Journal of Biomechanical Engineering

Lumbar spinal stenosis (LSS) is a common degenerative disease among the elderly. The role that mechanical stress-induced hypertrophic ligamentum flavum (HLF) plays in patients with LSS remains unclear. Here, we used a finite element analysis to investigate the stress characteristics on the ligamentum flavum (LF) and evaluate the feasibility of a mouse model of HLF. First, we induced a bipedal posture in mice by taking advantage of their hydrophobia. A micro-CT scan was performed to examine their spinal change during bipedal posture. A finite element analysis showed that the stress and strain on the upright posture were significantly increased compared with those on the sprawling posture. Tissue staining showed that the degeneration degree of the LF in bipedal standing group gradually increased over the modeling period. The amount of elastic fibers decreased under HLF, whereas the amount of collagen fibers, the number of the LF cells, and the expression of fibrosis-related factors increased. Compared with aged group, LF degeneration was more severe in the bipedal standing group. Our findings demonstrate that the increased stress caused by a posture change causes HLF and that a bipedal mouse model can be used to study HLF in vivo.

The literature supports the existence of a strain threshold, above which cortical bone adapts to exogenous mechanical loading by forming new bone. This strain threshold, however, varies with loading conditions, locations, waveforms, frequency etc. and there is a need to mathematically express the strain threshold in terms of these parameters. There have been several parametric, mathematical or numerical models in the literature for the cortical bones adaptation to mechanical loading, which may be already fitting some of the experimental data; however, they may not be easily and confidently derived from the first principles. To fill the gap, this work has attempted to derive the corresponding bone formation rate (BFR) rather from the first principles, namely using the energy principles. The derived model has been compared to the existing parametric models and validated with respect to the diverse experimental data available in the literature. The developed model is able to not only predict the BFR, but also helps to understand the nature and possible mathematical form of the strain threshold for cortical bones adaptation to mechanical loading.

IntroductionLumbar spinal stenosis is a common cause of lower back pain and weakness in elderly patients. The gold standard treatment for this is lumbar laminectomy which involves widespread muscle damage to the multifidus, a complete loss of the posterior tension band which contains the supraspinous and interspinous ligaments. However, in recent years minimally invasive techniques such as bilateral and unilateral laminotomy have become more popular and are showing efficacy in the decompression of spinal stenosis. Due to its minimally invasive approach, the muscle retraction required for laminotomy is less intensive than that required for laminectomy. The overall body of literature on the surgical treatment of spinal stenosis is sparse in its interrogation of the biomechanical outcomes of these techniques and to our knowledge, there are no current publications that incorporate muscle forces. MethodsA previously validated thoracolumbar ribcage finite element (FE) model was used for this study. Three different surgeries, traditional laminectomy, unilateral and bilateral midline sparing approaches at L4-L5 segment were simulated by removing the spinous process, supraspinous, and interspinous ligaments. The segmental range of motion (ROM) for all models were acquired and input into a musculoskeletal modelling software to calculate muscle forces. ResultsUnilateral and bilateral laminotomy showed similar muscle forces for every muscle group in both flexion and extension motion. While comparing the muscle forces in laminotomy to the laminectomy in extension motion displayed an increase in Iliocostalis lumborum (IL) by 12 % and multifidus (MF) by 16% and decrease in transverse abdominus (TA) by 138% and erector spine (ES) by 12%. For flexion, there was an increase in IL by 35%, and MF by 12%. ConclusionOur results highlight that laminectomy, which involves the removal of paraspinal muscles and posterior ligamentous structures to relieve stenosis, can lead to increased instability and necessitate muscle compensation, particularly in adjacent and thoracic spine segments. Conversely, midline sparing approaches such as laminotomies, are associated with decreased muscle compensation across spinal segments and enhanced stability.

