Michel R. Labrosse

Mechanical properties of abdominal aortic aneurysm wall.

There is a need to understand why and where the abdominal aortic aneurysm may rupture. Our goal therefore is to investigate whether the mechanical properties are different in different regions of the aneurysm. Aorta samples from five freshly excised whole aneurysms, U 5 cm in diameter, from five patients, average age 71 - 10 years, were subjected to uniaxial testing. We report the wall thickness, yield stress and strain, and parameters that describe nonlinear stress-strain curves for the anterior, lateral and posterior regions of the aneurysm. The posterior region was thicker than the anterior region ( 2.73 - 0.46 mm versus 2.09 - 0.51 mm). The stress-strain curves were described by † = a k b, where † is true stress and k is engineering strain. In the circumferential direction, the wall stiffness increased from posterior to anterior to lateral. In the longitudinal direction, the lateral and anterior regions showed greater wall stiffness than the posterior region. The wall stiffness was greater in the circumferential than longitudinal direction. The anterior region was the weakest, especially in the longitudinal direction (yield stress † Y = 0.38 - 0.18 N mm -2 ). For a less complex model the aneurysmal wall could be considered orthotropic with † = 12.89 k 2.92 and 4.95 k 2.84 in the circumferential and longitudinal directions. For the isotropic model, † = 7.89 k 2.88. In conclusion, different regions of the aneurysm have different yield stress, yield strains, and other mechanical properties, and this must be considered in understanding where the rupture might occur.There is a need to understand why and where the abdominal aortic aneurysm may rupture. Our goal therefore is to investigate whether the mechanical properties are different in different regions of the aneurysm. Aorta samples from five freshly excised whole aneurysms, > or = 5 cm in diameter, from five patients, average age 71 +/- 10 years, were subjected to uniaxial testing. We report the wall thickness, yield stress and strain, and parameters that describe nonlinear stress-strain curves for the anterior, lateral and posterior regions of the aneurysm. The posterior region was thicker than the anterior region (2.73 +/- 0.46 mm versus 2.09 +/- 0.51 mm). The stress-strain curves were described by sigma = a epsilon(b), where sigma is true stress and epsilon is engineering strain. In the circumferential direction, the wall stiffness increased from posterior to anterior to lateral. In the longitudinal direction, the lateral and anterior regions showed greater wall stiffness than the posterior region. The wall stiffness was greater in the circumferential than longitudinal direction. The anterior region was the weakest, especially in the longitudinal direction (yield stress sigmaY = 0.38 +/- 0.18 N mm(-2)). For a less complex model the aneurysmal wall could be considered orthotropic with sigma = 12.89epsilon(2.92) and 4.95epsilon(2.84) in the circumferential and longitudinal directions. For the isotropic model, sigma =7.89epsilon(2.88). In conclusion, different regions of the aneurysm have different yield stress, yield strains, and other mechanical properties, and this must be considered in understanding where the rupture might occur.

Role of Aortic Root Motion in the Pathogenesis of Aortic Dissection

Background—The downward movement of the aortic root during the cardiac cycle may be responsible for producing the circumferential tear observed in aortic dissections. Methods and Results—Contrast injections were investigated in 40 cardiac patients, and a finite element model of the aortic root, arch, and branches of the arch was built to assess the influence of aortic root displacement and pressure on the aortic wall stress. The axial displacement of the aortic root ranged from 0 to 14 mm. It was increased in patients with aortic insufficiency (22±13% of the sino-tubular junction diameter versus 12±9%) and reduced in patients with hypokinesis of the left ventricle (10±9% of sino-tubular junction versus 17±12%). The largest stress increase due to aortic root displacement was found approximately 2 cm above the sino-tubular junction, where the longitudinal stress increased by 50% to 0.32 Nmm−2 when 8.9-mm axial displacement was applied in addition to 120-mm Hg luminal pressure. A similar result was observed when the pressure load was increased to 180 mm Hg without axial displacement. Conclusions—Both aortic root displacement and hypertension significantly increase the longitudinal stress in the ascending aorta. For patients with hypertension who are at risk of dissection, aortic root movement may be monitored as an important risk factor.

