Aging effects on the Achilles tendon moment arm during walking

The Achilles tendon (AT) moment arm transforms triceps surae muscle forces into a moment about the ankle which is critical for functional activities like walking. Moreover, the AT moment arm changes continuously during walking, as it depends on both ankle joint rotation and triceps surae muscle loading (presumably due to bulging of the muscle belly). Here, we posit that aging negatively effects the architecturally complex AT moment arm during walking, which thereby contributes to well-documented reductions in ankle moment generation during push-off. We used motion capture-guided ultrasound imaging to quantify instantaneous variations in the AT moment arms of young (23.9 ± 4.3 years) and older (69.9 ± 2.6 years) adults during walking, their dependence on triceps surae muscle loading, and their association with ankle moment generation during push-off. Older adults walked with 11% smaller AT moment arms and 11% smaller peak ankle moments during push-off than young adults. Moreover, as hypothesized, these unfavourable changes were significantly and positively correlated (r² = 0.38, p < 0.01). More surprisingly, aging attenuated load-dependent increases in the AT moment arm (i.e., those between heel-strike and push-off at the same ankle angle); only young adults exhibited a significant increase in their AT moment arm due to triceps surae muscle-loading. Age-associated reductions in triceps surae volume or activation, and thus muscle bulging during force generation, may compromise the mechanical advantage of the AT during the critical push-off phase of walking in older adults. Thus, strategies to restore and/or improve locomotor performance in our aging population should consider these functionally important changes in musculoskeletal behavior.     

Variation in the human Achilles tendon moment arm during walking

The Achilles tendon (AT) moment arm is an important determinant of ankle moment and power generation during locomotion. Load and depth-dependent variations in the AT moment arm are generally not considered, but may be relevant given the complex triceps surae architecture. We coupled motion analysis and ultrasound imaging to characterize AT moment arms during walking in 10 subjects. Muscle loading during push-off amplified the AT moment arm by 10% relative to heel strike. AT moment arms also varied by 14% over the tendon thickness. In walking, AT moment arms are not strictly dependent on kinematics, but exhibit important load and spatial dependencies.     

A simple but reliable method for measuring 3D Achilles tendon moment arm geometry from a single,static magnetic resonance scan

Current methods for measuring in vivo 3D muscle-tendon moment arms generally rely on the acquisition of magnetic resonance imaging (MRI) scans at multiple joint angles. However, for patients with musculoskeletal pathologies such as fixed contractures, moving a joint through its full range of motion is not always feasible. The purpose of this research was to develop a simple, but reliable in vivo 3D Achilles tendon moment arm (ATMA) technique from a single static MRI scan. To accomplish this, for nine healthy adults (5 males, 4 females), the geometry of a cylinder was fit to the 3D form of the talus dome, which was used to estimate the talocrural flexion/extension axis, and a fifth-order polynomial fit to the line of action of the Achilles tendon. The single static scan in vivo 3D ATMA estimates were compared to estimates obtained from the same subjects at the same ankle joint angles using a previously validated 3D dynamic MRI based in vivo ATMA measurement technique. The ATMA estimates from the single scan in vivo 3D method (52.5 mm ± 5.6) were in excellent agreement (ICC = 0.912) to the validated in vivo 3D method (51.5 mm ± 5.1). These data show reliable in vivo 3D ATMA can be obtained from a single MRI scan for healthy adult populations. The single scan, in vivo 3D ATMA technique provides researchers with a simple, but reliable method for obtaining subject-specific ATMAs for musculoskeletal modelling purposes.     

Achilles tendon moment arm length is smaller in children with cerebral palsy than in typically developing children

When studying muscle and whole-body function in children with cerebral palsy (CP), knowledge about both internal and external moment arms is essential since they determine the mechanical advantage of a muscle over an external force. Here we asked if Achilles tendon moment arm (MA_AT) length is different in children with CP and age-matched typically developing (TD) children, and if MA_AT can be predicted from anthropometric measurements. Sixteen children with CP (age: 10y 7 m ± 3y, 7 hemiplegia, 12 diplegia, GMFCS level: I (11) and II (8)) and twenty TD children (age: 10y 6 m ± 3y) participated in this case-control study. MA_AT was calculated at 20° plantarflexion by differentiating calcaneus displacement with respect to ankle angle. Seven anthropometric variables were measured and related to MA_AT. We found normalized MA_AT to be 15% (∼7 mm) smaller in children with CP compared to TD children (p = 0.003). MA_AT could be predicted by all anthropometric measurements with tibia length explaining 79% and 72% of variance in children with CP and TD children, respectively. Our findings have important implications for clinical decision making since MA_AT influences the mechanical advantage about the ankle, which contributes to movement function and is manipulated surgically.     

