Estimation of trunk mechanical properties using system identification: effects of experimental setup and modelling assumptions

The use of system identification to quantify trunk mechanical properties is growing in biomechanics research. The effects of several experimental and modelling factors involved in the system identification of trunk mechanical properties were investigated. Trunk kinematics and kinetics were measured in six individuals when exposed to sudden trunk perturbations. Effects of motion sensor positioning and properties of elements between the perturbing device and the trunk were investigated by adopting different models for system identification. Results showed that by measuring trunk kinematics at a location other than the trunk surface, the deformation of soft tissues is erroneously included into trunk kinematics and results in the trunk being predicted as a more damped structure. Results also showed that including elements between the trunk and the perturbing device in the system identification model did not substantially alter model predictions. Other important parameters that were found to substantially affect predictions were the cut-off frequency used when low-pass filtering raw data and the data window length used to estimate trunk properties.     

Soft tissue wobbling affects trunk dynamic response in sudden perturbations

Soft tissue wobbling reduces the transferred impact of external loads on lower limb joints. The present study investigated whether soft tissue wobbling has similar effects on trunk dynamic response to sudden perturbations. Three healthy males were subjected to a series of anteriorly directed trunk position perturbations at three different velocities while trunk kinematics and kinetics were measured. A nonlinear active-passive finite element model of the human trunk was then used to study the effects of soft tissue wobbling on trunk response. Also investigated were the effects on model predictions of including elements simulating the apparatus (rod-harness assembly) transferring motor-generated perturbations to the trunk. Predicted and measured trunk kinematics and kinetics, when accounting for the dynamic effects of both wobbling mass and rod-harness assembly, were in good agreement for all velocities especially early (<120 ms) after the perturbations (ρ>0.97). Root mean square errors in model predictions increased considerably when neglecting the aforementioned modeling considerations. The trunk wobbling mass and connecting elements between the trunk and the perturbing device, particularly during faster perturbations, substantially attenuated the transferred impact of external loads on the spine (by 33-90 N across perturbation velocities). Such reductions in the impacts transferred, in turn, reduced the predicted demands on the neuromuscular system for control and maintenance of spinal loads and stability. As such, these features should be considered in future biodynamic models of the human trunk aimed at estimating trunk neuromuscular behaviors during sudden perturbations.     

Trunk response analysis under sudden forward perturbations using a kinematics-driven model

Accurate quantification of the trunk transient response to sudden loading is crucial in prevention, evaluation, rehabilitation and training programs. An iterative dynamic kinematics-driven approach was used to evaluate the temporal variation of trunk muscle forces, internal loads and stability under sudden application of an anterior horizontal load. The input kinematics is hypothesized to embed basic dynamic characteristics of the system that can be decoded by our kinematics-driven approach. The model employs temporal variation of applied load, trunk forward displacement and surface EMG of select muscles measured on two healthy and one chronic low-back pain subjects to a sudden load. A finite element model accounting for measured kinematics, nonlinear passive properties of spine, detailed trunk musculature with wrapping of global extensor muscles, gravity load and trunk biodynamic characteristics is used to estimate the response under measured sudden load. Results demonstrate a delay of ～200 ms in extensor muscle activation in response to sudden loading. Net moment and spinal loads substantially increase as muscles are recruited to control the trunk under sudden load. As a result and due also to the trunk flexion, system stability significantly improves. The reliability of the kinematics-driven approach in estimating the trunk response while decoding measured kinematics is demonstrated. Estimated large spinal loads highlight the risk of injury that likely further increases under larger perturbations, muscle fatigue and longer delays in activation.     

Spinal stability and role of passive stiffness in dynamic squat and stoop lifts

The spinal stability and passive-active load partitioning under dynamic squat and stoop lifts were investigated as the ligamentous stiffness in flexion was altered. Measured in vivo kinematics of subjects lifting 180 N at either squat or stoop technique was prescribed in a nonlinear transient finite element model of the spine. The Kinematics-driven approach was utilized for temporal estimation of muscle forces, internal spinal loads and system stability. The finite element model accounted for nonlinear properties of the ligamentous spine, wrapping of thoracic extensor muscles and trunk dynamic characteristics while subject to measured kinematics and gravity/external loads. Alterations in passive properties of spine substantially influenced muscle forces, spinal loads and system stability in both lifting techniques, though more so in stoop than in squat. The squat technique is advocated for resulting in smaller spinal loads. Stability of spine in the sagittal plane substantially improved with greater passive properties, trunk flexion and load. Simulation of global extensor muscles with curved rather than straight courses considerably diminished loads on spine and increased stability throughout the task.     

