Latest Articles Include:
- Editorial Board and Publication Information
- J Biomech 44(4):IFC (2011)
- In Memoriam: Rik Huiskes (1944–2010)
- J Biomech 44(4):575-576 (2011)
- Hip extension, knee flexion paradox: A new mechanism for non-contact ACL injury
- J Biomech 44(4):577-585 (2011)
Considering that an athlete performs at-risk sports activities countless times throughout the course of his or her career prior to the instance of anterior cruciate ligament (ACL) injury, one may conclude that non-contact ACL injury is a rare event. Nevertheless, the overall number of non-contact ACL injuries, both in the US and worldwide, remains alarming due to the growing number of recreational and professional athletes participating in high-risk activities. To date, numerous non-contact ACL injury mechanisms have been proposed, but none provides a detailed picture of sequence of events leading to injury and the exact cause of this injury remains elusive. In this perspective article, we propose a new conception of non-contact ACL injury mechanism that comprehensively integrates risk factors inside and outside the knee joint. The proposed mechanism is robust in the sense that it is biomechanically justifiable and addresses a number of confounding issues related to AC! L injury.
- Fatigue and tensile properties of radicular dentin substrate
- J Biomech 44(4):586-592 (2011)
The purpose of this study was to compare the fatigue and tensile strengths of radicular dentin. Forty bovine lower central incisors were used, twenty teeth for the fatigue test and twenty teeth for the tensile test. Bovine teeth were each sectioned into coronal and radicular portions. Dentin slabs of 1 mm thickness were prepared along the radicular tooth using a low-speed cutting machine and trimmed into dumbbell-shaped specimens. A dentin slab was harvested from each tooth. Subsequently, fatigue and tensile tests were performed in Hank's balanced saline solution at 37 °C. The staircase method was employed to determine fatigue strength and its standard deviation. Fracture surfaces were observed by scanning electron microscopy. Mean fatigue strength and tensile strength were 44.3±5.0 and 84.4±8.3 MPa, respectively. The fatigue strength of radicular dentin was significantly lower than the tensile strength. The fatigue strength of radicular dentin was only approximatel! y one half of the tensile strength.
- Mechanical signal influence on mesenchymal stem cell fate is enhanced by incorporation of refractory periods into the loading regimen
- J Biomech 44(4):593-599 (2011)
Mechanical signals of both low and high intensity are inhibitory to fat and anabolic to bone in vivo, and have been shown to directly affect mesenchymal stem cell pools from which fat and bone precursors emerge. To identify an idealized mechanical regimen which can regulate MSC fate, low intensity vibration (LIV; <10 microstrain, 90 Hz) and high magnitude strain (HMS; 20,000 microstrain, 0.17 Hz) were examined in MSC undergoing adipogenesis. Two×twenty minute bouts of either LIV or HMS suppressed adipogenesis when there was at least a 1 h refractory period between bouts; this effect was enhanced when the rest period was extended to 3 h. Mechanical efficacy to inhibit adipogenesis increased with additional loading bouts if a refractory period was incorporated. Mechanical suppression of adipogenesis with LIV involved inhibition of GSK3β with subsequent activation of β-catenin as has been shown for HMS. These data indicate that mechanical biasing of MSC lineage selecti! on is more dependent on event scheduling than on load magnitude or duration. As such, a full day of rest should not be required to "reset" the mechanical responsiveness of MSCs, and suggests that incorporating several brief mechanical challenges within a 24 h period may improve salutary endpoints in vivo. That two diverse mechanical inputs are enhanced by repetition after a refractory period suggests that rapid cellular adaptation can be targeted.
- Forces and deformations of the abdominal wall—A mechanical and geometrical approach to the linea alba
- J Biomech 44(4):600-606 (2011)
Force-elongation responses of the human abdominal wall in the linea alba region were determined by tensile tests in which the linea alba was seen to exhibit a nonlinear elastic, anisotropic behavior as is frequently observed in soft biological tissues. In addition, the geometry of the abdominal wall was determined, based on MRI data. The geometry can be specified by principal radii of curvature in longitudinal of approximately 470 mm and in the transverse direction of about 200 mm. The determined radii agree with values found in other studies. Mechanical stresses, deformations and abdominal pressures for load cases above 6% elongation can be related using Laplace's formula and our constitutive and geometrical findings. Results from uni- and biaxial tensile tests can thus be compared using this model. Calculations confirm that abdominal pressures of approximately 20 kPa correspond to related biaxial forces of about 3.4 N/mm in the transverse and 1.5 N/mm in the longitud! inal direction. Young's moduli can be calculated with respect to the uniaxial as well as the biaxial loading. At these physiological loadings, a compliance ratio of about 2:1 between the longitudinal and transversal directions is found. Young's moduli of about 50 kPa occur in transversal direction and of about 20 kPa in longitudinal direction at transverse and longitudinal strains both in the order of 6%. These findings coincide with results from other investigations in which the properties of the abdominal wall have been examined.
