Biomechanical analysis of a posterior transfer maneuver on a level surface in individuals with high and low-level spinal cord injuries

Upper extremity effort during the sit-to-stand task in able-bodied and in individuals with spinal cord injury: A preliminary study

OBJECTIVE

To investigate the association between the presence of spinal cord injury (SCI) on biomechanical variables by comparing individuals with SCI and able-bodied individuals during the sit-to-stand (STS) task assisted by a walker device. Specifically, we compared the upper-extremity joint angles and moments, trunk forward tilt angle, vertical forces of the instrumented walker, and ground reaction forces between groups.

DESIGN

Case-control study.

SETTING

Department of Orthopedics and Traumatology, UNICAMP-Brazil.

PARTICIPANTS

Six individuals with SCI and fourteen able-bodied individuals.

MAIN OUTCOME MEASURES

Kinematics and kinetics of the shoulder, elbow, and wrist joints; trunk forward tilt angle, vertical walker forces, and ground reaction forces (GRF) were analyzed during the STS task in two phases: before and after the seat-off event.

RESULTS

A higher peak elbow flexion angle and higher vertical walker forces were observed before the seat-off, whereas the lower peak vertical GRF was found, after the seat-off, in the SCI group compared with the control group.

CONCLUSIONS

SCI affects kinematics and kinetics variables during the STS task compared to able-bodied controls. Individuals with SCI adopted different standing-up strategies that affected the distribution of the forces in the upper and lower extremities of the human body.

Utilizing spinal cord injury stratification during classification for allocation of para surfing sport classes

OBJECTIVES

The purpose of this study was to determine which stratification (anatomical versus functional) forms a better construct for classification of para surfers with spinal cord injury; to assess the groupings of these para surfers; and to evaluate the strength of association between manual muscle testing and surfing performance.

DESIGN

Cross-sectional.

METHODS

Archived data from classification records including demographics, spinal cord injury levels, trunk strength, and limb strength were compared to judged wave scores and competition rankings.

RESULTS

Participants (n = 70, male n = 56; female n = 14) met inclusion criteria and were classified into Para Surfing Kneeling (n = 9); Sit (n = 11); Prone 1 (n = 25); and Prone 2 (n = 25) sport classes. Reliability statistics showed that functional grouping (Cronbach's α = 0.759) is better grouped with strength testing and rankings compared to anatomical grouping (Cronbach's α = 0.721). Under exploratory factor analysis with 2 fixed components, based on the factor loadings (rank and strength) functional stratification (0.978) is better aligned compared to anatomical stratification (0.785) for grouping of surfers. Further, the association and impact of strength with functional spinal cord level stratification were confirmed using regression analysis (chi-square of 74.06 with p-value <.0001).

CONCLUSIONS

Trunk and limb strengths have been shown to influence wave riding performance in surfers with spinal cord injury. Surfers with spinal cord injury can equitably be classified into one of the four para surfing sport classes. The use of functional stratification of spinal cord injury with trunk and limb strengths should be considered as an integral component in para surfing athlete sport classification.

Upper limb electromyographic analysis of manual wheelchair transfer techniques in individuals with spinal cord injury: A systematic review

BACKGROUND AND PURPOSE

The objective of this study is to determine the upper limb muscle electromyographic (EMG) activity required during various manual wheelchair transfers in the population of spinal cord injury (SCI).

METHODS

This review included observational studies reporting the (EMG) activity of upper limb muscles during wheelchair transfers in people with SCI. We searched electronic databases and reference lists of relevant literature between 1995 and March 2022 with English language limits, yielding 3870 total articles. Two independent researchers performed data extraction and conducted quality assessment using two checklists, the Modified Downs and Blacks and National Heart, Lung, and Blood Institute for observational cohort and cross-sectional studies.

RESULTS

After eligibility screening, seven studies were included in this review. The sample size ranged from 10 to 32 participants aged 31-47 years. They assessed four types of transfers and mostly evaluated six upper limb muscles were biceps, triceps, anterior deltoid, pectoralis major, latissimus dorsi and ascending fibres of the trapezius. The peak EMG value indicated that muscle recruitment varied in both upper limbs according to the task demand, and the highest activity was seen during the lift-pivot transfer phase. Because of the data heterogeneity, a meta-analysis of study results was not feasible.

