Identification of passive elastic joint moment-angle relationships in the lower extremity

The purpose of this study was to develop a method for identifying subject-specific passive elastic joint moment-angle relationships in the lower extremity, which could subsequently be used to estimate passive contributions to joint kinetics during gait. Twenty healthy young adults participated in the study. Subjects were positioned side-lying with their dominant limb supported on a table via low-friction carts. A physical therapist slowly manipulated the limb through full sagittal hip, knee, and ankle ranges of motion using two hand-held 3D load cells. Lower extremity kinematics, measured with a passive marker motion capture system, and load cell readings were used to compute joint angles and associated passive joint moments. We formulated a passive joint moment-angle model that included eight exponential functions to account for forces generated via the passive stretch of uni-articular structures and bi-articular muscles. Model parameters were estimated for individual subjects by minimizing the sum of squared errors between model predicted and experimentally measured moments. The model predictions closely replicated measured joint moments with average root-mean-squared errors of 2.5, 1.4, and 0.7 Nm about the hip, knee, and ankle respectively. We show that the models can be coupled with gait kinematics to estimate passive joint moments during walking. Passive hip moments were substantial from terminal stance through initial swing, with energy being stored as the hip extended and subsequently returned during pre- and initial swing. We conclude that the proposed methodology could provide quantitative insights into the potentially important role that passive mechanisms play in both normal and abnormal gait.     

The effect of three-dimensional postural change on shear elastic modulus of the iliotibial band

To understand and treat iliotibial band (ITB) syndrome, caused by excessive compression between the ITB and lateral femoral condyle, it is important to identify factors contributing to an increase in ITB stiffness. The purpose of this study was to clarify the factors that contribute to an increase in ITB stiffness by examining the relationship between three-dimensional postural changes and ITB stiffness. Fourteen healthy individuals performed one-leg standing under 7 conditions (including normal one-leg standing as a control condition) in which the pelvic position was changed in three planes. The shear elastic modulus in the ITB was measured using shear-wave elastography, as a measure of ITB stiffness. The three-dimensional joint angles and external joint moments in the hip and knee joints were also measured to confirm the changes in joint angles and external load. Compared to the normal one-leg standing condition, ITB stiffness was significantly increased in the pelvic posterior tilted position (i.e. hip extension), contralateral pelvic dropped position (i.e. hip adduction), and contralateral pelvic posterior rotated position (i.e. hip external rotation). The findings suggest that interventions to reduce hip extension, adduction, and external rotation might be useful if these excessive positional changes are detected in patients with ITB syndrome.     

Muscular coordination of knee motion during the terminal-swing phase of normal gait

Children with cerebral palsy often walk with diminished knee extension during the terminal-swing phase, resulting in a troublesome "crouched" posture at initial contact and a shortened stride. Treatment of this gait abnormality is challenging because the factors that extend the knee during normal walking are not well understood, and because the potential of individual muscles to limit terminal-swing knee extension is unknown. This study analyzed a series of three-dimensional, muscle-driven dynamic simulations to quantify the angular accelerations of the knee induced by muscles and other factors during swing. Simulations were generated that reproduced the measured gait dynamics and muscle excitation patterns of six typically developing children walking at self-selected speeds. The knee was accelerated toward extension in the simulations by velocity-related forces (i.e., Coriolis and centrifugal forces) and by a number of muscles, notably the vasti in mid-swing (passive), the hip extensors in terminal swing, and the stance-limb hip abductors, which accelerated the pelvis upward. Knee extension was slowed in terminal swing by the stance-limb hip flexors, which accelerated the pelvis backward. The hamstrings decelerated the forward motion of the swing-limb shank, but did not contribute substantially to angular motions of the knee. Based on these data, we hypothesize that the diminished knee extension in terminal swing exhibited by children with cerebral palsy may, in part, be caused by weak hip extensors or by impaired hip muscles on the stance limb that result in abnormal accelerations of the pelvis.     

The passive elastic moment at the hip

The passive elastic moment at the hip was measured in normal male subjects in situ. The influence of two joint muscles crossing the hip was evaluated by performing hip moment measurements over a continuous range of hip angles and at prescribed knee angles. The experimentally acquired data was fitted by exponential functions which separately modeled the moment contribution of tissues deformed by hip flexion and extension. The results of the investigation are discussed with regard to the possible role of the passive joint moments as an energy storage and release mechanism during human walking.     

