A Mathematical Formulation for 3D Quasi-Static Multibody Models of Diarthrodial Joints

This study describes a genera] set of equations for quasi-static analysis of three-dimensional multibody systems, with a particular emphasis on modeling of diarthrodial joints. The model includes articular contact, muscle forces, tendons and tendon pulleys, ligaments, and the wrapping of soft tissue structures around bone and cartilage surfaces. The general set of equations governing this problem are derived using a consistent notation for all types of links, which can be converted conveniently into efficient computer codes. The computational efficiency of the model is enhanced by the use of analytical Jacobians, particularly in the analysis of articular surface contact and wrapping of soft tissue structures around bone and cartilage surfaces. The usefulness of the multibody model is demonstrated by modeling the patellofemoral joint of six cadaver knees, using cadaver-specific data for the articular surface and bone geometries, as well as tendon and ligament insertions and muscle lines of actions. Good accuracy was observed when comparing the model patellar kinematic predictions to experimental data (mean ± stand, dev. error in translation: 0.63 ± 1.19 mm, 0.10 ± 0.71 mm, -0.29 ± 0.84 mm along medial, proximal, and anterior directions, respectively; in rotation: -1.41 ± 1.71°, 0.27 ±2.38°, -1.13 ± 1.83° in flexion, tilt and rotation, respectively). The accuracy which can be achieved with this type of model, and the computational efficiency of the algorithm employed in this study may serve in many applications such as computer-aided surgical planning, and real-time computer-assisted surgery in the operating room.     

Development and validation of a subject-specific moving-axis tibiofemoral joint model using MRI and EOS imaging during a quasi-static lunge

The aims of this study were to introduce and validate a novel computationally-efficient subject-specific tibiofemoral joint model. Subjects performed a quasi-static lunge while micro-dose radiation bi-planar X-rays (EOS Imaging, Paris, France) were captured at roughly 0°, 20°, 45°, 60°, and 90° of tibiofemoral flexion. Joint translations and rotations were extracted from this experimental data through 2D-to-3D bone reconstructions, using an iterative closest point optimization technique, and employed during model calibration and validation. Subject-specific moving-axis and hinge models for comparisons were constructed in the AnyBody Modeling System (AMS) from Magnetic Resonance Imaging (MRI)-extracted anatomical surfaces and compared against the experimental data. The tibiofemoral axis of the hinge model was defined between the epicondyles while the moving-axis model was defined based on two tibiofemoral flexion angles (0° and 90°) and the articulation modeled such that the tibiofemoral joint axis moved linearly between these two positions as a function of the tibiofemoral flexion. Outside this range, the joint axis was assumed to remain stationary. Overall, the secondary joint kinematics (ML: medial–lateral, AP: anterior-posterior, SI: superior-inferior, IE: internal-external, AA: adduction-abduction) were better approximated by the moving-axis model with mean differences and standard errors of (ML: −1.98 ± 0.37 mm, AP: 6.50 ± 0.82 mm, SI: 0.05 ± 0.20 mm, IE: 0.59 ± 0.36°, AA: 1.90 ± 0.79°) and higher coefficients of determination (R²) for each clinical measure. While the hinge model achieved mean differences and standard errors of (ML: −0.84 ± 0.45 mm, AP: 10.11 ± 0.88 mm, SI: 0.66 ± 0.62 mm, IE: −3.17 ± 0.86°, AA: 11.60 ± 1.51°).     

Finite element analysis to characterize how varying patellar loading influences pressure applied to cartilage: model evaluation

A finite element analysis (FEA) modeling technique has been developed to characterize how varying the orientation of the patellar tendon influences the patellofemoral pressure distribution. To evaluate the accuracy of the technique, models were created from MRI images to represent five knees that were previously tested in vitro to determine the influence of hamstrings loading on patellofemoral contact pressures. Hamstrings loading increased the lateral and posterior orientation of the patellar tendon. Each model was loaded at 40°, 60°, and 80° of flexion with quadriceps force vectors representing the experimental loading conditions. The orientation of the patellar tendon was represented for the loaded and unloaded hamstrings conditions based on experimental measures of tibiofemoral alignment. Similar to the experimental data, simulated loading of the hamstrings within the FEA models shifted the center of pressure laterally and increased the maximum lateral pressure. Significant (p < 0.05) differences were identified for the center of pressure and maximum lateral pressure from paired t-tests carried out at the individual flexion angles. The ability to replicate experimental trends indicates that the FEA models can be used for future studies focused on determining how variations in the orientation of the patellar tendon related to anatomical or loading variations or surgical procedures influence the patellofemoral pressure distribution.     

