Two-dimensional Sagittal Plane Research Articles

Neuromechanical stabilisation of the centre of mass during running

BackgroundStabilisation of the centre of mass (COM) trajectory is thought to be important during running. There is emerging evidence of the importance of leg length and angle regulation during running, which could contribute to stability in the COM trajectory The present study aimed to understand if leg length and angle stabilises the vertical and anterior-posterior (AP) COM displacements, and if the stability alters with running speeds. MethodsData for this study came from an open-source treadmill running dataset (n = 28). Leg length (m) was calculated by taking the resultant distance of the two-dimensional sagittal plane leg vector (from pelvis segment to centre of pressure). Leg angle was defined by the angle subtended between the leg vector and the horizontal surface. Leg length and angle were scaled to a standard deviation of one. Uncontrolled manifold analysis (UCM) was used to provide an index of motor abundance (IMA) in the stabilisation of the vertical and AP COM displacement. ResultsIMAAP and IMAvertical were largely destabilising and always stabilising, respectively. As speed increased, the peak destabilising effect on IMAAP increased from −0.66(0.18) at 2.5 m/s to −1.12(0.18) at 4.5 m/s, and the peak stabilising effect on IMAvertical increased from 0.69 (0.19) at 2.5 m/s to 1.18 (0.18) at 4.5 m/s. ConclusionTwo simple parameters from a simple spring-mass model, leg length and angle, can explain the control behind running. The variability in leg length and angle helped stabilise the vertical COM, whilst maintaining constant running speed may rely more on inter-limb variation to adjust the horizontal COM accelerations.

Stability Region-Based Analysis of Walking and Push Recovery Control

Abstract To achieve walking and push recovery successfully, a biped robot must be able to determine if it can maintain its current contact configuration or transition into another one without falling. In this study, the ability of a humanoid robot to maintain single support (SS) or double support (DS) contact and to achieve a step are represented by balanced and steppable regions, respectively, as proposed partitions of an augmented center-of-mass-state space. These regions are constructed with an optimization method that incorporates full-order system dynamics, system properties such as kinematic and actuation limits, and contact interactions with the environment in the two-dimensional sagittal plane. The SS balanced, DS balanced, and steppable regions are obtained for both experimental and simulated walking trajectories of the robot with and without the swing foot velocity constraint to evaluate the contribution of the swing leg momentum. A comparative analysis against one-step capturability, the ability of a biped to come to a stop after one step, demonstrates that the computed steppable region significantly exceeds the one-step capturability of an equivalent reduced-order model. The use of balanced regions to characterize the full balance capability criteria of the system and benchmark controllers is demonstrated with three push recovery controllers. The implemented hip–knee–ankle controller resulted in improved stabilization with respect to decreased foot tipping and time required to balance, relative to an existing hip–ankle controller and a gyro balance feedback controller.

Effects of Inertial Load on Sagittal Plane Kinematics of the Lower Extremity During Flywheel-Based Squats.

Worcester, KS, Baker, PA, and Bollinger, LM. Effects of inertial load on sagittal plane kinematics of the lower extremity during flywheel-based squats. J Strength Cond Res 36(1): 63-69, 2022-Increasing load increases flexion of lower extremity joints during weighted squats; however, the effects of inertial load on lower extremity kinematics during flywheel-based resistance training (FRT) squats remain unclear. The purpose of this study was to evaluate sagittal plane kinematics of lower extremity joints during FRT squats at various inertial loads. Nine recreationally resistance-trained subjects (3M, 6F) completed a bout of FRT squats with inertial loads of 0.050, 0.075, and 0.100 kg·m2. Two-dimensional sagittal plane kinematics were monitored with retroreflective markers at a rate of 60 Hz. Joint angles and angular velocities of the knee, trunk + hip, trunk inclination, and ankle were quantified throughout concentric and eccentric actions. Effects of inertial load were determined by repeated-measures analysis of variance with α = 0.05. Average power and average vertical velocity decreased with increasing inertial load, whereas average force increased. Minimal and maximal sagittal plane joint angles of the knee, trunk + hip, trunk inclination, and ankle were not significantly different among inertial loads. However, peak joint angular velocities of the knee and trunk + hip tended to decrease with increasing inertial load. Conversely trunk inclination and ankle dorsiflexion velocities were not significantly different among inertial loads. Increasing inertial load from 0.050 to 0.100 kg·m2 significantly reduces average power during FRT squats primarily by decreasing movement velocity, which seems to be specific to the knee and hip joints. It is possible that lower concentric energy input at high inertial loads prevents increased joint flexion during FRT squats.