Collagen fiber alignment does not explain mechanical anisotropy in fibroblast populated collagen gels

Many load-bearing soft tissues exhibit mechanical anisotropy. In order to understand the behavior of natural tissues and to create tissue engineered replacements, quantitative relationships must be developed between the tissue structures and their mechanical behavior. We used a novel collagen gel system to test the hypothesis that collagen fiber alignment is the primary mechanism for the mechanical anisotropy we have reported in structurally anisotropic gels. Loading constraints applied during culture were used to control the structural organization of the collagen fibers of fibroblast populated collagen gels. Gels constrained uniaxially during culture developed fiber alignment and a high degree of mechanical anisotropy, while gels constrained biaxially remained isotropic with randomly distributed collagen fibers. We hypothesized that the mechanical anisotropy that developed in these gels was due primarily to collagen fiber orientation. We tested this hypothesis using two mathematical models that incorporated measured collagen fiber orientations: a structural continuum model that assumes affine fiber kinematics and a network model that allows for nonaffine fiber kinematics. Collagen fiber mechanical properties were determined by fitting biaxial mechanical test data from isotropic collagen gels. The fiber properties of each isotropic gel were then used to predict the biaxial mechanical behavior of paired anisotropic gels. Both models accurately described the isotropic collagen gel behavior. However, the structural continuum model dramatically underestimated the level of mechanical anisotropy in aligned collagen gels despite incorporation of measured fiber orientations; when estimated remodeling-induced changes in collagen fiber length were included, the continuum model slightly overestimated mechanical anisotropy. The network model provided the closest match to experimental data from aligned collagen gels, but still did not fully explain the observed mechanics. Two different modeling approaches showed that the level of collagen fiber alignment in our uniaxially constrained gels cannot explain the high degree of mechanical anisotropy observed in these gels. Our modeling results suggest that remodeling-induced redistribution of collagen fiber lengths, nonaffine fiber kinematics, or some combination of these effects must also be considered in order to explain the dramatic mechanical anisotropy observed in this collagen gel model system.     

An adaptive system identification model of the biomechanical response of the human trunk during sudden loading

Sudden loading injuries to the low back are a concern. Current models are limited in their ability to quantify the time-varying nature of the sudden loading event. The method of approach used six males who were subjected to sudden loads. Response data (EMG and kinematics) were input into a system identification model to yield time-varying torso stiffness estimates. The results show estimates of system stiffness in good agreement with values in the literature. The average root mean square error of the model's predictions of sagittal motion was equal to 0.1 deg. In conclusion, system identification can be implemented with minimal error and used to gain more insight into the time-dependent trunk response to sudden loads.     

A sensitivity analysis method for the body segment inertial parameters based on ground reaction and joint moment regressor matrices

This paper presents a method allowing a simple and efficient sensitivity analysis of dynamics parameters of complex whole-body human model. The proposed method is based on the ground reaction and joint moment regressor matrices, developed initially in robotics system identification theory, and involved in the equations of motion of the human body. The regressor matrices are linear relatively to the segment inertial parameters allowing us to use simple sensitivity analysis methods. The sensitivity analysis method was applied over gait dynamics and kinematics data of nine subjects and with a 15 segments 3D model of the locomotor apparatus. According to the proposed sensitivity indices, 76 segments inertial parameters out the 150 of the mechanical model were considered as not influent for gait. The main findings were that the segment masses were influent and that, at the exception of the trunk, moment of inertia were not influent for the computation of the ground reaction forces and moments and the joint moments. The same method also shows numerically that at least 90% of the lower-limb joint moments during the stance phase can be estimated only from a force-plate and kinematics data without knowing any of the segment inertial parameters.     