On the relation between joint moments and pedalling rates at constant power in bicycling

Joint moments are of interest because they bear some relation to muscular effort and hence rider performance. The general objective of this study is to explore the relation between joint moments and pedalling rate (i.e. cadence). Joint moments are computed by modelling the leg-bicycle system as a five-bar linkage constrained to plane motion. Using dynamometer pedal force data and potentiometer crank and pedal position data, system equations are solved on a computer to produce moments at the ankle, knee and hip joints. Cadence and pedal forces are varied inversely to maintain constant power. Results indicate that average joint moments vary considerably with changes in cadence. Both hip and knee joints show an average moment which is minimum near 105 rotations min-1 for cruising cycling. It appears that an optimum rotations min-1 can be determined from a mechanical approach for any given power level and bicycle-rider geometry.     

A new method for gravity correction of dynamometer data and determining passive elastic moments at the joint

Moments measured by a dynamometer in biomechanics testing often include the gravitational moment and the passive elastic moment in addition to the moment caused by muscle contraction. Gravitational moments result from the weight of body segments and dynamometer attachment, whereas passive elastic moments are caused by the passive elastic deformation of tissues crossing the joint being assessed. Gravitational moments are a major potential source of error in dynamometer measurements and must be corrected for, a procedure often called gravity correction. While several approaches to gravity correction have been presented in the literature, they generally assume that the gravitational moment can be adequately modeled as a simple sine or cosine function. With this approach, a single passive data point may be used to specify the model, assuming that passive elastic moments are negligible at that point. A new method is presented here for the gravity correction of dynamometer data. Gravitational moment is represented using a generalized sinusoid, which is fit to passive data obtained over the entire joint range of motion. The model also explicitly accounts for the presence of passive elastic moments. The model was tested for cases of hip flexion-extension, knee flexion-extension, and ankle plantar flexion-dorsiflexion, and provided good fits in all cases.     

Segment-interaction analysis of the stance limb in sprint running

A high angular velocity of the thigh of the stance limb, generated by hip extensor musculature, is commonly thought to be a performance-determining factor in sprint running. However, the thigh segment is a component of a linked system (i.e., the lower limb), therefore, it is unlikely that the kinematics of the thigh will be due exclusively to the resultant joint moment (RJM) at the hip. The purpose of this study was to quantify, by means of segment-interaction analysis, the determinants of sagittal plane kinematics of the lower limb segments during the stance phase of sprint running. Video and ground reaction force data were collected from four male athletes performing maximal-effort sprints. The analysis revealed that during the first-third of the stance phase, a hip extension moment was the major determinant of the increasing angular velocity of the thigh. However, during the mid-third of stance, hip and knee extension moments and segment interaction effects all contributed to the thigh attaining its peak angular velocity. Extension moments at the ankle, and to a lesser extent the knee, were attributed with preventing the 'collapse' of the shank under the effects of the interactive moment due to ground reaction force. The angular acceleration of the foot was determined almost completely by the RJM at the ankle and the interactive moment due to ground reaction force. Further research is required to determine if similar results exit for a wide range of athletes and for other stages of a sprint race (e.g. early acceleration, maximal velocity, and deceleration phases).     

Prestress revealed by passive co-tension at the ankle joint

This study was designed to test the assumption that elastic tissues of the ankle are prestressed, by investigating the presence of simultaneous opposite passive elastic moments and thus, passive co-tension, at the ankle joint. A prestressed two-spring model used to generate qualitative predictions of the effects of stretching the posterior elastic structures of the ankle on the net passive moment of this joint was used. Twenty-seven healthy individuals were subjected to passive evaluation of the net elastic moment of the ankle in the sagittal plane, with the knee positioned at 90°, 60°, 30° and 0° of flexion, in order to change the length of the posterior biarticular elastic structures. The placement of the knee in the more extended positions caused changes in the net passive moment as predicted by the prestressed model. The ankle position in which the net passive moment was equal to zero was shifted to more plantar flexed positions (p<0.001) and there was a global increase in ankle stiffness since both passive dorsiflexion stiffness (p≤0.037) and passive plantar flexion stiffness (p≤0.029) increased. The normalized terminal plantar flexion stiffness also increased (p≤0.047), suggesting that biarticular posterior elastic structures are pre-strained and still under tension when the ankle is maximally plantar flexed and the knee is positioned at 60° of flexion. Resting positions were indicative of equilibrium between opposite passive elastic moments. The results revealed that there is passive co-tension at the ankle, demonstrating the existence of prestress in elastic structures of this joint.     