- Finding consistent strain distributions in the glenohumeral capsule between two subjects: Implications for development of physical examinations
- J Biomech 44(4):607-613 (2011)
The anterior-inferior glenohumeral capsule is the primary passive stabilizer to the glenohumeral joint during anterior dislocation. Physical examinations following dislocation are crucial for proper diagnosis of capsule pathology; however, they are not standardized for joint position which may lead to misdiagnoses and poor outcomes. To suggest joint positions for physical examinations where the stability provided by the capsule may be consistent among patients, the objective of this study was to evaluate the distribution of maximum principal strain on the anterior-inferior capsule using two validated subject-specific finite element models of the glenohumeral joint at clinically relevant joint positions. The joint positions with 25 N anterior load applied at 60° of glenohumeral abduction and 10°, 20°, 30° and 40° of external rotation resulted in distributions of strain that were similar between shoulders (r2≥0.7). Furthermore, those positions with 20–40° of ex! ternal rotation resulted in capsule strains on the glenoid side of the anterior band of the inferior glenohumeral ligament that were significantly greater than in all other capsule regions. These findings suggest that anterior stability provided by the anterior-inferior capsule may be consistent among subjects at joint positions with 60° of glenohumeral abduction and a mid-range (20–40°) of external rotation, and that the glenoid side has the greatest contribution to stability at these joint positions. Therefore, it may be possible to establish standard joint positions for physical examinations that clinicians can use to effectively diagnose pathology in the anterior-inferior capsule following dislocation and lead to improved outcomes.
- Dynamics of wrist rotations
- J Biomech 44(4):614-621 (2011)
Understanding the dynamics of wrist rotations is important for many fields, including biomechanics, rehabilitation and motor neuroscience. This paper provides an experimentally based mathematical model of wrist rotation dynamics in Flexion–Extension (FE) and Radial–Ulnar Deviation (RUD), and characterizes the torques required to overcome the passive mechanical impedance of wrist rotations. We modeled the wrist as a universal joint with non-intersecting axes. The equations of motion of the hand rotating about the wrist joint include inertial, damping, and stiffness terms, with parameter values based on direct measurements (stiffness) or measurements combined with data available in the literature (inertia, damping). We measured the wrist kinematics of six young, healthy subjects making comfortable and fast-paced wrist rotations (±15° in FE, RUD, and combinations) and inserted these kinematic data into the model of wrist rotation dynamics. With this we quantified the torques required to overcome the impedance of wrist rotations and evaluated the relative importance of individual impedance terms as well as interactions between the degrees of freedom. We found that the wrist's passive stiffness is the major impedance the neuromuscular system must overcome to rotate the wrist. Inertia and passive damping only become important for very fast movements. Unlike elbow and shoulder reaching movements, inertial interaction torques are negligible for wrist rotations. Interaction torques due to stiffness and damping, however, are significant. Finally, we found that some model terms (inertial interaction torques, axis offset, and, for moderately sized rotations, non-linearities) can be neglected with little loss of accuracy, resulting in a simple, linear model useful for studies in biomechanics, motor neuroscience, and rehabilitation.
- Characterization of blood clot viscoelasticity by dynamic ultrasound elastography and modeling of the rheological behavior
- J Biomech 44(4):622-629 (2011)
Dynamic elastography (DE) is a new tool to study mechanical behavior of soft tissues via their motion response to propagating shear waves. This technique characterized viscoelasticity of 9 porcine whole blood samples (3 animals) during coagulation for a shearing frequency of 70 Hz, and after complete clot formation between 50 and 160 Hz. Clot storage (G′) and loss (G″) moduli were calculated from shear wave velocity and attenuation. Temporal evolutions of G′ and G″ during coagulation were typified with 4 parameters: maximum change in elasticity (G′ slopemax), elasticity after 120 min of coagulation (G′max), time occurrence of G″ maximum (te) and G″ at the plateau (G″plateau). G′ and G″ frequency dependence of completely formed blood clots was fitted with 5 standard rheological models: Maxwell, Kelvin–Voigt, Jeffrey, Zener and third-order generalized Maxwell. DE had sufficient sensitivity to follow the coagulation kinetics described by a progress! ive increase in G′, while G″ transitory increased followed by a rapid stabilization. Inter- and intra-animal dispersions (InterAD and IntraAD) of G′max (InterAD=15.9%, IntraAD=9.1%) showed better reproducibility than G′ slopemax (InterAD=40.4%, IntraAD=21.9%), te (InterAD=27.4%, IntraAD=18.7%) and G″plateau (InterAD=58.6%, IntraAD=40.2%). G′ evolution within the considered range of frequency exhibited an increase, followed by stabilization to a plateau, whereas G″ presented little variations with convergence at a quasi-constant value at highest frequencies. Residues χ, describing the goodness of fit between models and experimental data, showed statistically (p<0.05) that the Kelvin–Voigt model was less in agreement with experimental data than other models. The Zener model is recommended to predict G′ and G″ dispersion of coagulated blood over the explored frequency range.
- Biomechanics of actin filaments: A computational multi-level study
- J Biomech 44(4):630-636 (2011)
The actin microfilament (F-actin) is a structural and functional component of the cell cytoskeleton. Notwithstanding the primary role it plays for the mechanics of the cell, the mechanical behaviour of F-actin is still not totally explored. In particular, the relationship between the mechanics of F-actin and its molecular architecture is not completely understood. In this study, the mechanical properties of F-actin were related to the molecular topology of its building monomers (G-actin) by employing a computational multi-level approach. F-actins with lengths up to 500 nm were modelled and characterized, using a combination of equilibrium molecular dynamics (MD) simulations and normal mode analysis (NMA). MD simulations were performed to analyze the molecular rearrangements of G-actin in physiological conditions; NMA was applied to compute the macroscopic properties of F-actin from its vibrational modes of motion. Results from this multi-level approach showed that bending stiffness, bending modulus and persistence length are independent from the length of F-actin. On the contrary, the orientations and motions of selected groups of residues of G-actin play a primary role in determining the filament flexibility. In conclusion, this study (i) demonstrated that a combined computational approach of MD and NMA allows to investigate the biomechanics of F-actin taking into account the molecular topology of the filament (i.e., the molecular conformations of G-actin) and (ii) that this can be done using only crystallographic G-actin, without the need of introducing experimental parameters nor of reducing the number of residues.