Human Knee Inverse Dynamics Model of Vertical Jump Exercise

Abstract This work deals with the dynamics of the human knee during vertical jump exercise. The focus is on the joint forces necessary to produce the jump and to dissipate energy during landing. A two-dimensional (2D) sagittal plane, inverse dynamics human leg model is developed. This model uses data from a motion capture system and force plates in order to predict knee and hip joint forces during the vertical jump exercise. The model consists of three bony structures femur, tibia, and patella, ligament structures to include both cruciate and collateral ligaments, and knee joint muscles. The inverse dynamics model is solved using optimization in order to predict joint forces during this exercise. matlab software package is used for the optimization computations. Results are compared with data available in the literature. This work provides insight regarding contact forces and ligaments forces, muscle forces, and knee and hip contact forces in the vertical jump exercise.

Special Issue: Nonlinear and Computational Dynamics in Biomedical Applications

Special Issue: Nonlinear and Computational Dynamics in Biomedical Applications

Exploration of the validity of the two-dimensional sagittal plane assumption in modeling the standing long jump

Most previous standing long jump studies have been based on the assumption of two-dimensional sagittal plane motion with bilateral symmetry. The purpose of this study was to investigate the validity of this assumption. Standing long jump trials were collected using six adult male participants. Each participant stood with a foot on each of two force plates and performed eight standing long jumps for maximal distance. Inverse dynamics analyses were performed for two-dimensional (2D) and three-dimensional (3D) models, and joint moments, powers, and work values were compared. The differences between these models with respect to the validity of the common planar jumping assumption were analyzed. Good agreement was observed between 2D and 3D methods for the lower body, with minimal differences in sagittal plane moments, power, and work for the ankle, knee, and lower back. There were significant, but relatively small differences in the sagittal plane kinematics and kinetics at the hip. For the upper body, the results contradicted the sagittal plane assumption in that significant moments and power were generated about the abduction/adduction axis of the shoulder and a similar amount of work was performed about both abduction/adduction and flexion/extension axes of the shoulder. The elbow also showed significant differences in power and work. These results indicate that an assumption of planar motion should be sufficient for many studies of the standing long jump that only examine lower body movement. However, for studies that include upper body motion, diagnosing injury risk, or investigating gender differences, a 3D model may be more appropriate.

SU-F-303-02: Achieving 4D MRI in Regular Breathing Cycle with Extended Acquisition Time of Dynamic MR Images

Purpose: The purpose of this study is to develop a technique to obtain four-dimensional (4D) magnetic resonance (MR) images that are more representative of a patient's typical breathing cycle by utilizing an extended acquisition time while minimizing the image artifacts. Methods: The 4D MR data were acquired with the balanced steady state free precession in two-dimensional sagittal plane of view. Each slice was acquired repeatedly for about 15 s, thereby obtaining multiple images at each of the 10 phases in the respiratory cycle. This improves the probability that at least one of the images were acquired at the desired phase during a regular breathing cycle. To create optimal 4D MR images, an iterative approach was used to identify the set of images that yielded the highest slice-to-slice similarity. To assess the effectiveness of the approach, the data set was truncated into periods of 7 s (50 time points), 11 s (75 time points) and the full 15 s (100 time points). The 4D MR images were then sorted with data of the three different acquisition periods for comparison. Results: In general, the 4D MR images sorted using data from longer acquisition periods showed less mismatched artifacts. In addition, the normalized cross correlation (NCC) between slices of a 4D volume increases with increased acquisition period. The average NCC was 0.791 from the 7 s period, 0.794 from the 11 s period and 0.796 from the 15 s period. Conclusion: Our preliminary study showed that extending the acquisition time with the proposed sorting technique can improve image quality and reduce artifact presence in the 4D MR images. Data acquisition over two breathing cycles is a good trade-off between artifact reduction and scan time. This research was partially funded by the the Center for Radiation Oncology Research from UT MD Anderson Cancer Center.

