Modeling lamellar disruption within the aortic wall using a particle-based approach

Mathematical modeling and numerical simulation of arterial dissection based on a novel surgeon's view

This paper presents a mathematical model for arterial dissection based on a novel hypothesis proposed by a surgeon, Axel Haverich, see Haverich (Circulation 135(3):205-207, 2017. https://doi.org/10.1161/circulationaha.116.025407 ). In an attempt and based on clinical observations, he explained how three different arterial diseases, namely atherosclerosis, aneurysm and dissection have the same root in malfunctioning Vasa Vasorums (VVs) which are micro capillaries responsible for artery wall nourishment. The authors already proposed a mathematical framework for the modeling of atherosclerosis which is the thickening of the artery walls due to an inflammatory response to VVs dysfunction. A multiphysics model based on a phase-field approach coupled with mechanical deformation was proposed for this purpose. The kinematics of mechanical deformation was described using finite strain theory. The entire model is three-dimensional and fully based on a macroscopic continuum description. The objective here is to extend that model by incorporating a damage mechanism in order to capture the tearing (rupture) in the artery wall as a result of micro-injuries in VV. Unlike the existing damage-based model of the dissection in the literature, here the damage is driven by the internal bleeding (hematoma) rather than purely mechanical external loading. The numerical implementation is carried out using finite element method (FEM).

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

The Constrained Mixture Model (CMM) is a novel approach to describe arterial wall mechanics, whose formulation is based on a referential physiological state. The CMM considers the arterial wall as a mixture of load-bearing constituents, each of them with characteristic mass fraction, material properties, and deposition stretch levels from its stress-free state to the in-vivo configuration. Although some reports of this model successfully assess its capabilities, they barely explore experimental approaches to model patient-specific scenarios. In this sense, we propose an iterative fitting procedure of numerical-experimental nature to determine material parameters and deposition stretch values. To this end, the model has been implemented in a finite element framework, and it is calibrated using reported experimental data of descending thoracic aorta. The main results obtained from the proposed procedure consist of a set of material parameters for each constituent. Moreover, a relationship between deposition stretches and residual strain measurements (opening angle and axial stretch) has been numerically proved, establishing a strong consistency between the model and experimental data.

A novel constitutive model considering the role of elastic lamellae' structural heterogeneity in homogenizing transmural stress distribution in arteries

Understanding how the homeostatic stress state can be reached in arterial tissues can provide new insights into vascular physiology. Even though the function of maintaining homeostasis is often linked to the concentric layers of medial elastic lamellae, how the lamellae are capable of evenly distributing the stress transmurally remains to be understood. The recent microstructural study by Yu et al. (2018 J. R. Soc. Interface 15, 20180492) revealed that, circumferentially, lamellar layers closer to the lumen are wavier than the ones further away from it and, thus, experience more unfolding when subjected to blood pressure. Motivated by this peculiar finding, the current study, for the first time, proposes a novel approach to model elastic lamellae and such structural heterogeneity using the extensible worm-like chain model. When implemented into the material description of the conventional two-layer artery model, in which adventitial collagen is modelled using the inextensible worm-like chain model, it is demonstrated that structural heterogeneity in elastic lamellae plays an important role in dictating transmural stress distribution and, therefore, the homeostasis of the arterial wall.

Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems

Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's response. The solver with lower fidelity (coarse) is responsible for simulating domains with homogeneous features, whereas the expensive high-fidelity (fine) model describes microscopic features with refined discretization, often making the overall cost prohibitively high, especially for time-dependent problems. In this work, we explore the idea of multiscale modeling with machine learning and employ DeepONet, a neural operator, as an efficient surrogate of the expensive solver. DeepONet is trained offline using data acquired from the fine solver for learning the underlying and possibly unknown fine-scale dynamics. It is then coupled with standard PDE solvers for predicting the multiscale systems with new boundary/initial conditions in the coupling stage. The proposed framework significantly reduces the computational cost of multiscale simulations since the DeepONet inference cost is negligible, facilitating readily the incorporation of a plurality of interface conditions and coupling schemes. We present various benchmarks to assess the accuracy and efficiency, including static and time-dependent problems. We also demonstrate the feasibility of coupling of a continuum model (finite element methods, FEM) with a neural operator, serving as a surrogate of a particle system (Smoothed Particle Hydrodynamics, SPH), for predicting mechanical responses of anisotropic and hyperelastic materials. What makes this approach unique is that a well-trained over-parametrized DeepONet can generalize well and make predictions at a negligible cost.