Effect of intervertebral translational flexibilities on estimations of trunk muscle forces,kinematics, loads,and stability

Due to the complexity of the human spinal motion segments, the intervertebral joints are often simulated in the musculoskeletal trunk models as pivots thus allowing no translational degrees of freedom (DOFs). This work aims to investigate, for the first time, the effect of such widely used assumption on trunk muscle forces, spinal loads, kinematics, and stability during a number of static activities. To address this, the shear deformable beam elements used in our nonlinear finite element (OFE) musculoskeletal model of the trunk were either substantially stiffened in translational directions (SFE model) or replaced by hinge joints interconnected through rotational springs (HFE model). Results indicated that ignoring intervertebral translational DOFs had in general low to moderate impact on model predictions. Compared with the OFE model, the SFE and HFE models predicted generally larger L4–L5 and L5–S1 compression and shear loads, especially for tasks with greater trunk angles; differences reached ～15% for the L4–L5 compression, ～36% for the L4–L5 shear and ～18% for the L5–S1 shear loads. Such differences increased, as location of the hinge joints in the HFE model moved from the mid-disc height to either the lower or upper endplates. Stability analyses of these models for some select activities revealed small changes in predicted margin of stability. Model studies dealing exclusively with the estimation of spinal loads and/or stability may, hence with small loss of accuracy, neglect intervertebral translational DOFs at smaller trunk flexion angles for the sake of computational simplicity.     

Trunk kinematic,kinetic, and neuro-muscular response to foot center of pressure translation along the medio-lateral foot axis during gait

Footwear devices that shift foot center of pressure (COP), thereby impacting lower-limb biomechanics to produce clinical benefit, have been studied regarding degenerative diseases of knee and hip joints, exhibiting evidence of clinical success. Ability to purposefully affect trunk biomechanics has not been investigated for this type of footwear. Fifteen healthy young male subjects underwent gait and electromyography analysis using a biomechanical device that shifts COP via moveable convex elements attached to the shoe sole. Analyses were performed in three COP configurations for pairwise comparison: (1) neutral (control) (2) laterally deviated, and (3) medially deviated. Sagittal and frontal-plane pelvis and spine kinematics, external oblique activity, and frontal and transverse-plane lumbar moments were affected by medio-lateral COP shift. Transverse-plane trunk kinematics, activity of the lumbar longissimus, latissimus dorsi, rectus abdominus, and quadratus lumborum, and sagittal-plane lumbar moment, were not significantly impacted. Two linear mixed effects models assessed predictive impact of (I) COP location, and (II) trunk kinematics and neuromuscular activity, on the significant lumbar moment parameters. The COP was a significant predictor of all modeled frontal and transverse-plane lumbar moment parameters, while pelvic and spine rotation, and lumbar longissimus activity were significant predictors of one frontal-plane lumbar moment parameter. Model results suggest that, although trunk biomechanics and muscle activity were altered by COP shift, COP offset influences lumbar kinetics directly, or via lower-limb changes not assessed in this study, but not by means of alteration of trunk kinematics or muscle activity. Further study may reveal implications in treatment of low back pain.     

Model and in vivo studies on human trunk load partitioning and stability in isometric forward flexions

To resolve the trunk redundancy to determine muscle forces, spinal loads, and stability margin in isometric forward flexion tasks, combined in vivo-numerical model studies was undertaken. It was hypothesized that the passive resistance of both the ligamentous spine and the trunk musculature plays a crucial role in equilibrium and stability of the system. Fifteen healthy males performed free isometric trunk flexions of approximately 40 degrees and approximately 65 degrees +/- loads in hands while kinematics by skin markers and EMG activity of trunk muscles by surface electrodes were measured. A novel kinematics-based approach along with a nonlinear finite element model were iteratively used to calculate muscle forces and internal loads under prescribed measured postures and loads considered in vivo. Stability margin was investigated using nonlinear, linear buckling, and perturbation analyses under various postures, loads and alterations in ligamentous stiffness. Flexion postures significantly increased activity in extensor muscles when compared with standing postures while no significant change was detected in between flexed postures. Compression at the L5-S1 substantially increased from 570 and 771 N in upright posture, respectively, for +/-180 N, to 1912 and 3308 N at approximately 40 degrees flexion, and furthermore to 2332 and 3850 N at approximately 65 degrees flexion. Passive ligamentous/muscle components resisted up to 77% of the net moment. In flexion postures, the spinal stability substantially improved due both to greater passive stiffness and extensor muscle activities so that, under 180 N, no muscle stiffness was required to maintain stability. The co-activity of abdominal muscles and the muscle stiffness were of lesser concern to maintain stability in forward flexion tasks as compared with upright tasks. An injury to the passive system, on one hand, required a substantial compensatory increase in active muscle forces which further increased passive loads and, hence, the risk of injury and fatigue. On the other hand, it deteriorated the system stability which in turn could require greater additional muscle activation. This chain of events would place the entire trunk active-passive system at higher risks of injury, fatigue and instability.     

