Age-Related Changes in Inter-Joint Interactions for Global and Local Kinematics While Standing

Inter-joint interactions are involved in human standing. These interactions work not only for global kinematics that control the center of mass (COM) of the entire body, but also for local kinematics that control joint angular movements. Age-related changes in these interactions are thought to cause unstable standing postures in older people. Interactions of global kinematics are known to be deficient owing to aging. However, it is unclear whether the interaction of local kinematics is affected by aging. We investigated the age-related changes in inter-joint interactions, especially local kinematics, during standing. Differences were investigated in these two inter-joint interactions between older and younger adults in three different postures: normal, eyes-closed, and foam-surface standings. The inter-joint interaction for local kinematics was computed using the induced-acceleration analysis with a double-inverted pendulum model and quantified using an uncontrolled manifold approach. Consistent with previous studies, the inter-joint interaction for COM acceleration (global kinematics) deteriorated in older adults. In contrast, the interactions for angular accelerations in the ankle and hip joints (local kinematics) were slightly better in the older adults. Moreover, the individual components of angular acceleration which were induced by net torques from homonymous and remote joints were significantly increased in older adults. Thus, global and local inter-joint interactions are driven by distinct neural mechanisms and the interaction of local kinematics can compensate for the increment of each component of joint angular acceleration in older adults.

T HE human standing posture is considered inherently unstable owing to physical restrictions, such as a narrow base of support, a multi-segmental structure linked by wellslipped joints, and insufficient passive torque against body weight.Feedback control of the central nervous system is required to compensate for these restrictions when maintaining an upright stance [1], [2].Since aging alters the structure and function of the neural system, physiological and biomechanical changes in the features of the standing posture appear in older people: increased co-contraction [3], higher joint stiffness [4], pronounced physiological tremor [5], and decline of sensorimotor function [6].Such changes can cause a rigid stance and increased susceptibility to falls in older adults.
Inter-joint interactions contribute to posture control.Previous studies have examined how joint angular displacements are coupled with one another during standing [7], [8].The variances in angular displacements are coordinated to suppress the center of mass (COM) displacement in the sagittal plane.Investigation using a simpler double-inverted pendulum model with ankle and hip joints [9], [10], [11] exhibited anti-phasing coupling between the upper and lower segments.When the upper segment moves anteriorly, the lower segment moves posteriorly, and vice versa.This coupling becomes more rigorous in the angular acceleration plane [12], [13], which implies that the control of standing posture prioritizes to minimizing the variance in COM acceleration rather than COM displacement.Reciprocal movements between adjacent segments enable the COM to stabilize with smaller fluctuations.Loss of inter-joint interaction is thought to be a cause of unstable posture and for higher prevalence of falls in older adults with balance deficits [14], [15], [16].
In addition to the inter-joint interaction of COM movements, individual joint movement is determined by the coupling of torque-induced actions induced by multiple joints.Torque at one joint is known to induce angular acceleration in both homonymous and remote joints [17], [18].For stance control, Sasagawa et al. [19] used the double-inverted pendulum model to explore whether each component of the joint angular accelerations induced by net torques in the ankle and hip joints couples with one another.These components counteracted to decrease the resultant angular accelerations.Hence, in addition to the COM acceleration (global kinematics), the joint angular acceleration (local kinematics) is adjusted by the inter-joint interaction while standing.Regarding the influence of aging, the inter-joint interaction for global kinematics is known to be deficient [14], [16], whereas the changes in local kinematics are unclear.If common neural mechanisms underlie both interactions, similar changes may occur.Exploration of the influence of aging could contribute to understanding the mechanisms of human standing or differences of postural strategies taken in younger and older adults.
The purpose of this study was to clarify whether the inter-joint interaction for local kinematics deteriorates with aging.The coupling between the ankle and hip joints was investigated using a double-inverted pendulum model in older and younger adults, with the goal of identifying novel differences between ankle and hip joints for postural control.Coupling was quantified using the uncontrolled manifold (UCM) approach [20], and its effect was verified as a reduction rate based on compensation by a remote joint.In previous studies, challenging postures have highlighted the influence of aging, and the predictability of future falls as age-related changes are more apparent when postural demand increases [21], [22].Thus, we expected that the influence of aging on inter-joint interactions would be observed more clearly in a posture with higher demand.

