A Contemporary Look at Biomechanical Models of Myocardium.

Understanding and predicting the mechanical behavior of myocardium under healthy and pathophysiological conditions are vital to developing novel cardiac therapies and promoting personalized interventions. Within the past 30 years, various constitutive models have been proposed for the passive mechanical behavior of myocardium. These models cover a broad range of mathematical forms, microstructural observations, and specific test conditions to which they are fitted. We present a critical review of these models, covering both phenomenological and structural approaches, and their relations to the underlying structure and function of myocardium. We further explore the experimental and numerical techniques used to identify the model parameters. Next, we provide a brief overview of continuum-level electromechanical models of myocardium, with a focus on the methods used to integrate the active and passive components of myocardial behavior. We conclude by pointing to future directions in the areas of optimal form as well as new approaches for constitutive modeling of myocardium.

Geometric surrogates of abdominal aortic aneurysm wall mechanics.

The maximum diameter criterion is the most important factor in the clinical management of abdominal aortic aneurysms (AAA). Consequently, interventional repair is recommended when an aneurysm reaches a critical diameter, typically 5.0 cm in the United States. Nevertheless, biomechanical measures of the aneurysmal abdominal aorta have long been implicated in AAA risk of rupture. The purpose of this study is to assess whether other geometric characteristics, in addition to maximum diameter, may be highly correlated with the AAA peak wall stress (PWS). Using in-house segmentation and meshing algorithms, 30 patient-specific AAA models were generated for finite element analysis using an isotropic constitutive material for the AAA wall. PWS, evaluated as the spatial maximum of the first principal stress, was calculated at a systolic pressure of 120 mmHg. The models were also used to calculate 47 geometric indices characteristic of the aneurysm geometry. Statistical analyses were conducted using a feature reduction algorithm in which the 47 indices were reduced to 11 based on their statistical significance in differentiating the models in the population (p < 0.05). A subsequent discriminant analysis was performed and 7 of these indices were identified as having no error in discriminating the AAA models with a significant nonlinear regression correlation with PWS. These indices were: Dmax (maximum diameter), T (tortuosity), DDr (maximum diameter to neck diameter ratio), S (wall surface area), Kmedian (median of the Gaussian surface curvature), Cmax (maximum lumen compactness), and Mmode (mode of the Mean surface curvature). Therefore, these characteristics of an individual AAA geometry are the highest correlated with the most clinically relevant biomechanical parameter for rupture risk assessment. We conclude that the indices can serve as surrogates of PWS in lieu of a finite element modeling approach for AAA biomechanical evaluation.

An approach for patient-specific multi-domain vascular mesh generation featuring spatially varying wall thickness modeling.

In this work, we present a computationally efficient image-derived volume mesh generation approach for vasculatures that implements spatially varying patient-specific wall thickness with a novel inward extrusion of the wall surface mesh. Multi-domain vascular meshes with arbitrary numbers, locations, and patterns of both iliac bifurcations and thrombi can be obtained without the need to specify features or landmark points as input. In addition, the mesh output is coordinate-frame independent and independent of the image grid resolution with high dimensional accuracy and mesh quality, devoid of errors typically found in off-the-shelf image-based model generation workflows. The absence of deformable template models or Cartesian grid-based methods enables the present approach to be sufficiently robust to handle aneurysmatic geometries with highly irregular shapes, arterial branches nearly parallel to the image plane, and variable wall thickness. The assessment of the methodology was based on i) estimation of the surface reconstruction accuracy, ii) validation of the output mesh using an aneurysm phantom, and iii) benchmarking the volume mesh quality against other frameworks. For the phantom image dataset (pixel size 0.105 mm; slice spacing 0.7 mm; and mean wall thickness 1.401±0.120 mm), the average wall thickness in the mesh was 1.459±0.123 mm. The absolute error in average wall thickness was 0.060±0.036 mm, or about 8.6% of the largest image grid spacing (0.7 mm) and 4.36% of the actual mean wall thickness. Mesh quality metrics and the ability to reproduce regional variations of wall thickness were found superior to similar alternative frameworks.

The importance of patient-specific regionally varying wall thickness in abdominal aortic aneurysm biomechanics.

