Uncertainty quantification of the wall thickness and stiffness in an idealized dissected aorta.

Personalized treatment informed by computational models has the potential to markedly improve the outcome for patients with a type B aortic dissection. However, existing computational models of dissected walls significantly simplify the characteristic false lumen, tears and/or material behavior. Moreover, the patient-specific wall thickness and stiffness cannot be accurately captured non-invasively in clinical practice, which inevitably leads to assumptions in these wall models. It is important to evaluate the impact of the corresponding uncertainty on the predicted wall deformations and stress, which are both key outcome indicators for treatment optimization. Therefore, a physiology-inspired finite element framework was proposed to model the wall deformation and stress of a type B aortic dissection at diastolic and systolic pressure. Based on this framework, 300 finite element analyses, sampled with a Latin hypercube, were performed to assess the global uncertainty, introduced by 4 uncertain wall thickness and stiffness input parameters, on 4 displacement and stress output parameters. The specific impact of each input parameter was estimated using Gaussian process regression, as surrogate model of the finite element framework, and a δ moment-independent analysis. The global uncertainty analysis indicated minor differences between the uncertainty at diastolic and systolic pressure. For all output parameters, the 4th quartile contained the major fraction of the uncertainty. The parameter-specific uncertainty analysis elucidated that the material stiffness and relative thickness of the dissected membrane were the respective main determinants of the wall deformation and stress. The uncertainty analysis provides insight into the effect of uncertain wall thickness and stiffness parameters on the predicted deformation and stress. Moreover, it emphasizes the need for probabilistic rather than deterministic predictions for clinical decision making in aortic dissections.

Growth and remodeling of the dissected membrane in an idealized dissected aorta model.

While transitioning from the acute to chronic phase, the wall of a dissected aorta often expands in diameter and adaptations in thickness and microstructure take place in the dissected membrane. Including the mechanisms, leading to these changes, in a computational model is expected to improve the accuracy of predictions of the long-term complications and optimal treatment timing of dissection patients. An idealized dissected wall was modeled to represent the elastin and collagen production and/or degradation imposed by stress- and inflammation-mediated growth and remodeling, using the homogenized constrained mixture theory. As no optimal growth and remodeling parameters have been defined for aortic dissections, a Latin hypercube sampling with 1000 parameter combinations was assessed for four inflammation patterns, with a varying spatial extent (full/local) and temporal evolution (permanent/transient). The dissected membrane thickening and microstructure was considered together with the diameter expansion over a period of 90 days. The highest success rate was found for the transient inflammation patterns, with about 15% of the samples leading to converged solutions after 90 days. Clinically observed thickening rates were found for 2-4% of the transient inflammation samples, which represented median total diameter expansion rates of about 5 mm/year. The dissected membrane microstructure showed an elastin decrease and, in most cases, a collagen increase. In conclusion, the model with the transient inflammation pattern allowed the reproduction of clinically observed dissected membrane thickening rates, diameter expansion rates and adaptations in microstructure, thus providing guidance in reducing the parameter space in growth and remodeling models of aortic dissections.

Pulse wave velocity: A clinical measure to aid material parameter estimation in computational arterial biomechanics.

Determining proper material parameters from clinical data remains a large, though unavoidable, challenge in patient-specific computational cardiovascular modeling. In an attempt to couple the clinical and modelling practice, this study investigated whether pulse wave velocity (PWV), a clinical arterial stiffness measure, can guide in determining appropriate parameter values for the Gasser-Ogden-Holzapfel (GOH) constitutive model. The reduction and uncertainty analysis was demonstrated on a cylindrical descending thoracic aorta model. Starting from discretized ranges of GOH parameters and using a full factorial design, the parameter sets yielding a physiological PWV (3.5-12.5 m/s) at diastolic pressure (80 mmHg; PWV80) were selected and their PWV at dicrotic notch pressure (110 mmHg; PWV110) was determined. These PWV measures were applied to determine the reduction of the 7D GOH parameter space, the 2D subspaces and the remaining uncertainty in case only PWV80 or both measurements are available. The resulting 12,032 parameter sets lead to a 7D parameter space reduction of ≥ 82.5 % using PWV80, which increased to 96.0 % when including PWV110, in particular at 3.5-8.5 m/s. A similar trend was observed for the remaining uncertainty and the 2D subspaces comprised of medial collagen fiber parameters, while scarce reductions were found for the adventitial and elastin parameters. In conclusion, PWV80 and PWV110 are complementary measures with the potential to reduce the GOH parameter space in arterial models, in particular for media- and collagen-related parameters. Moreover, this approach has the advantage that it allows the estimation of the remaining uncertainty after parameter space reduction.