About prestretch in homogenized constrained mixture models simulating growth and remodeling in patient-specific aortic geometries

Abstract

Evolution of mechanical and structural properties in the Ascending Thoracic Aorta (ATA) is the results of complex mechanobiological processes. In this work, we address some numerical challenges in order to elaborate computational models of these processes. For that, we extend the state of the art of homogenized constrained mixture (hCM) models. In these models, prestretches are assigned to the mixed constituents in order to ensure local mechanical equilibrium macroscopically, and to maintain a homeostatic level of tension in collagen fibers microscopically. Although the initial prestretches were assumed as homogeneous in idealized straight tubes, more elaborate prestretch distributions need to be considered for curved geometrical models such as patient-specific ATA. Therefore, we introduce prestretches having a three-dimensional gradient across the ATA geometry in the homeostatic reference state. We test different schemes with the objective to ensure stable growth and remodeling (G&R) simulations on patient-specific curved vessels. In these simulations, aneurysm progression is triggered by tissue changes in the constituents such as mass degradation of intramural elastin. The results show that the initial prestretches are not only critical for the stability of numerical simulations, but they also affect the G&R response. Eventually, we submit that initial conditions required for G&R simulations need to be identified regionally for ensuring realistic patient-specific predictions of aneurysm progression.

Preliminary establishment and validation of the inversion method for growth and remodeling parameters of patient-specific abdominal aortic aneurysms

“…Each unit volume of the middle layer and adventitia layer of the aorta was considered a mixture composed of elastin, four clusters of collagen fibers, and one cluster of smooth muscle fibers. The mass densities of these six components in each layer are different according to reference, as shown in Table 2 [23] . The partial material parameters of different components are shown in Table 3.…”

Patient-Specific Finite Element Modeling of Aneurysmal Dilatation After Chronic Type B Aortic Dissection

“…inner side of adventitia layer and outer side of media layer), is created by breaking springs in a selected region where tears are assumed to be present. The force induced by the pressure in the false lumen is then applied on each mesh surface, 𝑆 𝑑𝑖𝑠𝑠𝑒𝑐𝑡𝑖𝑜𝑛 , of the newly created free surfaces 𝒑 𝑑𝑖𝑠𝑠𝑒𝑐𝑡𝑖𝑜𝑛 = 𝑃 𝐹𝐿 𝒏 𝑆 𝑑𝑖𝑠𝑠𝑒𝑐𝑡𝑖𝑜𝑛 (25) where 𝑃 𝐹𝐿 is the constant pressure in the false lumen and 𝒏 𝑆 𝑑𝑖𝑠𝑠𝑒𝑐𝑡𝑖𝑜𝑛 is the outward pointing unit vector normal to the free mesh surfaces in the false lumen. Finally, it is worth noting that the presence of such pressurized false lumen will break the mechanical equilibrium of the arterial initial homeostatic state, and therefore trigging the G&R of the arterial wall over a long period of time in case of cTBAD, until the achievement of a new preferred mechanical state or eventually an excessive aneurysmal degeneration.…”

“…Similarly, a pure sliding boundary condition is assigned to cross-sections at the two extremities while the outer surface of the adventitia is let free. Mechanical parameters, as well as simulation parameters, are reported in Table 2, based on Laubrie et al [25]. The initial tear of the dissection is created by breaking springs in the regions defined by √𝑥 2 + 𝑦 2 ≥ 70 and 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥 𝑦 ⁄ ) ≤ 60°, to model a representative initial tear of cTBAD.…”

“…The same material properties and simulation parameters as summarized in Table 2. Finally, it is worth noting that the non-uniform prestretches were used in this patient-specific artery, which was computed based on an iterative method previously developed by Laubrie et al [25]. In order to better describe the initial dissection tear of cTBAD, we introduce a numerical parameter, 𝛼, for each circumferential cross-section of the arterial segment, as shown in Figure 5.…”

An inverse fitting strategy to determine the constrained mixture model parameters: application in patient-specific aorta

“…In contrast, collagen is continuously produced and degraded (short half-life), which may be further reduced by arterial diseases, like hypertension or aneurysms ( Cyron and Humphrey, 2017 ). On the other hand, the CMM takes into consideration potential structural changes of each component; for example, through degradation of their material properties ( Latorre and Humphrey, 2020 ), or alteration of its stressed configuration over time ( Laubrie et al, 2022 ). Particular attention is put on this last point since, as the in-vivo configuration is taken as a referential state, the definition of a characteristic deposition stretch (pre-strain) by each constituent is necessary, which quantifies its deformation from a stress-free (natural) configuration to the referential state.…”