Prediction of extracellular matrix stiffness in engineered heart valve tissues based on nonwoven scaffolds

The in vitro development of tissue engineered heart valves (TEHV) exhibiting appropriate structural and mechanical characteristics remains a significant challenge. An important step yet to be addressed is establishing the relationship between scaffold and extracellular matrix (ECM) mechanical properties. In the present study, a composite beam model accounting for nonwoven scaffold-ECM coupling and the transmural collagen concentration distribution was developed, and utilized to retrospectively estimate the ECM effective stiffness in TEHV specimens incubated under static and cyclic flexure conditions (Engelmayr Jr et~al. in Biomaterials 26(2):175-187 2005). The ECM effective stiffness was expressed as the product of the local collagen concentration and the collagen specific stiffness (i.e., stiffness/concentration), and was related to the overall TEHV effective stiffness via an empirically determined scaffold-ECM coupling parameter and measured transmural collagen concentration distributions. The scaffold-ECM coupling parameter was determined by flexural mechanical testing of polyacrylamide gels (i.e., ECM analogs) of variable stiffness and associated scaffold-polyacrylamide gel composites (i.e., engineered tissue analogs). The transmural collagen concentration distributions were quantified from fluorescence micrographs of picro-sirius red stained TEHV sections. As suggested by a previous structural model of the nonwoven scaffold (Engelmayr Jr and Sacks in J Biomech Eng 128(4):610-622, 2006), nonwoven scaffold-ECM composites did not follow a traditional rule of mixtures. The present study provided further evidence that the primary mode of reinforcement in nonwoven scaffold-ECM composites is an increase in the number fiber-fiber bonds with a concomitant increase in the effective stiffness of the spring-like fiber segments. Simulations of potential ECM deposition scenarios using the current model indicated that the present approach is sensitive to the specific time course of tissue deposition, and is thus very suitable for studies of ECM formation in engineered heart valve tissues.     

Virtualisation of stress distribution in heart valve tissue

This study presents an image-based finite element analysis incorporating histological photomicrographs of heart valve tissues. We report stress fields inside heart valve tissues, where heterogeneously distributed collagen fibres are responsible for transmitting forces into cells. Linear isotropic and anisotropic tissue material property models are incorporated to quantify the overall stress distributions in heart valve tissues. By establishing an effective predictive method with new computational tools and by performing virtual experiments on the heart valve tissue photomicrographs, we clarify how stresses are transferred from matrix to cell. The results clearly reveal the roles of heterogeneously distributed collagen fibres in mitigating stress developments inside heart valve tissues. Moreover, most local peak stresses occur around cell nuclei, suggesting that higher stress may be mediated by cells for biomechanical regulations.     

Structural effects of an innovative surgical technique to repair heart valve defects

The structural and functional effects of the “edge-to-edge” technique on the human mitral valve have been investigated, paying particular attention to the diastolic phase. An advanced finite element model of the valve has been developed, using a hyperelastic material schematization, suitable geometry and constraint conditions, and an effective fluidodynamic analysis. The edge-to-edge suture has been applied on this model and the diastolic phase has been simulated. The results of this calculation show that the operation increases the transvalvular pressure and the maximum stress in the leaflets, which reaches a level similar to that of the systolic phase. The influence of suture position and extension, and the mitral annulus dimension has also been investigated. The results indicate that a lateral location of the stitch is better than a central one, both regarding valve functionality (pressure level and mobility) and internal stresses level, that a longer suture worsens the valve functionality but reduces the stresses level, finally, that the dilatation of the mitral annulus does not affect the valve functionality but increases the stresses level.     

Cell-mediated retraction versus hemodynamic loading – A delicate balance in tissue-engineered heart valves

Preclinical studies of tissue-engineered heart valves (TEHVs) showed retraction of the heart valve leaflets as major failure of function mechanism. This retraction is caused by both passive and active cell stress and passive matrix stress. Cell-mediated retraction induces leaflet shortening that may be counteracted by the hemodynamic loading of the leaflets during diastole. To get insight into this stress balance, the amount and duration of stress generation in engineered heart valve tissue and the stress imposed by physiological hemodynamic loading are quantified via an experimental and a computational approach, respectively.     