Intervertebral disc (IVD) degeneration is a potential contributor to low-back pain. While experimental IVD injury models have demonstrated IVD structural changes, the early mechanical consequences remain unclear. This study aimed to establish a rat model of lumbar spine instability via IVD injury and assess back musculature adaptations to IVD injury. Thirty-one adult male Wistar rats were assigned to three groups: IVD knife stab lesion (knife), IVD needle puncture (needle), and sham surgery control (control). In the knife and needle groups, L4/L5 IVDs were injured at 14 weeks of age. One-two weeks post-intervention, lumbar multifidus (MF) and medial longissimus (ML) muscles were excised, L4-L5 spinal segments were harvested for mechanical testing, and IVDs were collected for histology. The needle group exhibited lower peak stiffness, peak moment, and hysteresis than controls in flexion, with no difference in lateral bending. IVD height and area did not differ between groups, but the needle group had a smaller nucleus relative to annulus area compared to controls. Morphological changes were observed in both injury groups. The needle group showed higher normalized ML mass, while normalized MF mass was unchanged. In conclusion, a rat model of lumbar spine instability was successfully established via IVD needle injury.

Female athletes are significantly more likely to tear their anterior cruciate ligament (ACL) compared to their male counterparts. While there are several potential reasons for this, previous data from our lab demonstrated that female ACL explants have an impaired remodeling response to loading, which may prevent the repair of fatigue damage and lead to increased ACL rupture. The objective of this study was to identify the mechanisms driving the impaired remodeling of female ACLs to cyclic loading, including the role of estrogen. ACLs were harvested from male and female New Zealand white rabbits and cyclically loaded in a tensile bioreactor followed by bulk RNA-sequencing. Additional ACL explants treated with or without estradiol were analyzed using RT-qPCR to determine the regulatory effect of estrogen on markers for tissue remodeling and inflammatory cytokines with cyclic loading. We found that female ACLs exhibited significantly fewer differentially expressed genes (DEGs) in response to loading compared to male ACLs. Additionally, multiple mechanotransduction pathways were enriched with loading only in the male ACLs. While a few estrogen-related pathways were enriched in both male and female ACLs with loading, the expression of tissue remodeling markers was not different between estrogen treatment and vehicle control. Together, our findings highlight specific mechanotransduction pathways that may be responsible for the muted biological response of female ACLs to load, which provides a potential explanation for the increased rate of ACL tears in women.

This work attempts to derive long-term, time-dependent cortical bone adaptation to mechanical loading. Linear control theory is used to model the adaptation process, with the stimulus defined in terms of dissipation energy density. The newly adapted area is expressed as a function of the stimulus in the form of a differential equation, which is analyzed to obtain closed-form solutions. The study explores different possibilities, such as varying the order of differential equations (including fractional order) and examining different types of responses, e.g., critically damped and overdamped. Such model diversity will help identify the most appropriate formulation that fits experimental data.

Anterior cruciate ligament (ACL) injuries disproportionately affect female adolescent athletes, with hormonal influences implicated in this sex disparity. However, the relationship between pubertal hormonal changes and ACL gene and protein expression remains poorly understood. This study characterized hormone receptor expression and transcriptional profiles in the anteromedial (AM) and posterolateral (PL) bundles of female porcine ACLs before and after puberty. ACL bundles were collected from pre-pubescent (8 weeks) and post-pubescent (>8 months) female Yorkshire cross-breed pigs (n=6/group) and analyzed using gene expression profiling, western blotting, and immunofluorescence. Pre-pubescent ACLs exhibited greater expression of primary matrix genes (COL1A1, COL1A2, ELN, TNMD), suggesting active matrix synthesis, while post-pubescent ACLs showed elevated secondary matrix genes (COL3A1, LUM, COMP), indicating a homeostatic state. Notably, estrogen receptor alpha (ER) gene and protein expression were significantly greater in post-pubescent ACLs, particularly in AM bundles, whereas G-protein coupled estrogen receptor (GPR30) expression was elevated pre-puberty. Both receptors were distributed homogeneously throughout the tissue. Progesterone receptor protein expression was not detected in any samples. Histologically, post-pubescent ACLs demonstrated decreased cellularity and thicker fascicles compared to pre-pubescent tissues. These findings indicate that ACL sensitivity to estrogen varies across development, with increased ER expression post-puberty potentially rendering the ligament more responsive to circulating estrogen. This work provides foundational evidence for age-dependent hormonal responsiveness in the ACL and motivates further investigation into how sex hormones influence ACL injury risk in adolescent females.