Is There Enough Evidence to Support the Role of Glycosaminoglycans and Proteoglycans in Thoracic Aortic Aneurysm and Dissection?—A Systematic Review

Altered proteoglycan (PG) and glycosaminoglycan (GAG) distribution within the aortic wall has been implicated in thoracic aortic aneurysm and dissection (TAAD). This review was conducted to identify literature reporting the presence, distribution and role of PGs and GAGs in the normal aorta and differences associated with sporadic TAAD to address the question; is there enough evidence to establish the role of GAGs/PGs in TAAD? 75 studies were included, divided into normal aorta (n = 51) and TAAD (n = 24). There is contradictory data regarding changes in GAGs upon ageing; most studies reported an increase in GAG sub-types, often followed by a decrease upon further ageing. Fourteen studies reported changes in PG/GAG or associated degradation enzyme levels in TAAD, with most increased in disease tissue or serum. We conclude that despite being present at relatively low abundance in the aortic wall, PGs and GAGs play an important role in extracellular matrix maintenance, with differences observed upon ageing and in association with TAAD. However, there is currently insufficient information to establish a cause-effect relationship with an underlying mechanistic understanding of these changes requiring further investigation. Increased PG presence in serum associated with aortic disease highlights the future potential of these biomolecules as diagnostic or prognostic biomarkers.

18F-Sodium Fluoride Positron Emission Tomography and Computed Tomography in Acute Aortic Syndrome

BACKGROUND

Acute aortic syndrome is associated with aortic medial degeneration. 18F-sodium fluoride (18F-NaF) positron emission tomography (PET) detects microscopic tissue calcification as a marker of disease activity.

OBJECTIVES

In a proof-of-concept study, this investigation aimed to establish whether 18F-NaF PET combined with computed tomography (CT) angiography could identify aortic medial disease activity in patients with acute aortic syndrome.

METHODS

Patients with aortic dissection or intramural hematomas and control subjects underwent 18F-NaF PET/CT angiography of the aorta. Aortic 18F-NaF uptake was measured at the most diseased segment, and the maximum value was corrected for background blood pool activity (maximum tissue-to-background ratio [TBRmax]). Radiotracer uptake was compared with change in aortic size and major adverse aortic events (aortic rupture, aorta-related death, or aortic repair) over 45 ± 13 months.

RESULTS

Aortic 18F-NaF uptake co-localized with histologically defined regions of microcalcification and elastin disruption. Compared with control subjects, patients with acute aortic syndrome had increased 18F-NaF uptake (TBRmax: 1.36 ± 0.39 [n = 20] vs 2.02 ± 0.42 [n = 47] respectively; P < 0.001) with enhanced uptake at the site of intimal disruption (+27.5%; P < 0.001). 18F-NaF uptake in the false lumen was associated with aortic growth (+7.1 mm/year; P = 0.011), and uptake in the outer aortic wall was associated with major adverse aortic events (HR: 8.5 [95% CI: 1.4-50.4]; P = 0.019).

CONCLUSIONS

In patients with acute aortic syndrome, 18F-NaF uptake was enhanced at sites of disease activity and was associated with aortic growth and clinical events. 18F-NaF PET/CT holds promise as a noninvasive marker of disease severity and future risk in patients with acute aortic syndrome. (18F Sodium Fluoride PET/CT in Acute Aortic Syndrome [FAASt]; NCT03647566).