A mechanical supination sprain simulator for studying ankle supination sprain kinematics

This study presents a free-fall mechanical supination sprain simulator for evaluating the ankle joint kinematics during a simulated ankle supination sprain injury. The device allows the foot to be in an anatomical position before the sudden motion, and also allows different degrees of supination, or a combination of inversion and plantarflexion. Five subjects performed simulated supination sprain trials in five different supination angles. Ankle motion was captured by a motion analysis system, and the ankle kinematics were reported in plantarflexion/dorsiflexion, inversion/eversion and internal/external rotation planes. Results showed that all sprain motions were not pure single-plane motions but were accompanied by motion in other two planes, therefore, different degrees of supination were achieved. The presented sprain simulator allows a more comprehensive study of the kinematics of ankle sprain when compared with some previous laboratory research designs.     

Comparison of two trunk electromagnetic sensor placement methods during shoulder motion analysis

For kinematic studies of the shoulder, electromagnetic sensors are commonly placed on the humerus, scapula, and trunk. The trunk sensor is used to describe humeral and scapular kinematics with respect to the trunk. There are two common trunk sensor placements, the sternum or third thoracic vertebrae (T3). It is currently unclear if placement of the trunk sensor affects kinematics, making it difficult to compare data across studies. The purpose of this study was to compare two trunk sensor placements (T3 and sternum) on trunk and scapular kinematics during arm elevation. An electromagnetic tracking system was used to collect kinematic data during five consecutive repetitions of ascending and descending arm elevation in the sagittal plane. The results indicate that trunk sensor placement had no significant effect on trunk kinematics or scapular upward/downward rotation and internal/external rotation. Scapular anterior/posterior tilt was significantly greater when the trunk sensor was on the sternum compared to the T3 vertebrae during ascending 30°–120°: mean difference = −3.51° (95%CI: −5.61, −1.40), and descending 120°–30°: mean difference = −3.27° (95%CI: −6.07, −0.48). However, the difference in anterior/posterior tilt did not exceed the error (minimal detectable change), and thus is likely not a meaningful difference. These results indicate the trunk sensors can be affixed on T3 or the sternum, depending on the needs of the study.     

A least-squares identification algorithm for estimating squat exercise mechanics using a single inertial measurement unit

This study investigated the possibility of estimating lower-limb joint kinematics during a squat exercise performed in the sagittal plane based on data collected from a single inertial measurement unit located on the lower trunk. The human body was modeled as a three-degrees-of-freedom planar chain and the relevant joint angles (ankle, knee, and hip) are represented by Fourier series. A least-squares approach based on the minimization of the difference between the measured and estimated linear accelerations and the angular velocity of the lower trunk was used to solve the related analytical problem. The approach was validated on ten healthy young volunteers (ten trials each) using a force plate and a stereophotogrammetric system to collect reference data. The root mean square differences between the estimated joint angles and those reconstructed with the stereophotogrammetric system were lower than 4° with correlation coefficients higher than 0.99. The ankle joint resultant vertical force component was estimated with an accuracy of about 3% and a high correlation coefficient of r=0.95, whereas much lower percentage accuracies were found for the horizontal force and couple components. The latter accuracies were similar to those affecting these force and couple components as estimated through inverse dynamics and the stereophotogrammetric data in conjunction with the same mechanical model, which suggests that only minor errors were introduced by the proposed algorithm and measurement tools.     

