCs) like dead-load and fluid-pressure (FP), coupled with constitutive parameters, on the existence and levels of bifurcation loads is compared and discussed. It is argued that the selection of the appropriate type of homogeneous RBC can have a critical effect on the level of bifurcation loads and even exclude the emergence of bifurcation instabilities.

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.

Constitutive modeling of coronary arterial media--comparison of three model classes.

Accurate modeling of arterial elasticity is imperative for predicting pulsatile blood flow and transport to the periphery, and for evaluating the mechanical microenvironment of the vessel wall. The goal of the present study is to compare a recently developed structural model of porcine left anterior descending artery media to two commonly used typical representatives of phenomenological and structure-motivated invariant-based models, in terms of the number of model parameters, model descriptive and predictive powers, and requisite different test protocols for reliable parameter estimation. The three models were compared against 3D data of radial inflation, axial extension, and twist tests. Also checked are the models predictive capabilities to response data not used for estimation, including both tests outside the range of estimation database, as well as protocols of a different nature. The results show that the descriptive estimation error (model fit to estimation database), measured by the sum of squared residuals (SSE) between full 3D data and model predictions, was about twice as low for the structural (4.58%) model compared to the other two (9.71 and 8.99% for the phenomenological and structure-motivated models, respectively). Similar SSE ratios were obtained for the predictive capabilities. Prediction SSE at high stretch based on estimation of two low stretches yielded an SSE value of 2.81% for the structural model, and 10.54% and 7.87% for the phenomenological and structure-motivated models, respectively. For the prediction of twist from inflation-extension data, SSE values for the torsional stiffness was 1.76% for the structural model and 39.62 and 2.77% for the phenomenological and structure-motivated models. The required number of model parameters for the structural model is four, whereas the phenomenological model requires six to nine and the structure-motivated has four parameters. These results suggest that modeling based on the tissue structural features improves model reliability in describing given data and in predicting the tissue general response.

Experimentally validated microstructural 3D constitutive model of coronary arterial media.

Accurate modeling of arterial response to physiological or pathological loads may shed light on the processes leading to initiation and progression of a number of vascular diseases and may serve as a tool for prediction and diagnosis. In this study, a microstructure based hyperelastic constitutive model is developed for passive media of porcine coronary arteries. The most general model contains 12 independent parameters representing the three-dimensional inner fibrous structure of the media and includes the effects of residual stresses and osmotic swelling. Parameter estimation and model validation were based on mechanical data of porcine left anterior descending (LAD) media under radial inflation, axial extension, and twist tests. The results show that a reduced four parameter model is sufficient to reliably predict the passive mechanical properties. These parameters represent the stiffness and the helical orientation of each lamellae fiber and the stiffness of the interlamellar struts interconnecting these lamellae. Other structural features, such as orientational distribution of helical fibers and anisotropy of the interlamellar network, as well as possible transmural distribution of structural features, were found to have little effect on the global media mechanical response. It is shown that the model provides good predictions of the LAD media twist response based on parameters estimated from only biaxial tests of inflation and extension. In addition, good predictive capabilities are demonstrated for the model behavior at high axial stretch ratio based on data of law stretches.