Regional delamination strength in the human aorta underlies the anatomical localization of the dissection channel

Aortic dissection is a life-threatening event, during which a primary tear propagates along the aorta causing catastrophic delamination of the inner (intima with most of the media) from the outer layers (leftover media with adventitia). Our understanding of mode-I fracture resistance at different aortic regions is incomplete, although the anatomical localization of the dissection channel may be assigned to this factor. To determine whether the susceptibility to dissection propagation varied with aortic region, the average and standard deviation of peel tension (indices of adhesive strength between layers when pulled apart and its fluctuation) were measured in 24 cadaveric subjects. Measurements were made in the inner and outer quadrants of 9 consecutive regions. Strong regional heterogeneity was established that was age-related based on the following evidence: (1) the average and standard deviation of peel tension peaked in the ascending aorta, decreasing to almost constant values in the descending thoracic aorta, but increasing across the abdominal aorta; (2) axial differences were more pronounced in the inner quadrant, with differences among quadrants reaching significance proximally; (3) the average peel tension was greatly impaired from <40 to 40-60 but much less to >60-year-old subjects at most regions/quadrants, leading to non-uniform axial variations in all age groups; (4) gender affected little the data. This comprehensive series of delamination tests explains the clinical observation of most dissections initiating in the ascending aorta to extend distally and of few dissections initiating in the descending thoracic aorta to extend proximally, while supporting the increased vulnerability in aged subjects.

Differences in Aortic Histopathology in Patients Undergoing Valve Reimplantation Surgery for Various Clinical Syndromes

Objectives  The study aims to investigate aortic histopathologic differences among patients undergoing aortic valve reimplantation, suggest different mechanisms of aortic root aneurysm pathogenesis, and identify factors associated with long-term success of reimplantation.

Methods  From 2006 to 2017, 568 adults who underwent reimplantation for repair of aortic root aneurysm, including patients with tricuspid aortic valves with no connective tissue disease (TAV/NoCTD, n  = 314/568; 55.3%), bicuspid aortic valves (BAVs, n  = 86/568; 15.1%), or connective tissue disease (CTD, n  = 177/568; 31.2%), were compiled into three comparison groups. Patients with both BAV and CTD ( n  = 9/568; 1.6%) were omitted to increase study power. Patient records were analyzed retrospectively, focusing on pathology reports, which were available for 98.42% of patients, and were classified based on their descriptions of aortic tissue samples, primarily from the noncoronary sinus. Mean follow-up time available for patients was 2.97 years.

Results  Aortitis, medial fibrosis, and smooth muscle loss were more common histopathologic findings in patients with TAV/NoCTD than in patients with BAV and CTD ( p  < 0.05). Cystic medial degeneration was most often found in patients with CTD, then TAV/NoCTD, and least in BAV ( p  < 0.01). Increases in mucopolysaccharides were found more often in the BAV group than in the TAV/NoCTD and CTD groups ( p  < 0.01). There were no differences in the frequency of elastic laminae fragmentation/loss across these three groups. Among all patients, 1.97% ( n  = 11/559) had an unplanned reintervention on the aortic valve after reimplantation, but no significant demographic or histopathologic differences were identified.

Conclusion  Despite some common histopathologic features among patients undergoing aortic valve reimplantation, there were enough distinguishing features among aortic tissue samples of TAV/NoCTD, BAV, and CTD patients to suggest that these groups develop root aneurysms by different mechanisms. No histopathologic features were able to predict the need for late reintervention on the aortic valve.

A phantom and in vivo simulation of coronary flow to calculate fractional flow reserve using a mesh-free model

Moving particle semi-implicit (MPS) method is a mesh-free method to perform computational fluid dynamics (CFD). The purpose of this study was to calculate the simulated fractional flow reserve (sFFR) using a coronary stenosis model, and to validate the MPS-derived sFFR against invasive FFR using clinical coronary CT data. Coronary flow simulation included 21 stenosis models with stenosis ranging 30-70%. Patient coronary analysis was performed in 76 consecutive patients (100 vessels) who underwent coronary CT angiography and subsequent invasive FFR between November 2016 and March 2020. Accuracy of sFFR and CT angiography for diagnosis of invasive FFR ≤ 0.80 was compared. Quantitative morphological stenosis data of CT angiography were also obtained. Area stenosis showed a good correlation to sFFR (R2 = 0.996, p < 0.001) in coronary stenosis models. In the patient study, the mean FFR value was 0.82 ± 0.10, and 37 out of 100 vessels showed FFR ≤ 0.80. FFR and sFFR values showed a good correlation (R2 = 0.59, p < 0.001) with a slight underestimation of sFFR as compared with FFR (mean difference - 0.015 ± 0.096, p = 0.12). The sensitivity, specificity, positive predictive value, and negative predictive value of sFFR to predict FFR ≤ 0.80 was 86%, 89%, 82%, 92%, respectively. The accuracy to predict FFR ≤ 0.80 using sFFR was greater than using diameter stenosis and minimum lumen area (88% vs. 74%, p = 0.008). CFD using the MPS method showed feasible results validated against invasive FFR. The accuracy to predict significant stenosis was higher than morphological stenosis.