An analytical approach to spatio-temporal dynamics of neutral community models

We propose a spatial version of the neutral community model on a network of interconnected patches. The dynamical equations for the abundances and higher order moments of the abundances are established. Due to the neutrality assumption these equations are autonomous, enabling an exact analysis of spatio-temporal dynamics. We compute local (i.e., inside a patch) and global (i.e., between patches) diversities, and illustrate our results with two examples: (1) a non-spatial community, for which we recover previous results, and (2) a model with a finite number of patches which are all connected to each other with equal migration intensity. We discuss the relevance of this model for experiments in microbial ecology.     

Does epimuscular myofascial force transmission occur between the human quadriceps muscles in vivo during passive stretching?

This study sought to examine the shear modulus (i.e., an force index) of three quadriceps muscles [i.e., vastus medialis (VM), vastus lateralis (VL), and rectus femoris (RF)] during passive stretching to determine whether epimuscular myofascial force transmission occurs across muscles. Secondly, this study compared the shear modulus between the quadriceps muscles, in both proximal and distal regions. Twelve healthy individuals were assessed during a passive knee flexion maneuver between 0° and 90° of knee flexion with the hip in two positions: flexed (80°) vs. neutral (0°). Muscle electrical activity was also assessed during the testing. No differences were observed between the hip testing positions for myoelectric activity (p > 0.43), and for VL and VM shear modulus (p = 0.12–0.98). Similarly, there were no differences between the proximal and distal regions for all muscles (p = 0.42–0.93). RF showed a higher shear modulus with the hip in the neutral position (p = 0.004). With the hip flexed, the VL showed the greatest shear modulus among the tested muscles (p < 0.025); while with the hip in the neutral position, no differences were observed for shear modulus between VL and RF (p = 0.817). These findings suggest that epimuscular myofascial force transmission (at a muscle belly level) does not occur between the quadriceps muscles when passively flexing the knee until 90°. Whether epimuscular myofascial force transmission occurs in the quadriceps muscles bellies with greater muscle stretch (either through knee flexion or hip extension) remains to be examined.     

Identification of passive elastic joint moments in the lower extremities.

Musculotendon actuators produce active and passive moments at the joints they span. Due to the existence of bi-articular muscles, the passive elastic joint moments are influenced by the angular positions of adjacent joints. To obtain quantitative information about this passive elastic coupling between lower limb joints, we examined the passive elastic joint properties of the hip, knee, and ankle joint of ten healthy subjects. Passive elastic joint moments were found to considerably depend on the adjacent joint angles. We present a simple mathematical model that describes these properties on the basis of a double-exponential expression. The model can be implemented in biomechanical models of the lower extremities, which are generally used for the simulation of multi-joint movements such as standing-up, walking, running, or jumping.     

Tests for independence between marks and points of a marked point process

A convenient assumption while modeling a marked point process is that the observations (i.e., marks) and the locations (i.e., points) are independent. We propose new graphical and formal testing approaches to test for this assumption. The proposed graphical procedures are easy to obtain and can be used to diagnose the nature and range of dependence between marks and points. The formal testing procedures require only minimal conditions on marks and thus can be applied to a variety of settings. We illustrate these procedures through a simulation study and an application to some real data.     

Paired nonlinear behavior of active and passive joint torques associated with preparation for walk-to-run gait transition

This study investigated the lower extremity torque's active and passive features during the walk-to-run gait transition with continuously increased walking speed. Fourteen volunteers participated in the experiment. Kinematic and kinetic data were collected synchronously. Five strides leading up the gait transition were examined. Peaks of the passive (e.g., contact) and active (e.g., generalized muscle torques), along with net joint torque, and time to peak torques exhibited significant differences at the last stride before gait transition, compared to the first four strides, at the ankle, knee, and hip joints, respectively. Selected peak joint active and passive torques showed significant and opposite trends at critical events within a stride cycle: such ankle joint right after heel-contact, knee joint during weight acceptance, and both hip and knee joints right before toe-off. The magnitude and the corresponding time to active and passive peak torque changed in a nonlinear pattern before the transition from walk to run. The lower extremity segment-interaction during gait transition appeared to be an active reorganization exemplified by the interaction between the lower extremity's active and passive torque components.     