CONCLUSION

There were various ways of reporting the upper limb EMG muscle activity profile across all the included studies with a limited sample size. The crucial role of upper limb muscles during different types of manual wheelchair transfers was interpreted in this review. This is essential for predicting functional independence of individuals with SCI and warranting optimal rehabilitation strategies for wheelchair transfer skills.

The influence of gender on shoulder kinematics and head-hip technique during non-level transfers in full-time wheelchair users

BACKGROUND

Non-level transfers are some of the most demanding tasks for manual wheelchair users. Safely performing these transfer tasks may be needed for maintaining long-term upper limb health. This cross-sectional study aimed to examine the influence of gender on the head-hip technique and lead arm kinematics during multi-height transfers in manual wheelchair users.

METHODS

Motion analysis was used to obtain lead-arm shoulder kinematics (flexion/extension and abduction/adduction) and trunk flexion during level, uphill, and floor-to-table transfers in full-time manual wheelchair users.

FINDINGS

Twelve male (N = 12) and fifteen female (N = 15) manual wheelchair users with a mean age of 23 ± 5 years and no signs of shoulder pain participated in the study. Lead-arm shoulder flexion and abduction increased as vertical displacement requirements increased during the various transfer tasks (p < 0.01). Women displaced greater trunk flexion during level transfers at approaching significant levels (p = 0.07). During uphill transfers, women displayed significantly greater trunk flexion than men (p < 0.05).

INTERPRETATION

Manual wheelchair users use unique kinematic requirements when using the head-hip during level and non-level transfers. Women may be at decreased risk of chronic shoulder pain due to a greater use of the head-hip technique during non-level transfers. Nonetheless, more research that integrates kinetics and strength assessments during non-level transfer biomechanical analyses is needed to better understand technical requirements of non-level transfers in manual wheelchair users.

Impact of spasticity on transfers and activities of daily living in individuals with spinal cord injury

CONTEXT/OBJECTIVE

For persons with spinal cord injury, spasticity commonly interferes with activities of daily living such as transfers. Electromyography can be used to objectively measure muscle spasms during transfers, but how electromyographic measures relate to the impact spasticity has on life, or to clinically-rated spasticity, is unclear. We aimed to characterize relationships among spasm duration and magnitude, impact of spasticity on daily life, and a clinical measure of extensor spasticity, as well as to determine reliability of the electromyographic measures.

DESIGN

Participants (N=19) underwent electromyographic measurements of involuntary muscle activity (spasm duration and magnitude) evoked in quadriceps muscles during transfers on two days. Impact of spasticity on daily life was measured with the Spinal Cord Injury Spasticity Evaluation Tool. Clinically-rated spasticity severity was measured with the Spinal Cord Assessment Tool for Spastic reflexes.

RESULTS

No significant associations were found between impact of spasticity and spasm duration, spasm magnitude, or clinical extensor spasticity score. Absolute and normalized spasm duration were positively associated with clinical extensor spasticity score (rho=0.510-0.667, P < 0.05). Spasm measures during transfers had good to excellent day-to-day reliability (rho=0.656-0.846, P < 0.05).

CONCLUSIONS

Electromyographic and clinical measures of involuntary activity in the lower extremity do not significantly relate to perceived impact of spasticity on daily life. However, quadriceps spasm duration during transfers is related to clinically-rated extensor spasticity. Electromyography is a reliable method of quantifying quadriceps spasms during transfers. Future investigations should identify factors that influence the impact of spasticity on life, which may help direct treatment strategies to reduce problematic impact.

Surface electromyography as a measure of trunk muscle activity in patients with spinal cord injury: a meta-analytic review

CONTEXT

Surface electromyography (SEMG) may be a sensitive marker for distinguishing the activity of trunk muscles, which are critical to functional mobility recovery in patients with spinal cord injury (SCI).

OBJECTIVES

This manuscript presents a systematic review and meta-analysis of the published literature on the effect of SEMG as a measure of trunk muscle activity in patients with SCI.

METHODS

A comprehensive search of the research literature included Pubmed, Medline, CNKI, WANFANG DATA, Web of Science, Elsevier, Wiley-Blackwell, Karger, OVID, and a review of reference lists within found articles. Case-control, cohort, and cross-sectional studies were included in the review.

