A new finite-element shell model for arterial growth and remodeling after stent implantation

Load-sharing characteristics of stenting and post-dilation in heavily calcified coronary artery

In this work, stenting in non-calcified and heavily calcified coronary arteries was quantified in terms of diameter-pressure relationships and load transfer from the balloon to the artery. The efficacy of post-dilation in non-calcified and heavily calcified coronary arteries was also characterized in terms of load sharing and the changes in tissue mechanics. Our results have shown that stent expansion exhibits a cylindrical shape in non-calcified lesions, while it exhibits a dog bone shape in heavily calcified lesions. Load-sharing analysis has shown that only a small portion of the pressure load (1.4 N, 0.8% of total pressure load) was transferred to the non-calcified lesion, while a large amount of the pressure load (19 N, 12%) was transferred to the heavily calcified lesion. In addition, the increasing inflation pressure (from 10 to 20 atm) can effectively increase the minimal lumen diameter (from 1.48 to 2.82 mm) of the heavily calcified lesion, the stress (from 1.5 to 8.4 MPa) and the strain energy in the calcification (1.77 mJ to 26.5 mJ), which are associated with the potential of calcification fracture. Results indicated that increasing inflation pressure can be an effective way to improve the stent expansion if a dog bone shape of the stenting profile is observed. Considering the risk of a balloon burst, our results support the design and application of the high-pressure balloon for post-dilation. This work also sheds some light on the stent design and choice of stent materials for improving the stent expansion at the dog bone region and mitigating stresses on arterial tissues.

Load-sharing characteristics of stenting and post-dilation in heavily calcified coronary artery

In this work, stenting in non-calcified and heavily calcified coronary arteries was quantified in terms of diameter-pressure relationships and load transfer from the balloon to the artery. The efficacy of post-dilation in non-calcified and heavily calcified coronary arteries was also characterized in terms of load sharing and the changes in tissue mechanics. Our results have shown that stent expansion exhibits a cylindrical shape in non-calcified lesions, while it exhibits a dog bone shape in heavily calcified lesions. Load-sharing analysis has shown that only a small portion of the pressure load (1.4 N, 0.8% of total pressure load) was transferred to the non-calcified lesion, while a large amount of the pressure load (19 N, 12%) was transferred to the heavily calcified lesion. In addition, the increasing inflation pressure (from 10 to 20 atm) can effectively increase the minimal lumen diameter (from 1.48 mm to 2.82 mm) of the heavily calcified lesion, the stress (from 1.5 MPa to 8.4 MPa) the strain energy in the calcification (1.77 mJ to 26.5 mJ), which associated with the potential of calcification fracture. Results indicated that increasing inflation pressure can be an effective way to improve the stent expansion if a dog bone shape of the stenting profile is observed. Considering the risk of a balloon burst, our results support the design and application of the high-pressure balloon for post-dilation.

Modeling planar response of vascular tissues using quadratic functions of effective strain

Simulation-based studies of the cardiovascular structure such as aorta have become increasingly popular for many biomedical problems such as predictions of aneurysm rupture. A critical step in these simulations is the development of constitutive models that accurately describe the tissue's mechanical behavior. In this work, we present a new constitutive model, which explicitly accounts for the gradual recruitment of collagen fibers. The recruitment is considered using an effective stretch, which is a continuum-scale kinematic variable measuring the uncrimped stretch of the tissue in an average sense. The strain energy of a fiber bundle is described by a quadratic function of the effective strain. Constitutive models formulated in this manner are applied to describe the responses of ascending thoracic aortic aneurysm and porcine thoracic aorta tissues. The heterogeneous properties of the ATAA tissue are extracted from bulge inflation test data, and then used in finite element analysis to simulate the inflation test. The descriptive and predictive capabilities are further assessed using planar testing data of porcine thoracic aortic tissues. It is found that the constitutive model can accurately describe the stress-strain relations. In particular, the finite element simulation replicates the displacement, strain, and stress distributions with excellent fidelity.

