Glycosaminoglycans modulate compressive stiffness and circumferential residual stress in the porcine thoracic aorta.

The mechanical properties of the aorta are influenced by the extracellular matrix, a network mainly comprised of fibers and glycosaminoglycans (GAG). In this work, we demonstrate that GAG contribute to the opening angle (a marker of circumferential residual stresses) in intact and glycated aortic tissue. Enzymatic GAG depletion was associated with a decrease in the opening angle, by approximately 25% (p = 0.009) in the ascending (AS) region, 32% (p = 0.003) in the aortic arch (AR), and 42% (p = 0.001) in the lower descending thoracic (LDT) region. A similar effect of GAG depletion on aortic ring opening angle was also observed in previously glycated tissues. Using indentation testing, we found that the radial compressive stiffness significantly increased in the AS region following GAG depletion, compared to fresh (p = 0.006) and control samples (p = 0.021), and that the compressive properties are heterogeneous along the aortic tree. A small loss of water content was also detected after GAG depletion, which was most prominent under hypotonic conditions. Finally, the AS region was also associated with a significant loss of compressive deformation (circumferential stretch that is < 1) in the inner layer of the aorta following GAG depletion, suggesting that GAG interact with ECM fibers in their effect on aortic mechanics. The importance of this work lies in its identification of the role of GAG in modulating the mechanical properties of the aorta, namely the circumferential residual stresses and the radial compressive stiffness, as well as contributing to the swelling state and the level of circumferential prestretch in the tissue. STATEMENT OF SIGNIFICANCE: The mechanical properties of the aorta are influenced by the composition and organization of its extracellular matrix (ECM) and are highly relevant to medical conditions affecting the structural integrity of the aorta. The extent of contribution of glycosaminoglycans (GAG), a relatively minor ECM component, to the mechanical properties of the aorta, remains poorly characterized. This works shows that GAG contribute on average 30% to the opening angle (an indicator of circumferential residual stresses) of porcine aortas, and that GAG-depletion is associated with an increased radial compressive stiffness of the aorta. GAG-depletion was also associated with a loss of water content and compressive deformation in the inner layers of the aortic wall providing insight into potential mechanisms for their biomechanical role.

Intramural Distributions of GAGs and Collagen vs. Opening Angle of the Intact Porcine Aortic Wall.

The heterogeneity and contribution of collagen and elastin to residual stresses have been thoroughly studied, but more recently, glycosaminoglycans (GAGs) also emerged as potential regulators. In this study, the opening angle of aortic rings (an indicator of circumferential residual stresses) and the mural distributions of sulfated GAGs (sGAG), collagen, and elastin were quantified in the ascending, aortic arch and descending thoracic regions of 5- to 6-month-old pigs. The opening angle correlated positively with the aortic ring's mean radius and thickness, with good and moderate correlations respectively. The correlations between the sGAG, collagen, elastin, and collagen:sGAG ratio and the opening angle were evaluated to identify aortic compositional factors that could play roles in regulating circumferential residual stresses. The total collagen:sGAG ratio displayed the strongest correlation with the opening angle (r = - 0.715, p < 0.001), followed by the total sGAG content which demonstrated a good correlation (r = 0.623, p < 0.001). Additionally, the intramural gradients of collagen, sGAG and collagen:sGAG correlated moderately with the opening angle. We propose that, in addition to the individual role sGAG play through their content and intramural gradient, the interaction between collagen and sGAG should be considered when evaluating circumferential residual stresses in the aorta.

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.

Intramural Glycosaminoglycans Distribution vs. Residual Stress in Porcine Ascending Aorta: a Computational Study.

In this computational modelling work, we explored the mechanical roles that various glycosaminoglycans (GAGs) distributions may play in the porcine ascending aortic wall, by studying both the transmural residual stress as well as the opening angle in aortic ring samples. A finite element (FE) model was first constructed and validated against published data generated from rodent aortic rings. The FE model was then used to simulate the response of porcine ascending aortic rings with different GAG distributions prescribed through the wall of the aorta. The results indicated that a uniform GAG distribution within the aortic wall did not induce residual stresses, allowing the aortic ring to remain closed when subjected to a radial cut. By contrast, a heterogeneous GAG distribution led to the development of residual stresses which could be released by a radial cut, causing the ring to open. The residual stresses and opening angle were shown to be modulated by the GAG content, gradient, and the nature of the transmural distribution.