RESULTS

Eleven studies were included in this meta-analysis. Trunk muscle activities for the sitting condition were greater in patients with SCI than normal subjects. SEMG activity of trunk muscles for the sitting condition and posterior transfer was greater in patients with high level (HL)-SCI compared to those with low level (LL)-SCI. In addition, across studies, the level of trunk muscle activity for various difficulty settings was different for a given SCI group.

CONCLUSION

This systematic review evaluated the value of trunk muscles for patients with SCI. We recommend use of SEMG as an assessment tool for improving the comparability and interpretability of trunk muscle activity of SCI therapeutic strategies.

Upper limb joint kinetics of three sitting pivot wheelchair transfer techniques in individuals with spinal cord injury

STUDY DESIGN

Repeated measures design.

OBJECTIVE

This study compared the upper extremity (UE) joint kinetics between three transfer techniques.

SETTING

Research laboratory.

METHODS

Twenty individuals with spinal cord injury performed three transfer techniques from their wheelchair to a level tub bench. Two of the techniques involved a head-hips method with leading hand position close (HH-I) and far (HH-A) from the body, and the third technique with the trunk upright (TU) and hand far from body. Motion analysis equipment recorded upper body movements and force sensors recorded their hand and feet reaction forces during the transfers.

RESULTS

Several significant differences were found between HH-A and HH-I and TU and HH-I transfers indicating that hand placement was a key factor influencing the UE joint kinetics. Peak resultant hand, elbow, and shoulder joint forces were significantly higher for the HH-A and TU techniques at the trailing arm (P < 0.036) and lower at the leading arm (P < 0.021), compared to the HH-I technique.

CONCLUSION

Always trailing with the same arm if using HH-A or TU could predispose that arm to overuse related pain and injuries. Technique training should focus on initial hand placement close to the body followed by the amount of trunk flexion needed to facilitate movement.

Upper limb kinematics after cervical spinal cord injury: a review

Although a number of upper limb kinematic studies have been conducted, no review actually addresses the key-features of open-chain upper limb movements after cervical spinal cord injury (SCI). The aim of this literature review is to provide a clear understanding of motor control and kinematic changes during open-chain upper limb reaching, reach-to-grasp, overhead movements, and fast elbow flexion movements after tetraplegia. Using data from MEDLINE between 1966 and December 2014, we examined temporal and spatial kinematic measures and when available electromyographic recordings. We included fifteen control case and three series case studies with a total of 164 SCI participants and 131 healthy control participants. SCI participants efficiently performed a broad range of tasks with their upper limb and movements were planned and executed with strong kinematic invariants like movement endpoint accuracy and minimal cost. Our review revealed that elbow extension without triceps brachii relies on increased scapulothoracic and glenohumeral movements providing a dynamic coupling between shoulder and elbow. Furthermore, contrary to normal grasping patterns where grasping is prepared during the transport phase, reaching and grasping are performed successively after SCI. The prolonged transport phase ensures correct hand placement while the grasping relies on wrist extension eliciting either whole hand or lateral grip. One of the main kinematic characteristics observed after tetraplegia is motor slowing attested by increased movement time. This could be caused by (i) decreased strength, (ii) triceps brachii paralysis which disrupts normal agonist-antagonist co-contractions, (iii) accuracy preservation at movement endpoint, and/or (iv) grasping relying on tenodesis. Another feature is a reduction of maximal superior reaching during overhead movements which could be caused by i) strength deficit in agonist muscles like pectoralis major, ii) strength deficit in proximal synergic muscles responsible for scapulothoracic and glenohumeral joint stability, iii) strength deficit in distal synergic muscles preventing the maintenance of elbow extension by shoulder elbow dynamic coupling, iv) shoulder joint ankyloses, and/or v) shoulder pain. Further studies on open chain movements are needed to identify the contribution of each of these factors in order to tailor upper limb rehabilitation programs for SCI individuals.

Evidence-Based Strategies for Preserving Mobility for Elderly and Aging Manual Wheelchair Users

Elderly and aging manual wheelchair (MWC) users have increased risk for accelerated loss of function and mobility that greatly limits independence and affects quality of life. This review paper addresses important issues for preserving function and mobility for elderly and aging individuals who use a MWC by presenting the current available evidence and recommendations. These include recommendations for maximizing function, by decreasing pain, improving the ability to self-propel, and prolonging mobility and endurance through ergonomics, individualized wheelchair selection and configuration, and adaptations for increasing the capacity to handle the daily mobility demands through training, strengthening, and exercise. Each recommendation is supported by current research in each relevant area.