Straightening of curved pattern of collagen fibers under load controls aortic valve shape

The network of collagen fibers in the aortic valve leaflet is believed to play an important role in the strength and durability of the valve. However, in addition to its stress-bearing role, such a fiber network has the potential to produce functionally important shape changes in the closed valve under pressure load. We measured the average pattern of the collagen network in porcine aortic valve leaflets after staining for collagen. We then used finite element simulation to explore how this collagen pattern influences the shape of the closed valve. We observed a curved or bent pattern, with collagen fibers angled downward from the commissures toward the center of the leaflet to form a pattern that is concave toward the leaflet free edge. Simulations showed that these curved fiber trajectories straighten under pressure load, leading to functionally important changes in closed valve shape. Relative to a pattern of straight collagen fibers running parallel to the leaflet free edge, the concave pattern of curved fibers produces a closed valve with a 40% increase in central leaflet coaptation height and with decreased leaflet billow, resulting in a more physiological closed valve shape. Furthermore, simulations show that these changes in loaded leaflet shape reflect changes in leaflet curvature due to modulation of in-plane membrane stress resulting from straightening of the curved fibers. This effect appears to play an important role in normal valve function and may have important implications for the design of prosthetic and tissue engineered replacement valves.     

Stress–strain behavior of mitral valve leaflets in the beating ovine heart

Excised anterior mitral leaflets exhibit anisotropic, non-linear material behavior with pre-transitional stiffness ranging from 0.06 to 0.09 N/mm² and post-transitional stiffness from 2 to 9 N/mm². We used inverse finite element (FE) analysis to test, for the first time, whether the anterior mitral leaflet (AML), in vivo, exhibits similar non-linear behavior during isovolumic relaxation (IVR). Miniature radiopaque markers were sewn to the mitral annulus, AML, and papillary muscles in 8 sheep. Four-dimensional marker coordinates were obtained using biplane videofluoroscopic imaging during three consecutive cardiac cycles. A FE model of the AML was developed using marker coordinates at the end of isovolumic relaxation (when pressure difference across the valve is approximately zero), as the reference state. AML displacements were simulated during IVR using measured left ventricular and atrial pressures. AML elastic moduli in the radial and circumferential directions were obtained for each heartbeat by inverse FEA, minimizing the difference between simulated and measured displacements. Stress–strain curves for each beat were obtained from the FE model at incrementally increasing transmitral pressure intervals during IVR. Linear regression of 24 individual stress–strain curves (8 hearts, 3 beats each) yielded a mean (±SD) linear correlation coefficient (r²) of 0.994±0.003 for the circumferential direction and 0.995±0.003 for the radial direction. Thus, unlike isolated leaflets, the AML, in vivo, operates linearly over a physiologic range of pressures in the closed mitral valve.     

The effects of stent interaction on porcine urinary bladder matrix employed as stent-graft materials

Deployment of stent-grafts, derived from synthetic biomaterials, is an established minimally invasive approach for effectively treating abdominal aortic aneurysms (AAAs). However, a notable disadvantage associated with this surgical technique is migration of the deployed stent-graft due to poor biocompatibility and inadequate integration in vivo. Recently, tissue-engineered extracellular matrices (ECMs) have shown early promise as integrating stabilisation collars in this setting due to their ability to induce a constructive tissue remodelling response after in vivo implantation. In the present study the effects of stent loading on an ECM?s mechanical properties were investigated by characterising the compression and loading effects of endovascular stents on porcine urinary bladder matrix (UBM) scaffolds. Results demonstrated that the maximum stress was induced when the stent force was 8-times higher than a standard commercially available stent-graft and this represented about 20% of the failure strength of the UBM material. In addition, the influence of stent shape was also investigated. Findings demonstrated that the stress induced was higher for circular stents at low forces and a higher stress was induced on square stents when increased force was applied. Our findings demonstrate that porcine UBM possesses sufficient mechanical strength to withstand the compression and loading effects of commercially available stent-grafts in the setting of endovascular aneurysm repair.     