Structural analysis of the natural aortic valve in dynamics: from unpressurized to physiologically loaded.

A novel finite element model of the natural aortic valve was developed implementing anisotropic hyperelastic material properties for the leaflets and aortic tissues, and starting from the unpressurized geometry. Static pressurization of the aortic root, silicone rubber moulds and published data helped to establish the model parameters, while high-speed video recording of the leaflet motion in a left-heart simulator allowed for comparisons with simulations. The model was discretized with brick elements and loaded with time-varying pressure using an explicit commercial solver. The aortic valve model produced a competent valve whose dynamic behavior (geometric orifice area vs. time) closely matched that observed in the experiment. In both cases, the aortic valve took approximately 30 ms to open to an 800 mm(2) orifice and remained completely or more than half open for almost 200 ms, after which it closed within 30-50 ms. The highest values of stress were along the leaflet attachment line and near the commissure during diastole. Von Mises stress in the leaflet belly reached 600-750 kPa from early to mid-diastole. While the model using the unpressurized geometry as initial configuration was specially designed to satisfy the requirements of continuum mechanics for large deformations of hyperelastic materials, it also clearly demonstrated that dry models can be adequate to analyze valve dynamics. Although improvements are still needed, the advanced modeling and validation techniques used herein contribute toward improved and quantified accuracy over earlier simplified models.

Mechanical behavior of human aortas: Experiments, material constants and 3-D finite element modeling including residual stress

Segments of fresh human ascending, thoracic descending and abdominal aortas from eight male sexagenarians were pressurized under closed-end and free extension conditions. The median unpressurized inner radii for the ascending, thoracic and abdominal locations were 14.21, 9.67 and 7.16mm, respectively. The median thickness was similar in the ascending and thoracic regions, at about 1.6mm, while it was 1.2mm in the abdominal region. The opening angle was not statistically different between regions, with a median of -38 degrees . Under 13.3kPa pressure, the median circumferential stretch ratio was about 1.26 in all three aortic locations; the median longitudinal stretch ratio was similar in the ascending and thoracic regions, at about 1.13, while it was 1.05 in the abdominal region. Material constants for a three-dimensional hyperelastic anisotropic constitutive model were determined. Experimental, analytical and finite element results showed excellent agreement, validating the novel experimental approach and the numerical methods used. When residual stress was not taken into account, stresses were highest on the inside of the aorta, with a gradient across the wall of about 200 and 50kPa in the circumferential and longitudinal directions, respectively. When residual stress was included as described by negative opening angles, stresses were highest on the outside of the aorta, with a gradient across the wall in excess of 400kPa for the circumferential direction, and on the order of 150kPa for the longitudinal direction. The mechanical consequences of negative opening angles had not been appreciated so far, and deserve further investigation.

Finite element modeling of the thoracic aorta: including aortic root motion to evaluate the risk of aortic dissection

Objective: We propose that the aortic root motion plays an important role in aortic dissection. Methods and results: A finite element model of the aortic root, arch and branches of the arch was built to assess the influence of aortic root displacement and pressure on the aortic wall stress. The largest stress increase due to aortic root displacement was found at approximately 2 cm above the top of the aortic valve. There, the longitudinal stress increased by 50% to 0.32 MPa when 8.9 mm axial displacement was applied in addition to 120 mmHg luminal pressure. A similar result was observed when the pressure load was increased to 180 mmHg without axial displacement. Conclusions: Both aortic root displacement and hypertension significantly increase the longitudinal stress in the ascending aorta, which could play a decisive role in the development of various aortic pathologies, including aortic dissection.

Mechanical characterization of human aortas from pressurization testing and a paradigm shift for circumferential residual stress.