A Computational Study on Deformed Bioprosthetic Valve Geometries: Clinically Relevant Valve Performance Metrics.

Transcatheter aortic valves (TAV) are symmetrically designed, but they are often not deployed inside cylindrical conduits with circular cross-sectional areas. Many TAV patients have heavily calcified aortic valves, which often result in deformed prosthesis geometries after deployment. We investigated the effects of deformed valve annulus configurations on a surgical bioprosthetic valve as a model for TAV. We studied valve leaflet motions, stresses and strains, and analog hydrodynamic measures (using geometric methods), via finite element (FE) modeling. Two categories of annular deformations were created to approximate clinical observations: (1) noncircular annulus with valve area conserved, and (2) under-expansion (reduced area) compared to circular annulus. We found that under-expansion had more impact on increasing stenosis (with geometric orifice area metrics) than noncircularity, and that noncircularity had more impact on increasing regurgitation (with regurgitation orifice area metrics) than under-expansion. We found durability predictors (stress/strain) to be the highest in the commissure regions of noncircular configurations such as EllipMajor (noncircular and under-expansion areas). Other clinically relevant performance aspects such as leaflet kinematics and coaptation were also investigated with the noncircular configurations. This study provides a framework for choosing the most challenging TAV deformations for acute and long-term valve performance in the design and testing phase of device development.

Cam FAI and Smaller Neck Angles Increase Subchondral Bone Stresses During Squatting: A Finite Element Analysis.

BACKGROUND: Individuals with a cam deformity and a decreased (varus) femoral neck-shaft angle may be predisposed to symptomatic femoroacetabular impingement (FAI). However, it is unclear what combined effects the cam deformity and neck angle have on acetabular cartilage and subchondral bone stresses during an impinging squat motion. We therefore used finite element analysis to examine the combined effects of cam morphology and femoral neck-shaft angle on acetabular cartilage and subchondral bone stresses during squatting, examining the differences in stress characteristics between symptomatic and asymptomatic individuals with cam deformities and individuals without cam deformities and no hip pain. QUESTIONS/PURPOSES: Using finite element analysis in this population, we asked: (1) What are the differences in acetabular cartilage stresses? (2) What are the differences in subchondral bone stresses? (3) What are the effects of high and low femoral neck-shaft angles on these stresses? METHODS: Six male participants were included to represent three groups (symptomatic cam, asymptomatic cam, control without cam deformity) with two participants per group, one with the highest femoral neck-shaft angle and one with the lowest (that is, most valgus and most varus neck angles, respectively). Each participant's finite element hip models were reconstructed from imaging data and assigned subject-specific bone material properties. Hip contact forces during squatting were determined and applied to the finite element models to examine maximum shear stresses in the acetabular cartilage and subchondral bone. RESULTS: Both groups with cam deformities experienced higher subchondral bone stresses than cartilage stresses. Both groups with cam deformities also had higher subchondral bone stresses (symptomatic with high and low femoral neck-shaft angle = 14.1 and 15.8 MPa, respectively; asymptomatic with high and low femoral neck-shaft angle = 10.9 and 13.0 MPa, respectively) compared with the control subjects (high and low femoral neck-shaft angle = 6.4 and 6.5 MPa, respectively). The symptomatic and asymptomatic participants with low femoral neck-shaft angles had the highest cartilage and subchondral bone stresses in their respective subgroups. The asymptomatic participant with low femoral neck-shaft angle (123°) demonstrated anterolateral subchondral bone stresses (13.0 MPa), similar to the symptomatic group. The control group also showed no differences between cartilage and subchondral bone stresses. CONCLUSIONS: The resultant subchondral bone stresses modeled here coincide with findings that acetabular subchondral bone is denser in hips with cam lesions. Future laboratory studies will expand the parametric finite element analyses, varying these anatomic and subchondral bone stiffness parameters to better understand the contributions to the pathomechanism of FAI. CLINICAL RELEVANCE: Individuals with a cam deformity and more varus neck orientation may experience elevated subchondral bone stresses, which may increase the risks of early clinical signs and degenerative processes associated with FAI, whereas individuals with cam morphology and normal-to-higher femoral neck-shaft angles may be at lesser risk of disease progression that would potentially require surgical intervention.