Structural and functional left ventricular impairment in subjects with chronic spinal cord injury and no overt cardiovascular disease

CONTEXT

Cardiovascular disease (CVD) is the leading cause of morbidity and mortality in subjects with long-term spinal cord injury (SCI). More specific recommendations for CVD prevention in this population are needed.

METHODS

One hundred thirty male subjects (47 subjects with SCI and 83 able-bodied persons (ABPs), mean age 43.89 ± 1.9 and 45.44 ± 12.2 years; P = 0.48) underwent transthoracic echocardiography (TTE). The effects of age, weight, mean arterial pressure (MAP) and level of physical training on cardiac adaptations were evaluated through multiple regression analysis.

RESULTS

In subjects with SCI, TTE revealed increased wall thickness (P < 0.05), lower E wave, E/A ratio and early diastolic myocardial relaxation velocity on Tissue Doppler Imaging (TDI) (P < 0.05) and higher systolic myocardial contraction velocity on TDI (0.10 ± 0.02 vs. 0.09 ± 0.02 m/seconds, P = 0.002) and peak systolic pressure to end-systolic volume ratio (3.62 ± 1.39 vs. 2.82 ± 0.90, P < 0.001) compared with ABPs. Aortic diameters were larger in subjects with SCI than ABPs. Differences remained statistically significant even after adjustment for age, weight, MAP, and level of physical training. Weight and age were found to be independent variables that substantially affected left ventricular structure and function in subjects with SCI.

CONCLUSIONS

Subjects with post-traumatic chronic SCI and no overt cardiovascular risk factors, exhibit initial left ventricular remodeling (as assessed by TTE) compared with ABPs. Lifestyle modifications, including regular physical exercise and weight control, should be implemented in all subjects with SCI, even at a very early stage, in order to reduce cardiovascular risk and prevent the development of CVD.

Effects of sensorimotor trunk impairments on trunk and upper limb joint kinematics and kinetics during sitting pivot transfers in individuals with a spinal cord injury

BACKGROUND

Depending on the level and severity of the sensorimotor impairment in individuals with a spinal cord injury, the subsequent reduced seated postural stability and strength generating-capacity at the upper limbs could affect performance during sitting pivot transfer. This study aimed to determine the effects of sensorimotor impairments on head, trunk and upper limb movement and efforts during sitting pivot transfers.

METHODS

Twenty-six individuals with a spinal cord injury participated and were stratified in two subgroups: with (N=15) and without voluntary motor control (N=11) of their lower back and abdominal muscles. Kinematics and kinetics of sitting pivot transfer were collected using a transfer assessment system. Mean joint angles and movement amplitudes and peak and average joint moments were compared between subgroups using independent Student t-tests (P<0.05) for the weight-bearing sitting pivot transfer phases.

FINDINGS

The subgroup without voluntary control of their lower back and abdominal muscles had significantly greater forward trunk flexion compared to the other subgroup resulting in higher wrist extension and elbow flexion at both upper limbs. No significant joint moment difference was found between the subgroups.

INTERPRETATION

Individuals with spinal cord injury who have no voluntary motor control of their abdominal and lower back muscles increase forward trunk flexion during sitting pivot transfers 1) to increase stiffness of their spine that may optimize the strength-generating ability of their thoracohumeral muscles and 2) to lower their center of mass that may facilitate lift-off and enhance the overall stability during sitting pivot transfers.

Movement strategies during car transfers in individuals with tetraplegia: a preliminary study

STUDY DESIGN

Three-dimensional kinematic analysis of car transfer (CT) movement in four adult males with C6 tetraplegia.

OBJECTIVES

The aim of the present study was to assess the normal transfer technique movement from a wheelchair to a car (that is, CT) in subjects with tetraplegia. A better understanding of CT movement is invaluable knowledge for spinal cord injury rehabilitation. This type of knowledge will improve rehabilitation programs so that patients with tetraplegia will have greater societal participation.

SETTING

School of Comprehensive Rehabilitation, Osaka Prefecture University, Osaka, Japan.