BackgroundBone tunnel enlargement is considered as a potential problem following ACL reconstruction and can cause a fixation failure and complicate its revision surgery. This study evaluates post tibial tunnel expansion in ACL reconstruction using an interference screw. MethodsA series of in-vitro experimental tests on animal bone and tissues were used to simulate post ACL reconstruction. The study believes an unbalanced lateral force can cause a local enlargement on the contact zone inside the tunnel. Grayscale X-ray images were used to assess the screw alignment inside the tunnel. ResultsThey showed a slight misalignment between the screw and the tunnel axis as the tendon strands moved along the side of the tunnel, and the screw had partial contact with the tendon and bone along the tunnel. According to the results, increased stress in the tunnel wall causes tunnel enlargement. Although the tunnel created away from the tibial central axis produced a higher strength, it results in higher stress on the wall of the tunnel which can increase the risk of tunnel expansion. ConclusionsThe current study believes the use of an unguided interference screw insertion potentially increases risks of the misaligned fixation and cause a tunnel enlargement. This risk may be controlled by restricting the post-operative rehabilitation.

Load removal from the load-bearing bone, such as in the case of extended space travel and prolonged bed rest, harms bone health and leads to severe bone loss. However, the constitutive idea relating the quantity of bone loss to the absence of physiological loading is poorly understood. This work attempts to develop a mathematical model that predicts cortical bone loss at three sections: distal, mid-section, and proximal along the length of a mouse tibia. Load-induced interstitial fluid flow-based dissipation energy density has been adopted as a stimulus to trigger mechanotransduction. The developed model takes the loss of stimulus due to the disuse of bone as an input and predicts the quantity of bone loss with spatial accuracy. We hypothesized that the bone loss site would be the site of maximum stimulus loss due to disuse. To test the hypothesis, we calculated stimulus loss, i.e., loss of dissipation energy density due to bone disuse, based on the poroelastic analysis of the bone using a finite element method. A novel mathematical model has been then developed that successfully relates this loss of stimulus to the in-vivo bone loss data in the literature. According to the developed model, the site-specific mineral rate is found to be proportional to the square root of the loss of dissipation energy density. To the authors best knowledge, this model is the first of its kind to compute site-specific bone loss. The developed model can be extended to predict bone loss due to other disuse conditions such as long space travel, prolonged bed rest, etc.

This study aims at evaluating femoral bone-related mechanical properties in female patients with long-term remission of Cushings Syndrome (CS). Sixty-four female subjects were included in this study and stratified in two groups: (a) 32 long-term remission of CS patients, and (b) 32 healthy (paired) control subjects. Quantitative Computed Tomography (QCT) was used to derive patient-specific Finite Element (FE) models. A sideways-fall impact was simulated for each subject and the resulting stress and strain values were compare among the two different groups. Our findings indicate that women with CS in remission exhibit impaired biomechanical properties in the femoral neck compared to controls, suggesting compromised bone properties in this population.

BackgroundAlthough deformation and fracture of the vertebral endplate have been implicated in spinal conditions such as vertebral fracture and disc degeneration, few biomechanical studies of this structure are available. The goal of this study was to quantify the mechanical behavior of the vertebral endplate. MethodsEight-five rectangular specimens were dissected from the superior and/or inferior central endplates of human lumbar spine segments L1-L4. Micro-computed tomography (CT) imaging, four-point-bend testing, and ashing were performed to quantify the apparent elastic modulus and yield stress (modulus and yield stress, respectively, of the porous vertebral endplate), tissue yield stress (yield stress of the tissue of the vertebral endplate, excluding pores), ultimate strain, fracture strain, bone volume fraction (BV/TV), bone mineral density (BMD), and various measures of tissue density and composition (tissue mineral density, ash fraction, and ash density). Regression was used to assess the dependence of mechanical properties on density and composition. ResultsWide variations in elastic and failure properties, and in density and tissue composition, were observed. BMD and BV/TV were good predictors of many of the apparent-level mechanical properties, including modulus, yield stress, and in the case of the inferior vertebral endplate, failure strains. Similar values of the mechanical properties were noted between superior and inferior vertebral endplates. In contrast to the dependence of apparent stiffness and strength on BMD and BV/TV, none of the mechanical properties depended on any of the tissue-level density measurements. ConclusionThe dependence of many of the mechanical properties of the vertebral endplate on BV/TV and BMD suggests possibilities for non-invasive assessment of how this region of the spine behaves during habitual and injurious loading. Further study of the non-mineral components of the endplate tissue is required to understand how the composition of this tissue may influence the overall mechanical behavior of the vertebral endplate.

