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In this study, we aimed to develop an in-silico synthesis of the effect of critical surgical design parameters on articular contact behavior for a bone-patellar-tendon-bone anterior cruciate ligament reconstruction (ACL-R) surgery. A previously developed finite element model of the knee joint consisting of all relevant soft tissues was employed. The knee model was further updated with additional features to develop the parametric FE model of the biomechanical experiments that depicted the ACL-R surgery. The parametricity was created involving femoral tunnel architecture (orientations and locations) and graft fixation characteristics (pretension and angle of fixation). A global sensitivity analysis based on variance decomposition was used to investigate the contribution of the surgical parameters to the uncertainty in response to the ACL-R joint. Our examinations indicated that the total contact force was primarily influenced by either combined or individual action of the graft pretension and fixation angle, with a modest contribution of the graft insertion sites. The joint contact center and area were affected mainly by the angle of fixation and the tunnel placements. Graft pretension played the dominant role in the maximum contact pressure variability, an observation that has been well-documented in the literature. Interestingly, the joint contact behavior was almost insensitive to the tunnel's coronal and sagittal orientations. Our data provide an evaluation of how the surgical parameters affect the knee joint's contact behavior after ACL-R and may provide additional information to better explain the occurrence of osteoarthritis as an aftermath of such surgery.

A characteristic feature of arthritic diseases is cartilage extracellular matrix (ECM) degradation, often orchestrated by the overexpression of matrix metalloproteinases (MMPs) and other proteases. The interplay between fibril level degradation and the tissue-level aggregate response to biomechanical loading was explored in this work by a computational multiscale cartilaginous model. We considered the relative abundance of collagenases (MMP-1) and gelatinases (MMP-9) in surrogate models, where the diffusion (spatial distribution) of these enzymes and the subsequent, co-localized fibrillar damage were spatially randomized with Latin Hypercube Sampling. The computational model was constructed by incorporating the results from prior molecular dynamics simulations (tensile test) of microfibril degradation into a hyper-elastoplastic fibril-reinforced cartilage model. Including MMPs-mediated collagen fibril-level degradation in computational models may help understand the ECM pathomechanics at the tissue level. The mechanics of cartilage tissue and fibril show variations in mechanical integrity depending on the different combinations of MMPs-1 and 9 with a concentration ratio of 1:1, 3:1, and 1:3 in simulated indentation tests. The fibril yield (local failure) was initiated at 20.2 ± 3.0 (%) and at 23.0 ± 2.8 (%) of bulk strain for col 1:gel 3 and col 3: gel 1, respectively. The reduction in failure stress (global response) was 39.8% for col 1:gel 3, 37.5% for col 1:gel 1, and 36.7% for col 3:gel 1 compared with the failure stress of the degradation free tissue. These findings indicate that cartilage's global and local mechanisms of failure largely depend on the relative abundance of the two key enzymes-collagenase (MMP-1) and gelatinase (MMP-9) and the spatial characteristics of diffusion across the layers of the cartilage ECM.

Matrix metalloproteinases (MMPs) degrade the extracellular matrix (ECM) subsequently damaging cartilage and altering biomechanical properties. Collectively, MMPs cleave every ECM macromolecule. However, MMPs present complex substrate interactions and digest differing ECM components making it difficult to understand the individual role each MMP plays in cartilage degradation. To understand the combined impact MMPs have on cartilage biomechanical properties, MMPs from two subfamilies: collagenase and gelatinase were investigated. Three ratios of MMP-1 (c) and MMP-9 (g), c1:g1, c1:g0 and c0:g1 were considered. Cartilage plugs (n = 30) were collected from the femoral condyles of 3 bovine stifle joints. In groups of 10, samples were treated with MMP-1, MMP-9, or a combination. Samples were subjected to indentation loading up to 20% bulk strain and were assessed mechanically and histologically to determine the degradative impact. Young's modulus and peak load were compared between the control and degraded explants. In comparison to samples degraded by MMP-1 or MMP-9 individually, cartilage degraded with both enzymes resulted in a 9-15% greater reduction in stiffness and peak load. Individually, MMP-1 and MMP-9 have a minimum effect on cartilage micromechanical properties, but synergistically the two enzymes digest ECM components and a much greater degradative effect is observed.