A. Participants
A dataset used in our previous study [21], which included 49 adults (younger: 18 individuals, 13 females, older: 31 individuals, 15 females), was utilized for the current study.None of the participants had any orthopedic and/or neuromuscular diseases or physical disabilities.We calculated the appropriate sample size using G power software [23] (version 3.1.9.6, Germany) with a desired power of 0.85, medium effect size of 0.25 (patrial η 2 = 0.06) and alpha of 0.05.Hence, the minimum number of participants was 32.Finally, 16 younger and 16 older participants were allocated by random sampling from all participants (younger: 12 females, ages 20.3 ± 0.6 years; older: 8 females, ages 76.1 ± 2.0 years).Participants provided written informed consent in accordance with the Declaration of Helsinki, and the experimental procedure was approved by the ethics committee of Chiba Prefectural University of Health and Sciences.

B. Equipment and Procedures
The standing posture was recorded using a motion capture system that included eight infrared cameras (Mac3D system, Motion Analysis, Corp) and two force-plates (BR400600, AMTI, Inc.).Twenty-nine reflective markers were attached to body landmarks for Helen Hayes-marker set.The time series of their position data were filtered using a fourth-order, zerophase-lag Butterworth low-pass filter with a cut-off frequency of 10 Hz.Every trial was recorded for 60 s, and the first 10 s were excluded from subsequent analysis.The sampling frequency was set at 100 Hz for both the motion capture and force-plate data.
To reveal the effects of postural demands on inter-joint interactions, three different postures were analyzed: bipedal θ ank, is the tilt angle which is formed by the vertical line and lower link, and θ hip is the difference between the tilt angle in the lower link and that in the upper link.θ ank, and θ hip were offset on average.stance with eyes opened (QS), bipedal stance with eyes closed (EC), and standing on foam rubber with eyes opened (Foam).Participants stood with their right and left heels separated by 15.0 cm on each force-plate and aligned parallelly in the anteroposterior (AP) direction.In the Foam condition, participants stood on foam rubber containing natural rubber with a tensile strength of 2.1 kgf/ cm 2 , a density of 0.06 g/ cm 3 , an elongation stretch percentage of 110%, and a thickness of 3.5 cm.The order of the trials for the experimental conditions was randomized for each participant.Details are described in our previous study [21].