An improved OpenSim gait model with multiple degrees of freedom knee joint and knee ligaments

Musculoskeletal models are widely used to investigate joint kinematics and predict muscle force during gait. However, the knee is usually simplified as a one degree of freedom joint and knee ligaments are neglected. The aim of this study was to develop an OpenSim gait model with enhanced knee structures. The knee joint in this study included three rotations and three translations. The three knee rotations and mediolateral translation were independent, with proximodistal and anteroposterior translations occurring as a function of knee flexion/extension. Ten elastic elements described the geometrical and mechanical properties of the anterior and posterior cruciate ligaments (ACL and PCL), and the medial and lateral collateral ligaments (MCL and LCL). The three independent knee rotations were evaluated using OpenSim to observe ligament function. The results showed that the anterior and posterior bundles of ACL and PCL (aACL, pACL and aPCL, pPCL) intersected during knee flexion. The aACL and pACL mainly provided force during knee flexion and adduction, respectively. The aPCL was slack throughout the range of three knee rotations; however, the pPCL was utilised for knee abduction and internal rotation. The LCL was employed for knee adduction and rotation, but was slack beyond 20° of knee flexion. The MCL bundles were mainly used during knee adduction and external rotation. All these results suggest that the functions of knee ligaments in this model approximated the behaviour of the physical knee and the enhanced knee structures can improve the ability to investigate knee joint biomechanics during various gait activities.     

基于土壤水分模拟的干旱动态监测指标及其适用性

根据土壤水分平衡原理,采用Penman-Monteith公式计算可能蒸散,逐日滚动模拟土壤有效水分,提出基于土壤水分(SM)的逐日干旱动态监测指标。通过与《气象干旱等级》国家标准中标准化降水指数(SPI)、相对湿润度指数(MI)和综合气象干旱指数(CI)相比较,分析了SM干旱动态监测指标在广东的适用性特征。结果表明:(1)基于SM统计的干旱频发时段(11月—翌年4月)比少雨时段(10月—翌年3月)滞后1个月,SM指标能够刻画干旱相对于降水年变化的滞后效应和逐渐发展的特征,客观反映广东干旱频率季节变化特征;(2)SM干旱指标自动隐含了降水-蒸发过程的时间累积效应,物理意义清晰,能够刻画干旱发生、发展和结束过程的丰富细节,在对干旱过程发展渐进性、降水敏感性和过程完整性方面,具有较好的应用价值。     

Development and validation of a computational model of the knee joint for the evaluation of surgical treatments for osteoarthritis

A three-dimensional (3D) knee joint computational model was developed and validated to predict knee joint contact forces and pressures for different degrees of malalignment. A 3D computational knee model was created from high-resolution radiological images to emulate passive sagittal rotation (full-extension to 65°-flexion) and weight acceptance. A cadaveric knee mounted on a six-degree-of-freedom robot was subjected to matching boundary and loading conditions. A ligament-tuning process minimised kinematic differences between the robotically loaded cadaver specimen and the finite element (FE) model. The model was validated by measured intra-articular force and pressure measurements. Percent full scale error between FE-predicted and in vitro-measured values in the medial and lateral compartments were 6.67% and 5.94%, respectively, for normalised peak pressure values, and 7.56% and 4.48%, respectively, for normalised force values. The knee model can accurately predict normalised intra-articular pressure and forces for different loading conditions and could be further developed for subject-specific surgical planning.     

Sub-millimetre accurate human hand kinematics: from surface to skeleton

A highly accurate human hand kinematics model and identification are proposed. The model includes the five digits and the palm arc based on mapping function between surface landmarks and estimated joint centres of rotation. Model identification was experimentally performed using a motion tracking system. The evaluation of the marker position estimation error, which is on sub-millimetre level across all digits, underlines model quality and accuracy. Noticeably, with the development of this model, we were able to improve various modelling assumptions from literature and found a basic linear relationship between surface and skeleton rotational angles.     