Material characterization of cardiovascular biomaterials using an inverse finite-element method and an explicit solver.

The ability to accurately model soft tissue behavior, such as that of heart valve tissue, is essential for developing reliable numerical simulations and determining patient-specific care options. Although several material models can predict soft tissue behavior, complications may arise when these models are implemented into finite element (FE) programs, due to the addition of an arbitrary penalty parameter for numerically enforcing material incompressibility. Herein, an inverse methodology was developed in MATLAB to use previously published stress-strain data from experimental planar equibiaxial testing of five biomaterials used in heart valve cusp replacements, in conjunction with commercial explicit FE solver LS-DYNA, to optimize the material parameters and the penalty parameter for an anisotropic hyperelastic strain energy function. A two-parameter optimization involving the scaling constant of the strain energy function and the penalty parameter proved sufficient to produce acceptable material responses when compared with experimental behaviors under the same testing conditions, as long as analytically derived material constants were available for the other non-optimized parameters and the actual tissue thickness was not much less than 1 mm. Variations in the penalty parameter had a direct effect on the accuracy of the simulated responses, with a practical range determined to be 5×108-9×108 times the scaling constant of the strain energy function.

Investigation of raphe function in the bicuspid aortic valve and its influence on clinical criteria-A patient-specific finite element study.

The aortic valve is normally composed of 3 cusps. In one common lesion, 2 cusps are fused together. The conjoined area of the fused cusps is termed raphe. Occurring in 1% to 2% of the population, the bicuspid aortic valve (BAV) is the most common congenital cardiac malformation. The majority of BAV patients eventually require surgery. There is a lack in the literature regarding modeling of the raphe (geometry and material properties), its role and its influence on BAV function. The present study aims to propose improvements on these aspects. Three patient-specific finite element models of BAVs were created based on 3D trans-esophageal echocardiography measurements, and assuming age-dependent material properties. The raphe was initially given the same material properties as its underlying cusps. Two levels of validation were performed; one based on the anatomical validation of the pressurized geometry in diastole (involving 7 anatomical measures), as simulated starting from the unpressurized geometry, and the other based on a functional assessment using clinical measurements in both systole and diastole (involving 16 functional measures). The pathology was successfully reproduced in the FE models of all 3 patients. To further investigate the role of the raphe, 2 additional scenarios were considered; (1) the raphe was considered as almost rigid, (2) the raphe was totally removed. The results confirmed the interpretation of the raphe as added stiffness in the fused cusp's rotation with respect to the aortic wall, as well as added support for stress distribution from the fused cusps to the aortic wall.

UROKIN: A Software to Enhance Our Understanding of Urogenital Motion.

Transperineal ultrasound (TPUS) allows for objective quantification of mid-sagittal urogenital mechanics, yet current practice omits dynamic motion information in favor of analyzing only a rest and a peak motion frame. This work details the development of UROKIN, a semi-automated software which calculates kinematic curves of urogenital landmark motion. A proof of concept analysis, performed using UROKIN on TPUS video recorded from 20 women with and 10 women without stress urinary incontinence (SUI) performing maximum voluntary contraction of the pelvic floor muscles. The anorectal angle and bladder neck were tracked while the motion of the pubic symphysis was used to compensate for the error incurred by TPUS probe motion during imaging. Kinematic curves of landmark motion were generated for each video and curves were smoothed, time normalized, and averaged within groups. Kinematic data yielded by the UROKIN software showed statistically significant differences between women with and without SUI in terms of magnitude and timing characteristics of the kinematic curves depicting landmark motion. Results provide insight into the ways in which UROKIN may be useful to study differences in pelvic floor muscle contraction mechanics between women with and without SUI and other pelvic floor disorders. The UROKIN software improves on methods described in the literature and provides unique capacity to further our understanding of urogenital biomechanics.