Within- and between-day reliability of trunk mechanical behaviors estimated using position-controlled perturbations

Recent applications of position-controlled perturbation techniques to the human trunk have allowed separate estimation of intrinsic and reflexive trunk mechanical behaviors. These mechanical behaviors play an important role in spinal stability and have been associated with low back pain risk, yet the reliability of these measures remains unknown. Therefore, the objective of the current study was to assess within- and between-day reliability of several measures of trunk mechanical behaviors obtained from position-controlled trunk perturbations. A secondary objective was to assess if different harness designs, used to connect a participant to the perturbing device, influenced reliability. Data were analyzed from baseline measurements obtained from two previously published studies, and a third unpublished study. The total combined subject pool included 33 healthy young adults (17 M, 16 F). Relative and absolute reliability was quantified using intraclass correlation coefficients (ICCs) and standard errors of measurement (SEM), respectively. Within-day ICCs of intrinsic trunk stiffness (0.84-0.90) and effective mass (0.91-95) were excellent, and were generally higher than ICCs for reflex gain (0.55-0.85), maximum reflex force (0.65-0.85), and timing of maximum reflex force (0.48-0.86). Within-day ICCs (0.48-0.95) were consistently superior to between-day values (0.19-0.72). Improvements in harness design increased both within- and between-day reliability and reduced SEMs for most measures.     

Comparison of mechanical behavior among the extrapulmonary arteries from rats

Results of comparative tests on pulmonary arteries from untreated Long-Evans rats are presented from three sections of the artery: the trunk, and the right and left main extrapulmonary arteries. Analyses were conducted looking for mechanical differences between the flow (longitudinal) and circumferential directions, between the right and left main arteries, and between each of the mains and the trunk. The mechanical properties of rat pulmonary arteries were obtained with a bubble inflation technique. A flat disk of rat pulmonary artery was constrained at the periphery and inflated, and the geometry of the resulting bubble of material recorded from six different angles. To analyze the data, the area under the stress-strain curve was calculated for each test and orientation. This area, related to the strain-energy density, was calculated at stress equal to 200kPa, for the purpose of statistical comparison. The mean values for the area show that the trunk is less compliant than the main arteries; this difference is supported by histological evidence. When comparing the circumferential and longitudinal properties of the arteries, differences are found for the trunk and left main arteries, but with opposite orientations being more compliant. The mean values for the two orientations for the right main artery are statistically identical. There was indication of significant difference in mechanical properties between the trunk and the main arteries. The left main artery in the circumferential orientation is highly compliant and appears to strongly influence the likelihood that significant differences will exist when included in a statistical population. These data show that each section of the extrapulmonary arterial system should not be expected to behave identically, and they provide the baseline mechanical behavior of the pulmonary artery from normotensive rats.     

Identification of ankle sprain motion from common sporting activities by dorsal foot kinematics data

This study presented a method to identify ankle sprain motion from common sporting activities by dorsal foot kinematics data. Six male subjects performed 300 simulated supination sprain trials and 300 non-sprain trials in a laboratory. Eight motion sensors were attached to the right dorsal foot to collect three-dimensional linear acceleration and angular velocity kinematics data, which were used to train up a support vector machine (SVM) model for the identification purpose. Results suggested that the best identification method required only one motion sensor located at the medial calcaneus, and the method was verified on another group of six subjects performing 300 simulated supination sprain trials and 300 non-sprain trials. The accuracy of this method was 91.3%, and the method could help developing a mobile motion sensor system for ankle sprain detection.     