C. Data Analyses
To analyze the inter-joint interactions between body segments, the standing posture was modeled using a double-inverted pendulum model based on marker positions (leg and head-and-trunk segments, Fig. 1).We analyzed this model in the sagittal plane, and the leg movement was averaged between the right and left sides based on the assumption that both legs moved almost equally.Computing length and weight of both links, and hip and ankle joint angles (θ hip and θ ank ) were calculated in each sample, and angular velocities ( θhip , θank ) and accelerations ( θhip , θank ) were obtained by differentiation of the time series of angular displacement.θ ank was defined as the tilt angle of the lower link from the vertical line and θ hip was the difference between the tilt angle of the upper link and that of the lower link (appendix).Positive values represent dorsiflexion and flexion of the ankle and hip joints, respectively.The time series of the COM acceleration was calculated in the AP direction as follows: Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
where m and l denote the mass and length of each segment, respectively; h is the distance from the COM to the distal end of the segments.The above formula can be converted as follows: Thus, the COM acceleration was expressed by a two-variable function ( θhip and θank ).When the COM acceleration is zero, the joint angular acceleration in the hip joint is represented by the product of the constant and ankle-joint angular acceleration ( θhip = k * θank ).
The equation of motion for the double-inverted pendulum model was described as: Transforming this equation, the joint torque can be obtained: where T denotes the vector of joint torque; M (θ ) is the inertial matrix; θ , θ , and θ are the vector of joint angular acceleration, velocity, and displacement, respectively; G (θ ) is the gravitational torque and V θ, θ is the velocity-dependent torque.
The calculation procedures are presented in Supplementary Materials.To separate each contribution of these torques on the angular accelerations, the above equation was transformed by multiplying the inverse of the inertial matrix [24]: M −1 is the inverse of the inertial matrix.This equation can be expanded as follow: where j and i represent the ankle and hip joint, and C ji is the matrix component of M −1 , where the product of C ji and each torque (T i , G i , and V i ) indicates an individual component of the angular acceleration generated from either its own joint ( j) or in the other joint.The sum of the individual components produces the net angular acceleration.As an example of an ankle joint: θ T i ank , θ Gi ank and θ V i ank represent the components of ankle joint angular acceleration induced by T , G, and V in the ankle (homonymous) and hip (remote) joints, respectively.θank is the sum of the net angular acceleration in the ankle and hip joints.).The velocity-dependent torques V were negligible compared to T or G, as was the case in a previous study [19].Thus, we did not present these in the results.
To quantify the inter-joint interaction, we applied the UCM approach, which is defined as a null space of the Jacobian for controlled (task) and control (elemental) variables.We postulated that the central nervous system attempts to control the joint angular accelerations for zero COM acceleration during standing.Thus, the variance structure of the ankle and hip joint angular acceleration was focused on global kinematics.For local kinematics, the joint angular acceleration was regarded as a task variable, and the variance structure of the components of angular acceleration induced by net torques θ N E T ank/ hi p j was focused.The UCM was defined as a null space of the Jacobian matrix for COM acceleration (UCM global ) and joint angular accelerations (UCM local ): where, task is a task variable that is the COM acceleration for UCM global and the ankle and hip joint angular acceleration for UCM local .element ank/ hi p indicates the elemental variables in the ankle and hip joints, respectively, which are joint angular accelerations for UCM global and net angular accelerations induced by components from the ankle and hip torques for UCM local .The number of basis vectors for this null space was one, based on two elemental and single task variables.
The deviation into the null and orthogonal space was as follows: N where ε is the null space of the Jacobian matrix, i indicates ankle and hip joints, and t is a time index of total N .GEV is the goal equivalent variance that represents good coordination along the UCM subspace for a task variable and NGEV is a non-goal equivalent variance.Finally, each variable is normalized by the degrees of freedom: one for GEV and two for NGEV.The inter-joint interaction was compared using the ratio [25].
Since the torque from the remote joint was counteracted in a quiet stance, we calculated the reduction rate of the residual angular acceleration suppressed by the acceleration from the remote joint.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
where θ N E T j j represents the component of the joint angular acceleration in j joint, and thus this rate indicates how θ j was changed relative to θ N E T j j , which is not decreased by the interaction from the remote joint.
We further evaluated the group differences in task and elemental variables using root-mean square (RMS) of COM acceleration, joint angular acceleration, and net-torque-induced acceleration in the ankle and hip joints.In addition, principal component analysis was applied to the time series of the angular accelerations in the ankle and hip joints.The eigenvector of the first principal component was calculated to compare the slope of the long axis on the angular acceleration plane, which represents the ratio of hip kinematics relative to ankle one.