METHODS

Four adult males with C6 tetraplegia, an impairment grade of A according to the American Spinal Injury Association guidelines, took part in the study. The subjects used their own wheelchair and car in our assessments of their CT movement technique. Movements were assessed using a three-dimensional video analysis system with six digital video cameras. CT data, which included lateral displacement of the head and buttocks, and angular displacement of neck flexion and trunk forward inclination, were collected and correlation coefficients were calculated.

RESULTS

All four subjects demonstrated negative correlations in lateral displacements greater than 0.70. As for correlation coefficients of angular displacement, two subjects demonstrated negative correlations (r = -0.98 and r = -0.77) and one subject demonstrated a positive correlation (r = 0.75). The neck flexion and trunk forward inclination strategy was different among the four subjects.

CONCLUSIONS

Each subject with C6 tetraplegia demonstrated different strategies during CT movement.

Upper limb kinetic analysis of three sitting pivot wheelchair transfer techniques

BACKGROUND

The objective of this study was to investigate differences in shoulder, elbow and hand kinetics while performing three different SPTs that varied in terms of hand and trunk positioning.

METHODS

Fourteen unimpaired individuals (8 male and 6 female) performed three variations of sitting pivot transfers in a random order from a wheelchair to a level tub bench. Two transfers involved a forward flexed trunk (head-hips technique) and the third with the trunk remaining upright. The two transfers involving a head hips technique were performed with two different leading hand initial positions. Motion analysis equipment recorded upper body movements and force sensors recorded hand reaction forces. Shoulder and elbow joint and hand kinetics were computed for the lift phase of the transfer.

FINDINGS

Transferring using either of the head hips techniques compared to the trunk upright style of transferring resulted in reduced superior forces at the shoulder (P<0.002), elbow (P<0.004) and hand (P<0.013). There was a significant increase in the medial forces in the leading elbow (P=0.049) for both head hip transfers and the trailing hand for the head hip technique with the arm further away from the body (P<0.028). The head hip techniques resulted in higher shoulder external rotation, flexion and extension moments compared to the trunk upright technique (P<0.021).

INTERPRETATION

Varying the hand placement and trunk positioning during transfers changes the load distribution across all upper limb joints. The results of this study may be useful for determining a technique that helps preserve upper limb function overtime.

An expert review of the scientific literature on independent wheelchair transfers

PURPOSE

The purpose of this study was to perform a literature review and seek expert opinion on the relevance and strength of the evidence concerning setup and transfer performance.

METHODS

Scientific literature databases were searched until June 2009 using 43 keywords resulting in 339 articles. These were internally reviewed and narrowed to 41 articles which were formally assessed by 13 external experts. Articles that 80% or more of the reviewers scored as moderately or highly relevant were included in the final results.

RESULTS

Nineteen articles met the relevancy criteria. The aspects of setup that experts felt were addressed to some degree included vertical transfer distance, transferring across a gap and position of the mobility device relative to target destination. None of the 19 articles were scored as having strong to very strong resulting evidence.

CONCLUSIONS

There is a consensus among studies that transferring to a higher surface implies greater exertion of the upper limb. However, there is no evidence concerning how high or low, how close, and how much space is needed next to the target surface so it can be accessible by a majority of wheelchair users.

Trunk and upper extremity kinematics during sitting pivot transfers performed by individuals with spinal cord injury

BACKGROUND

Although reaching an optimal level of independence during sitting pivot transfer is crucial for individuals with spinal cord injury, little is known regarding the kinematic requirements of this functional task.

METHODS

Ten males with spinal cord injury performed independent sitting pivot transfers between an initial seat and a target one placed at same (50 cm), lower (40 cm), and higher heights (60 cm) than the initial one, using their usual movement strategies. Three-dimensional trunk, shoulder, elbow and wrist kinematics were collected bilaterally during sitting pivot transfers. Each sitting pivot transfer was divided into three phases for analysis: pre-lift, lift-pivot and post-lift. Temporal parameters were also documented.

FINDINGS

Peak shoulder extension displacement and velocities were always higher at the leading shoulder compared to the trailing one (P<0.004), and almost coincided with peak trunk velocities early during the lift phase. With increasing target seat height, shoulder flexion (P<0.011) and elbow extension (P<0.013) displacements and velocities of the trailing upper extremity augmented and reached higher values at this upper extremity compared to the leading upper extremity, with one exception at the shoulder. Elbows generally remained flexed (min=28-56 degrees ) during the lift phase of all transfers whereas extreme wrist extension positions (max=84-88 degrees ) were documented across all transfers. Total durations of transfers (2.6-2.8s) and lift-pivot phases (1.0-1.3s) were not affected by target seat heights.