Use of biorobotic models of highly deformable fins for studying the mechanics and control of fin forces in fishes

Bony fish swim with a level of agility that is unmatched in human-developed systems. This is due, in part, to the ability of the fish to carefully control hydrodynamic forces through the active modulation of the fins' kinematics and mechanical properties. To better understand how fish produce and control forces, biorobotic models of the bluegill sunfish's (Lepomis macrochirus) caudal fin and pectoral fins were developed. The designs of these systems were based on detailed analyses of the anatomy, kinematics, and hydrodynamics of the biological fins. The fin models have been used to investigate how fin kinematics and the mechanical properties of the fin-rays influence propulsive forces and to explore kinematic patterns that were inspired by biological motions but that were not explicitly performed by the fish. Results from studies conducted with the fin models indicate that subtle changes to the kinematics and mechanical properties of fin rays can significantly impact the magnitude, direction, and time course of the 3D forces used for propulsion and maneuvers. The magnitude of the force tends to scale with the fin's stiffness, but the direction of the force is not invariant, and this causes disproportional changes in the magnitude of the thrust, lift, and lateral components of force. Results from these studies shed light on the multiple strategies that are available to the fish to modulate fin forces.     

Comparison of Trunk Activity during Gait Initiation and Walking in Humans

To understand the role of trunk muscles in maintenance of dynamic postural equilibrium we investigate trunk movements during gait initiation and walking, performing trunk kinematics analysis, Erector spinae muscle (ES) recordings and dynamic analysis. ES muscle expressed a metachronal descending pattern of activity during walking and gait initiation. In the frontal and horizontal planes, lateroflexion and rotation occur before in the upper trunk and after in the lower trunk. Comparison of ES muscle EMGs and trunk kinematics showed that trunk muscle activity precedes corresponding kinematics activity, indicating that the ES drive trunk movement during locomotion and thereby allowing a better pelvis mobilization. EMG data showed that ES activity anticipates propulsive phases in walking with a repetitive pattern, suggesting a programmed control by a central pattern generator. Our findings also suggest that the programs for gait initiation and walking overlap with the latter beginning before the first has ended.     

Trunk Muscle Activation at the Initiation and Braking of Bilateral Shoulder Flexion Movements of Different Amplitudes

The aim of this study was to investigate if trunk muscle activation patterns during rapid bilateral shoulder flexions are affected by movement amplitude. Eleven healthy males performed shoulder flexion movements starting from a position with arms along sides (0°) to either 45°, 90° or 180°. EMG was measured bilaterally from transversus abdominis (TrA), obliquus internus (OI) with intra-muscular electrodes, and from rectus abdominis (RA), erector spinae (ES) and deltoideus with surface electrodes. 3D kinematics was recorded and inverse dynamics was used to calculate the reactive linear forces and torque about the shoulders and the linear and angular impulses. The sequencing of trunk muscle onsets at the initiation of arm movements was the same across movement amplitudes with ES as the first muscle activated, followed by TrA, RA and OI. All arm movements induced a flexion angular impulse about the shoulders during acceleration that was reversed during deceleration. Increased movement amplitude led to shortened onset latencies of the abdominal muscles and increased level of activation in TrA and ES. The activation magnitude of TrA was similar in acceleration and deceleration where the other muscles were specific to acceleration or deceleration. The findings show that arm movements need to be standardized when used as a method to evaluate trunk muscle activation patterns and that inclusion of the deceleration of the arms in the analysis allow the study of the relationship between trunk muscle activation and direction of perturbing torque during one and the same arm movement.     

Feasibility of using a magnetic tracking device for measuring carpal kinematics

While several different methods have been used to measure carpal kinematics, biplanar radiography is generally considered to be the most accurate and popular one. However, biplanar radiography is tedious and so only pseudo-dynamic kinematics can be measured. Recently, magnetic tracking system has been developed for the measurement of joint kinematics which is versatile and easy to use and so the possibility of measuring motions dynamically. In this study, the capability of a magnetic tracking device to accurately measure carpal kinematics was investigated by comparing it with biplanar radiography. The kinematics of the third metacarpal, scaphoid, and lunate in five fresh cadaveric specimens were measured using both methods as the wrists were placed in eight positions. The finite screw rotation of each bone with respect to the distal radius during selecting the seven wrist motions was calculated for both measuring techniques and compared. In general, the kinematics for all three bones measured by using either magnetic tracking device or biplanar radiography was identical and showed no statistical difference. The averaged differences ranged from 0.0 to 2.0°. These differences were due to the potential effect of the weight of the sensors and the interference of the attaching rod to the surrounding tissue. It is concluded that the application of the magnetic tracking device to carpal kinematics is warranted, if proper technical procedures as suggested are followed.