Differences Between Types Of Constant Resistance On Torque And Muscle Activation During Elbow Flexion Exercise

Constant resistance is the most common method to enhance strength. Constant resistance load is always the same across the full range of movement. However, pulleys can generate forces in different directions (x and y axis) while free-weights only generate force in one direction (y axis). PURPOSE: To investigate torque and muscle activation between elbow flexion exercise performed with free-weights and pulleys. METHODS: Five resistance trained males (body mass: 73.43±17.32 kg; height: 176.03 ±12.73 cm) and two females (body mass: 53.9±6.79 kg; height: 163.75 ±8.84 cm) participated. Maximal voluntary isometric contraction of the elbow flexors was measured at 90° of flexion for 5 seconds. Subjects performed 10 unilateral elbow flexions using free-weights and pulleys with 40% of their maximal isometric contraction load. Exercises were performed in a randomized order and at a pre-established rhythm of 2 seconds for each dynamic action controlled by a metronome. Ten minutes of rest between protocols was given. Surface electromyography of the biceps brachii was collected at 2400 Hz and synchronized with two-dimensional sagittal plane video at 60 Hz. Anatomical markers on the upper-limb and an electrogoniometer were used. During the pulley exercise, a load cell was used to record force. Five repetitions were analyzed. Root mean square (RMS) and mean sum of torques (MST) were calculated with a specific routine written in Matlab. Paired t-tests were used to determine significant (p≤0.05) differences between exercises. RESULTS: For the load used, there was no significant difference between pulley and free-weight. Similarly, there was no significant difference between pulley and free-weight for RMS (free-weight: 0.025 ± 0.006 mV; pulley: 0.026 ± 0.005 mV). However, MST was significantly greater for pulley (3,942.9 ± 1,013.7 N.m) than for free-weight (2,604.3 ± 705.6 N.m). CONCLUSION: The use of a pulley during elbow flexion exercise produced greater torque when compared with free-weight. However, biceps brachii activation was not different. More studies are necessary to investigate muscle activation in other muscles performed with different types of constant resistance.

A Deterministic Model of Human Motion Based on Algebraic Techniques and a Sensor Network to Simulate Shoulder Kinematics.

Limiting the quantitative characterization of ambulatory mobility to only the two-dimensional sagittal plane through the investigation of key kinematic parameters, may still inform scientists and bioengineers of critical elements of joint locomotion. This paper presents the initial validation of a deterministic biomechanical gait model that was derived from an inverse kinematic analysis of three-dimensional upper extremity movement. Algebraic methods were applied to generate shoulder flexion and extension angles during a single gait cycle during normal walking. The direct kinematic measurements from a motion capture system were analyzed and compared to the predicted measurements from the algebraic model for eight healthy, human subjects. The predicted results over all subjects varied from the actual joint angle measurements with a nominal amount of mean error (23%), while correlations were quite strong (mean R2 = 0.97). These findings indicate the potential value of deterministic modeling with algebraic techniques as an alternative to existing methods.

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.

A Work-Loop Method for Characterizing Leg Function During Sagittal Plane Movements

The work-loop method is frequently used to determine the mechanical work performed by a system, for instance, when analyzing muscles or describing the work balance at the joint level. While for these examples usually only one-dimensional movements are investigated, for two- or three-dimensional movements, such as leg function during walking and running, the work-loop has to be adapted. In this paper, we present an analytical derivation that extends the work-loop method to two-dimensional sagittal plane movements. Three effects contribute to the mechanical work of the leg: (1) forces directed along the leg axis, (2) forces acting perpendicular to the leg axis, and (3) a shift of the center of pressure (COP) during stance. These three contributors to the mechanical work performed can be interpreted as three general tasks of the leg. To demonstrate the new work-loop method, we analyzed experimental data on hopping, running and walking. The results indicate that the proposed new generalized work-loop concept is suitable for describing the overall mechanical work performed on the COM during stance with energy consistent net work balances. Depending on the type of gait, specific contributions of each work term were found that characterize leg function during locomotion.

Paper 8: Lower Extremity Neuromuscular Compensations During Instrumented Single Leg Hop Five Years Following ACL Reconstruction