Gait analysis in chronic heart failure: The calf as a locus of impaired walking capacity

Reduced walking capacity, a hallmark of chronic heart failure (CHF), is strongly correlated with hospitalization and morbidity. The aim of this work was to perform a detailed biomechanical gait analysis to better identify mechanisms underlying reduced walking capacity in CHF. Inverse dynamic analyses were conducted in CHF patients and age- and exercise level-matched control subjects on an instrumented treadmill at self-selected treadmill walking speeds and at speeds representing +20% and –20% of the subjects’ preferred speed. Surprisingly, no difference in preferred speed was observed between groups, possibly explained by an optimization of the mechanical cost of transport in both groups (the mechanical cost to travel a given distance; J/kg/m). The majority of limb kinematics and kinetics were also similar between groups, with the exception of greater ankle dorsiflexion angles during stance in CHF. Nevertheless, over two times greater ankle plantarflexion work during stance and per distance traveled is required for a given triceps surae muscle volume in CHF patients. This, together with a greater reliance on the ankle compared to the hip to power walking in CHF patients, especially at faster speeds, may contribute to the earlier onset of fatigue in CHF patients. This observation also helps explain the high correlation between triceps surae muscle volume and exercise capacity that has previously been reported in CHF. Considering the key role played by the plantarflexors in powering walking and their association with exercise capacity, our findings strongly suggest that exercise-based rehabilitation in CHF should not omit the ankle muscle group.     

The interaction of muscle moment arm,knee laxity,and torque in a multi-scale musculoskeletal model of the lower limb

IntroductionMusculoskeletal modeling allows insight into the interaction of muscle force and knee joint kinematics that cannot be measured in the laboratory. However, musculoskeletal models of the lower extremity commonly use simplified representations of the knee that may limit analyses of the interaction between muscle forces and joint kinematics. The goal of this research was to demonstrate how muscle forces alter knee kinematics and consequently muscle moment arms and joint torque in a musculoskeletal model of the lower limb that includes a deformable representation of the knee.MethodsTwo musculoskeletal models of the lower limb including specimen-specific articular geometries and ligament deformability at the knee were built in a finite element framework and calibrated to match mean isometric torque data collected from 12 healthy subjects. Muscle moment arms were compared between simulations of passive knee flexion and maximum isometric knee extension and flexion. In addition, isometric torque results were compared with predictions using simplified knee models in which the deformability of the knee was removed and the kinematics at the joint were prescribed for all degrees of freedom.ResultsPeak isometric torque estimated with a deformable knee representation occurred between 45° and 60° in extension, and 45° in flexion. The maximum isometric flexion torques generated by the models with deformable ligaments were 14.6% and 17.9% larger than those generated by the models with prescribed kinematics; by contrast, the maximum isometric extension torques generated by the models were similar. The change in hamstrings moment arms during isometric flexion was greater than that of the quadriceps during isometric extension (a mean RMS difference of 9.8 mm compared to 2.9 mm, respectively).DiscussionThe large changes in the moment arms of the hamstrings, when activated in a model with deformable ligaments, resulted in changes to flexion torque. When simulating human motion, the inclusion of a deformable joint in a multi-scale musculoskeletal finite element model of the lower limb may preserve the realistic interaction of muscle force with knee kinematics and torque.     

A mechanism accounting for independence on starting length of tension increase in ramp stretches of active skeletal muscle at short half-sarcomere lengths

Based on previous experimental results of independence on starting length of the tension gradient in constant-velocity stretches of active skeletal muscle at muscle lengths including the ascending limb and the plateau of the tension-length relation, a possible physiological mechanism determining the tension increase in lengthening active muscle is discussed. Considering the sliding filament theory, it is suggested that the tension-length relation of a half-sarcomere in lengthening contractions is different from that in isometric contractions. The assumed mechanism predicts, among others, that the thick filament retains its shortened length in lengthening contractions starting from a half-sarcomere length where this filament is compressed. An example model is implemented and checked with simulations.     