Development and validation of a multi-body model of the canine stifle joint

Multi-body musculoskeletal models that can be used concurrently to predict joint contact pressures and muscle forces would be extremely valuable in studying the mechanics of joint injury. The purpose of this study was to develop an anatomically correct canine stifle joint model and validate it against experimental data. A cadaver pelvic limb from one adult dog was used in this study. The femoral head was subjected to axial motion in a mechanical tester. Kinematic and force data were used to validate the computational model. The maximum RMS error between the predicted and measured kinematics during the complete testing cycle was 11.9 mm translational motion between the tibia and the femur and 4.3° rotation between patella and femur. This model is the first step in the development of a musculoskeletal model of the hind limb with anatomically correct joints to study cartilage loading under dynamic conditions.     

A screening method to analyse the sensitivity of a lower limb multibody kinematic model

The study presents a screening method used to identify the influential parameters of a lower limb model including ligaments, at low numerical cost. Concerning multibody kinematics optimisation, the ligament parameters (isometric length) were found the most influential ones in a previous study. The screening method tested if they remain influential with minimised length variations. The most important parameters for tibiofemoral kinematics were the skin markers, segment lengths and joint parameters, including two ligaments. This was confirmed by a quantitative sensitivity analysis. The screening method has the potential to be used as a stand-alone procedure for a sensitivity analysis.     

深圳市龙华地区城镇用地动态模型建设及模拟研究

在１９８８～１９９６年时段景面遥感制的基础上,利用细胞自组织模型对深圳市龙华地区城镇成区的动态变化过程进行了模拟研究。模型其选择了高程,城率、限最近干线公路的生趣距离,斑块相邻度指数和形状指数等５个变量参与非域镇用地单元的综合转移概率计算,利用１９８８～１９９０年的城镇扩张结果确定不同变量的权重参数,利用１９９２、１９９４和１９６年的数据进行模型验证。结果表明,细胞自组织模型可以很好地反映模拟起始     

Approximation of the functional kinematics of posterior stabilised total knee replacements using a two-dimensional sagittal plane patello-femoral model: comparing model approximation to in vivo measurement

Previous in vivo studies have observed that current designs of posterior stabilised (PS) total knee replacements (TKRs) may be ineffective in restoring normal kinematics in Late flexion. Computer-based models can prove a useful tool in improving PS knee replacement designs. This study investigates the accuracy of a two-dimensional (2D) sagittal plane model capable of predicting the functional sagittal plane kinematics of PS TKR implanted knees against direct in vivo measurement. Implant constraints are often used as determinants of anterior–posterior tibio-femoral positioning. This allowed the use of a patello-femoral modelling approach to determine the effect of implant constraints. The model was executed using motion simulation software which uses the constraint force algorithm to achieve a solution. A group of 10 patients implanted with Scorpio PS implants were recruited and underwent fluoroscopic imaging of their knees. The fluoroscopic images were used to determine relative implant orientation using a three-dimensional reconstruction method. The determined relative tibio-femoral orientations were then input to the model. The model calculated the patella tendon angles (PTAs) which were then compared with those measured from the in vivo fluoroscopic images. There were no significant differences between the measured and calculated PTAs. The average root mean square error between measured and modelled ranged from 1.17° to 2.10° over the flexion range. A sagittal plane patello-femoral model could conceivably be used to predict the functional 2D kinematics of an implanted knee joint. This may prove particularly useful in optimising PS designs.     

Comparative Study on Biomechanics of Two Legs in the Action of Single-Leg Landing in Men’s Badminton

This study aims to analyze the biomechanical difference between the two legs of male badminton players when they land on one leg, thereby providing some guidance for preventing sports injury. Ten male badminton players were selected as the subjects. They did the single-leg landing movement successfully three times. The kinematic data were obtained by the Vicon infrared high-speed motion capture system. The kinetic data were obtained by the KISTLER three-dimensional forcing measuring platform. The data were processed and analyzed. The center of gravity of the right leg on the X and Y axes were 0.25 ± 0.05 and 0.21 ± 0.04 m, respectively, which were lower than that of the left leg (p < 0.05). At the moment of landing by a single leg, the hip angle of the left and right legs was 164.78 ± 6.12° and 156.29 ± 6.89°, respectively (p < 0.05), the hip joint speed of the left and right legs was 2.21 ± 0.32 and 1.98 ± 0.31 m/s, respectively (p < 0.05), the knee joint speed of the left and right legs was 2.51 ± 0.21 and 2.21 ± 0.21 m/s, respectively (p < 0.05). Although there was no significant difference in the range of joint motion, the motion range of the right leg was larger than that of the left leg, and the buffering time of the knee joint of the right leg was also significantly less than that of the left leg. The comparison of the kinetic data demonstrated that the ground reaction force (GRF), peak vertical ground reaction force (PVGRF), and lower limb stiffness of the right leg were significantly smaller than those of the left leg, and the time to peak force was greater than that of the left leg (p < 0.05). The injury risk of the left leg is greater than that of the right leg when the athlete land on a single leg. In the process of training, the athlete should strengthen the stability training of two legs, especially the left leg, in order to reduce sports injury.     

