Study of the variations of fall induced hip fracture risk between right and left femurs using CT-based FEA.

BACKGROUND: Hip fracture of elderly people-suffering from osteoporosis-is a severe public health concern, which can be reduced by providing a prior assessment of hip fracture risk. Image-based finite element analysis (FEA) has been considered an effective computational tool to assess the hip fracture risk. Considering the femoral neck region is the weakest, fracture risk indicators (FRI) are evaluated for both single-legged stance and sideways fall configurations and are compared between left and right femurs of each subject. Quantitative Computed Tomography (QCT) scan datasets of thirty anonymous patients' left and right femora have been considered for the FE models, which have been simulated with an equal magnitude of load applied to the aforementioned configurations. The requirement of bilateral hip assessment in predicting the fracture risk has been explored in this study. RESULTS: Comparing the sideways fall and single-legged stance, the FRI varies by 64 to 74% at the superior aspects and by 14 to 19% at the inferior surfaces of both the femora. The results of this in vivo analysis clearly substantiate that the fracture is expected to initiate at the superior surface of femoral neck region if a patient falls from his/her standing height. The distributions of FRI between the femurs vary considerably, and the variability is significant at the superior aspects. The p value (= 0.02) obtained from paired sample t-Test yields p value ≤ 0.05, which shows the evidence of variability of the FRI distribution between left and right femurs. Moreover, the comparison of FRIs between the left and right femur of men and women shows that women are more susceptible to hip fracture than men. CONCLUSIONS: The results and statistical variation clearly signify a need for bilateral hip scanning in predicting hip fracture risk, which is clinically conducted, at present, based on one hip chosen randomly and may lead to inaccurate fracture prediction. This study, although preliminary, may play a crucial role in assessing the hip fractures of the geriatric population and thereby, reducing the cost of treatment by taking predictive measure.

Computational study of the elastic properties of Rheum rhabarbarum tissues via surrogate models of tissue geometry.

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.

QCT-based 3D finite element modeling to assess patient-specific hip fracture risk and risk factors.

Early assessment of hip fracture risk may play a critical role in designing preventive mechanisms to reduce the occurrence of hip fracture in geriatric people. The loading direction, clinical, and morphological variables play a vital role in hip fracture. Analyzing the effects of these variables helps predict fractures risk more accurately; thereby suggesting the critical variable that needs to be considered. Hence, this work considered the fall postures by varying the loading direction on the coronal plane (α) and on the transverse plane (ß) along with the clinical variables-age, sex, weight, and bone mineral density, and morphological variables-femoral neck axis length, femoral neck width, femoral neck angle, and true moment arm. The strain distribution obtained via finite element analysis (FEA) shows that the angle of adduction (α) during a fall increases the risk of fracture at the greater trochanter and femoral neck, whereas with an increased angle of rotation (ß) during the fall, the FRI increases by ∼1.35 folds. The statistical analysis of clinical, morphological, and loading variables (αandß) delineates that the consideration of only one variable is not enough to realistically predict the possibility of fracture as the correlation between individual variables and FRI is less than 0.1, even though they are shown to be significant (p<0.01). On the contrary, the correlation (R2=0.48) increases as all variables are considered, suggesting the need for considering different variables fork predicting FRI. However, the effect of each variable is different. While loading, clinical, and morphological variables are considered together, the loading direction on transverse plane (ß) has high significance, and the anatomical variabilities have no significance.

SSDL-an automated semi-supervised deep learning approach for patient-specific 3D reconstruction of proximal femur from QCT images.

Deep Learning (DL) techniques have recently been used in medical image segmentation and the reconstruction of 3D anatomies of a human body. In this work, we propose a semi-supervised DL (SSDL) approach utilizing a CNN-based 3D U-Net model for femur segmentation from sparsely annotated quantitative computed tomography (QCT) slices. Specifically, QCT slices at the proximal end of the femur forming ball and socket joint with acetabulum were annotated for precise segmentation, where a segmenting binary mask was generated using a 3D U-Net model to segment the femur accurately. A total of 5474 QCT slices were considered for training among which 2316 slices were annotated. 3D femurs were further reconstructed from segmented slices employing polynomial spline interpolation. Both qualitative and quantitative performance of segmentation and 3D reconstruction were satisfactory with more than 90% accuracy achieved for all of the standard performance metrics considered. The spatial overlap index and reproducibility validation metric for segmentation-Dice Similarity Coefficient was 91.8% for unseen patients and 99.2% for validated patients. An average relative error of 12.02% and 10.75% for volume and surface area, respectively, were computed for 3D reconstructed femurs. The proposed approach demonstrates its effectiveness in accurately segmenting and reconstructing 3D femur from QCT slices.

The effect of body weight on the knee joint biomechanics based on subject-specific finite element-musculoskeletal approach.

Knee osteoarthritis (OA) and obesity are major public health concerns that are closely intertwined. This intimate relationship was documented by considering obesity as the most significant preventable risk factor associated with knee OA. To date, however, the effects of obesity on the knee joint's passive-active structure and cartilage loading have been inconclusive. Hence, this study investigates the intricate relationship between obesity and knee OA, centering on the biomechanical changes in knee joint active and passive reactions during the stance phase of gait. Using a subject-specific musculoskeletal and finite element approach, muscle forces, ligament stresses, and articular cartilage contact stresses were analyzed among 60 individuals with different body mass indices (BMI) classified under healthy weight, overweight, and obese categories. Our predicted results showed that obesity significantly influenced knee joint mechanical reaction, increasing muscle activations, ligament loading, and articular cartilage contact stresses, particularly during key instances of the gait cycle-first and second peak loading instances. The study underscores the critical role of excessive body weight in exacerbating knee joint stress distribution and cartilage damage. Hence, the insights gained provide a valuable biomechanical perspective on the interaction between body weight and knee joint health, offering a clinical utility in assessing the risks associated with obesity and knee OA.