深龋修复的力学模型分析

目的:模拟下颌第一磨牙Ⅰ类洞深龋,计算机分析得到修复体最佳应力分布时基底材料与修复材料厚度比例。方法 采用三维有限元法建立数值模型,利用SAP84(V4.2)程序计算并作力学分析。结果:在能护髓前提下应尽量减少次基厚度(1)银汞修复时,银汞合金厚度应大于基底厚度时应力分布最佳。(2)树脂修复时,树脂厚度与基底厚度相近,应力分布最佳。结论 根据材料弹性模量来决定基底材料与修复材料厚度比例。     

Effect of screw position on load transfer in lumbar pedicle screws: a non-idealized finite element analysis

Angled screw insertion has been advocated to enhance fixation strength during posterior spine fixation. Stresses on a pedicle screw and surrounding vertebral bone with different screw angles were studied by finite element analysis during simulated multidirectional loading. Correlations between screw-specific vertebral geometric parameters and stresses were studied. Angulations in both the sagittal and axial planes affected stresses on the cortical and cancellous bones and the screw. Pedicle screws pointing laterally (vs. straight or medially) in the axial plane during superior screw angulation may be advantageous in terms of reducing the risk of both screw loosening and screw breakage.     

A computational model for collagen fibre remodelling in the arterial wall

As the interaction between tissue adaptation and the mechanical condition within tissues is complex, mathematical models are desired to study this interrelation. In this study, a mathematical model is presented to investigate the interplay between collagen architecture and mechanical loading conditions in the arterial wall. It is assumed that the collagen fibres align along preferred directions, situated in between the principal stretch directions. The predicted fibre directions represent symmetrically arranged helices and agree qualitatively with morphometric data from literature. At the luminal side of the arterial wall, the fibres are oriented more circumferentially than at the outer side. The discrete transition of the fibre orientation at the media-adventitia interface can be explained by accounting for the different reference configurations of both layers. The predicted pressure-radius relations resemble experimentally measured sigma-shaped curves. As there is a strong coupling between the collagen architecture and the mechanical loading condition within the tissue, we expect that the presented model for collagen remodelling is useful to gain further insight into the processes involved in vascular adaptation, such as growth and smooth muscle tone adaptation.     

How plate positioning impacts the biomechanics of the open wedge tibial osteotomy; A finite element analysis

A numerical model of the medial open wedge tibial osteotomy based on the finite element method was developed. Two plate positions were tested numerically. In a configuration, (a), the plate was fixed in a medial position and (b) in an anteromedial position. The simulation took into account soft tissues preload, muscular tonus and maximal gait load.

The maximal stresses observed in the four structural elements (bone, plate, wedge, screws) of an osteotomy with plate in medial position were substantially higher (1.13–2.8 times more) than those observed in osteotomy with an anteromedial plate configuration. An important increase (1.71 times more) of the relative micromotions between the wedge and the bone was also observed. In order to avoid formation of fibrous tissue at the bone wedge interface, the osteotomy should be loaded under 18.8% (～50 kg) of the normal gait load until the osteotomy interfaces union is achieved.     

A novel methodology for generating 3D finite element models of the hip from 2D radiographs

Finite element (FE) modelling has been proposed as a tool for estimating fracture risk and patient-specific FE models are commonly based on computed tomography (CT). Here, we present a novel method to automatically create personalised 3D models from standard 2D hip radiographs. A set of geometrical parameters of the femur were determined from seven a–p hip radiographs and compared to the 3D femoral shape obtained from CT as training material; the error in reconstructing the 3D model from the 2D radiographs was assessed. Using the geometry parameters as the input, the 3D shape of another 21 femora was built and meshed, separating a cortical and trabecular compartment. The material properties were derived from the homogeneity index assessed by texture analysis of the radiographs, with focus on the principal tensile and compressive trabecular systems. The ability of these FE models to predict failure load as determined by experimental biomechanical testing was evaluated and compared to the predictive ability of DXA. The average reconstruction error of the 3D models was 1.77 mm (±1.17 mm), with the error being smallest in the femoral head and neck, and greatest in the trochanter. The correlation of the FE predicted failure load with the experimental failure load was r²=64% for the reconstruction FE model, which was significantly better (p<0.05) than that for DXA (r²=24%). This novel method for automatically constructing a patient-specific 3D finite element model from standard 2D radiographs shows encouraging results in estimating patient-specific failure loads.     

