Numerical investigation on circular and elliptical bulge tests for inverse soft tissue characterization

The acquisition of insights concerning the mechanobiology of aneurysmatic aortic tissues is an important field of investigation. The complete characterization of aneurysm mechanical behaviour can be carried out by biaxial experimental tests on ex vivo specimens. In literature, several works proposed bulge inflation tests as a valid method to analyse aneurysmatic tissue. Bulge test data processing requires the adoption of digital image correlation and inverse analysis approaches to estimate strain and stress distributions, respectively. In this context, however, the accuracy of inverse analysis method has not been evaluated yet. This aspect appears particularly interesting given the anisotropic behaviour of the soft tissue and the possibility to adopt different die geometries. The goal of this study is to provide an accuracy characterization of the inverse analysis applied to the bulge test technique using a numerical approach. In particular, different cases of bulge inflation were simulated in a finite element environment as a reference. To investigate the effect of tissue anisotropic degree and bulge die geometries (circular and elliptical), different input parameters were considered to obtain multiple test cases. The specimen deformed shapes, resulting from the reference finite element simulations, were then analysed through an inverse analysis approach to produce an estimation of stress distributions. The estimated stresses were, at last, compared with the values from the reference finite element simulations. The results demonstrated that the circular die geometry produces a satisfactory estimation accuracy only under certain conditions of material quasi-isotropy. On the other hand, the choice of an elliptical bulge die was proven to be more suitable for the analysis of anisotropic tissues.

Uncertainty Quantification in the In Vivo Image-Based Estimation of Local Elastic Properties of Vascular Walls

Introduction: Patient-specific computational models are a powerful tool for planning cardiovascular interventions. However, the in vivo patient-specific mechanical properties of vessels represent a major source of uncertainty. In this study, we investigated the effect of uncertainty in the elastic module (E) on a Fluid–Structure Interaction (FSI) model of a patient-specific aorta. Methods: The image-based χ-method was used to compute the initial E value of the vascular wall. The uncertainty quantification was carried out using the generalized Polynomial Chaos (gPC) expansion technique. The stochastic analysis was based on four deterministic simulations considering four quadrature points. A deviation of about ±20% on the estimation of the E value was assumed. Results: The influence of the uncertain E parameter was evaluated along the cardiac cycle on area and flow variations extracted from five cross-sections of the aortic FSI model. Results of stochastic analysis showed the impact of E in the ascending aorta while an insignificant effect was observed in the descending tract. Conclusions: This study demonstrated the importance of the image-based methodology for inferring E, highlighting the feasibility of retrieving useful additional data and enhancing the reliability of in silico models in clinical practice.

An image-based approach for the estimation of arterial local stiffness in vivo

The analysis of mechanobiology of arterial tissues remains an important topic of research for cardiovascular pathologies evaluation. In the current state of the art, the gold standard to characterize the tissue mechanical behavior is represented by experimental tests, requiring the harvesting of ex-vivo specimens. In recent years though, image-based techniques for the in vivo estimation of arterial tissue stiffness were presented. The aim of this study is to define a new approach to provide local distribution of arterial stiffness, estimated as the linearized Young's Modulus, based on the knowledge of in vivo patient-specific imaging data. In particular, the strain and stress are estimated with sectional contour length ratios and a Laplace hypothesis/inverse engineering approach, respectively, and then used to calculate the Young's Modulus. After describing the method, this was validated by using a set of Finite Element simulations as input. In particular, idealized cylinder and elbow shapes plus a single patient-specific geometry were simulated. Different stiffness distributions were tested for the simulated patient-specific case. After the validation from Finite Element data, the method was then applied to patient-specific ECG-gated Computed Tomography data by also introducing a mesh morphing approach to map the aortic surface along the cardiac phases. The validation process revealed satisfactory results. In the simulated patient-specific case, root mean square percentage errors below 10% for the homogeneous distribution and below 20% for proximal/distal distribution of stiffness. The method was then successfully used on the three ECG-gated patient-specific cases. The resulting distributions of stiffness exhibited significant heterogeneity, nevertheless the resulting Young's moduli were always contained within the 1-3 MPa range, which is in line with literature.

Biomechanics of Hollow Organs: Experimental Testing and Computational Modeling

Hollow organs are visceral organs that are hollow tubes or pouches (such as the intestine or the stomach, respectively) or that include a cavity (such as the heart) and which subserve a vital function [...].