Material properties needed for accurate stress analysis of the human aorta are still incompletely known, especially as many reports have ignored the presence of residual stresses in the aortic wall. To contribute new material regarding these issues, we carried out measurements and pressurization testing on ascending, thoracic and abdominal aortic samples from 24 human subjects aged 38-77 years, and evaluated the opening angle describing the circumferential residual stress level present in the aorta. We determined material constants for the aorta by gender, anatomic location and age group, according to a simple phenomenological constitutive model. The unpressurized aortic radius positively correlated with age, and the circumferential and longitudinal stretch ratios under systemic pressure negatively correlated with age, confirming the known enlargement and stiffening of the aorta with aging. The opening angle was measured to range from a minimum of 89° to above 360° for extreme cases. For given aortic dimensions and material properties, analysis of the in vivo circumferential and longitudinal mural stress distributions indicated a profound influence of the opening angle. For instance, in the thoracic aorta of males aged 38-66, opening angles in the range of 0° to 80° (resp. 60°) may equalize the gradient of in vivo circumferential (resp. longitudinal) stress between the inner and outer layers of the aorta, as commonly expected; however, opening angles above 160° (resp. 120°) may cause the gradient of circumferential (resp. longitudinal) stress to reverse and increase compared to the case without residual stress, putting the maximum stresses toward the adventitia instead of the intima. Even though the analysis of the aortic wall excluded possible longitudinal residual stresses as well as material inhomogeneities, such as constitutive differences between the intimal, medial and adventitial layers, the experimental data reported herein are important to aortic modeling at large and the better understanding of aortic pathophysiology in particular.

Modeling leaflet correction techniques in aortic valve repair: A finite element study

In aortic valve sparing surgery, cusp prolapse is a common cause of residual aortic insufficiency. To correct cusp pathology, native leaflets of the valve frequently require adjustment which can be performed using a variety of described correction techniques, such as central or commissural plication, or resuspension of the leaflet free margin. The practical question then arises of determining which surgical technique provides the best valve performance with the most physiologic coaptation. To answer this question, we created a new finite element model with the ability to simulate physiologic function in normal valves, and aortic insufficiency due to leaflet prolapse in asymmetric, diseased or sub-optimally repaired valves. The existing leaflet correction techniques were simulated in a controlled situation, and the performance of the repaired valve was quantified in terms of maximum leaflets stress, valve orifice area, valve opening and closing characteristics as well as total coaptation area in diastole. On the one hand, the existing leaflet correction techniques were shown not to adversely affect the dynamic properties of the repaired valves. On the other hand, leaflet resuspension appeared as the best technique compared to central or commissural leaflet plication. It was the only method able to achieve symmetric competence and fix an individual leaflet prolapse while simultaneously restoring normal values for mechanical stress, valve orifice area and coaptation area.

Hip Joint Stresses Due to Cam-Type Femoroacetabular Impingement: A Systematic Review of Finite Element Simulations

Background The cam deformity causes the anterosuperior femoral head to obstruct with the acetabulum, resulting in femoroacetabular impingement (FAI) and elevated risks of early osteoarthritis. Several finite element models have simulated adverse loading conditions due to cam FAI, to better understand the relationship between mechanical stresses and cartilage degeneration. Our purpose was to conduct a systematic review and examine the previous finite element models and simulations that examined hip joint stresses due to cam FAI. Methods The systematic review was conducted to identify those finite element studies of cam-type FAI. The review conformed to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines and studies that reported hip joint contact pressures or stresses were included in the quantitative synthesis. Results Nine articles studied FAI morphologies using finite element methods and were included in the qualitative synthesis. Four articles specifically examined contact pressures and stresses due to cam FAI and were included in the quantitative synthesis. The studies demonstrated that cam FAI resulted in substantially elevated contact pressures (median = 10.4 MPa, range = 8.5–12.2 MPa) and von Mises stresses (median 15.5 MPa, range = 15.0–16.0 MPa) at the acetabular cartilage; and elevated maximum-shear stress on the bone (median = 15.2 MPa, range = 14.3–16.0 MPa), in comparison with control hips, during large amplitudes of hip motions. Many studies implemented or adapted idealized, ball-and-cup, parametric models to predict stresses, along with homogeneous bone material properties and in vivo instrumented prostheses loading data. Conclusion The formulation of a robust subject-specific FE model, to delineate the pathomechanisms of FAI, remains an ongoing challenge. The available literature provides clear insight into the estimated stresses due to the cam deformity and provides an assessment of its risks leading to early joint degeneration.