Critical Pressure of Intramural Delamination in Aortic Dissection

Computational models of aortic dissection can examine mechanisms by which this potentially lethal condition develops and propagates. We present results from phase-field finite element simulations that are motivated by a classical but seldom repeated experiment. Initial simulations agreed qualitatively and quantitatively with data, yet because of the complexity of the problem it was difficult to discern trends. Simplified analytical models were used to gain further insight. Together, simplified and phase-field models reveal power-law-based relationships between the pressure that initiates an intramural tear and key geometric and mechanical factors-insult surface area, wall stiffness, and tearing energy. The degree of axial stretch and luminal pressure similarly influence the pressure of tearing, which was ~88 kPa for healthy and diseased human aortas having sub-millimeter-sized initial insults, but lower for larger tear sizes. Finally, simulations show that the direction a tear propagates is influenced by focal regions of weakening or strengthening, which can drive the tear towards the lumen (dissection) or adventitia (rupture). Additional data on human aortas having different predisposing disease conditions will be needed to extend these results further, but the present findings show that physiologic pressures can propagate initial medial defects into delaminations that can serve as precursors to dissection.

Simulating progressive intramural damage leading to aortic dissection using DeepONet: an operator-regression neural network

Aortic dissection progresses mainly via delamination of the medial layer of the wall. Notwithstanding the complexity of this process, insight has been gleaned by studying in vitro and in silico the progression of dissection driven by quasi-static pressurization of the intramural space by fluid injection, which demonstrates that the differential propensity of dissection along the aorta can be affected by spatial distributions of structurally significant interlamellar struts that connect adjacent elastic lamellae. In particular, diverse histological microstructures may lead to differential mechanical behaviour during dissection, including the pressure-volume relationship of the injected fluid and the displacement field between adjacent lamellae. In this study, we develop a data-driven surrogate model of the delamination process for differential strut distributions using DeepONet, a new operator-regression neural network. This surrogate model is trained to predict the pressure-volume curve of the injected fluid and the damage progression within the wall given a spatial distribution of struts, with in silico data generated using a phase-field finite-element model. The results show that DeepONet can provide accurate predictions for diverse strut distributions, indicating that this composite branch-trunk neural network can effectively extract the underlying functional relationship between distinctive microstructures and their mechanical properties. More broadly, DeepONet can facilitate surrogate model-based analyses to quantify biological variability, improve inverse design and predict mechanical properties based on multi-modality experimental data.

On a phase-field approach to model fracture of small intestine walls

We address anisotropic elasticity and fracture in small intestine walls (SIWs) with both experimental and computational methods. Uniaxial tension experiments are performed on porcine SIW samples with varying alignments and quantify their nonlinear elastic anisotropic behavior. Fracture experiments on notched SIW strips reveal a high sensitivity of the crack propagation direction and the failure stress on the tissue orientation. From a modeling point of view, the observed anisotropic elastic response is studied with a continuum mechanical model stemming from a strain energy density with a neo-Hookean component and an anisotropic component with four families of fibers. Fracture is addressed with the phase-field approach, featuring two-fold anisotropy in the fracture toughness. Elastic and fracture model parameters are calibrated based on the experimental data, using the maximum and minimum limits of the experimental stress-stretch data set. A very good agreement between experimental data and computational results is obtained, the role of anisotropy being effectively captured by the proposed model in both the elastic and the fracture behavior. STATEMENT OF SIGNIFICANCE: This article reports a comprehensive experimental data set on the mechanical failure behavior of small intestinal tissue, and presents the corresponding protocols for preparing and testing the samples. On the one hand, the results of this study contribute to the understanding of small intestine mechanics and thus to understanding of load transfer mechanisms inside the tissue. On the other hand, these results are used as input for a phase-field modelling approach, presented in this article. The presented model can reproduce the mechanical failure behavior of the small intestine in an excellent way and is thus a promising tool for the future mechanical description of diseased small intestinal tissue.