The present study reports the anisotropy effects of uniaxial and multiaxial loading on cancellous bone in order to mimic true physiological conditions as well as pathological reactions and thereby provides improved data that represents clinical and real life conditions. Cancellous bone samples were CT-scanned for morphological analysis and model construction. The models were then computationally loaded on three different directions; horizontal, vertical, and at 45{degrees}. Lower BV/TV, Tb.Th, and Conn.D resulted in lower number of cycles to failure, regardless to the loading conditions. However, the number of cycles to failure was found to be negatively correlated to the value of structural model index. Dramatic increased in effective plastic strain and decrease in cycles to failure were demonstrated by the cancellous bone models under multiaxial loading. The reduction of fatigue life was five times lower in multiaxial condition in comparison to the fatigue life under uniaxial loading. Off-axis orientation effect on the fatigue life of the trabecular bone was demonstrated the worst in horizontal trabecular bone model. Effective plastic strain was recorded the highest in horizontal model, while the model at 45{degrees} demonstrated 1.6 times higher effective plastic strain than the vertical ones. This is due to several numbers of thin trabeculae which are susceptible to fatigue at higher stress concentration. In conclusion, the anisotropic effect of uniaxial and multiaxial loading onto the mechanical behaviour of bovine cancellous bone was demonstrated throughout this study. It is apparent that multiaxial with off-axis forces are important to be considered as the loading direction manifests the fatigue lifetime of cancellous bone.

BackgroundAdolescent idiopathic scoliosis (AIS) is a three-dimensional deformity of the spinal column in otherwise healthy adolescents. The underlying mechanisms associated with the spinal deformity development have been explored which delineated the role of the sagittal curvature of the spine. The patterns of the spinal deformity vary between the AIS patients as shown in several classification systems. It remains to further investigate how variations in sagittal profiles result in different coronal plane deformities in AIS and how these deformation patterns are intrinsically different. MethodsA total of 71 Lenke 1 and 52 Lenke 5 AIS patients were included retrospectively. The 3D models of the spine were generated from biplanar radiographs to calculate the clinical spinal parameters, vertebral axial rotations, and the 3D centerline of the spinal curvature. A classification based on the centerlines axial plane projection was developed. The 3D curvature of the centerline was calculated at each point. A 2D elastic rod finite element model (FEM) of the sagittal spinal curvature for each axial subtype was developed to calculate the 3D deformity of the spine under gravity and axial torsion. Differences in the axial clusters clinical parameters, curvature of the spine, and the deformation patterns of the FEM were compared. The characteristics of the sagittal curvature of these axial clusters were determined. ResultsLenke1 was divided into two axial groups (I and II) whereas the Lenke 5 cohort all had the same axial projection pattern (loop shape). T5-T12 kyphosis was significantly different between Lenke1-Group I and the other two groups, p=0.04. The vertebral rotation in both Lenke1-Group I and Lenke 5 had only one maximum value and the FEM deformed in a loop shaped whereas Lenke1-group II showed two maximum values for vertebral rotation and the FEM of the centerline deformed in a lemniscate shape. The ratio of the spinal arc lengths above and below the sagittal inflection points for Lenke1-Groups I and II and Lenke 5 were 0.52, 1.16, and 3.24, respectively. ConclusionVariations in the axial plane projection of the curve were observed within Lenke types. Lenke 1- Group I and Lenke 5 showed similar 3D curve characteristics suggesting one 3D curve whereas Lenke1-Group II, with two 3D curves, behaved differently. The length of the spinal arcs above and below the sagittal inflection point related to the patterns of axial deformity.