单端固定式下颌骨修复体的应力分析

目的：针对包括一侧髁状突的下颌骨缺损,通过有限元应力分析,了解单端固定式下颌骨修复体在功能运动时的受力与变形规律,以期寻求更加合理的修复体的设计和固定方式。方法：建立下颌骨断端和修复体的简易三维模型,模拟咀嚼运动,施加垂直方向载荷,进行有限元法应力分析,计算出该模型各组成部分的应力分布和受力变形。结果：在该模型加载时,延伸板基部和近断端处上部的螺钉颈部是应力集中的部位,近断端处下部的螺钉颈部和修复体的远端舌侧为形变最大的部位。结论：单端固定式下颌骨修复体在加载时,延伸板的基部和靠近断端的固定螺钉是应力集中的部位,修复体远离固定的一侧是变形最大的部位,提示我们应将延伸板形态设计为尽可能加宽,并应增加下颌骨下缘处的固定,使修复体与下颌骨断端受力更加合理,变形也尽可能缩小。     

Simulation of planar soft tissues using a structural constitutive model: Finite element implementation and validation

Computational implementation of physical and physiologically realistic constitutive models is critical for numerical simulation of soft biological tissues in a variety of biomedical applications. It is well established that the highly nonlinear and anisotropic mechanical behaviors of soft tissues are an emergent behavior of the underlying tissue microstructure. In the present study, we have implemented a structural constitutive model into a finite element framework specialized for membrane tissues. We noted that starting with a single element subjected to uniaxial tension, the non-fibrous tissue matrix must be present to prevent unrealistic tissue deformations. Flexural simulations were used to set the non-fibrous matrix modulus because fibers have little effects on tissue deformation under three-point bending. Multiple deformation modes were simulated, including strip biaxial, planar biaxial with two attachment methods, and membrane inflation. Detailed comparisons with experimental data were undertaken to insure faithful simulations of both the macro-level stress–strain insights into adaptations of the fiber architecture under stress, such as fiber reorientation and fiber recruitment. Results indicated a high degree of fidelity and demonstrated interesting microstructural adaptions to stress and the important role of the underlying tissue matrix. Moreover, we apparently resolve a discrepancy in our 1997 study (Billiar and Sacks, 1997. J. Biomech. 30 (7), 753–756) where we observed that under strip biaxial stretch the simulated fiber splay responses were not in good agreement with the experimental results, suggesting non-affine deformations may have occurred. However, by correctly accounting for the isotropic phase of the measured fiber splay, good agreement was obtained. While not the final word, these simulations suggest that affine fiber kinematics for planar collagenous tissues is a reasonable assumption at the macro level. Simulation tools such as these are imperative in the design and simulation of native and engineered tissues.     

Pharmacological consequences of oxidative stress in ocular tissues

The eye is a unique organ because of its constant exposure to radiation, atmospheric oxygen, environmental chemicals and physical abrasion. That oxidative stress mechanisms in ocular tissues have been hypothesized to play a role in diseases such as glaucoma, cataract, uveitis, retrolental fibroplasias, age-related macular degeneration and various forms of retinopathy provides an opportunity for new approaches to their prevention and treatment, In the anterior uvea, both H₂O₂ and synthetic peroxides exert pharmacological/toxicological actions tissues of the anterior uvea especially on the sympathetic nerves and smooth muscles of the iris–ciliary bodies of several mammalian species. Effects produced by peroxides require the presence of trace amounts of extracellular calcium and the functional integrity of mitochondrial calcium stores. Arachidonic acid metabolites appear to be involved in both the excitatory action of peroxides on sympathetic neurotransmission and their inhibitory effect on contractility of the iris smooth muscle to muscarinic receptor activation. In addition to the peroxides, isoprostanes (products of free radical catalyzed peroxidation of arachidonic acid independent of the cyclo-oxygenase enzyme) can also alter sympathetic neurotransmission in anterior uveal tissues. In the retina, both H₂O₂ and synthetic peroxides produced an inhibitory action on potassium depolarization induced release of [³H] d-aspartate, in vitro and on the endogenous glutamate and glycine concentrations in vivo. Effects caused by peroxides in the retina are mediated, at least in part, by second messengers such as nitric oxide, prostaglandins and isoprostanes. The ability of H₂O₂ to alter the integrity of neurotransmitter pools from sympathetic nerves in the anterior uvea and glutaminergic nerves in the retina could underlie its role in the etiology of glaucoma.     