Anterior cruciate ligament (ACL) injury may lead to neuromuscular activation changes long after surgical reconstruction and rehabilitation. This study compared bilateral lower extremity EMG and kinematic characteristics during the performance of a single leg hop. Our hypothesis was that lower extremity neuromuscular activation characteristics would differ between the lower extremity that had undergone ACL reconstruction and the noninvolved contralateral lower extremity. Seventy subjects at a mean of 5 years (range 2-10 years) following unilateral ACL reconstruction using allograft tissue participated in this study. All subjects had complied with rehabilitation program recommendations. Active knee range of motion was bilaterally equivalent and knee laxity was within 2 mm. Most subjects (66%) displayed normal or nearly normal 2000 IKDC SelfReported Knee Evaluation scores. EMG (1000 Hz) and two-dimensional sagittal plane kinematic (60 Hz) data were collected as subjects performed 3 single leg hops with each lower extremity. Gluteus maximus, vastus medialis, medial hamstring, and gastrocnemius EMG amplitudes were standardized to levels attained during single repetition, maximal volitional effort isometric contractions (%MVIC) using conventional manual muscle tests. Paired t-tests were used to compare side-to-side differences (P .05). Peak bilateral lower extremity joint displacement (noninvolved, involved) did not differ at the knee (56.7 13° vs. 57.8 14°) or ankle (13.8 5° vs. 13.3 5°) during single leg hop performance. Hip displacement however was increased (63.9 17° vs. 67.2 16°, P .03) and single leg hop distance was decreased at the involved side (42.3 15 cm vs. 40.0 15 cm, P .001). EMG activation sequence and duration did not differ between extremities. Vastus medialis and medial hamstring EMG amplitudes did not display differences during single leg hop propulsion or landing. Gluteus maximus EMG amplitudes did not display differences during single leg hop propulsion. Gastrocnemius EMG amplitudes during both single leg hop propulsion (1.2 .4%MVIC vs. 1.3 .3%MVIC, P .04) and landing (1.2 .5%MVIC vs. 1.3 .5%MVIC, P .01), and gluteus maximus muscle EMG amplitudes during landing (1.3 .5%MVIC vs. 1.5 1%MVIC, P .04) were increased at the involved lower extremity compared to the noninvolved lower extremity. Despite predominantly satisfactory self-reported knee outcome scores evidence of side-to-side neuromuscular differences were observed. Increased gluteus maximus and gastrocnemius muscle activation amplitudes and increased hip displacement magnitude at the involved lower extremity at a mean 5 years post-ACL reconstruction suggest long-term compensatory changes toward a hip and ankle joint bias to decrease knee joint loading forces. ACL reconstruction corrects knee joint ligamentous laxity, however compensatory neuromuscular changes still occur. Paper 9: What Can We Really Do Following TKA, UKA and HTO? MICHEL P BONNIN, MD, FRANCE, PRE-

Effect of take-off from prosthetic versus intact limb on transtibial amputee long jump technique

Increasing numbers of long jumpers with lower limb amputations choose to take off from their prosthetic limb. It is not yet known what difference in technique, if any, this requires, or which is more advantageous. To investigate kinematic differences in long jump technique in athletes with a unilateral transtibial ampution (TT) who take off from their prosthetic limb versus those who take off from their intact limb. Naturalistic, field-based, observational; independent group, nonparametric comparison. Two-dimensional sagittal plane kinematic analysis was performed on all athletes competing in the men's Paralympic TT long jump finals. Five athletes took off from their prosthetic limb (TO(prosth)) and five from their intact limb (TO(intact)). No differences were seen between the two groups in terms of jump distance, approach speed or vertical velocity at touch down. While in contact with the take-off board, the two groups gained a similar amount of vertical velocity. However, the TO(prosth) group appeared to conserve horizontal velocity by using the prosthesis as a 'springboard', minimizing the large hip and knee range of motion displayed by the TO(intact) group and athletes in previous studies. While differences in technique were observed, no difference was found for jump distance.

Does saddle height affect patellofemoral and tibiofemoral forces during bicycling for rehabilitation?

The aim of the present study was to measure saddle height effects on knee joint load. Nine uninjured non-cyclists were evaluated in three saddle heights: 100% of trochanteric height-REF; 103% of REF-HIGH; and 97% of REF-LOW. Two-dimensional sagittal plane force applied on the pedal and kinematics were recorded. After inverse dynamics of the lower limb, knee resultant force was computed as tibiofemoral normal and shear components and compressive patellofemoral force. Peak patellofemoral compressive force and peak compressive and shear tibiofemoral forces did not differ when saddle height was changed. Knee angle at the lower crank position increased at LOW compared to REF and HIGH saddle height (p<0.02). Small saddle height changes (±3%) did not affect knee joint load, at low workloads on uninjured subjects, while changes in knee angle did not relate to effects on joint forces. These findings suggest that setting saddle height by knee angle secures the maintenance of joint load at low workloads on uninjured subjects.