Subject-specific finite-element modeling of normal aortic valve biomechanics from 3D+t TEE images

In the past decades, developments in transesophageal echocardiography (TEE) have opened new horizons in reconstructive surgery of the aortic valve (AV), whereby corrections are made to normalize the geometry and function of the valve, and effectively treat leaks. To the best of our knowledge, we propose the first integrated framework to process subject-specific 3D+t TEE AV data, determine age-matched material properties for the aortic and leaflet tissues, build a finite element model of the unpressurized AV, and simulate the AV function throughout a cardiac cycle. For geometric reconstruction purposes, dedicated software was created to acquire the 3-D coordinates of 21 anatomical landmarks of the AV apparatus in a systematic fashion. Measurements from ten 3D+t TEE datasets of normal AVs were assessed for inter- and intra-observer variability. These tests demonstrated mean measurement errors well within the acceptable range. Simulation of a complete cardiac cycle was successful for all ten valves and validated the novel schemes introduced to evaluate age-matched material properties and iteratively scale the unpressurized dimensions of the valves such that, given the determined material properties, the dimensions measured in vivo closely matched those simulated in late diastole. The leaflet coaptation area, describing the quality of the sealing of the valve, was measured directly from the medical images and was also obtained from the simulations; both approaches correlated well. The mechanical stress values obtained from the simulations may be interpreted in a comparative sense whereby higher values are indicative of higher risk of tearing and/or development of calcification.

Planar biaxial testing of heart valve cusp replacement biomaterials: Experiments, theory and material constants.

OBJECTIVES Aortic valve (AV) repair has become an attractive option to correct aortic insufficiency. Yet, cusp reconstruction with various cusp replacement materials has been associated with greater long-term repair failures, and it is still unknown how such materials mechanically compare with native leaflets. We used planar biaxial testing to characterize six clinically relevant cusp replacement materials, along with native porcine AV leaflets, to ascertain which materials would be best suited for valve repair. METHODS We tested at least six samples of: 1) fresh autologous porcine pericardium (APP), 2) glutaraldehyde fixed porcine pericardium (GPP), 3) St Jude Medical pericardial patch (SJM), 4) CardioCel patch (CC), 5) PeriGuard (PG), 6) Supple PeriGuard (SPG) and 7) fresh porcine AV leaflets (PC). We introduced efficient displacement-controlled testing protocols and processing, as well as advanced convexity requirements on the strain energy functions used to describe the mechanical response of the materials under loading. RESULTS The proposed experimental and data processing pipeline allowed for a robust in-plane characterization of all the materials tested, with constants determined for two Fung-like hyperelastic, anisotropic strain energy models. CONCLUSIONS Overall, CC and SPG (respectively PG) patches ranked as the closest mechanical equivalents to young (respectively aged) AV leaflets. Because the native leaflets as well as CC, PG and SPG patches exhibit significant anisotropic behaviors, it is suggested that the fiber and cross-fiber directions of these replacement biomaterials be matched with those of the host AV leaflets. STATEMENT OF SIGNIFICANCE The long-term performance of cusp replacement materials would ideally be evaluated in large animal models for AV disease and cusp repair, and over several months or more. Given the unavailability and impracticality of such models, detailed information on stress-strain behavior, as studied herein, and investigations of durability and valve dynamics will be the best surrogates, as they have been for prosthetic valves. Overall, comparison with Fig. 3 suggests that CC and SPG (respectively PG) patches may be the closest mechanical equivalents to young (respectively aged) AV leaflets. Interestingly, the thicknesses of these materials are close to those reported for porcine and younger human AV leaflets, which may facilitate surgical implantation, by contrast to the thinner APP which has poor handling qualities. Because the native leaflets as well as CC, PG and SPG patches exhibit anisotropic behaviors, from a mechanistic perspective alone, it stands to reason that cardiac surgeons should seek to intraoperatively match the fiber and cross-fiber directions of these replacement biomaterials with those of the repaired AV leaflets.