Effect of Surgical Design Variations on the Knee Contact Behavior during Anterior Cruciate Ligament Reconstruction.

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.

Knee joint biomechanics and cartilage damage prediction during landing: A hybrid MD-FE-musculoskeletal modeling.

Understanding the mechanics behind knee joint injuries and providing appropriate treatment is crucial for improving physical function, quality of life, and employability. In this study, we used a hybrid molecular dynamics-finite element-musculoskeletal model to determine the level of loads the knee can withstand when landing from different heights (20, 40, 60 cm), including the height at which cartilage damage occurs. The model was driven by kinematics-kinetics data of asymptomatic subjects at the peak loading instance of drop landing. Our analysis revealed that as landing height increased, the forces on the knee joint also increased, particularly in the vastus muscles and medial gastrocnemius. The patellar tendon experienced more stress than other ligaments, and the medial plateau supported most of the tibial cartilage contact forces and stresses. The load was mostly transmitted through cartilage-cartilage interaction and increased with landing height. The critical height of 126 cm, at which cartilage damage was initiated, was determined by extrapolating the collected data using an iterative approach. Damage initiation and propagation were mainly located in the superficial layers of the tibiofemoral and patellofemoral cartilage. Finally, this study provides valuable insights into the mechanisms of landing-associated cartilage damage and could help limit joint injuries and improve training programs.

Surrogate modeling of articular cartilage degradation to understand the synergistic role of MMP-1 and MMP-9: a case study.

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.

Study of the significance of parameters and their interaction on assessing femoral fracture risk by quantitative statistical analysis.

Early assessment of hip fracture helps develop therapeutic and preventive mechanisms that may reduce the occurrence of hip fracture. An accurate assessment of hip fracture risk requires proper consideration of the loads, the physiological and morphological parameters, and the interactions between these parameters. Hence, this study aims at analyzing the significance of parameters and their interactions by conducting a quantitative statistical analysis. A multiple regression model was developed considering different loading directions during a sideways fall (angle [Formula: see text] and [Formula: see text] on the coronal and transverse planes, respectively), age, gender, patient weight, height, and femur morphology as independent parameters and Fracture Risk Index (FRI) as a dependent parameter. Strain-based criteria were used for the calculation of FRI with the maximum principal strain obtained from quantitative computed tomography-based finite element analysis. The statistical result shows that [Formula: see text] [Formula: see text], age [Formula: see text], true moment length [Formula: see text], gender [Formula: see text], FNA [Formula: see text], height [Formula: see text], and FSL [Formula: see text] significantly affect FRI where [Formula: see text] is the most influential parameter. The significance of two-level interaction [Formula: see text] and three-level interaction [Formula: see text] shows that the effect of parameters is dissimilar and depends on other parameters suggesting the variability of FRI from person to person.

Mechanical characterization of articular cartilage degraded combinedly with MMP-1 and MMP-9.

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.

Sensitivity analysis of the knee ligament forces to the surgical design variation during anterior cruciate ligament reconstruction: a finite element analysis.

The purpose of this study is to understand the effect of essential surgical design parameters on collateral and cruciate ligaments behavior for a Bone-Patellar-Tendon-Bone (BPTB) anterior cruciate ligament reconstruction (ACL-R) surgery. A parametric finite element model of biomechanical experiments depicting the ACL-R surgery associated with a global sensitivity analysis was adopted in this work. The model parameters were six intraoperative variables, two-quadrant coordinates of femoral tunnel placement, femoral tunnel sagittal and coronal angles, graft pretension, and the joint angle at which the BPTB graft is tensioned (fixation angle). Our results indicated that cruciate ligaments (posterior cruciate ligament (PCL) and graft) were mainly sensitive to graft pretension (23%), femoral tunnel sites (56%), and the angle at which the surgeon decided to fix the graft (14%). The collateral ligaments (medial and lateral) were also affected by the same set of surgical parameters as the cruciate ligaments except for graft pretension. The output data of this study may help to identify a better role for the ACL-R intraoperative variables in optimizing the knee joint ligaments' postsurgical functionality.

An in vitro investigation to understand the synergistic role of MMPs-1 and 9 on articular cartilage biomechanical properties.

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.

Computational frame of ligament in situ strain in a full knee model.

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.

A multiscale synthesis: characterizing acute cartilage failure under an aggregate tibiofemoral joint loading.

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.

The effect of fibrillar degradation on the mechanics of articular cartilage: a computational model.

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 (ß) 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.

The twist-to-bend compliance of the Rheum rhabarbarum petiole: integrated computations and experiments.

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.

Study of stress variations in single-stance and sideways fall using image-based finite element analysis.

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.

Experimental determination of Philodendron melinonii and Arabidopsis thaliana tissue microstructure and geometric modeling via finite-edge centroidal Voronoi tessellation.

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.