Kinematic evaluation of cruciate-retaining total knee replacement patients during level walking: A comparison with the displacement-controlled ISO standard

Differences between wear-scar features of simulator-tested and retrieved tibial total knee replacement (TKR) liners have been reported. This disagreement may result from differences between in vivo kinematic profiles and those defined by the International Organization for Standardization (ISO). The purpose of this study was to determine the knee kinematics of a TKR subject group during level walking and compare them with the motion profiles defined by the ISO standard for a displacement-controlled knee wear testing simulator. Twenty-nine patients with a posterior cruciate ligament-retaining TKR design were gait tested using the point cluster technique to obtain flexion–extension (FE) rotation, anterior–posterior (AP) translation and internal–external (IE) rotation knee motions during a complete cycle of level walking. Relative ranges of motion and timing of key points within the in vivo motion data were compared against the same ranges and same key points from the input profiles of the displacement-controlled wear testing standard ISO14243-3. The subjects exhibited a FE pattern similar to ISO, with an insignificant difference in range of FE rotation from midstance to terminal stance. However, the subjects had a significantly higher range of knee flexion from terminal stance into swing. The subjects also exhibited a phase delay for the entire gait cycle. For AP translation, the standard profile had statistically significant lower magnitudes than seen in vivo. Opposite pattern of AP motion was also apparent from midstance and swing. Similarly, ISO specified a smaller IE total range of rotation with a motion pattern in complete opposition to that seen in vivo. In conclusion, significant differences were found in both the magnitudes and pattern of in vivo motion compared with ISO.     

Dynamic model of the lactating dairy cow metabolism

The whole-animal model described in this paper is intended to be a research model with an intermediary structure between sophisticated and simple cow models. The mechanistic model structure integrates the main metabolic pathways of the lactating dairy cow. Milk yield and related feed intake for varying production potentials were considered to be the driving forces and were empirically defined. The model was designed to explain the main metabolic flows and variations in body reserves associated with the push of nutrients from dry matter intake and their pull by the mammary gland to synthesise milk components throughout lactation. The digestive part of the model uses either known feed unit systems (e.g. PDI system for protein) or published empirical equations for the prediction of digestive flows of organic matter, starch and fatty acids and ruminal volatile fatty acid production. The metabolic sub-system is made up of four tissue compartments (body protein, body lipid, protein in the uterus and triglycerides in the liver) and five circulating metabolites (glucose, amino acids, acetate + butyrate, propionate, and triglycerides and non-esterified fatty acids). A major original aspect of the model is its homeorhetic control system. It was assumed that flows relating to adipose and protein tissue anabolism and catabolism were driven by a couple of linked theoretical hormones controlling mobilisation and anabolism. The evolution in body composition and body weight were outcomes of this control. Another originality of the model is its suitability for milk yields varying from 10 to 50 kg at peak production. This was achieved by homeorhetic control of milk potential acting on several key metabolic flows. Homeostatic regulation was also introduced in order to confine the behaviour of the model within realistic physiological values. For some basic aspects (e.g. Uterine involution, standard kinetics of body protein and fat), it was necessary to build specific databases from the literature and interpret these by meta-analysis. Fairly realistic simulated kinetics were obtained for body composition, liver triglycerides, blood plasma metabolite concentrations, milk protein and fat contents, and also for major groups of milk fatty acids.     

Finite element simulation of the behavior of the periodontal ligament: A validated nonlinear contact model

Due to its significance in tooth movement, the stress/deformation field of periodontium and the alveolar bone remodeling process, periodontal ligament (PDL) cannot be excluded from the studies investigating dental biomechanics regarding its excessive deformability. Therefore, many analytical and numerical researches are carried out to simulate its response and to create a constitutive model via experiments intending to discover the material properties of PDL. The aim of this study is to formulate a user specified contact model that can be used in conjunction with finite element (FE) software and reflects PDL’s influence on neighboring structures based on the currently available information, without requiring an actual volumetric finite element mesh of ligament. The results show good agreement with available experimental tooth mobility data. Smooth stress fields are obtained on the tooth root and alveolar bone, which is a significant aspect in bone-remodeling studies. The advantage of simulating PDL as a contact model at the interface of tooth root and the alveolar process instead of a solid-meshed FE model with poor geometric morphology and/or very dense mesh is expected to save pre/post-processing workforce, to increase the accuracy and to contribute to the smoothness of interface stress distributions.     