"In vivo" determination of hip joint separation and the forces generated due to impact loading conditions

Numerous supporting structures assist in the retention of the femoral head within the acetabulum of the normal hip joint including the capsule, labrum, and ligament of the femoral head (LHF). During total hip arthroplasty (THA), the LHF is often disrupted or degenerative and is surgically removed. In addition, a portion of the remaining supporting structures is transected or resected to facilitate surgical exposure. The present study analyzes the effects of LHF absence and surgical dissection in THA patients. Twenty subjects (5 normal hip joints, 10 nonconstrained THA, and 5 constrained THA) were evaluated using fluoroscopy while performing active hip abduction. All THA subjects were considered clinically successful. Fluoroscopic videos of the normal hips were analyzed using digitization, while those with THA were assessed using a computerized interactive model-fitting technique. The distance between the femoral head and acetabulum was measured to determine if femoral head separation occurred. Error analysis revealed measurements to be accurate within 0.75mm. No separation was observed in normal hips or those subjects implanted with constrained THA, while all 10 (100%) with unconstrained THA demonstrated femoral head separation, averaging 3.3mm (range 1.9-5.2mm). This study has shown that separation of the prosthetic femoral head from the acetabular component can occur. The normal hip joint has surrounding capsuloligamentous structures and a ligament attaching the femoral head to the acetabulum. We hypothesize that these soft tissue supports create a passive, resistant force at the hip, preventing femoral head separation. The absence of these supporting structures after THA may allow increased hip joint forces, which may play a role in premature polyethylene wear or prosthetic loosening.     

Gender differences exist in the hip joint moments of healthy older walkers

Gender differences in the incidence of symptomatic hip osteoarthritis (OA), changes in hip cartilage volume and hip joint space and rates hip arthroplasty of older people are reported in the literature. As the rate of progression of OA is in part mechanically modulated it is possible that this gender bias may be related to inherent differences (if they exist) in walking mechanics between older males and females. The purpose of this study was to examine potential mechanisms for gender differences in hip joint mechanics during walking by testing the hypotheses that females would exhibit higher hip flexion, adduction and internal rotation moments but not significantly greater normalized ground reaction forces (GRFs). Forty-two healthy subjects (21 male, 21 female), ages 50–79 yr were recruited for gait analysis. In support of the hypotheses, greater external hip adduction and internal rotation along with hip extension moments were found for females compared to males after normalizing for body size for all self-selected walking speeds. Differences in walking style (kinematics) were the main determinants in the joint kinetic differences as no differences in the normalized GRFs were found. As external joint moments are surrogate measures of the joint contact forces, the results of this study suggest the hip joint stress for the female population is higher compared to male population. This is in favor of a hypothesis that the increased joint contact stress in a female population could contribute to a greater joint degeneration at the hip in females as compared with males.     

Identifying grasslands suitable for cellulosic feedstock crops in the Greater Platte River Basin: dynamic modeling of ecosystem performance with 250 m eMODIS

This study dynamically monitors ecosystem performance (EP) to identify grasslands potentially suitable for cellulosic feedstock crops (e.g., switchgrass) within the Greater Platte River Basin (GPRB). We computed grassland site potential and EP anomalies using 9‐year (2000–2008) time series of 250 m expedited moderate resolution imaging spectroradiometer Normalized Difference Vegetation Index data, geophysical and biophysical data, weather and climate data, and EP models. We hypothesize that areas with fairly consistent high grassland productivity (i.e., high grassland site potential) in fair to good range condition (i.e., persistent ecosystem overperformance or normal performance, indicating a lack of severe ecological disturbance) are potentially suitable for cellulosic feedstock crop development. Unproductive (i.e., low grassland site potential) or degraded grasslands (i.e., persistent ecosystem underperformance with poor range condition) are not appropriate for cellulosic feedstock development. Grassland pixels with high or moderate ecosystem site potential and with more than 7 years ecosystem normal performance or overperformance during 2000–2008 are identified as possible regions for future cellulosic feedstock crop development (ca. 68 000 km² within the GPRB, mostly in the eastern areas). Long‐term climate conditions, elevation, soil organic carbon, and yearly seasonal precipitation and temperature are important performance variables to determine the suitable areas in this study. The final map delineating the suitable areas within the GPRB provides a new monitoring and modeling approach that can contribute to decision support tools to help land managers and decision makers make optimal land use decisions regarding cellulosic feedstock crop development and sustainability.     