- Vertical ground reaction forces diminish in mice after botulinum toxin injection
- J Biomech 44(4):637-643 (2011)
We examined changes in weight-bearing ability in mice after injection with botulinum toxin type A (BTX) to determine whether BTX can be used to isolate the effects of muscle on bone. As ambulation patterns were previously shown to improve within two weeks post-injection, we hypothesized that BTX injection to the posterior hindlimb would not significantly affect the mouse's ability to bear weight in the affected limb one week post-injection. Female BALB/c mice (N=13, 16–17 week old) were injected with either 20 μL of BTX (1 U/100 g) or saline (SAL) in the left posterior hindlimb. Vertical ground reaction forces (GRF), hindlimb muscle cross-sectional area (MCSA), and tibial bone micro-architecture were assessed for 42 d following injection. Peak and average vertical GRF were 11±1% and 23±3% lower, respectively, in the BTX-injected hindlimb within 4 d post-injection and remained lower than the SAL-injected hindlimb 14–21 d post-injection (15±4% and 10±2%, respe! ctively). Time between forelimb and hindlimb peaks was 30–40% greater in the BTX-injected hindlimb than SAL-injected hindlimb 4–14 d post-injection. Peak vertical GRF recovered earlier following BTX injection than MCSA or bone volume fraction. These results indicate that weight-bearing ability recovered despite persistent muscle atrophy, and that weight-bearing alone was insufficient to maintain bone in the absence of muscle activity. We suggest that the absence of high-frequency signals typically associated with fast-twitch muscle activity may be contributing to the ongoing degradation of bone after BTX injection.
- Dynamic stability of human walking in visually and mechanically destabilizing environments
- J Biomech 44(4):644-649 (2011)
Understanding how humans remain stable during challenging locomotor activities is critical to developing effective tests to diagnose patients with increased fall risk. This study determined if different continuous low-amplitude perturbations would induce specific measureable changes in measures of dynamic stability during walking. We applied continuous pseudo-random oscillations of either the visual scene or support surface in either the anterior–posterior or mediolateral directions to subjects walking in a virtual environment with speed-matched optic flow. Floquet multipliers and short-term local divergence exponents both increased (indicating greater instability) during perturbed walking. These responses were generally much stronger for body movements occurring in the same directions as the applied perturbations. Likewise, subjects were more sensitive to both visual and mechanical perturbations applied in the mediolateral direction than to those applied in the ante! rior–posterior direction, consistent with previous experiments and theoretical predictions. These responses were likewise consistent with subjects' anecdotal perceptions of which perturbation conditions were most challenging. Contrary to the Floquet multipliers and short-term local divergence exponents, which both increased, long-term local divergence exponenets decreased during perturbed walking. However, this was consistent with specific changes in the mean log divergence curves, which indicated that subjects' movements reached their maximum local divergence limits more quickly during perturbed walking. Overall, the Floquet multipliers were less sensitive, but reflected greater specificity in their responses to the different perturbation conditions. Conversely, the short-term local divergence exponents exhibited less specificity in their responses, but were more sensitive measures of instability in general.
- Individual muscle force parameters and fiber operating ranges for elbow flexion–extension and forearm pronation–supination
- J Biomech 44(4):650-656 (2011)
We have quantified individual muscle force and moment contributions to net joint moments and estimated the operating ranges of the individual muscle fibers over the full range of motion for elbow flexion/extension and forearm pronation/supination. A three dimensional computer graphics model was developed in order to estimate individual muscle contributions in each degree of freedom over the full range of motion generated by 17 muscles crossing the elbow and forearm. Optimal fiber length, tendon slack length, and muscle specific tension values were adjusted within the literature range from cadaver studies such that the net isometric joint moments of the model approximated experimental joint moments within one standard deviation. Analysis of the model revealed that the muscles operate on varying portions of the ascending limb, plateau region, and descending limb of the force–length curve. This model can be used to further understand isometric force and moment contribut! ions of individual muscles to net joint moments of the arm and forearm and can serve as a comprehensive reference for the forces and moments generated by 17 major muscles crossing the elbow and wrist.
- Sickle cell trait human erythrocytes are significantly stiffer than normal
- J Biomech 44(4):657-661 (2011)
Atomic force microscopy (AFM) allows for high-resolution topography studies of biological cells and measurement of their mechanical properties in physiological conditions. In this work, AFM was employed to measure the stiffness of abnormal human red blood cells from human subjects with the genotype for sickle cell trait. The determined Young's modulus was compared with that obtained from measurements of erythrocytes from healthy subjects. The results showed that Young's modulus of pathological erythrocytes was approximately three times higher than in normal cells. Observed differences indicate the effect of the polymerization of sickle hemoglobin as well as possible changes in the organization of the cell cytoskeleton associated with the sickle cell trait.
- A nonlinear characteristic regime of biomembrane force probe
- J Biomech 44(4):662-668 (2011)
A linear relation between stiffness and aspiration pressure is the basis for biomembrane force probe (BFP), a widely used technique to measure minuscule forces. Here we perform finite element simulations and semi-analytical modeling of the BFP operation to show that, at low aspiration pressures, there exists a characteristic regime in which the relation between stiffness and aspiration pressure is actually nonlinear. We find that this nonlinear characteristic regime arises from a transition in configuration of a partially aspirated biomembrane force probe under increasing aspiration pressure. We discuss both the conditions for the transition and the characteristics of the nonlinear characteristic regime, as well as its potential applications.