Statistical shape modelling versus linear scaling: Effects on predictions of hip joint centre location and muscle moment arms in people with hip osteoarthritis

Marker-based dynamic functional or regression methods are used to compute joint centre locations that can be used to improve linear scaling of the pelvis in musculoskeletal models, although large errors have been reported using these methods. This study aimed to investigate if statistical shape models could improve prediction of the hip joint centre (HJC) location. The inclusion of complete pelvis imaging data from computed tomography (CT) was also explored to determine if free-form deformation techniques could further improve HJC estimates. Mean Euclidean distance errors were calculated between HJC from CT and estimates from shape modelling methods, and functional- and regression-based linear scaling approaches. The HJC of a generic musculoskeletal model was also perturbed to compute the root-mean squared error (RMSE) of the hip muscle moment arms between the reference HJC obtained from CT and the different scaling methods. Shape modelling without medical imaging data significantly reduced HJC location error estimates (11.4 ± 3.3 mm) compared to functional (36.9 ± 17.5 mm, p = <0.001) and regression (31.2 ± 15 mm, p = <0.001) methods. The addition of complete pelvis imaging data to the shape modelling workflow further reduced HJC error estimates compared to no imaging (6.6 ± 3.1 mm, p = 0.002). Average RMSE were greatest for the hip flexor and extensor muscle groups using the functional (16.71 mm and 8.87 mm respectively) and regression methods (16.15 mm and 9.97 mm respectively). The effects on moment-arms were less substantial for the shape modelling methods, ranging from 0.05 to 3.2 mm. Shape modelling methods improved HJC location and muscle moment-arm estimates compared to linear scaling of musculoskeletal models in patients with hip osteoarthritis.     

Effects of lumbo-pelvic rhythm on trunk muscle forces and disc loads during forward flexion: A combined musculoskeletal and finite element simulation study

Previous in-vivo studies suggest that the ratio of total lumbar rotation over pelvic rotation (lumbo-pelvic rhythm) during trunk sagittal movement is essential to evaluate spinal loads and discriminate between low back pain and asymptomatic population. Similarly, there is also evidence that the lumbo-pelvic rhythm is key for evaluation of realistic muscle and joint reaction forces and moments predicted by various computational musculoskeletal models. This study investigated the effects of three lumbo-pelvic rhythms defined based on in-vivo measurements on the spinal response during moderate forward flexion (60°) using a combined approach of musculoskeletal modeling of the upper body and finite element model of the lumbosacral spine. The muscle forces and joint loads predicted by the musculoskeletal model, together with the gravitational forces, were applied to the finite element model to compute the disc force and moment, intradiscal pressure, annular fibers strain, and load-sharing. The results revealed that a rhythm with high pelvic rotation and low lumbar flexion involves more global muscles and increases the role of the disc in resisting spinal loads, while its counterpart, with low pelvic rotation, recruits more local muscles and engages the ligaments to lower the disc loads. On the other hand, a normal rhythm that has balanced pelvic and lumbar rotations yields almost equal disc and ligament load-sharing and results in more balanced synergy between global and local muscles. The lumbo-pelvic rhythm has less effect on the intradiscal pressure and annular fibers strain. This work demonstrated that the spinal response during forward flexion is highly dependent on the lumbo-pelvic rhythm. It is therefore, essential to adapt this parameter instead of using the default values in musculoskeletal models for accurate prediction of muscle forces and joint reaction forces and moments. The findings provided by this work are expected to improve knowledge of spinal response during forward flexion, and are clinically relevant towards low back pain treatment and disc injury prevention.     