Aortic Valve Cusp Coaptation Surface Area Using 3-Dimensional Transesophageal Echocardiography Correlates with Severity of Aortic Valve Insufficiency.

OBJECTIVE: The aim of this study was to test both in humans and using finite element (FE) aortic valve (AV) models whether the coaptation surface area (CoapSA) correlates with aortic insufficiency (AI) severity due to dilated aortic roots to determine the validity and utility of 3-dimensional transesophageal echocardiographic-measured CoapSA. DESIGN: Two-pronged, clinical and computational approach. SETTING: Single university hospital. PARTICIPANTS: The study comprised 10 patients with known AI and 98 FE simulations of increasingly dilated human aortic roots. INTERVENTIONS: The CoapSA was calculated using intraoperative 3-dimensional transesophageal echocardiography data of patients with isolated AI and compared with established quantifiers of AI. In addition, the CoapSA and effective regurgitant orifice area (EROA) were determined using FE simulations. MEASUREMENTS AND MAIN RESULTS: In the 10 AI patients, regurgitant fraction (RF) increased with EROA (R2 = 0.77, p = 0.0008); CoapSA decreased with RF (R2 = 0.72, p = 0.0020); CoapSA decreased with EROA (R2 = 0.71, p = 0.0021); and normalized CoapSA (CoapSA / [Ventriculo-Aortic Junction × Sinotubular Junction]) decreased with EROA (R2 = 0.60, p = 0.0088). In the 98 FE simulations, normalized CoapSA decreased with EROA (R2 = 0.50, p = 0.0001). CONCLUSIONS: In both human and FE AV models, CoapSA was observed to be inversely correlated with AI severity, EROA, and RF, thereby supporting the validity and utility of 3D TEE-measured CoapSA. A clinical implication is the expectation that high values of CoapSA, measured intraoperatively after AV repairs, would correlate with better long-term outcomes of those repairs.

Increased Hip Stresses Resulting From a Cam Deformity and Decreased Femoral Neck-Shaft Angle During Level Walking.

BACKGROUND: It is still unclear why many individuals with a cam morphology of the hip do not experience pain. It was recently reported that a decreased femoral neck-shaft angle may also be associated with hip symptoms. However, the effects that different femoral neck-shaft angles have on hip stresses in symptomatic and asymptomatic individuals with cam morphology remain unclear. QUESTIONS/PURPOSES: We examined the effects of the cam morphology and femoral neck-shaft angle on hip stresses during walking by asking: (1) Are there differences in hip stress characteristics among symptomatic patients with cam morphology, asymptomatic individuals with cam morphology, and individuals without cam morphology? (2) What are the effects of high and low femoral neck-shaft angles on hip stresses? METHODS: Six participants were selected, from a larger cohort, and their cam morphology and femoral neck-shaft angle parameters were measured from CT data. Two participants were included in one of three groups: (1) symptomatic with cam morphology; (2) asymptomatic with a cam morphology; and (3) asymptomatic control with no cam morphology with one participant having the highest femoral neck-shaft angle and the other participant having the lowest in each subgroup. Subject-specific finite element models were reconstructed and simulated during the stance phase, near pushoff, to examine maximum shear stresses on the acetabular cartilage and labrum. RESULTS: The symptomatic group with cam morphology indicated high peak stresses (6.3-9.5 MPa) compared with the asymptomatic (5.9-7.0 MPa) and control groups (3.8-4.0 MPa). Differences in femoral neck-shaft angle influenced both symptomatic and asymptomatic groups; participants with the lowest femoral neck-shaft angles had higher peak stresses in their respective subgroups. There were no differences among control models. CONCLUSIONS: Our study suggests that the hips of individuals with a cam morphology and varus femoral neck angle may be subjected to higher mechanical stresses than those with a normal femoral neck angle. CLINICAL RELEVANCE: Individuals with a cam morphology and decreased femoral neck-shaft angle are likely to experience severe hip stresses. Although asymptomatic participants with cam morphology had elevated stresses, a higher femoral neck-shaft angle was associated with lower stresses. Future research should examine larger amplitudes of motion to assess adverse subchondral bone stresses.