- A simulation analysis of the combined effects of muscle strength and surgical tensioning on lateral pinch force following brachioradialis to flexor pollicis longus transfer
- J Biomech 44(4):669-675 (2011)
Biomechanical simulations of tendon transfers performed following tetraplegia suggest that surgical tensioning influences clinical outcomes. However, previous studies have focused on the biomechanical properties of only the transferred muscle. We developed simulations of the tetraplegic upper limb following transfer of the brachioradialis (BR) to the flexor pollicis longus (FPL) to examine the influence of residual upper limb strength on predictions of post-operative transferred muscle function. Our simulations included the transfer, ECRB, ECRL, the three heads of the triceps, brachialis, and both heads of the biceps. Simulations were integrated with experimental data, including EMG and joint posture data collected from five individuals with tetraplegia and BR-FPL tendon transfers during maximal lateral pinch force exertions. Given a measured co-activation pattern for the non-paralyzed muscles in the tetraplegic upper limb, we computed the highest activation for the tr! ansferred BR for which neither the elbow nor the wrist flexor moment was larger than the respective joint extensor moment. In this context, the effects of surgical tensioning were evaluated by comparing the resulting pinch force produced at different muscle strength levels, including patient-specific scaling. Our simulations suggest that extensor muscle weakness in the tetraplegic limb limits the potential to augment total pinch force through surgical tensioning. Incorporating patient-specific muscle volume, EMG activity, joint posture, and strength measurements generated simulation results that were comparable to experimental results. Our study suggests that scaling models to the population of interest facilitates accurate simulation of post-operative outcomes, and carries utility for guiding and developing rehabilitation training protocols.
- Post-yield nanomechanics of human cortical bone in compression using synchrotron X-ray scattering techniques
- J Biomech 44(4):676-682 (2011)
The ultrastructural response to applied loads governs the post-yield deformation and failure behavior of bone, and is correlated with bone fragility fractures. Combining a novel progressive loading protocol and synchrotron X-ray scattering techniques, this study investigated the correlation of the local deformation (i.e., internal strains of the mineral and collagen phases) with the bulk mechanical behavior of bone. The results indicated that the internal strains of the longitudinally oriented collagen fibrils and mineral crystals increased almost linearly with respect to the macroscopic strain prior to yielding, but markedly decreased first and then gradually leveled off after yielding. Similar changes were also observed in the applied stress before and after yielding of bone. However, the collagen to mineral strain ratio remained nearly constant throughout the loading process. In addition, the internal strains of longitudinal mineral and collagen phases did not exhib! it a linear relationship with either the modulus loss or the plastic deformation of bulk bone tissue. Finally, the time-dependent response of local deformation in the mineral phase was observed after yielding. Based on the results, we speculate that the mineral crystals and collagen fibrils aligned with the loading axis only partially explain the post-yield deformation, suggesting that shear deformation involving obliquely oriented crystals and fibrils (off axis) is dominant mechanism of yielding for human cortical bone in compression.
- Optimization-based prediction of asymmetric human gait
- J Biomech 44(4):683-693 (2011)
An optimization-based formulation and solution method are presented to predict asymmetric human gait for a large-scale skeletal model. Predictive dynamics approach is used in which both the joint angles and joint torques are treated as unknowns in the equations of motion. For the optimization formulation, the joint angle profiles are treated as the primary unknowns, and velocities and accelerations are calculated using them. In numerical implementation, the joint angle profiles are discretized using the B-spline interpolation. An algorithm is presented to inversely calculate the joint torques and the ground reaction forces. The sum of the joint-torques squared, called the dynamic effort, is minimized as the human performance measure. Constraints are imposed on the joint strengths (torques) and joint ranges of motion along with other physical constraints. The formulation is validated by simulating a symmetric gait and comparing the results with the experimental data. Th! en asymmetric gait motion is simulated, where the left and right step lengths are different. The kinematics and kinetics results from the simulation are presented and discussed. Predicted ground reaction forces are explained by using the inverted pendulum model. Predicted kinematics and kinetics have trends that are similar to those reported in the literature. Potential practical applications of the formulation and the solution approach are discussed.
- Evaluation of a hydrogel–fiber composite for ACL tissue engineering
- J Biomech 44(4):694-699 (2011)
The anterior cruciate ligament (ACL) is necessary for normal knee stability and movement. Unfortunately the ACL is also the most frequently injured ligament of the knee with severe disruptions requiring surgical intervention. In response to this, tissue engineering has emerged as an option for ACL replacement and repair. In this study we present a novel hydrogel-fibrous scaffold as a potential option for ACL replacement. The scaffold was composed of PLLA fibers, in a previously evaluated braid-twist structure, combined with a polyethylene glycol diacrylate (PEGDA) hydrogelto improve viscoelastic properties. Both hydrogel concentration (10%, 15%, and 20%) and amount of hydrogel (soaking the fibrous scaffold in hydrogel solution or encasing the scaffold in a block of hydrogel) were evaluated. It was found that the braid-twist scaffold had a greater porosity and larger number of pores above 100 μm than braided scaffolds with the same braiding angle. After testing for the! ir effects on swelling, fiber degradation, and protein release, as well as viscoelastic and tensile testing (when combined with fibrous scaffolds), it was found that the composite scaffold soaked in 10% hydrogel had the best chemical release and mechanical properties. The optimized structure behaved similarly to natural ligament in tension with the addition of the hydrogel decreasing the ultimate tensile stress (UTS), but the UTS was still comparable to natural ACL. In addition, cellular studies showed that the hydrogel–PLLA fiber composite supported fibroblast growth.