Passive joint stiffness reflects the stiffness of various soft tissues across a joint. However, no previous studies have investigated the relationship between passive joint stiffness and muscle, nerve, and tendon stiffness. This study aimed to clarify whether passive ankle joint stiffness is related to stiffness in the triceps surae muscles, tibial nerve, and Achilles tendon. Thirty-eight healthy adults participated in the study. The passive ankle joint stiffness (slope of angle-passive torque curve) and shear wave velocities, which indicate soft tissue stiffness, of the triceps surae muscles and tibial nerve were measured at 5{degrees} of ankle plantarflexion and 5{degrees}, 15{degrees}, and 25{degrees} of ankle dorsiflexion. The shear wave velocity of the Achilles tendon was measured only at 5{degrees} of plantarflexion. A multiple regression model (forced-entry method) was constructed at each angle, specifying the shear wave velocities as the independent variables and passive joint stiffness as the dependent variable. At 5{degrees} of plantarflexion, no shear wave velocities were significantly related to passive joint stiffness (all p [≥] 0.05). At 5{degrees} and 15{degrees} of dorsiflexion, only the shear wave velocities of the tibial nerve were significantly positively related to passive joint stiffness (p = 0.024 and 0.008, respectively). At 25{degrees} of dorsiflexion, the shear wave velocities of the lateral gastrocnemius muscle and tibial nerve were significantly positively related to passive joint stiffness (p = 0.002 and 0.001, respectively). It can be concluded that both triceps surae muscles stiffness and tibial nerve stiffness are related to passive ankle joint stiffness.

Intervertebral disc degeneration is the most recognized cause of low back pain, characterized by the decline of tissue structure and mechanics. Image-based mechanical parameters (e.g., strain, stiffness) may provide an ideal assessment of disc function that is lost with degeneration but unfortunately remains underdeveloped. Moreover, it is unknown whether strain or stiffness of the disc may be predicted by MRI relaxometry (e.g. T1 or T2), an increasingly accepted quantitative measure of disc structure. In this study, we quantified T1 and T2 relaxation times and in-plane strains using displacement-encoded MRI within the disc under physiological levels of compression and bending. We then estimated shear modulus in orthogonal image planes and compared these values to relaxation times and strains within regions of the disc. Intratissue strain depended on the loading mode, and shear modulus in the nucleus pulposus was typically an order of magnitude lower than the annulus fibrosis, except in bending, where the apparent stiffness depended on the loading. Relative shear moduli estimated from strain data derived under compression generally did not correspond with those from bending experiments, with no correlations in the sagittal plane and only 4 of 15 regions correlated in the coronal plane, suggesting that future inverse models should incorporate multiple loading conditions. Strain imaging and strain-based estimation of material properties may serve as imaging biomarkers to distinguish healthy and diseased discs. Additionally, image-based elastography and relaxometry may be viewed as complementary measures of disc structure and function to assess degeneration in longitudinal studies.

Artificial tendons may be an effective alternative to autologous and allogenic tendon grafts for repairing critically sized tendon defects. The goal of this study was to quantify the in vivo hindlimb biomechanics (ground contact pressure and sagittal-plane motion) during hopping gait of rabbits having a critically sized tendon defect of the tibialis cranialis and either with or without repair using an artificial tendon. In five rabbits, the tibialis cranialis tendon of the left hindlimb was surgically replaced with a polyester, silicone-coated artificial tendon (PET-SI); five operated control rabbits underwent complete surgical excision of the biological tibialis cranialis tendon in the left hindlimb with no replacement (TE). At 8 weeks post-surgery, peak vertical ground contact force in the left hindlimb was statistically significantly less compared to baseline for the TE group (p=0.0215). Statistical parametric mapping (SPM) analysis showed that, compared to baseline, the knee was significantly more extended during stance at 2 weeks post-surgery and during the swing phase of stride at 2 and 8 weeks post-surgery for the TE group (p<0.05). Also, the ankle was significantly more plantarflexed during swing at 2 and 8 weeks postoperative for the TE group (p<0.05). In contrast, there were no significant differences in the SPM analysis among timepoints in the PET-SI group for the knee or ankle. These findings suggest that the artificial tibialis cranialis tendon effectively replaced the biomechanical function of the native tendon.