Introduction of a Novel Image-Based and Non-Invasive Method for the Estimation of Local Elastic Properties of Great Vessels

Background: In the context of a growing demand for the use of in silico models to meet clinical requests, image-based methods play a crucial role. In this study, we present a parametric equation able to estimate the elasticity of vessel walls, non-invasively and indirectly, from information uniquely retrievable from imaging. Methods: A custom equation was iteratively refined and tuned from the simulations of a wide range of different vessel models, leading to the definition of an indirect method able to estimate the elastic modulus E of a vessel wall. To test the effectiveness of the predictive capability to infer the E value, two models with increasing complexity were used: a U-shaped vessel and a patient-specific aorta. Results: The original formulation was demonstrated to deviate from the ground truth, with a difference of 89.6%. However, the adoption of our proposed equation was found to significantly increase the reliability of the estimated E value for a vessel wall, with a mean percentage error of 9.3% with respect to the reference values. Conclusion: This study provides a strong basis for the definition of a method able to estimate local mechanical information of vessels from data easily retrievable from imaging, thus potentially increasing the reliability of in silico cardiovascular models.

On the Role and Effects of Uncertainties in Cardiovascular in silico Analyses

The assessment of cardiovascular hemodynamics with computational techniques is establishing its fundamental contribution within the world of modern clinics. Great research interest was focused on the aortic vessel. The study of aortic flow, pressure, and stresses is at the basis of the understanding of complex pathologies such as aneurysms. Nevertheless, the computational approaches are still affected by sources of errors and uncertainties. These phenomena occur at different levels of the computational analysis, and they also strongly depend on the type of approach adopted. With the current study, the effect of error sources was characterized for an aortic case. In particular, the geometry of a patient-specific aorta structure was segmented at different phases of a cardiac cycle to be adopted in a computational analysis. Different levels of surface smoothing were imposed to define their influence on the numerical results. After this, three different simulation methods were imposed on the same geometry: a rigid wall computational fluid dynamics (CFD), a moving-wall CFD based on radial basis functions (RBF) CFD, and a fluid-structure interaction (FSI) simulation. The differences of the implemented methods were defined in terms of wall shear stress (WSS) analysis. In particular, for all the cases reported, the systolic WSS and the time-averaged WSS (TAWSS) were defined.

Correlation between micro and macrostructural biaxial behavior of ascending thoracic aneurysm: a novel experimental technique

Mechanical properties and microstructural modifications of vessel tissues are strongly linked, as established in the state of the art of cardiovascular diseases. Techniques to obtain both mechanical and structural information are reported, but the possibility to obtain real-time microstructural and macrostructural data correlated is still lacking. An experimental approach to characterize the aortic tissue is presented. A setup integrating biaxial traction and Small Angle Light Scattering (SALS) analysis is described. The system was adopted to test ex-vivo aorta specimens from healthy and aneusymatic (aTAA) cases. A significant variation of the fiber dispersion with respect to the unloaded state was encountered during the material traction. The corresponding microstructural and mechanical data were successfully used to fit a given anisotropic constitutive model, with satisfactory R² values (0.97±0.11 and 0.96±0.17, for aTAA and healthy population, respectively) and fiber dispersion parameters variations between the aTAA and healthy populations (0.39±0.23 and 0.15±0.10). The method integrating the biaxial/SALS technique was validated, allowing for real-time synchronization between mechanical and microstructural analysis of anisotropic biological tissues.

A novel formulation for the study of the ascending aortic fluid dynamics with in vivo data

Numerical simulations to evaluate thoracic aortic hemodynamics include a computational fluid dynamic (CFD) approach or fluid-structure interaction (FSI) approach. While CFD neglects the arterial deformation along the cardiac cycle by applying a rigid wall simplification, on the other side the FSI simulation requires a lot of assumptions for the material properties definition and high computational costs. The aim of this study is to investigate the feasibility of a new strategy, based on Radial Basis Functions (RBF) mesh morphing technique and transient simulations, able to introduce the patient-specific changes in aortic geometry during the cardiac cycle. Starting from medical images, aorta models at different phases of cardiac cycle were reconstructed and a transient shape deformation was obtained by proper activating incremental RBF solutions during the simulation process. The results, in terms of main hemodynamic parameters, were compared with two performed CFD simulations for the aortic model at minimum and maximum volume. Our implemented strategy copes the actual arterial variation during cardiac cycle with high accuracy, capturing the impact of geometrical variations on fluid dynamics, overcoming the complexity of a standard FSI approach.