Matrix metalloproteinases (MMPs) play a crucial role in enzymatically digesting cartilage extracellular matrix (ECM) components, resulting in degraded cartilage with altered mechanical loading capacity. Overexpression of MMPs is often caused by trauma, physiologic conditions and by disease. To understand the synergistic impact MMPs have on cartilage biomechanical properties, MMPs from two subfamilies: collagenase (MMP-1) and gelatinase (MMP-9) were investigated in this study. Three different ratios of MMP-1 (c) and MMP-9 (g), c1:g1, c3:g1 and c1:g3 were considered to develop a degradation model. Thirty samples, harvested from bovine femoral condyles, were treated in groups of 10 with one concentration of enzyme mixture. Each sample was tested in a healthy state prior to introducing degradative enzymes to establish a baseline. Samples were subjected to indentation loading up to 20% bulk strain. Both control and treated samples were mechanically and histologically assessed to determine the impact of degradation. Young’s modulus and peak load of the tissue under indentation were compared between the control and degraded cartilage explants. Cartilage degraded with the c3:g1 enzyme concentration resulted in maximum 33% reduction in stiffness and peak load compared to the other two concentrations. The abundance of collagenase is more responsible for cartilage degradation and reduced mechanical integrity.

The pathogenesis and pathophysiological underpinnings of cartilage degradation are not well understood. Either mechanically or enzymatically mediated degeneration at the fibril level can lead to acute focal injuries that will, overtime, cause significant cartilage degradation. Understanding the relationship between external loading and the basic molecular structure of cartilage requires establishing a connection between the fibril-level defects and its aggregate effect on cartilage. In this work, we provide a multiscale constitutive model of cartilage to elucidate the effect of two plausible fibril degradation mechanisms on the aggregate tissue: tropocollagen crosslink failure (β) and a generalized surface degradation (δ). Using our model, the mechanics of aggregate tissue shows differed yield stress and post-yield behavior after crosslink failure and surface degradation compared to intact cartilage, and the tissue-level aggregate behaviors are different from the fibrillar behaviors observed in the molecular dynamics simulations. We also compared the effect of fibrillar defects in terms of crosslink failure and surface degradation in different layers of cartilage within the macroscale tissue construct during a simulated nanoindentation test. Although the mechanical properties of cartilage tissue were largely contingent upon the mechanical properties of the fibril, the macroscale mechanics of cartilage tissue showed ~ 10% variation in yield strain (tissue yield strain: ~ 27 to ~ 37%) compared to fibrillar yield strain (fibrillar yield strain: ~ 16 to ~ 26%) for crosslink failure and ~ 7% difference for the surface degradation (yield strain variations at the tissue: ~ 30 to ~ 37% and fibril: ~ 24 to ~ 26%) at the superficial layer. The yield strain was further delayed in middle layers at least up to 30% irrespective of the failure mechanisms. The cartilage tissue appeared to withstand more strain than the fibrils. The degeneration mechanisms of fibril differentially influenced the aggregate mechanics of cartilage, and the deviation may be attributed to fiber-matrix interplay, depth-dependent fiber orientation and fibrillar defects with different degradation mechanisms. The understanding of the aggregate stress-strain behavior of cartilage tissue, cartilage degradation and its underlying biomechanical factors is important for developing engineering approaches and therapeutic interventions for cartilage pathologies.

An accurate assessment of hip fracture risk requires a proper consideration of parameters affecting the fracture. In general, hip fracture is assessed based on bone mineral density (BMD) and load amount, but hip fracture is an outcome of the interaction of the parameters such as loading directions, bone density, which are often disregarded. Assessing the effect of the parameters individually may not correctly reflect the root cause of the hip fracture. Hence, this research aims at analyzing the significance of parameters and their interaction in assessing the fracture risk. A multiple regression analysis has been conducted considering bone density (ρash), different loading directions during sideways fall, represented by load angle (α) about femoral shaft on the coronal plane and angle (β) about femoral neck (FN) axis on the transverse plane as independent parameters and fracture risk index (FRI) as a dependent parameter. The statistical results showing the significant value of 0.7321 for α, and 0.0001 for β and ρash indicate that the effect of loading direction (α) does not have impact on fracture risk in comparison with the loading direction (β) and ρash. Furthermore, the analysis of the interaction of parameters shows that the impact of β on fracture risk may depends more on bone density.