- Comparison of glenohumeral motion using different rotation sequences
- J Biomech 44(4):700-705 (2011)
Glenohumeral motion presents challenges for its accurate description across all available ranges of motion using conventional Euler/Cardan angle sequences without singularity. A comparison of the description of glenohumeral motion was made using the ISB recommended YX′Y″ sequence to the XZ′Y″ sequence. A direct in-vivo method was used for the analysis of dynamic concentric glenohumeral joint motion in the scapular plane. An electromagnetic tracking system collected data from ten healthy individuals while raising their arm. There were differences in the description of angular position data between the two different sequences. The YX′Y″ sequence described the humerus to be in a more anteriorly rotated and externally rotated position compared to XZ′Y″ sequence, especially, at lower elevation angles. The description of motion between increments using XZ′Y″ sequence displacement decomposition was comparable to helical angles in magnitude and direction fo! r the study of arm elevation in the scapular plane. The description of the direction or path of motion of the plane of elevation using YX′Y″ angle decomposition would be contrary to that obtained using helical angles. We recommend that this alternate sequence (XZ′Y″) should be considered for describing glenohumeral motion.
- Altered control strategy between leading and trailing leg increases knee adduction moment in the elderly while descending stairs
- J Biomech 44(4):706-711 (2011)
The aim of the study was to examine the external knee adduction moments in a group of older and younger adults while descending stairs and thus the possibility of an increased risk of knee osteoarthritis due to altered knee joint loading in the elderly. Twenty-seven older and 16 younger adults descended a purpose-built staircase. A motion capture system and a force plate were used to determine the subjects' 3D kinematics and ground reaction forces (GRF) during locomotion. Calculation of the leg kinematics and kinetics was done by means of a rigid, three-segment, 3D leg model. In the initial portion of the support phase, older adults showed a more medio-posterior GRF vector relative to the ankle joint, leading to lower ankle joint moments (P<0.05). At the knee, the older adults demonstrated a more medio-posterior directed GRF vector, increasing in knee flexion and adduction in the second part of the single support phase (P<0.05). Further, GRF magnitude was lower in th! e initial and higher in the mid-portions of the support phase for the elderly (P<0.05). The results show that older adults descend stairs by using the trailing leg before the initiation of the double support phase more compared to the younger ones. The consequence of this altered control strategy while stepping down is a more medially directed GRF vector increasing the magnitude of external knee adduction moment in the elderly. The observed changes between leading and trailing leg in the elderly may cause a redistribution of the mechanical load at the tibiofemoral joint, affecting the initiation and progression of knee osteoarthritis in the elderly.
- Femur shape prediction by multiple regression based on quadric surface fitting
- J Biomech 44(4):712-718 (2011)
Quadric surface fitting of joint surface areas is often performed to allow further processing of joint component size, location and orientation (pose), or even to determine soft tissue wrapping by collision detection and muscle moment arm evaluation. This study aimed to determine, for the femoral bone, if the position of its morphological joint centers and the shape morphology could be approximated using regression methods with satisfactory accuracy from a limited amount of palpable anatomical landmarks found on the femoral bone surface. The main aim of this paper is the description of the pipeline allowing on one hand the data collection and database storage of femoral bone characteristics, and on the other hand the determination of regression relationships from the available database. The femoral bone components analyzed in this study included the diaphysis, all joint surfaces (shape, location and orientation of the head, condyles and femoro-patellar surface) and the! ir respective spatial relationships (e.g., cervico-diaphyseal angle, cervico-bicondylar angle, intercondylar angle, etc.). A total of 36 morphological characteristics are presented and can be estimated by regression method in in-vivo applications from the spatial location of 3 anatomical landmarks (lateral epicondyle, medial epicondyle and greater trochanter) located on the individual under investigation. The method does not require any a-priori knowledge on the functional aspect of the joint. In-vivo and in-vitro validations have been performed using data collected from medical imaging by virtual palpation and data collected directly on a volunteer using manual palpation through soft tissue. The prediction accuracy for most of the 36 femoral characteristics determined from virtual palpation was satisfactory, mean (SD) distance and orientation errors were 2.7(2.5) mm and 6.8(2.7)°, respectively. Manual palpation data allowed good accuracy for most femoral features, mean (S! D) distance and orientation errors were 4.5(5.2) mm and 7.5(5.! 3)°, respectively. Only the in-vivo location estimation of the femoral head was worse (position error=23.2 mm). In conclusion, results seem to show that the method allows in-vivo femoral joint shape prediction and could be used for further development (e.g., surface collision, muscle wrapping, muscle moment arm estimation, joint surface dimensions, etc.) in gait analysis-related applications.