3D finite-element modeling of vascular adaptation after endovascular aneurysm repair

Aneurysm shrinkage is clinically observed after successful endovascular aortic aneurysm repair (EVAR). However, global understanding of post-operative aneurysm evolutions remains weak. In this work, we propose to study these effects using numerical simulation. We set up a 3D finite-element model of post-EVAR vascular adaptation within an open-source finite-element code, which was initially developed for growth and remodeling (G&R). We modeled the endograft with a set of uniaxial prestrained springs that apply radial forces on the inner surface of the artery. Constitutive equations, momentum balance equations, and equations related to the mechanobiology of the artery were formulated based on the homogenized constrained mixture theory. We performed a sensitivity analysis by varying different selected parameters, namely oversizing and compliance of the stent-graft, gain parameters related to collagen G&R, and the residual pressure in the aneurysm sac. This permitted us to evaluate how each factor influences post-EVAR vascular adaptation. It was found that oversizing, compliance or gain parameters have a limited influence compared to that of the residual pressure in the aneurysm sac, which was found to play a critical role in the stability of aneurysm after stent-graft implantation. An excessive residual pressure larger than 50 mmHg can induce a continuous expansion of the aneurysm while a moderate residual pressure below this critical threshold yields continuous shrinkage of the aneurysm. Moreover, it was found that elderly patients, with relatively lower amounts of remnant elastin in the arterial wall, are more sensitive to the effect of residual pressure. Therefore, these results show that elderly patients may present a higher potential risk of aortic sac expansion due to intra-aneurysm sac pressure after EVAR than younger patients.

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

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.

Patient-specific computational modeling of endovascular aneurysm repair: State of the art and future directions

Endovascular aortic repair (EVAR) has become the preferred intervention option for aortic aneurysms and dissections. This is because EVAR is much less invasive than the alternative open surgery repair. While in-hospital mortality rates are smaller for EVAR than open repair (1%-2% vs. 3%-5%), the early benefits of EVAR are lost after 3 years due to larger rates of complications in the EVAR group. Clinicians follow instructions for use (IFU) when possible, but are left with personal experience on how to best proceed and what choices to make with respect to stent-graft (SG) model choice, sizing, procedural options, and their implications on long-term outcomes. Computational modeling of SG deployment in EVAR and tissue remodeling after intervention offers an alternative way of testing SG designs in silico, in a personalized way before intervention, to ultimately select the strategies leading to better outcomes. Further, computational modeling can be used in the optimal design of SGs in cases of complex geometries. In this review, we address some of the difficulties and successes associated with computational modeling of EVAR procedures. There is still work to be done in all areas of EVAR in silico modeling, including model validation, before models can be applied in the clinic, but much progress has already been made. Critical to clinical implementation are current efforts focusing on developing fast algorithms that can achieve (near) real-time solutions, as well as ways of dealing with inherent uncertainties related to patient aortic wall degradation on an individualized basis. We are optimistic that EVAR modeling in the clinic will soon become a reality to help clinicians optimize EVAR interventions and ultimately reduce EVAR-associated complications.

Machine learning approaches to surrogate multifidelity Growth and Remodeling models for efficient abdominal aortic aneurysmal applications

Computational Growth and Remodeling (G&R) models have been widely used to capture the pathological development of arterial diseases and have shown promise for aiding clinical diagnosis, prognosis prediction, and staging classification. However, due to the high complexity of the arterial adaptation mechanism, high-fidelity arterial G&R simulation usually takes hours or even days, which hinders its application in clinical practice. To remedy this problem, we develop a computationally efficient arterial G&R simulation framework that comprehensively combines the physics-based G&R simulations and data-driven machine learning approaches. The proposed framework greatly enhances the computational efficiency of arterial G&R simulations, thereby enabling more time-consuming arterial applications, including personalized parameter estimation and arterial disease progression prediction. In particular, we achieve significant computational cost reduction mainly through two methods: (1) constructing a Multifidelity Surrogate (MFS) to approximate multifidelity G&R simulations by using a cokriging approach and (2) developing a novel iterative optimization algorithm for personalized parameter estimation. The proposed framework is demonstrated by estimating G&R model parameters and predicting individual aneurysm growth using follow-up CT images of Abdominal Aortic Aneurysms (AAAs) from 21 patients. Results show that the personalized parameters are satisfactorily estimated and the growth of AAAs is predicted within the clinically relevant time frame, i.e., less than 2 h, without a loss of accuracy.