Cluster-based upper body marker models for three-dimensional kinematic analysis: Comparison with an anatomical model and reliability analysis

Quantifying angular joint kinematics of the upper body is a useful method for assessing upper limb function. Joint angles are commonly obtained via motion capture, tracking markers placed on anatomical landmarks. This method is associated with limitations including administrative burden, soft tissue artifacts, and intra- and inter-tester variability. An alternative method involves the tracking of rigid marker clusters affixed to body segments, calibrated relative to anatomical landmarks or known joint angles. The accuracy and reliability of applying this cluster method to the upper body has, however, not been comprehensively explored. Our objective was to compare three different upper body cluster models with an anatomical model, with respect to joint angles and reliability. Non-disabled participants performed two standardized functional upper limb tasks with anatomical and cluster markers applied concurrently. Joint angle curves obtained via the marker clusters with three different calibration methods were compared to those from an anatomical model, and between-session reliability was assessed for all models. The cluster models produced joint angle curves which were comparable to and highly correlated with those from the anatomical model, but exhibited notable offsets and differences in sensitivity for some degrees of freedom. Between-session reliability was comparable between all models, and good for most degrees of freedom. Overall, the cluster models produced reliable joint angles that, however, cannot be used interchangeably with anatomical model outputs to calculate kinematic metrics. Cluster models appear to be an adequate, and possibly advantageous alternative to anatomical models when the objective is to assess trends in movement behavior.     

基于元胞自动机的城市空间动态模拟

城市空间动态的模拟与预测可以为城市可持续发展规划与管理提供重要的参考依据。SLEUTH元胞自动机模型在城市空间模拟中较强的适用性和可移植性,该模型通过对历史数据的蒙特卡洛迭代自动寻找城市增长误差最小的参数组合,解决了传统元胞自动机模型中转换规则不易确定的问题。以武汉市为研究案例,运用SLEUTH模型进行了城市空间动态模拟与情景预测。2007年至2011年的城市空间模拟结果显示,模拟结果与实际历史数据可以获得良好的空间匹配度,Lee-Sallee形状指数均在0.6以上,显示SLEUTH元胞自动机模型经过本地化校正后具有较强的适用性和满意的模拟精度。进而,设置了现状趋势、基本保护、严格保护等3种情景对武汉2025年城市空间动态进行了预测,结果显示,各情景模式下城市居住用地均明显增长,农业用地、林地、水域等均有所减少;现状趋势情景和基本保护情景下农田、林地、水域减少的幅度较大,会加剧区域的生境破碎、耕地功能下降、水资源匮乏、湖滨湿地萎缩等生态问题,说明这两种情景不能有效满足城市生态系统健康和可持续发展的需要。严格保护情景下,城市居住用地扩张的程度得到了明显的控制,水域和林地得到了有效的保护,对于重要的自然生态系统组分保护及其服务能力维持可以起到显著作用。     

Biomechanical behaviour of cancellous bone on patellofemoral arthroplasty with Journey prosthesis: a finite element study

Isolated patellofemoral (PF) arthritis of the knee is a common cause of anterior knee pain and disability. Patellofemoral arthroplasty (PFA) is a bone conserving solution for patients with PF degeneration. Failure mechanisms of PFA include growing tibiofemoral arthritis and loosening of components. The implant loosening can be associated with bone resorption or fatigue-failure of bone by overload. This research work aims at determining the structural effects of the implantation of PF prosthesis Journey PFJ (Smith & Nephew, Inc., Memphis, TN, USA) on femoral cancellous bone. For this purpose, the finite element method is considered to perform computational simulations for different conditions, such as well-fixed and loosening scenarios. From the global results obtained, in the well-fixed scenario, a decrease in strain on cancellous bone was noticed, which can be related to bone resorption. In the loosening scenario, when the cement layer becomes inefficient, a significant increase in cancellous bone strain was observed, which can be associated with bone fatigue-failure.These strain changes suggest a weakness of the femur after PFA.