- True stress and Poisson's ratio of tendons during loading
- J Biomech 44(4):719-724 (2011)
Excessive axial tension is very likely involved in the aetiology of tendon lesions, and the most appropriate indicator of tendon stress state is the true stress, the ratio of instantaneous load to instantaneous cross-sectional area (CSA). Difficulties to measure tendon CSA during tension often led to approximate true stress by assuming that CSA is constant during loading (i.e. by the engineering stress) or that tendon is incompressible, implying a Poisson's ratio of 0.5, although these hypotheses have never been tested. The objective of this study was to measure tendon CSA variation during quasi-static tensile loading, in order to assess the true stress to which the tendon is subjected and its Poisson's ratio. Eight equine superficial digital flexor tendons (SDFT, about 30 cm long) were tested in tension until failure while the CSA of each tendon was measured in its metacarpal part by means of a linear laser scanner. Axial elongation and load were synchronously recorde! d during the test. CSA was found to linearly decrease with strain, with a mean decrease at failure of −10.7±2.8% (mean±standard deviation). True stress at failure was 7.1–13.6% higher than engineering stress, while stress estimation under the hypothesis of incompressibility differed from true stress of −6.6 to 2.3%. Average Poisson's ratio was 0.55±0.12 and did not significantly vary with load. From these results on equine SDFT it was demonstrated that tendon in axial quasi-static tension can be considered, at first approximation, as an incompressible material.
- A biomechanical assessment to evaluate breed differences in normal porcine medial collateral ligaments
- J Biomech 44(4):725-731 (2011)
Little information is available on the role of genetic factors and heredity in normal ligament behaviour and their ability to heal. Assessing these factors is challenging because of the lack of suitable animal models. Therefore, the purpose of this study was to develop a porcine model in order to evaluate and compare the biomechanical differences of normal medial collateral ligaments (MCLs) between Yorkshire (YK) and red Duroc (RD) breeds. It was hypothesized that biomechanical differences would not exist between normal YK and RD MCLs. Comparisons between porcine and human MCL were also made. A biomechanical testing apparatus and protocol specific to pig MCL were developed. Ligaments were subjected to cyclic and static creep tests and then elongated to failure. Pig MCL morphology, geometry, and low- and high-load mechanical behaviour were assessed. The custom-designed apparatus and protocol were sufficiently sensitive to detect mechanical property differences between b! reeds as well as inter-leg differences. The results reveal that porcine MCL is comparable in both shape and size to human MCL and exhibits similar structural and material failure properties, thus making it a feasible model. Comparisons between RD and YK breeds revealed that age-matched RD pigs weigh more, have larger MCL cross-sectional area, and have lower MCL failure stress than YK pigs. The effect of weight may have influenced MCL geometrical and biomechanical properties, and consequently, the differences observed may be due to breed type and/or animal weight. In conclusion, the pig serves as a suitable large animal model for genetic-related connective tissue studies.
- The 3D trajectory of the body centre of mass during adult human walking: Evidence for a speed–curvature power law
- J Biomech 44(4):732-740 (2011)
During straight walking, the body centre of mass (CM) follows a 3D figure-of-eight ("bow-tie") trajectory about 0.2 m long and with sizes around 0.05 m on each orthogonal axis. This was shown in 18 healthy adults walking at 0.3 to 1.4 m s−1 on a force-treadmill (Tesio and Rota, 2008). Double integration of force signals can provide both the changes of mechanical energy of the CM and its 3D displacements (Tesio et al., 2010). In the same subjects, the relationship between the tangential speed of the CM, Vt, the curvature, C, and its inverse—the radius of curvature, rc, were analyzed. A "power law" (PL) model was applied, i.e. log Vt was regressed over log rc. A PL is known to apply to the most various goal-directed planar movements (e.g. drawing), where the coefficient of log rc, β, usually takes values around . When the PL was fitted to the whole dataset, β was 0.346 and variance explanation, R2, was 59.8%. However, when the data were split into low- and ! high-curvature subsets (LC, HC, arbitrary cut-off of C=0.05 mm−1, rc=20 mm), β was 0.185 in the LC (R2 0.214) and 0.486 in the HC (R2 0.536) tracts. R2 on the whole dataset increased to 0.763 if the LC–HC classification of the forward speed and their interaction entered the model. The β coefficient, the curvature C, and the pendulum-like recovery of mechanical energy were lower during the double foot-ground contact phase, compared to the single contact. Along the CM trajectory, curvature and muscle power output peaked together around the inversions of lateral direction. Non-zero torsion values were randomly distributed along 60% of the trajectory, suggesting that this is not segmented into piecewise planar tracts. It is proposed that the trajectory can be segmented into one tract that is more actively controlled (tie) where a PL fits poorly and another tract which is more ballistic (bow) where a PL fits well. Results need confirmation through more appropriate 3D PL mo! delling.
- Mechanical force characterization in manipulating live cells with optical tweezers
- J Biomech 44(4):741-746 (2011)
Laser trapping with optical tweezers is a noninvasive manipulation technique and has received increasing attentions in biological applications. Understanding forces exerted on live cells is essential to cell biomechanical characterizations. Traditional numerical or experimental force measurement assumes live cells as ideal objects, ignoring their complicated inner structures and rough membranes. In this paper, we propose a new experimental method to calibrate the trapping and drag forces acted on live cells. Binding a micro polystyrene sphere to a live cell and moving the mixture with optical tweezers, we can obtain the drag force on the cell by subtracting the drag force on the sphere from the total drag force on the mixture, under the condition of extremely low Reynolds number. The trapping force on the cell is then obtained from the drag force when the cell is in force equilibrium state. Experiments on numerous live cells demonstrate the effectiveness of the propose! d force calibration approach.