INTERPRETATION

Sitting pivot transfers are characterized by substantial angular displacements and velocities at the trunk and upper extremities. Some kinematic parameters documented during sitting pivot transfers may increase the risk of developing secondary musculoskeletal impairments in this population.

Transfer from table to wheelchair in men and women with spinal cord injury: coordination of body movement and arm forces

STUDY DESIGN

A complex set-up was used to investigate kinematics and ground reaction forces.

SETTING

Motor Control and Physical Therapy Research Laboratory, Neurotec Department, Karolinska Institutet, Huddinge, Sweden.

OBJECTIVE

To investigate how men and women with spinal cord injury (SCI) perform transfers from table to wheelchair with regard to timing and magnitude of force generation beneath the hands and associated body movements.

METHODS

A total of 13 subjects (seven men, six women) with thoracic SCI. Kinematics of body movement were recorded (Elite 2000 system) simultaneously with the signals from three force plates (AMTI) placed beneath the buttocks and hands. Temporal and spatial parameters regarding head, trunk and trailing arm displacement, loading amplitudes and loading torque directions of both hands were analyzed for each trial and subject and compared between genders.

RESULTS

Men and women used similar amplitudes of head bending and forward displacement of the trailing shoulder, while female subjects had significantly larger trunk rotation. Both genders applied significantly more weight on the trailing hand. Differences between genders were seen in direction and timing of peak torque beneath the hands.

CONCLUSIONS

The forces beneath the trailing hand were larger than those in the leading, if there is weakness or pain in one arm, this arm should be selected as the leading. To avoid excessive load on the arms, technical aids and environmental factors should be very well adapted.

SPONSORSHIP

This project was funded by the Swedish Research Council and the Health Care Science Committee of Karolinska Institutet.

Movement patterns and muscular demands during posterior transfers toward an elevated surface in individuals with spinal cord injury

STUDY DESIGN

Three-dimensional kinematic analysis and surface electromyography (EMG) of 10 male adults with complete spinal cord injury (C7 to L2).

OBJECTIVE

To examine movement patterns and muscular demands in individuals with spinal cord injury (SCI) during posterior transfers.

SETTING

Pathokinesiology Laboratory at a Rehabilitation Centre, Montreal, Canada.

METHODS

Kinematic variables that described the positions and angular displacements of the head, trunk, shoulder and elbow were obtained by videotaping markers placed on the subject segments. EMG data were recorded for the biceps, triceps, anterior deltoid, pectoralis major, latissimus dorsi and trapezius muscles of the dominant upper extremity during posterior transfers using surface electrodes. To quantify the muscular demand, the EMG data recorded during the transfers were normalized to values obtained during maximal static contractions (EMGmax). The mean muscular demand was calculated for every muscle during the lift phase of the transfers. The lift phase was determined by pressure-sensitive contacts.

RESULTS

All subjects were able to execute the posterior transfers on an even surface, whereas nine subjects completed at least one of the transfers to the elevated surface. A forward-flexion pattern at the head and trunk was observed when either one or two hands remained on the lower surface, whereas a lift strategy was seen when both hands were placed on the elevated surface. Transferring to the elevated surface with hands on the lower surface required inferior electromyographic muscular utilization ratio (EMUR) than the transfer on the even surface for all muscles. The lowest EMUR were calculated for the transfer to the elevated surface with hands on the lower surface (triceps (18%), pectoralis major (53.8%), trapezius (66%) and latissimus dorsi (24.5%)) while performing the same transfer with hands on the elevated surface generated the highest EMUR (triceps (40.2%), anterior deltoid (73.2%), trapezius (83.6%) and latissimus dorsi (55.3%)).

CONCLUSIONS

Subjects presented different movement characteristics and muscular demands during the posterior transfers. It is suggested that the forward-flexion pattern improves the dynamic trunk stability and reduces the muscular demand required to transfer. High muscular demand developed when hands were positioned on the elevated surface might be due to increased postural control demands on the upper limb and reduced angular momentum.