An accurate assessment of hip fracture risk requires a proper consideration of parameters affecting the fracture. In general, hip fracture is affected by bone morphology, bone mineral Density (BMD), and load amount. Hip fracture is an outcome of the interaction of all those parameters including loading directions. Assessing the effect of the parameters individually may not correctly reflect the root cause of the hip fracture. Hence, this research aims at analyzing the significance of parameters and their interaction. A multivariate regression model was used considering bone density (ρash), different loading directions during sideways fall, represented by load angle (α) on the coronal plane and angle (β) on the transverse plane as independent parameters and Fracture Risk Index (FRI) as a dependent parameter. The statistical results showing the significant value of 0.7321 for α, and 0.0001 for β and ρash indicates that the effect of loading direction about femoral shaft on the coronal plane (α) does not have impact on fracture risk while loading direction about femoral neck axis on the transverse plane (β) and ρash have the significant impact. Furthermore, the analysis of the interaction of parameters shows that the impact of β on fracture risk may depends more on bone density as the significance of interaction of β and ρash is 0.0001.

Inspired by the nature, this study analyzes in-plane compressive responses of different modes of hierarchical architected structures with varying topologies. Architected cellular structures with two different unit cell topologies — square and kagome are considered, both having a relative density of 0.25. Each unit cell topology is designed with three different configurations. The base structure is the primitive one with solid homogeneous cell wall. The nested hierarchical structure is derived from the primitive one with cellular structuring in the cell wall. The third and final one is the fractal-like hierarchical structure, where same unit cells appear on different length scales. 3D printed structures were subjected to uniaxial compression to characterize their in-plane mechanical properties. The compressive stress-strain behaviors reveal that all the structures demonstrate the classical behavior of cellular structures followed by significant recovery of their initial shape upon load withdrawal. The energy absorptions demonstrated by the plateau regions before densification are not only governed by their structural topologies, but also largely governed by the configurations of hierarchical organizations. Hence, this study suggests the application specific design of hierarchical architected structures for defined loading conditions.

The biomechanical function of connective tissues in a knee joint is to stabilize the kinematics-kinetics of the joint by augmenting its stiffness and limiting excessive coupled motion. The connective tissues are characterized by an in vivo reference configuration (in situ strain) that would significantly contribute to the mechanical response of the knee joint. In this work, a novel iterative method for computing the in situ strain at reference configuration was presented. The framework used an in situ strain gradient approach (deformed reference configuration) and a detailed finite element (FE) model of the knee joint. The effect of the predicted initial configuration on the mechanical response of the joint was then investigated under joint axial compression, passive flexion, and coupled rotations (adduction and internal), and during the stance phase of gait. The inclusion of the reference configuration has a minimal effect on the knee joint mechanics under axial compression, passive flexion, and at two instances (0% and 50%) of the stance phase of gait. However, the presence of the ligaments in situ strains significantly increased the joint stiffness under passive adduction and internal rotations, as well as during the other simulated instances (25%, 75% and 100%) of the stance phase of gait. Also, these parameters substantially altered the local loading state of the ligaments and resulted in better agreement with the literature during joint flexion. Therefore, the proposed computational framework of ligament in situ strain will help to overcome the challenges in considering this crucial biological aspect during knee joint modeling. Besides, the current construct is advantageous for a better understanding of the mechanical behavior of knee ligaments under physiological and pathological states and provide relevant information in the design of reconstructive treatments and artificial grafts.

Plant petioles and stems are hierarchical structures comprising cellular tissues in one or more intermediate hierarchies displaying quasi random to heterogeneous cellularity that governs the overall structural properties. Exact replication of natural cellular tissue leads to the investigation of mechanical properties at the microstructural level. However, the micrographs often display artifacts due to experimental procedure and prevent representative spatial modeling of the tissues. Existing methods such as local thresholding or global thresholding (Otsu’s method) fail to effectively remove the artifacts. Hence, an efficient algorithm is required that can effectively help to reconstruct the geometric models of tissue microstructures by removing the noise. In this work, perception-based thresholding that conceptually works like human brain in differentiating noise from the actual ones based on color is introduced to remove discrete (within a cell) or adjacent (to the cell boundaries) noise. A variety of image dataset of non-woody plant tissues were tested with the algorithm, and its effectiveness in eliminating noise was quantitatively compared with existing noise removal techniques by Bivariate Similarity Index. The bivariate metrics indicate an enhanced performance of the perception-based thresholding over other considered algorithms.