D. Statistical Analyses
We performed two-way ANOVA with a mixed design (AGE × POSTURE).For the sphericity test, Mendoza's multisample sphericity test was applied.When sphericity could not be assumed, the variables were adjusted using the Greenhouse-Geisser correction.When an interaction was significant, simple main effects were tested at each level.In post-hoc comparisons, the Bonferroni correction was applied for all pairwise comparisons, and significant differences are depicted in the figures.The significance level was set at α = 0.05, and the results are presented as the means ± standard errors.Generalized eta (η 2 G ) represents an effect-size measure.III.RESULTS A. Age-and Posture-Related Changes in Inter-Joint Interaction for COM Acceleration (Global Kinematics) Figure 2A shows representative planar plots of ankle and hip joint movements with respect to angular displacement, velocity, and acceleration.Compared to the angular displacement trajectories, the trajectories of the angular velocities and accelerations were closer along a negative slope on which the task variables were zero, as calculated by the double-inverted pendulum model.This supports the previous results that joint angular movements were counteracted and more strictly constrained for COM acceleration than for COM displacement and velocity [12], [13].
To quantify these inter-joint interactions, UCM global was calculated using angular accelerations in the ankle and hip joints.There were main effects of AGE and POSTURE (Fig. 2B, AGE: F 1,30 = 19.68,p=0.001, η 2 G = 0.28; POSTURE: F 1.9,56.91= 12.62, p<0.001, η 2 G = 0.14).Hence, the segmental movements between the upper and lower segments were more significantly coupled in younger adults than in older adults.Post-hoc analysis for POSTURE further indicated a significantly larger UCM ratio in the Foam condition than in the other conditions (p=0.001 for QS vs. Foam, p<0.001 for EC vs. Foam).A significant main effect on AGE further appeared in the slope of the longitudinal axis on the angular acceleration plane (F  for the hip joint.Hence, the angular acceleration from the remote joint contributes to the deceleration in a homonymous joint.The distribution of these variables on the planar plane was depicted close to the negative slope, indicating zero angular acceleration (UCM local ).The group average of UCM local in both joints tended to be larger than that of UCM global , suggesting a higher inter-joint interaction for local kinematics.Two-way ANOVA demonstrated the main effects of UCM local on AGE and POSTURE in the hip joint (Fig. 3D, AGE: F 1,30 = 15.10,p<0.001, η 2 G = 0.22; POSTURE: F 1.71,51.32= 7.49, p=0.002, η 2 G = 0.09), whereas there was no significant difference in the ankle joint (Fig. 3B).
To determine the factors that accelerate ankle joint angular acceleration in older adults, we further focused on the amount of each acceleration component induced by the net torque in homonymous and remote joints.Figure 4A shows the time courses of the torque components (a) and their net torques in the ankle and hip joints (b), and the relation of net torques between those joints on the planar plane (c) in a representative participant.Consistent with a previous study [19], a positive correlation was observed between the ankle-and hip net torques which produced angular acceleration in each joint.In the comparison of the individual acceleration components induced by these torques, there were main effects of AGE and POSTURE in both  Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.angular acceleration was larger in older than younger participants (Fig. 4B

IV. DISCUSSION
This study explored the influence of aging on inter-joint interactions during standing.The results showed that the anti-phase coupling of the interaction for local kinematics (angular acceleration by net torque in the ankle and hip joints) was not affected even in older adults whereas that for global kinematics (COM acceleration) was significantly decreased.This implies that the two inter-joint interactions at different levels are regulated by distinct mechanisms, and the neural base that contributes to the interaction for local kinematics is not highly susceptible to aging.