Computational stability of human knee joint at early stance in Gait: Effects of muscle coactivity and anterior cruciate ligament deficiency

As one of the most complex and vulnerable structures of body, the human knee joint should maintain dynamic equilibrium and stability in occupational and recreational activities. The evaluation of its stability and factors affecting it is vital in performance evaluation/enhancement, injury prevention and treatment managements. Knee stability often manifests itself by pain, hypermobility and giving-way sensations and is usually assessed by the passive joint laxity tests. Mechanical stability of both the human knee joint and the lower extremity at early stance periods of gait (0% and 5%) were quantified here for the first time using a hybrid musculoskeletal model of the lower extremity. The roles of muscle coactivity, simulated by setting minimum muscle activation at 0–10% levels and ACL deficiency, simulated by reducing ACL resistance by up to 85%, on the stability margin as well as joint biomechanics (contact/muscle/ligament forces) were investigated. Dynamic stability was analyzed using both linear buckling and perturbation approaches at the final deformed configurations in gait. The knee joint was much more stable at 0% stance than at 5% due to smaller ground reaction and contact forces. Muscle coactivity, when at lower intensities (<3% of its maximum active force), increased dynamic stability margin. Greater minimum activation levels, however, acted as an ineffective strategy to enhance stability. Coactivation also substantially increased muscle forces, joint loads and ACL force and hence the risk of further injury and degeneration. A deficiency in ACL decreases total ACL force (by 31% at 85% reduced stiffness) and the stability margin of the knee joint at the heel strike. It also markedly diminishes forces in lateral hamstrings (by up to 39%) and contact forces on the lateral plateau (by up to 17%). Current work emphasizes the need for quantification of the lower extremity stability margin in gait.     

Contribution of muscle short-range stiffness to initial changes in joint kinetics and kinematics during perturbations to standing balance: A simulation study

Simulating realistic musculoskeletal dynamics is critical to understanding neural control of muscle activity evoked in sensorimotor feedback responses that have inherent neural transmission delays. Thus, the initial mechanical response of muscles to perturbations in the absence of any change in muscle activity determines which corrective neural responses are required to stabilize body posture. Muscle short-range stiffness, a history-dependent property of muscle that causes a rapid and transient rise in muscle force upon stretch, likely affects musculoskeletal dynamics in the initial mechanical response to perturbations. Here we identified the contributions of short-range stiffness to joint torques and angles in the initial mechanical response to support surface translations using dynamic simulation. We developed a dynamic model of muscle short-range stiffness to augment a Hill-type muscle model. Our simulations show that short-range stiffness can provide stability against external perturbations during the neuromechanical response delay. Assuming constant muscle activation during the initial mechanical response, including muscle short-range stiffness was necessary to account for the rapid rise in experimental sagittal plane knee and hip joint torques that occurs simultaneously with very small changes in joint angles and reduced root mean square errors between simulated and experimental torques by 56% and 47%, respectively. Moreover, forward simulations lacking short-range stiffness produced unreasonably large joint angle changes during the initial response. Using muscle models accounting for short-range stiffness along with other aspects of history-dependent muscle dynamics may be important to advance our ability to simulate inherently unstable human movements based on principles of neural control and biomechanics.     

Muscle compensation strategies to maintain glenohumeral joint stability with increased rotator cuff tear severity: A simulation study

Rotator cuff tear (RCT) in older adults may cause decreased muscle forces and disrupt the force balance at the glenohumeral joint, compromising joint stability. Our objective was to identify how increased RCT severity affects glenohumeral joint loading and muscle activation patterns using a computational model. Muscle volume measurements were used to scale a nominal upper limb model’s peak isometric muscle forces to represent force-generating characteristics of an average older adult male. Increased RCT severity was represented by systematically decreasing peak isometric muscle forces of supraspinatus, infraspinatus, and subscapularis. Five static postures in both scapular and frontal planes were evaluated. Results revealed that in both scapular and frontal planes, the peak glenohumeral joint contact force magnitude remained relatively consistent across increased RCT severity (average 1.5% and −4.2% change, respectively), and a relative balance of the transverse force couple is maintained even in massive RCT models. Predicted muscle activations of intact muscles, like teres minor, increased (average 5–30% and 4–17% in scapular and frontal planes, respectively) with greater RCT severity. This suggests that the system is prioritizing glenohumeral joint stability, even with severe RCT, and that unaffected muscles play a compensatory role to help stabilize the joint.     