Knee articular cartilage is characterized by a complex mechanical behavior, posing a challenge to develop an efficient and precise model. We argue that the cartilage damage, in general, can be traced to the fibril level as a plastic deformation, defined as micro-defects. To investigate these micro-defects, we have developed a detailed finite element model of the entire healthy tibiofemoral joint (TF) including a multiscale constitutive model which considers the structural hierarchies of the articular cartilage. The net model was simulated under physiological loading conditions to predict joint response under 2000 N axial compression and damage initiation under high axial loading (max 7 KN) when the TF joint flexed to 30°. Computed results sufficiently agreed with earlier experimental and numerical studies. Further, initiation and propagation of damage in fibrils were computed at the tibial cartilage located mainly in the superficial and middle layers. Our simulation results also indicated that the stiffer the fibril is (higher cross-link densities), the higher the contact stress required to elicit a fibril yield and the higher the rate of yielding as a function of increased contact stress. To the best of our knowledge, this is the first model that combines macro-continuum joint mechanics and micromechanics at the tissue level. The computational construct presented here serves as a simulation platform to explore the interplay between acute cartilage damage and micromechanics characteristics at the tropocollagen level.

Plant petioles can be considered as hierarchical cellular structures, displaying geometric features defined at multiple length scales. Their macroscopic mechanical properties are the cumulative outcome of structural properties attained at each level of the structural hierarchy. This work appraises the compliance of a rhubarb stalk by determining the stalk's bending and torsional stiffness both computationally and experimentally. In our model, the irregular cross-sectional shape of the petiole and the layers of the constituent tissues are considered to evaluate the stiffness properties at the structural level. The arbitrary shape contour of the petiole is generated with reasonable accuracy by the Gielis superformula. The stiffness and architecture of the constituent layered tissues are modeled by using the concept of shape transformers so as to obtain the computational twist-to-bend ratio for the petiole. The rhubarb stalk exhibits a ratio of flexural to torsional stiffness 4.04 (computational) and 3.83 (experimental) in comparison with 1.5 for isotropic, incompressible, circular cylinders, values that demonstrate the relative structural compliance to flexure and torsion.

Image-based finite element analysis (FEA) has been considered an effective computational tool to predict hip fracture risk. The patient specific FEA gives an insight into the inclusive effect of three-dimensional (3D) complex bone geometry, and the distribution of inhomogeneous isotropic material properties in conjunction with loading conditions. The neck region of a femur is primarily the weakest in which fracture is likely to happen, when someone falls. A sideways fall results in the development of greater tensile and compressive stresses, respectively, in the inferior and superior aspects of the femoral neck, whereas the state of stress is reversed in usual gait or stance configuration. Herein, the variations of stresses have been investigated at the femoral neck region considering both single-stance and sideways fall. Finite element models of ten human femora have been generated using Quantitative Computed Tomography (QCT) scan datasets and have been simulated with an equal magnitude of load applied to the aforementioned configurations. Fracture risk indicator, defined as the ratio of the maximum compressive or tensile stress computed at the superior and inferior surfaces to the corresponding yield stress, has been used in this work to measure the variations of fracture risk between single-stance and sideways fall. The average variations of the fracture risk indicators between the fall and stance are at least 24.3% and 8% at the superior and inferior surfaces, respectively. The differences may interpret why sideways fall is more dangerous for the elderly people, causing hip fracture.

This paper describes a study of petiole structural morphology in which tissue materials, cross-sectional geometry, layer-architecture and hydrostatic condition are variables that affect the overall structural properties of the organ. Philodendron melinonii is selected as a model species for characterizing the mechanical properties of the petiole. The shape of the petiole is modeled through the polar parameterization of the Lame’s curves, i.e. Gielis formulation. A multiscale model of bending stiffness is proposed to capture the impact of changing the constituent tissues and the cross-sectional geometry. Stiffness and density of different tissues are used to plot the domain bounded by the limiting curve of the respective tissue material. Shape parameters and the respective tissue properties are used to generate structural efficiency maps displaying property domains within which fall all possible combinations of tissues that are shaped into a certain geometry during growth. The turgor pressure is also taken into account to show how the domain of the effective material properties changes with water content. Finite element analysis besides experimental data is used to validate the theoretical results. The maps may offer a source of inspiration for biomimetic design, as they help to gain insight into the efficiency of biological beams described by different tissues properties, geometry and turgidity.

Femoral neck region is the weakest in which the fracture takes place when someone falls sideways. The sideways fall develops peak tensile and compressive stresses in the inferior and superior surfaces of the femoral neck, whereas the state of stress is reversed for a single-stance loading. Therefore, a CT based finite element analysis can be an effective tool for determining the state of stresses at the femoral neck region to predict the probability of fracture considering the 3D complex geometry of femur, its material properties and load conditions. The present work aims to represent the mechanism of hip fracture at the femoral neck region due to sideways fall, which results in greater tensile and compressive stresses at the femoral neck.