Muscle function may depend on model selection in forward simulation of normal walking

The purpose of this study was to quantify how the predicted muscle function would change in a muscle-driven forward simulation of normal walking when changing the number of degrees of freedom in the model. Muscle function was described by individual muscle contributions to the vertical acceleration of the center of mass (COM). We built a two-dimensional (2D) sagittal plane model and a three-dimensional (3D) model in OpenSim and used both models to reproduce the same normal walking data. Perturbation analysis was applied to deduce muscle function in each model. Muscle excitations and contributions to COM support were compared between the 2D and 3D models. We found that the 2D model was able to reproduce similar joint kinematics and kinetics patterns as the 3D model. Individual muscle excitations were different for most of the hip muscles but ankle and knee muscles were able to attain similar excitations. Total induced vertical COM acceleration by muscles and gravity was the same for both models. However, individual muscle contributions to COM support varied, especially for hip muscles. Although there is currently no standard way to validate muscle function predictions, a 3D model seems to be more appropriate for estimating individual hip muscle function.

Testing the Planar Assumption during Ergometer Cycling

Lower extremity motions during cycling are often assumed to occur in the sagittal plane. While seemingly logical, this assumption has not been rigorously tested. Frontal plane rotation of the ankle joint (inversion/eversion) has been studied extensively during gait but infrequently during cycling despite the suggestion that excessive eversion or pronation may be related to overuse knee injuries. Two-dimensional sagittal plane hip, knee, and ankle joint kinematics were generally found to be similar to simultaneously measured 3-D values. Despite the similarity in motion patterns, maximum hip angle was 34° more flexed in 2-D than 3-D. Maximum and minimum frontal plane ankle joint angles were similar in 2-D and 3-D. However, during the middle of the pedal cycle, 2-D frontal plane ankle joint motion deviated from 3-D, such that maximum ankle eversion was reached 36% of the pedal cycle later in 2-D versus 3-D. The discrepancy at the hip was due primarily to differences in hip angle definition for 2-D and 3-D approaches, and an alternate convention for hip angle in 2-D is suggested. Discrepancies in frontal plane ankle joint motion are due to weaknesses in the planar approach and would be difficult to overcome without resorting to 3-D measurement.

A method for the intravital measurement of interspinous kinematics

A novel non-radiographic technique for objectively quantifying quasi-static or dynamic intervertebral motion of a spinal motion segment in vivo in human subjects is presented here. The intervertebral motion device (IMD) is an instrumented linkage transducer system which can continuously measure over time two-dimensional sagittal plane rigid-body motion. Three custom-built omega-shaped displacement transducers are utilized. The IMD is rigidly fixed to the spinous processes of the lumbar motion segment by means of two intraosseous pins. Knowing the mechanoelectrical behavior and geometric configuration of the IMD, the relative spatial motion between the vertebral bodies can be resolved into sagittal rotation, axial translation, and anterior-posterior shear translation. Static calibrations of the IMD in the ranges of ±4° rotation and ±4 mm translation determined the absolute maximum errors to be 0.2° and 0.07 mm for rotation and translation measurements, respectively, with corresponding variances of 0.1° and 0.03 mm. For use in the vibration environment, negligible motion artifact content was detected in the IMD output signals when excited at discrete frequencies of 5.0 and 8.0 Hz. The first natural frequency of the IMD, specific for this design, was measured at 16.25 Hz. This technique may be used to study in vivo the spinal kinematics in healthy lumbar motion segments and in patients suspected of having segmental instability, and can perhaps be of clinical diagnostic significance.

Mechanical energy of walking of stroke patients

The mechanical energy costs of walking have been studied in ten stroke patients with hemiplegia. A two-dimensional sagittal plane cinematographic analysis of two strides of the subjects' normal walking was undertaken, yielding continuous information about the mechanical energy costs of the whole body and each of its parts, about the energy types involved, and the amounts of energy conservation. The large head, arms, and trunk (HAT) were found to dominate the total pattern. Three major disturbances were seen. In contrast to normal subjects who show energy-conserving negatively correlated potential and kinetic energy curves for the HAT, the subjects who demonstrated the first disturbance showed gross irregularity of the curves, with almost no opportunity for exchange between energy types. In a second disturbance the curves of the HAT showed some energy-conserving portions, but levels of kinetic energy curves were low, resulting in little energy exchange. In the third disturbance, some exchange was evident, but the pattern was dominated by potential energy changes in the form of a single large rise and fall, coinciding with swing phase of the affected leg. Each of these disturbances would require a different approach to treatment. Although mechanical energy analyses do not reflect certain energy costs, such as the effort required to hold the body up against the pull of gravity and that used in contracting antagonist muscles, they could be of considerable assistance in pinpointing costly variations in energy patterns during walking and in determining appropriate treatment procedures.