- Representation of planar motion of complex joints by means of rolling pairs. Application to neck motion
- J Biomech 44(4):747-750 (2011)
We propose to model planar movements between two human segments by means of rolling-without-slipping kinematic pairs. We compute the path traced by the instantaneous center of rotation (ICR) as seen from the proximal and distal segments, thus obtaining the fixed and moving centrodes, respectively. The joint motion is then represented by the rolling-without-slipping of one centrode on the other. The resulting joint kinematic model is based on the real movement and accounts for nonfixed axes of rotation; therefore it could improve current models based on revolute pairs in those cases where joint movement implies displacement of the ICR. Previous authors have used the ICR to characterize human joint motion, but they only considered the fixed centrode. Such an approach is not adequate for reproducing motion because the fixed centrode by itself does not convey information about body position. The combination of the fixed and moving centrodes gathers the kinematic informatio! n needed to reproduce the position and velocities of moving bodies. To illustrate our method, we applied it to the flexion–extension movement of the head relative to the thorax. The model provides a good estimation of motion both for position variables (mean Rpos=0.995) and for velocities (mean Rvel=0.958). This approach is more realistic than other models of neck motion based on revolute pairs, such as the dual-pivot model. The geometry of the centrodes can provide some information about the nature of the movement. For instance, the ascending and descending curves of the fixed centrode suggest a sequential movement of the cervical vertebrae.
- Double calibration: An accurate, reliable and easy-to-use method for 3D scapular motion analysis
- J Biomech 44(4):751-754 (2011)
The most recent non-invasive methods for the recording of scapular motion are based on an acromion marker (AM) set and a single calibration (SC) of the scapula in a resting position. However, this method fails to accurately measure scapular kinematics above 90° of arm elevation, due to soft tissue artifacts of the skin and muscles covering the acromion. The aim of this study was to evaluate the accuracy, and inter-trial and inter-session repeatability of a double calibration method (DC) in comparison with SC. The SC and DC data were measured with an optoelectronic system during arm flexion and abduction at different angles of elevation (0–180°). They were compared with palpation of the scapula using a scapula locator. DC data was not significantly different from palpation for 5/6 axes of rotation tested (Y, X, and Z in abduction and flexion), where as SC showed significant differences for 5/6 axes. The root mean square errors ranged from 2.96° to 4.48° for DC and! from 6° to 9.19° for SC. The inter-trial repeatability was good to excellent for SC and DC. The inter-session repeatability was moderate to excellent for SC and moderate to good for DC. Coupling AM and DC is an easy-to-use method, which yields accurate and reliable measurements of scapular kinematics for the complete range of arm motion. It can be applied to the measurement of shoulder motion in many fields (sports, orthopaedics, and rehabilitation), especially when large ranges of arm motion are required.
- A model for cell motility on soft bio-adhesive substrates
- J Biomech 44(4):755-758 (2011)
Mechanical stiffness of bio-adhesive substrates has been recognized as a major regulator of cell motility. We present a simple physical model to study the crawling locomotion of a contractile cell on a soft elastic substrate. The mechanism of rigidity sensing is accounted for using Schwarz's two-spring model Schwarz et al. (2006). The predicted dependency between the speed of motility and substrate stiffness is qualitatively consistent with experimental observations. The model demonstrates that the rigidity dependent motility of cells is rooted in the regulation of actomyosin contractile forces by substrate deformation at each anchorage point. On stiffer substrates, the traction forces required for cell translocation acquire larger magnitude but show weaker asymmetry which leads to slower cell motility. On very soft substrates, the model predicts a biphasic relationship between the substrate rigidity and the speed of locomotion, over a narrow stiffness range, which has! been observed experimentally for some cell types.
- Elliptical contact of thin biphasic cartilage layers: Exact solution for monotonic loading
- J Biomech 44(4):759-761 (2011)
A three-dimensional unilateral contact problem for articular cartilage layers is considered in the framework of the biphasic cartilage model. The articular cartilages bonded to subchondral bones are modeled as biphasic materials consisting of a solid phase and a fluid phase. It is assumed that the subchondral bones are rigid and shaped like elliptic paraboloids. The obtained analytical solution is valid for monotonically increasing loading conditions.
- Evaluation of the influence of growth medium composition on cell elasticity
- J Biomech 44(4):762-766 (2011)
Recently, there has been an increasing interest in using the biomechanical properties of cells as biomarkers to discriminate between normal and cancerous cells. However, few investigators have considered the influence of the growth medium composition when evaluating the biomechanical properties of the normal and diseased cells. In this study, we investigated the variation in Young's modulus of non-malignant MCF10A and malignant MDA-MB-231 breast cells seeded in five different growth media under controlled experimental conditions. The average Young's modulus of MDA-MB-231 cells was significantly lower (p<0.0001) than the mean Young's modulus of MCF10A cells when compared in identical medium compositions. However, we found that growth medium composition affected the elasticity of MCF10A and MDA-MB-231 cells. The average Young's modulus of both cell lines decreased by 10–18% when the serum was reduced from 10% to 5% and upon addition of epidermal growth factor (! EGF, 20 ng/ml) to the medium. Though these elasticity changes might have some biological impact, none was statistically significant. However, the elasticity of MCF10A was significantly more responsive than MDA-MB-231 cells to the medium composition supplemented with EGF, cholera toxin (CT), insulin (INS) and hydrocortisone (HC), which are recommended for routine cultivation of MCF10A cells (M5). MCF10A cells were significantly softer (p<0.002) when grown in medium M5 compared to a standard MDA-MB-231 medium (M1). The investigation of the effects of culture medium composition on the elastic properties of cells highlights the need to take these effects into consideration when interpreting elasticity measurements in cells grown in different media.