单端固定式下颌骨修复体的应力分析

目的:针对包括一侧髁状突的下颌骨缺损,通过有限元应力分析,了解单端固定式下颌骨修复体在功能运动时的受力与变形规律,以期寻求更加合理的修复体的设计和固定方式。方法:建立下颌骨断端和修复体的简易三维模型,模拟咀嚼运动,施加垂直方向载荷,进行有限元法应力分析,计算出该模型各组成部分的应力分布和受力变形。结果:在该模型加载时,延伸板基部和近断端处上部的螺钉颈部是应力集中的部位,近断端处下部的螺钉颈部和修复体的远端舌侧为形变最大的部位。结论:单端固定式下颌骨修复体在加载时,延伸板的基部和靠近断端的固定螺钉是应力集中的部位,修复体远离固定的一侧是变形最大的部位,提示我们应将延伸板形态设计为尽可能加宽,并应增加下颌骨下缘处的固定,使修复体与下颌骨断端受力更加合理,变形也尽可能缩小。     

An inverse modeling approach for stress estimation in mitral valve anterior leaflet valvuloplasty for in-vivo valvular biomaterial assessment

Estimation of regional tissue stresses in the functioning heart valve remains an important goal in our understanding of normal valve function and in developing novel engineered tissue strategies for valvular repair and replacement. Methods to accurately estimate regional tissue stresses are thus needed for this purpose, and in particular to develop accurate, statistically informed means to validate computational models of valve function. Moreover, there exists no currently accepted method to evaluate engineered heart valve tissues and replacement heart valve biomaterials undergoing valvular stresses in blood contact. While we have utilized mitral valve anterior leaflet valvuloplasty as an experimental approach to address this limitation, robust computational techniques to estimate implant stresses are required. In the present study, we developed a novel numerical analysis approach for estimation of the in-vivo stresses of the central region of the mitral valve anterior leaflet (MVAL) delimited by a sonocrystal transducer array. The in-vivo material properties of the MVAL were simulated using an inverse FE modeling approach based on three pseudo-hyperelastic constitutive models: the neo-Hookean, exponential-type isotropic, and full collagen–fiber mapped transversely isotropic models. A series of numerical replications with varying structural configurations were developed by incorporating measured statistical variations in MVAL local preferred fiber directions and fiber splay. These model replications were then used to investigate how known variations in the valve tissue microstructure influence the estimated ROI stresses and its variation at each time point during a cardiac cycle. Simulations were also able to include estimates of the variation in tissue stresses for an individual specimen dataset over the cardiac cycle. Of the three material models, the transversely anisotropic model produced the most accurate results, with ROI averaged stresses at the fully-loaded state of  432.6±46.5 kPa and 241.4±40.5 kPa in the radial and circumferential directions, respectively. We conclude that the present approach can provide robust instantaneous mean and variation estimates of tissue stresses of the central regions of the MVAL.     

A Gauss-Kronrod-Trapezoidal integration scheme for modeling biological tissues with continuous fiber distributions

Fibrous biological tissues may be modeled using a continuous fiber distribution (CFD) to capture tension–compression nonlinearity, anisotropic fiber distributions, and load-induced anisotropy. The CFD framework requires spherical integration of weighted individual fiber responses, with fibers contributing to the stress response only when they are in tension. The common method for performing this integration employs the discretization of the unit sphere into a polyhedron with nearly uniform triangular faces (finite element integration or FEI scheme). Although FEI has proven to be more accurate and efficient than integration using spherical coordinates, it presents three major drawbacks: First, the number of elements on the unit sphere needed to achieve satisfactory accuracy becomes a significant computational cost in a finite element (FE) analysis. Second, fibers may not be in tension in some regions on the unit sphere, where the integration becomes a waste. Third, if tensed fiber bundles span a small region compared to the area of the elements on the sphere, a significant discretization error arises. This study presents an integration scheme specialized to the CFD framework, which significantly mitigates the first drawback of the FEI scheme, while eliminating the second and third completely. Here, integration is performed only over the regions of the unit sphere where fibers are in tension. Gauss–Kronrod quadrature is used across latitudes and the trapezoidal scheme across longitudes. Over a wide range of strain states, fiber material properties, and fiber angular distributions, results demonstrate that this new scheme always outperforms FEI, sometimes by orders of magnitude in the number of computational steps and relative accuracy of the stress calculation.