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.

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.

A metric for the stiffness of calcified aortic valves using a combined computational and experimental approach.

Calcific aortic valve disease is the most common heart valve disease. It is associated with a significant increase in cardiovascular morbidity and mortality and independently increases the cardiovascular risk. It is then important to develop parameters that can estimate the stiffness of the valve. Such parameters may contribute to early detection of the disease or track its progression and optimize the timing for therapy. In this study, we introduce a metric representing the stiffness of the native aortic calcified valve over a wide range of stenosis severities. Our approach is based on three-dimensional structural finite-element simulations and in vitro measurements. The proposed method is developed first in a pulse duplicator; its clinical applicability is then evaluated in three patients with severe aortic stenosis. Our results indicate that the value of the proposed metric varies considerably between healthy valves and valves with very severe aortic stenosis, from 0.001 to 7.38 MPa, respectively. The method introduced in this study could give useful information regarding the stiffness of the valve leaflets with potential application to the evaluation of aortic sclerosis and aortic stenosis.

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.

A mechanobiological investigation of platelets.

Understanding mechanotransduction pathways leading to thrombosis will require progressive steps, including determination of the mechanical behavior of the platelet membrane in response to applied loads. The platelet membrane deformation capacity, as quantified by membrane progression into a borosilicate glass micropipette of defined internal diameter, was probed in murine platelets using a controlled range of negative pressure (0-7 cm H(2)O). Based on our observations that the platelet portion outside the micropipette was mostly spherical and that the platelet volume did not change upon aspiration, a novel continuum mechanics-based model of the platelet micropipette aspiration experiment was created, and a new hyperelastic isotropic material model including membrane residual tension was proposed for the platelet membrane. Murine platelet membranes maintained an average linear deformation behavior: L (p)/R (p) = 146,100p (i) × R (p) + 19.923, where L (p) is the platelet length aspirated in the micropipette (m), R (p) is micropipette radius (m) and p (i) is the aspiration pressure (Pa). The theoretical model was used to generate material constants for the murine platelet membrane that allowed for an accurate simulation of the micropipette aspiration experiments. From published results, another set of material constants was established for the human platelet membrane. Limited cases of platelet lysis upon aspiration were analyzed using the theoretical model to determine preliminary membrane tension strength values.

Usefulness and limitations of computational models in aortic disease risk stratification.

OBJECTIVE: In risk stratification of aortic diseases such as aneurysm and aortic dissection, diameter is one parameter whose influence on the average aortic wall stress is directly described by the Laplace law. More advanced mechanical models can be used and may yield additional information, such as transmural stress distributions. The question then arises of how refined models need to be to provide clinicians with practical help. METHODS: Two sets of finite element models were used. The relative roles of diameter, material stiffness, longitudinal stretch, blood pressure, wall thickness, and vessel curvature were explored using simplified aortic models for comparison with the Laplace law. The influences of the material properties nonlinearity and residual stress on the transmural stress distribution were investigated using an advanced aortic model including recent experimental findings in older humans. RESULTS: The Laplace law was confirmed as one effective, basic tool to assess the average wall stress in the aortic wall, both in the circumferential and longitudinal directions. However, the simplified models were sufficient to show that, as already reported in the literature, longitudinal stretch and vessel curvature have potentially equally strong or even stronger contributions to wall stress than the parameters included in the Laplace law. When the advanced model was used, and residual stress induced by large opening angles such as found in older subjects was introduced, the transmural stress gradient was found inverted compared with expectations, with the largest stresses now toward the adventitia. The results suggested that the intima may be increasingly shielded from higher stresses as one gets older, which might be protective against the initiation of dissection tears in the thoracic aorta. CONCLUSION: Biomechanical analysis of the aorta may be refined by using increasingly detailed computational models. Simplified models can readily improve on the Laplace law in the assessment of aortic wall stress, and as such, may already contribute to better risk stratification of aortic disease. Advanced models may also enhance our understanding of the mechanistic aspects in the pathogenesis of aortic disease. However, their applicability in a patient-specific context may be limited by the large number of input data they require, some of which might stay out of the clinicians' reach.

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.