Simple and complex models for studying muscle function in walking

While simple models can be helpful in identifying basic features of muscle function, more complex models are needed to discern the functional roles of specific muscles in movement. In this paper, two very different models of walking, one simple and one complex, are used to study how muscle forces, gravitational forces and centrifugal forces (i.e. forces arising from motion of the joints) combine to produce the pattern of force exerted on the ground. Both the simple model and the complex one predict that muscles contribute significantly to the ground force pattern generated in walking; indeed, both models show that muscle action is responsible for the appearance of the two peaks in the vertical force. The simple model, an inverted double pendulum, suggests further that the first and second peaks are due to net extensor muscle moments exerted about the knee and ankle, respectively. Analyses based on a much more complex, muscle-actuated simulation of walking are in general agreement with these results; however, the more detailed model also reveals that both the hip extensor and hip abductor muscles contribute significantly to vertical motion of the centre of mass, and therefore to the appearance of the first peak in the vertical ground force, in early single-leg stance. This discrepancy in the model predictions is most probably explained by the difference in model complexity. First, movements of the upper body in the sagittal plane are not represented properly in the double-pendulum model, which may explain the anomalous result obtained for the contribution of a hip-extensor torque to the vertical ground force. Second, the double-pendulum model incorporates only three of the six major elements of walking, whereas the complex model is fully 3D and incorporates all six gait determinants. In particular, pelvic list occurs primarily in the frontal plane, so there is the potential for this mechanism to contribute significantly to the vertical ground force, especially during early single-leg stance when the hip abductors are activated with considerable force.     

Decreased frontal plane hip joint moments in runners with excessive varus excursion at the knee

Knee varus position and motion have been correlated with increased medial knee loading during gait. The purpose of this study is to determine whether runners with excessive varus excursion (EVE) at the knee demonstrate frontal plane knee and hip kinetics that are different from those of runners with normal varus excursion (NVE). Twelve runners with EVE were compared with 12 NVE subjects using three-dimensional kinematics and kinetics. Frontal plane angles and moments were compared at the knee and hip. Runners with EVE had significantly greater abductor moment of the knee (p = .004) and lower peak abductor moment of the hip (p = .047). Runners with EVE demonstrate knee and hip mechanics thought to be associated with increased medial tibiofemoral loading. Further understanding of how changing hip abductor moments may affect changes in knee abductor moments during running may potentially lead to interventions that augment long-term risk of injury.     

Intracellular monosaccharide and amino acid concentrations and activities and the mechanisms of insulin action.

Current amino acid and monosaccharide transport models are based on an assumption which equates the intracellular chemical activity of a solute with its concentration. This assumption was tested for alpha-aminoisobutyric acid and 3-O-methylglucose in a giant cell, the amphibian oocyte, by using recently developed cryomicrodissection and internal reference phase techniques. We found the following. (i) alpha-Aminoisobutyric acid and 3-O-methylglucose activities were much greater in cytoplasm than was suggested by concentration data; i.e., activity coefficients were higher than in ordinary water solutions. This is attributable to the inaccessibility of considerable water as solvent (solute exclusion). (ii) Solute concentrations varied regionally as follows: nucleus > > animal cytoplasm > vegetal cytoplasm. Insulin increased the nucleus/cytoplasm concentration asymmetry, apparently by increasing cytoplasmic solute exclusion. (iii) Nuclear activity coefficients more closely resembled those of ordinary saline solutions so that nucleus/ extracellular concentration ratios reflected transmembrane activity gradients better than did cytoplasm (or whole cell)/extracellular ratios. (iv) Mediated passive alpha-aminoisobutyric acid and 3-O-methylglucose transport were constituent oocyte membrane properties. Membrane active transport was initiated with time (in the presence of substrate) and by insulin. (v) Increased temperature mimicked insulin in enhancing transmembrane alpha-aminoisobutyric acid activity gradients and increasing the nucleus/cytoplasm concentration asymmetry. These results indicated that concentration data are a misleading measure of cellular amino acid and monosaccharide activity; some consequences of this observation were explored. A model is proposed in which cell water has reduced solvent capacity or is compartmentalized (considered less likely) and is susceptible to physiological modulation. The model accounts for many observations in small cells, suggesting generality of the exclusion phenomenon and a previously unrecognized metabolic control mechanism.