The effects of misalignment during in vivo loading of bone: Techniques to detect the proximity of objects in three-dimensional models

Theories of mechanical adaptation of bone suggest that mechanical loading causes bone formation at discrete locations within bone microstructure experiencing the greatest mechanical stress/strain. Experimental testing of such theories requires in vivo loading experiments and high-resolution finite element models to determine the distribution of mechanical stresses. Finite element models of in vivo loading experiments typically assume idealized boundary conditions with applied load perfectly oriented on the bone, however small misalignments in load orientation during an in vivo experiment are unavoidable, and potentially confound the ability of finite element models to predict locations of bone formation at the scale of micrometers. Here we demonstrate two different three-dimensional spatial correlation methods to determine the effects of misalignment in load orientation on the locations of high mechanical stress/strain in the rodent tail loading model. We find that, in cancellous bone, the locations of tissue with high stress are maintained under reasonable misalignments in load orientation (p<0.01). In cortical bone, however, angular misalignments in the dorsal direction can alter the locations of high mechanical stress, but the locations of tissue with high stress are maintained under other misalignments (p<0.01). We conclude that, when using finite element models of the rodent tail loading model, small misalignments in loading orientation do not affect the predicted locations of high mechanical stress within cancellous bone.     

The importance of abductor pollicis longus in wrist motions: A physiological wrist simulator study

The abductor pollicis longus (APL) is one of the primary radial deviators of the wrist, owing to its insertion at the base of the first metacarpal and its large moment arm about the radioulnar deviation axis. Although it plays a vital role in surgical reconstructions of the wrist and hand, it is often neglected while simulating wrist motions in vitro. The aim of this study was to observe the effects of the absence of APL on the distribution of muscle forces during wrist motions. A validated physiological wrist simulator was used to replicate cyclic planar and complex wrist motions in cadaveric specimens by applying tensile loads to six wrist muscles – flexor carpi radialis (FCR), flexor carpi ulnaris, extensor carpi radialis longus (ECRL), extensor carpi radialis brevis, extensor carpi ulnaris (ECU) and APL. Resultant muscle forces for active wrist motions with and without actuating the APL were compared. The absence of APL resulted in higher forces in FCR and ECRL – the synergists of APL – and lower forces in ECU – the antagonist of APL. The altered distribution of wrist muscle forces observed in the absence of active APL control could significantly alter the efficacy of in vitro experiments conducted on wrist simulators, in particular when investigating those surgical reconstructions or rehabilitation of the wrist heavily reliant on the APL, such as treatments for basal thumb osteoarthritis.     

The effect of high-density genotypic data and different methods on joint genomic prediction: A case study in large white pigs

Joint genomic prediction (GP) is an attractive method to improve the accuracy of GP by combining information from multiple populations. However, many factors can negatively influence the accuracy of joint GP, such as differences in linkage disequilibrium phasing between single nucleotide polymorphisms (SNPs) and causal variants, minor allele frequencies and causal variants’ effect sizes across different populations. The objective of this study was to investigate whether the imputed high-density genotype data can improve the accuracy of joint GP using genomic best linear unbiased prediction (GBLUP), single-step GBLUP (ssGBLUP), multi-trait GBLUP (MT-GBLUP) and GBLUP based on genomic relationship matrix considering heterogenous minor allele frequencies across different populations (wGBLUP). Three traits, including days taken to reach slaughter weight, backfat thickness and loin muscle area, were measured on 67 276 Large White pigs from two different populations, for which 3334 were genotyped by SNP array. The results showed that a combined population could substantially improve the accuracy of GP compared with a single-population GP, especially for the population with a smaller size. The imputed SNP data had no effect for single population GP but helped to yield higher accuracy than the medium-density array data for joint GP. Of the four methods, ssGLBUP performed the best, but the advantage of ssGBLUP decreased as more individuals were genotyped. In some cases, MT-GBLUP and wGBLUP performed better than GBLUP. In conclusion, our results confirmed that joint GP could be beneficial from imputed high-density genotype data, and the wGBLUP and MT-GBLUP methods are promising for joint GP in pig breeding.     