Computational Study of Growth and Remodeling in Ascending Thoracic Aortic Aneurysms Considering Variations of Smooth Muscle Cell Basal Tone

In this paper, we investigate the progression of Ascending Thoracic Aortic Aneurysms (ATAA) using a computational model of Growth and Remodeling (G&R) taking into account the composite (elastin, four collagen fiber families and Smooth Muscle Cells—SMCs) and multi-layered (media and adventitia) nature of the aorta. The G&R model, which is based on the homogenized Constrained Mixture theory, is implemented as a UMAT in the Abaqus finite-element package. Each component of the mixture is assigned a strain energy density function: nearly-incompressible neo-Hookean for elastin and Fung-type for collagen and SMCs. Active SMCs tension is additionally considered, through a length-tension relationship having a classic inverted parabola shape, in order to investigate its effects on the progression of ATAA in a patient-specific model. A sensitivity analysis is performed to evaluate the potential impact of variations in the parameters of the length-tension relationships. These variations reflect in variations of SMCs normal tone during ATAA progression, with active stress contributions ranging between 30% (best case scenario) and 0% (worst case scenario) of the total wall circumferential stress. Low SMCs active stress in the worst case scenarios, in fact, affect the rates of collagen deposition by which the elastin loss is gradually compensated by collagen deposition in the simulated ATAA progression, resulting eventually in larger aneurysm diameters. The types of length-tension relationships leading to a drop of SMCs active stress in our simulations reveal a critical condition which could also result in SMCs apoptosis.

A nonlinear rotation-free shell formulation with prestressing for vascular biomechanics

We implement a nonlinear rotation-free shell formulation capable of handling large deformations for applications in vascular biomechanics. The formulation employs a previously reported shell element that calculates both the membrane and bending behavior via displacement degrees of freedom for a triangular element. The thickness stretch is statically condensed to enforce vessel wall incompressibility via a plane stress condition. Consequently, the formulation allows incorporation of appropriate 3D constitutive material models. We also incorporate external tissue support conditions to model the effect of surrounding tissue. We present theoretical and variational details of the formulation and verify our implementation against axisymmetric results and literature data. We also adapt a previously reported prestress methodology to identify the unloaded configuration corresponding to the medically imaged in vivo vessel geometry. We verify the prestress methodology in an idealized bifurcation model and demonstrate the significance of including prestress. Lastly, we demonstrate the robustness of our formulation via its application to mouse-specific models of arterial mechanics using an experimentally informed four-fiber constitutive model.

Fast, Rate-Independent, Finite Element Implementation of a 3D Constrained Mixture Model of Soft Tissue Growth and Remodeling

Constrained mixture models of soft tissue growth and remodeling can simulate many evolving conditions in health as well as in disease and its treatment, but they can be computationally expensive. In this paper, we derive a new fast, robust finite element implementation based on a concept of mechanobiological equilibrium that yields fully resolved solutions and allows computation of quasi-equilibrated evolutions when imposed perturbations are slow relative to the adaptive process. We demonstrate quadratic convergence and verify the model via comparisons with semi-analytical solutions for arterial mechanics. We further examine the enlargement of aortic aneurysms for which we identify new mechanobiological insights into factors that affect the nearby non-aneurysmal segment as it responds to the changing mechanics within the diseased segment. Because this new 3D approach can be implemented within many existing finite element solvers, constrained mixture models of growth and remodeling can now be used more widely.