Differential propensity of dissection along the aorta

Aortic dissections progress, in part, by delamination of the wall. Previous experiments on cut-open segments of aorta demonstrated that fluid injected within the wall delaminates the aorta in two distinct modes: stepwise progressive tearing in the abdominal aorta and a more prevalent sudden mode of tearing in the thoracic aorta that can also manifest in other regions. A microstructural understanding that delineates these two modes of tearing has remained wanting. We implemented a phase-field finite-element model of the aortic wall, motivated in part by two-photon imaging, and found correlative relations for the maximum pressure prior to tearing as a function of local geometry and material properties. Specifically, the square of the pressure of tearing relates directly to both tissue stiffness and the critical energy of tearing and inversely to the square root of the torn area; this correlation explains the sudden mode of tearing and, with the microscopy, suggests a mechanism for progressive tearing. Microscopy also confirmed that thick interlamellar radial struts are more abundant in the abdominal region of the aorta, where progressive tearing was observed previously. The computational results suggest that structurally significant radial struts increase tearing pressure by two mechanisms: confining the fluid by acting as barriers to flow and increasing tissue stiffness by holding the adjacent lamellae together. Collectively, these two phase-field models provide new insights into the mechanical factors that can influence intramural delaminations that promote aortic dissection.

The Contribution of Glycosaminoglycans/Proteoglycans to Aortic Mechanics in Health and Disease: A Critical Review

While elastin and collagen have received a lot of attention as major contributors to aortic biomechanics, glycosaminoglycans (GAGs) and proteoglycans (PGs) recently emerged as additional key players whose roles must be better elucidated if one hopes to predict aortic ruptures caused by aneurysms and dissections more reliably. GAGs are highly negatively charged polysaccharide molecules that exist in the extracellular matrix (ECM) of the arterial wall. In this critical review, we summarize the current understanding of the contributions of GAGs/PGs to the biomechanics of the normal aortic wall, as well as in the case of aortic diseases such as aneurysms and dissections. Specifically, we describe the fundamental swelling behavior of GAGs/PGs and discuss their contributions to residual stresses and aortic stiffness, thereby highlighting the importance of taking these polyanionic molecules into account in mathematical and numerical models of the aorta. We suggest specific lines of investigation to further the acquisition of experimental data to complement simulations and solidify our current understanding. We underscore different potential roles of GAGs/PGs in thoracic aortic aneurysm (TAAD) and abdominal aortic aneurysm (AAA). Namely, we report findings according to which the accumulation of GAGs/PGs in TAAD causes stress concentrations which may be sufficient to initiate and propagate delamination. On the other hand, there seems to be no clear indication of a relationship between the marked reduction in GAG/PG content and the stiffening and weakening of the aortic wall in AAA.

Aortic "Disease-in-a-Dish": Mechanistic Insights and Drug Development Using iPSC-Based Disease Modeling

Thoracic aortic diseases, whether sporadic or due to a genetic disorder such as Marfan syndrome, lack effective medical therapies, with limited translation of treatments that are highly successful in mouse models into the clinic. Patient-derived induced pluripotent stem cells (iPSCs) offer the opportunity to establish new human models of aortic diseases. Here we review the power and potential of these systems to identify cellular and molecular mechanisms underlying disease and discuss recent advances, such as gene editing, and smooth muscle cell embryonic lineage. In particular, we discuss the practical aspects of vascular smooth muscle cell derivation and characterization, and provide our personal insights into the challenges and limitations of this approach. Future applications, such as genotype-phenotype association, drug screening, and precision medicine are discussed. We propose that iPSC-derived aortic disease models could guide future clinical trials via “clinical-trials-in-a-dish”, thus paving the way for new and improved therapies for patients.