Finite element (FE) models have been effectively utilized in studying biomechanical aspects of myocardial infarction (MI). Although the rat is a widely used animal model for MI, there is a lack of material parameters based on anisotropic constitutive models for rat myocardial infarcts in literature. This study aimed at employing inverse methods to identify the parameters of an orthotropic constitutive model for myocardial infarcts in the acute, necrotic, fibrotic and remodelling phases utilizing the biaxial mechanical data developed in a previous study. FE model was developed mimicking the setup of the biaxial tensile experiment. The orthotropic case of the generalized Fung constitutive model was utilized to model the material properties of the infarct. The parameters of Fung model were optimized so that the FE solution best fitted the biaxial experimental stress-strain data. A genetic algorithm was used to minimize the objective function. Fung orthotropic material parameters for different infarct stages were identified. The FE model predictions best approximated the experimental data of the 28 days infarct stage with 3.0% mean absolute percentage error. The worst approximation was for the 7 days stage with 3.6% error. This study demonstrated that the experimental biaxial stress-strain data of healing rat infarcts could be successfully approximated using inverse FE methods and genetic algorithms. The material parameters identified in this study will provide an essential platform for FE investigations of biomechanical aspects of MI and the development of therapies.

Heart failure remains one of the leading causes of death especially among people over the age of 60 years worldwide. To develop effective therapy and suitable replacement materials for the heart muscle it is necessary to understand its biomechanical behaviour under load. This paper investigates the passive mechanical response of the sheep myocardia excised from three different regions of the heart. Due to the relatively higher cost and huge ethical demands in acquisition and testing of real animal heart models, this paper evaluates the fitting performances of five different constitutive models on the myocardial tissue responses. Ten sheep were sacrificed, and their hearts excised and transported within 3h to the testing biomechanical laboratory. The upper sections of the hearts above the short axes were carefully dissected out. Tissues were dissected from the mid-sections of the left ventricle, mid-wall and right ventricle for each heart. The epicardia and endocardia were then carefully sliced off each tissue to leave the myocardia. Stress-strain curves were calculated, filtered and resampled. The results show that Choi-Vito model was found to provide the best fit to the LV, the polynomial (Anisotropic) model to RV, the Four-Fiber Family model to RV, Holzapfel (2000) to RV, Holzapfel (2005) to RV and the Fung model to LV.

Residual stresses are considered as a significant factor influencing the stress-states in arteries. These stresses are typically observed through opening angle of a radially cut artery segment, often regarded as a primary descriptor of their stress-free state. However, the experimental evidence regarding the stress-free states of different artery layers is scarce. In this study, two experimental protocols, each employing different layer-separating sequences, were performed on 17 human common carotid arteries; the differences between both protocols were found statistically insignificant. While the media exhibited opening behaviour (reduced curvature), a contrasting trend was observed for the adventitia curvature, indicating its closing behaviour. In addition to the different bending effect, length changes of both layers after separation were observed, namely shortening of the adventitia and elongation of the media. The results point out that not all the residual stresses are released after a radial cut but a significant portion of them is released only after the layer separation. Considering the different mechanical properties of layers, this may significantly change the stress distribution in arterial wall and should be considered in its biomechanical models.

The purpose of this study was to develop Injury Risk Functions (IRFs) for the Anterior- and Posterior Cruciate Ligament (ACL and PCL, respectively) and the Medial- and Lateral Collateral Ligament (MCL and LCL, respectively) in the knee joint. The IRFs were based on Post-Mortem Human Subject (PMHS) tensile failure strains of either Bone-Ligament-Bone (BLB) or dissected LIGament (LIG) preparations. Due to insufficient sample sizes of the experimental data points available in the current literature, statistically-generated failure strains (virtual values) based on the reported mean- and standard deviation were used to accommodate for the unprovided specimen-specific results. All virtual and specimen-specific values were then categorized into groups of static and dynamic rates, respectively, and tested for the best fitting theoretical distribution to derive a ligament IRF. Ten IRFs were derived (3 for ACL, 2 for PCL, 2 for MCL and 3 for LCL). These IRFs are, to the best of the authors knowledge, the first attempt of knee ligament injury prediction tools based on PMHS data. For future improvements of the knee ligament IRFs, upcoming experiments need comparable testing and strain measurements. More emphasis on a clear definition of failure and transparent reporting of each specimen-specific result is necessary.