- Multiscale models of the hybrid palliation for hypoplastic left heart syndrome
- J Biomech 44(4):767-770 (2011)
A less-invasive procedure that combines interventional stent placement in the ductus arteriosus and surgical banding of the branch pulmonary arteries has been recently introduced in the treatment of the hypoplastic left heart syndrome (HLHS). The hemodynamic behaviour of this hybrid approach has not been examined before in a mathematical model. In this study, a mathematical model of the hybrid procedure for HLHS is described, applying a multiscale approach that couples 3D models of the area of the surgical operation and lumped parameter models of the remaining circulation. The effects of various degrees of pulmonary banding and different stent sizes inserted in the ductus arteriosus on pulmonary–systemic flow ratio, cardiac output and oxygen delivery were assessed. Computational results suggest that balanced systemic and pulmonary blood flow and optimal systemic oxygen delivery are sensitive to the degree of pulmonary arterial banding and not to the size of the ducta! l stent.
- Elucidation of extracellular matrix mechanics from muscle fibers and fiber bundles
- J Biomech 44(4):771-773 (2011)
The importance of the extracellular matrix (ECM) in muscle is widely recognized, since ECM plays a central role in proper muscle development (Buck and Horwitz, 1987), tissue structural support (Purslow, 2002), and transmission of mechanical signals between fibers and tendon (Huijing, 1999). Since substrate biomechanical properties have been shown to be critical in the biology of tissue development and remodeling ([Engler et al., 2006] and [Gilbert et al., 2010]), it is likely that mechanics are critical for ECM to perform its function. Unfortunately, there are almost no data available regarding skeletal muscle ECM viscoelastic properties. This is primarily due to the impossibility of isolating and testing muscle ECM. Therefore, this note presents a new method to quantify viscoelastic ECM modulus by combining tests of single muscle fibers and fiber bundles. Our results demonstrate that ECM is a highly nonlinearly elastic material, while muscle fibers are linearly elasti! c.
- The natural frequency of the foot-surface cushion during the stance phase of running
- J Biomech 44(4):774-779 (2011)
Researchers have reported on the stiffness of running in holistic terms, i.e. for the structures that are undergoing deformation as a whole rather than in terms of specific locations. This study aimed to estimate both the natural frequency and the viscous damping coefficient of the human foot-surface cushion, during the period between the heel strike and the mid-stance phase of running, using a purposely developed one degree-of-freedom inverted pendulum state space model of the leg. The model, which was validated via a comparison of measured and estimated ground reaction forces, incorporated a novel use of linearized and extended Kalman filter estimators. Investigation of the effect of variation of the natural frequency and/or the damping of the cushioning mechanism during running, using the said model, revealed the natural frequency of running on said foot-surface cushion, during the stance phase, to lie between 5 and 11 Hz. The "extended Kalman filter (EKF)" appr! oach, that was used here for the first time to directly apply measured ground forces, may be widely applicable to the identification process of combined estimation of both unknown physiological state and mechanical characteristics of the environment in an inverse dynamic model.
- Mixed-mode failure strength of implant–cement interface specimens with varying surface roughness
- J Biomech 44(4):780-783 (2011)
Aseptic loosening at the implant–cement interface is a well-documented cause of failure in joint arthroplasty. Traditionally, the strength of the implant–cement interface is determined using uni-axial normal and shear loading tests. However, during functional loading, the implant fixation sites are loaded under more complex stress conditions. For this purpose, the strength of the implant–cement interface under mixed-mode tensile and shear loading conditions was determined in this study using interface specimens with varying interface roughness. For the lowest roughness value analyzed (Ra=0.89 μm), the interface strength was 0.40–1.95 MPa at loading angles varying between pure tension and shear, whereas this was 4.90–9.90 MPa for the highest roughness value (Ra=2.76 μm). The interface strength during pure shear (1.95–9.90 MPa) was substantially higher than during pure tension (0.58–6.67 MPa). Polynomial regression was used to fit a second-order interpola! tion function through the experimental interface strength data (R2=0.85; p<0.001), relating the interface strength (S [MPa]) to the interface loading angle (α [degrees]) and interface roughness (Ra [μm]): . Finally, an interface failure criterion was derived from the interface strength measurements, describing the risk of failure at the implant–cement interface when subjected to a certain tensile and shear stress using only the interface strength in pure tensile and shear direction. The findings presented in this paper can be used in numerical models to simulate loosening at the implant–cement interface.
- Accuracy of single-plane fluoroscopy in determining relative position and orientation of total knee replacement components
- J Biomech 44(4):784-787 (2011)
The accuracy of estimating the relative pose between knee replacement components, in terms of clinical motion, is important in the study of knee joint kinematics. The objective of this study was to determine the accuracy of the single-plane fluoroscopy method in calculating the relative pose between the femoral component and the tibial component, along knee motion axes, while the components were in motion relative to one another. The kinematics of total knee replacement components were determined in vitro using two simultaneous methods: single-plane fluoroscopic shape matching and an optoelectronic motion tracking system. The largest mean differences in relative pose between the two methods for any testing condition were 2.1°, 0.3°, and 1.1° in extension, abduction, and internal rotation respectively, and 1.3, 0.9, and 1.9 mm in anterior, distal, and lateral translations, respectively. For the optimized position of the components during dynamic trials, the limits of! agreement, between which 95% of differences can be expected to fall, were −2.9 to 4.5° in flexion, −0.9 to 1.5° in abduction, −2.4 to 2.1° in external rotation, −2.0 to 3.9 mm in anterior-posterior translation, −2.2 to 0.4 mm in distal-proximal translation and −7.2 to 8.6 mm in medial–lateral translation. These mean accuracy values and limits of agreement can be used to determine whether the shape-matching approach using single-plane fluoroscopic images is sufficiently accurate for an intended motion tracking application.