Abdominal aortic aneurysm (AAA) is a vascular condition where the use of a biomechanics-based assessment for patient-specific risk assessment is a promising approach for clinical management of the disease. Among various factors that affect such assessment, AAA wall thickness is expected to be an important factor. However, regionally varying patient-specific wall thickness has not been incorporated as a modeling feature in AAA biomechanics. To the best our knowledge, the present work is the first to incorporate patient-specific variable wall thickness without an underlying empirical assumption on its distribution for AAA wall mechanics estimation. In this work, we present a novel method for incorporating regionally varying wall thickness (the "PSNUT" modeling strategy) in AAA finite element modeling and the application of this method to a diameter-matched cohort of 28 AAA geometries to assess differences in wall mechanics originating from the conventional assumption of a uniform wall thickness. For the latter, we used both a literature-derived population average wall thickness (1.5 mm; the "UT" strategy) as well as the spatial average of our patient-specific variable wall thickness (the "PSUT" strategy). For the three different wall thickness modeling strategies, wall mechanics were assessed by four biomechanical parameters: the spatial maxima of the first principal stress, strain, strain-energy density, and displacement. A statistical analysis was performed to address the hypothesis that the use of any uniform wall thickness model resulted in significantly different biomechanical parameters compared to a patient-specific regionally varying wall thickness model. Statistically significant differences were obtained with the UT modeling strategy compared to the PSNUT strategy for the spatial maxima of the first principal stress (p = 0.002), strain (p = 0.0005), and strain-energy density (p = 7.83 e-5) but not for displacement (p = 0.773). Likewise, significant differences were obtained comparing the PSUT modeling strategy with the PSNUT strategy for the spatial maxima of the first principal stress (p = 9.68 e-7), strain (p = 1.03 e-8), strain-energy density (p = 9.94 e-8), and displacement (p = 0.0059). No significant differences were obtained comparing the UT and PSUT strategies for the spatial maxima of the first principal stress (p = 0.285), strain (p = 0.152), strain-energy density (p = 0.222), and displacement (p = 0.0981). This work strongly recommends the use of patient-specific regionally varying wall thickness derived from the segmentation of abdominal computed tomography (CT) scans if the AAA finite element analysis is focused on estimating peak biomechanical parameters, such as stress, strain, and strain-energy density.

Fluid-structure interaction modeling of abdominal aortic aneurysms: the impact of patient-specific inflow conditions and fluid/solid coupling.

Rupture risk assessment of abdominal aortic aneurysms (AAA) by means of biomechanical analysis is a viable alternative to the traditional clinical practice of using a critical diameter for recommending elective repair. However, an accurate prediction of biomechanical parameters, such as mechanical stress, strain, and shear stress, is possible if the AAA models and boundary conditions are truly patient specific. In this work, we present a complete fluid-structure interaction (FSI) framework for patient-specific AAA passive mechanics assessment that utilizes individualized inflow and outflow boundary conditions. The purpose of the study is two-fold: (1) to develop a novel semiautomated methodology that derives velocity components from phase-contrast magnetic resonance images (PC-MRI) in the infrarenal aorta and successfully apply it as an inflow boundary condition for a patient-specific fully coupled FSI analysis and (2) to apply a one-way-coupled FSI analysis and test its efficiency compared to transient computational solid stress and fully coupled FSI analyses for the estimation of AAA biomechanical parameters. For a fully coupled FSI simulation, our results indicate that an inlet velocity profile modeled with three patient-specific velocity components and a velocity profile modeled with only the axial velocity component yield nearly identical maximum principal stress (σ1), maximum principal strain (ε1), and wall shear stress (WSS) distributions. An inlet Womersley velocity profile leads to a 5% difference in peak σ1, 3% in peak ε1, and 14% in peak WSS compared to the three-component inlet velocity profile in the fully coupled FSI analysis. The peak wall stress and strain were found to be in phase with the systolic inlet flow rate, therefore indicating the necessity to capture the patient-specific hemodynamics by means of FSI modeling. The proposed one-way-coupled FSI approach showed potential for reasonably accurate biomechanical assessment with less computational effort, leading to differences in peak σ1, ε1, and WSS of 14%, 4%, and 18%, respectively, compared to the axial component inlet velocity profile in the fully coupled FSI analysis. The transient computational solid stress approach yielded significantly higher differences in these parameters and is not recommended for accurate assessment of AAA wall passive mechanics. This work demonstrates the influence of the flow dynamics resulting from patient-specific inflow boundary conditions on AAA biomechanical assessment and describes methods to evaluate it through fully coupled and one-way-coupled fluid-structure interaction analysis.

The role of geometric and biomechanical factors in abdominal aortic aneurysm rupture risk assessment.

The current clinical management of abdominal aortic aneurysm (AAA) disease is based to a great extent on measuring the aneurysm maximum diameter to decide when timely intervention is required. Decades of clinical evidence show that aneurysm diameter is positively associated with the risk of rupture, but other parameters may also play a role in causing or predisposing the AAA to rupture. Geometric factors such as vessel tortuosity, intraluminal thrombus volume, and wall surface area are implicated in the differentiation of ruptured and unruptured AAAs. Biomechanical factors identified by means of computational modeling techniques, such as peak wall stress, have been positively correlated with rupture risk with a higher accuracy and sensitivity than maximum diameter alone. The objective of this review is to examine these factors, which are found to influence AAA disease progression, clinical management and rupture potential, as well as to highlight on-going research by our group in aneurysm modeling and rupture risk assessment.