The stiffness of plant tissue largely influences the overall mechanical response of plant organs, such as stems, branches and leaf petioles. This work examines the structural hierarchy of the plant tissue; in particular of the collenchyma tissue of the Rheum rhabarbarum. The goal of the paper is to develop a multiscale model capturing features of two orders of its structural hierarchy: cell wall and tissue architecture. The former is considered as a fiber reinforced composite, where the cellulose microfibril (CMF) is the main load bearing component. The longitudinal stiffness of the middle (S2) layer of the secondary cell wall is affected by the microfibril angle (MFA) up to 45° to a greater extent, which in turn plays a role in the overall wall stiffness. The latter, i.e. tissue architecture, influences the tissue stiffness through its random distribution of cells. Finite-edge Centroidal Voronoi Tessellation (FECVT) is used to model the non-periodic microstructure of the rhubarb collenchyma, whose effective elastic properties are obtained through finite element analysis. The results from the FECVT model show that the effective stiffness in the longitudinal direction is 15 to 25% higher than that in the transverse direction for relative density between 5 and 30%. The variation reflects the stiffening effect of the shape and size of the cells in the collenchyma tissue, as well as its aperiodic cellular distribution.Copyright © 2014 by ASME

Plant petioles and stems are hierarchical cellular structures, displaying geometrical features defined at multiple length scales. One or more of the intermediate hierarchical levels consists of tissues in which the cellular distribution is quasi-random, a factor that affects the elastic properties of the tissues. The current work focuses on the finite element analysis (FEA) of the constituent tissues of the plant Rheum rhabarbarum (rhubarb). The geometric model is generated via a recently introduced method: the finite edge centroidal Voronoi tessellation (FECVT), which is capable to capture the gradients of cellularity and diversified pattern of cellular materials, as opposed to current approaches in literature. The effective stiffness of the tissues is obtained by using an accurate numerical homogenization technique via detailed finite element analysis of the models of sub-regions of the tissues. As opposed to a large-scale representative volume element (RVE), statistical volume elements (SVE) are considered in this work to model tissue microstructures that are highly random. 2D finite element analyses demonstrate that the distribution of cells in collenchyma and parenchyma tissue make them stiffer in two different directions, while the overall effect of the combined tissues results in approximately equal stiffness in both directions. The rhubarb tissues, on the other hand, are more compliant than periodic and quasi-uniform random cellular materials by a factor of up to 47% and 44%, respectively. The variations of the stiffness shows the stiffening role that cell shape, size, and graded cellular distribution play in the mechanics of the rhubarb tissue.

Plant petioles and stems are hierarchical cellular structures, displaying structural features defined at multiple length scales. One or more of the intermediate hierarchical levels consists of tissues, in which the cellular distribution is quasirandom. The current work focuses on the realistic modeling of plant tissue microstructures. The finite-edge centroidal Voronoi tessellation (FECVT) is here introduced to overcome the drawbacks of the semi-infinite edges of a typical Voronoi model. FECVT can generate a realistic model of a tissue microstructure, which might have finite edges at its border, be defined by a boundary contour of any shape, and include complex heterogeneity and cellular gradients. The centroid-based Voronoi tessellation is applied to model the microstructure of the Philodendron melinonii petiole and the Arabidopsis thaliana stem, which both display intense cellular gradients. FECVT coupled with a digital image processing algorithm is implemented to capture the nonperiodic microstructures of plant tissues. The results obtained via this method satisfactorily obey the geometric, statistical, and topological laws of naturally evolved cellular solids. The predicted models are also validated by experimental data.

The leaf petiole is an organ that connects the leaf blade to the stem of a plant. From a structural viewpoint, the petiole resembles a cantilever beam that withstands torsional loading due to wind action and bending deformation due to gravity acting on the leaf blade. During growth, the petiole develops defined structural features at multiple length scales, which synergistically determine its mechanical response to external stimuli. The focus of this study is on the hierarchical level (n=3) of the cellular tissue. The goal is to capture the elastic properties of the cellular tissues of the leaf petiole in Philodendron melinonii at that hierarchy. Since the microstructure of the plant tissues resembles a non-periodic cellular pattern, we resort to a 2-D Finite Edge Centroidal Voronoi tessellation (FECVT) to generate a realistic network of polygonal cells. An analysis based on finite element analysis (FEA) is performed to explore the relation between the effective stiffness of Voronoi model and the properties of the cellular tissue. The effective (homogenized) elastic properties of the cellular tissue can be used to calculate the overall flexural and torsional stiffness of the P. melinonii petiole. The FEA of the Voronoi microstructure depicts the anisotropic stiffness properties of the P. melinonii tissue and its dependence with the graded cellularity.