城市主城区立体模型的构建与风环境模拟——以广州主城区为例

以22 km×21 km的广州主城区为例,以40 m建筑间距作为风道宽度低限、用容积高度对建筑高度赋值和垂向拔高为建模特色,概括构建了城市尺度的立体模型。在此基础上,分别模拟了广州主城区中性流条件下,弱风（2 m/s）和强风（5 m/s）、近地面10、25、50 m三个高度的风环境。模拟表明：来流5 m/s下主城区存在不同风速等级、不同平面形态以及不同高度面的风道;白云山、珠江新城等面积较大的地形或建筑高地形成了减速明显的背风区条带,并相互组合形成了重要的风口和具有较高基面的强风道;在不同高度上主城区风速均由周边向城市中心降低;风道风速强烈地依赖于风道走向,风道风速与走向夹角呈三次函数递减,两者拟合优度R²为0.512。模拟结果很好地呈现了城市尺度宏观地形白云山和建筑密集区相互间的作用,反映了城市尺度模型构建与模拟的优势。     

The bonnet monkey (Macaca radiata): A model for the study of gonadotropin dynamics during fasting in the human

General Hospital and Harvard Medical School, Boston Postmenopausal women excrete significantly greater quantities of radioimmunoassayable luteinizing hormone (LH) and follicle stimulating hormone (FSH) during fasting than during the control or refeeding periods. The concentrations of these gonadotropins in the serum, however, are not affected. In the present studies, ovariectomized Bonnet monkeys (Macaca radiata) and ovariectomized Sprague-Dawley rats were studied to compare the effects of fasting on gonadotropins dynamics in subhuman primates and rodents. Serum LH and FSH concentrations were not reduced by fasting of monkeys or rats. During a 4-day fast, rats excreted significantly (P ? 0.01) less LH, FSH, Na⁺, and K⁺ than during prefast or refeeding periods. Monkeys, on the other hand, excreted significantly (P ? 0.025) greater quantities of LH and FSH during the last 2 day of a 4-day fast as compared to prefast and refeeding periods. Like the human, they conserved Na+ and K+ on refeeding. These results indicate that the monkey is a better animal model than the rat with which to study the effects of fasting on gonadotropin excretion in the human.     

浅山区乡镇社会-生态系统脆弱性演化与模拟——以北京平谷为例

浅山区乡镇社会-生态系统相比于平原区受地形环境等因素制约更为脆弱,在国土空间开发与保护中更需要权衡。使用显式空间脆弱性(SERV)模型,从暴露度、敏感性、适应能力3个维度构建评价体系评估平谷浅山区12个乡镇社会-生态系统脆弱性,并使用有序加权平均算法(OWA)模拟多种决策风险下脆弱性情景。研究表明：(1)平谷浅山区2007-2017年总体脆弱性呈现中度脆弱水平,局部呈现上升态势,10年间中等以上脆弱乡镇面积比重由73.09%上升到80.74%。空间上呈现"东南高,西北低"的格局。(2)处于高脆弱水平乡镇应进行严格控制,增加水土保持林面积等提高适应能力;同时注重低脆弱乡镇的高暴露风险源及时进行生态修复。(3)通过设定不同决策风险系数预测不同发展导向下区域系统脆弱性差异,在倾向于可持续发展导向下优先生态环境治理,在经济发展导向下应推动绿色基础设施建设。评价结果可满足不同决策思路下指导区域发展实践。     

The 308‐nm excimer laser treatment does not increase the risk of skin cancer in patients with vitiligo: A population‐based retrospective cohort study

A 308‐nm excimer laser (EL) has been widely used to treat patients with localized vitiligo. However, data are rare on the influence of EL treatment on the risks of skin cancer. To evaluate the skin cancer risks after long‐term EL treatment, we performed a nationwide population‐based retrospective cohort study using the Korean National Health Insurance Claims Database. A total of 5,052 patients with vitiligo were classified into three groups according to the EL treatment sessions between 2009 and 2016: no, 50–99, and 100 or more EL treatments after 2‐year washout period (2007 and 2008). Using multivariable Cox proportional hazard models, we found that the risks of actinic keratosis, non‐melanoma skin cancers, and melanoma did not significantly differ among the groups, respectively. In conclusion, EL treatment would not increase the risks of premalignant skin lesions and skin cancers in patients with vitiligo. Based on our results, EL is likely to be a safe treatment option for patients with localized vitiligo.