A. Age-Related Changes in Body Kinematics and Inter-Joint Interaction
While standing, the time series of the ankle and hip joint angular accelerations counteract each other in the sagittal plane, resulting in a smaller body COM acceleration.The UCM showed that aging affects the inter-joint interaction and results in an increase in COM acceleration, supporting previous results [14], [16].Such deterioration has also been observed in multi-finger interactions during force production [26], finger-pointing [27], and stepping during a cognitive task [28].Taken together, when inter-joint interaction relates to task performance definitively, aging can influence its function.
Regarding the negative slope on the angular acceleration plane, the absolute values were significantly smaller in older adults.Since the values of slope represent the ratio of angular acceleration in the hip joint relative to that in the ankle joint, aging diminishes the counteraction effect of the hip joint on the decrease in ankle angular acceleration.In the double-inverted pendulum model, this negative slope was around -3 in the healthy young adults [12] and, when this is consistent with 1/k calculated in equation ( 2), COM acceleration becomes zero.The change in the negative slope is consistent with a decrease in the UCM ratio, which indicates the degree of joint coordination.Focusing on the elemental variables, we found a significant increase in angular acceleration in the ankle joint but not in the hip joint.Older adults rely more on the hip joint even when standing still [29], [30], and co-contraction of the ankle muscles is increased, which causes stiffer joint movements [31], [32], [33].Thus, the increased COM acceleration is due to decreased inter-joint interaction and increased angular acceleration in the ankle joint.
Contrary to the influence on global kinematics, the inter-joint interaction of local kinematics was not statistically different between older and younger adults.In the hip joint, the UCM local was significantly higher in older adults, although the difference in absolute value was small.Hence, the suppression mechanisms for joint angular acceleration function regardless of age.However, despite the same level of interaction, ankle joint angular acceleration is significantly increased in older adults.This could be due to the larger angular acceleration in the individual components induced by the net torques in the ankle and hip joints.These increments in the angular acceleration of each component may be attributed to a spontaneous physical distortion in the musculoskeletal system, which requires larger joint torques to maintain an upright stance.The prevalence of subtle bone and soft tissue deformities has increased in older populations [34], [35].In addition to the reorganization of the central nervous system, postural alignment can cause larger torque exertion that results in increased angular acceleration of the ankle joint during standing in older adults.
The increased angular acceleration in the ankle joint but not in the hip joints may reflect the different postural strategies between younger and older people.The change in the relation between ankle and hip kinematics was reflected in the decrease of the slope on the angular acceleration plane in older people.Older people tend to take a hip strategy in which the COM acceleration is controlled by moving the upper segment relative to the lower limb, which suggests the compensation mechanisms for the decline of the ankle strategy [29], [36].If increased angular acceleration in the ankle joint depends on less suppression from the hip joint, functional changes might be also observed in the hip joint.In this case, the inter-joint interaction from the hip joint would be insufficient to counteract the acceleration in the ankle joint.Due to inadequate compensation by the hip joint, changes in the COM kinematics could emerge finally.

B. Posture-Related Changes in Body Kinematics and Inter-Joint Interaction
Increased postural demand contributes to identification of age-related changes, particularly in the center of pressure (COP) measures [21], [29].The present results consistently showed a significant interaction and simple main effect of postural conditions in COM acceleration.In older people, COM velocity and acceleration were significantly increased in the EC compared to in the QS condition, while there was no significant difference in younger adults in COM displacement.This supports our previous study in which we reported that visual information becomes predominant in older people [21] and suggests that the distortion of visual input cannot be compensated by another sensory modality.This deficit of sensory reweighting is known to be one of the characteristics of older posture [38], [39].Similar to the COP analysis [21], it appears in more task-related parameters but not in COM displacement.
Regarding the inter-joint interaction for global kinematics, the results showed that it was larger in the Foam condition without statistical interaction by age, indicating that older adults have the potential to strengthen inter-joint interactions depending on postural demands.Moreover, the results of the slope of the angular acceleration on the plane were the same.This implies that the inter-joint interaction for global kinematics is modulated by postural demands, and such flexibility is not affected by age, although its own effect is decreased in older adults.
The inter-joint interaction for hip joint kinematics was slightly decreased when the postural demand increased.This can provoke a higher angular acceleration as indicated by the RMS of the angular accelerations in both ankle and hip joints.This result is inconsistent with that of global kinematics, implying distinct mechanisms between these two interactions.Since UCM local was reduced in the Foam condition, sufficient inter-joint interaction for angular acceleration might require mechanical stability on the surface.Similar to the inter-joint interaction for global kinematics, no statistical interaction by AGE was observed, suggesting that such posture-related modulation was preserved regardless of aging.

C. Potential Mechanisms for the Age-and Posture-Related Changes in Inter-Joint Interactions
As a cause of the different influences of aging between the two inter-joint interactions, we postulate that the neural bases for these mechanisms are distinct.A possible candidate for global kinematics is the sensorimotor cortex.This area involves a rapid feedback response that contributes to error correction if it is related to a behavioral goal [40].In this area, both anatomical and physiological changes are apparent due to aging, such as significant thinning of the gray matter [41], slowing of cortical oscillation [42], [43], [44], and greater activation in motor tasks [45].These changes could be linked to declines in sensory integration, which cause difficulty in correcting errors in the feedback process.In addition to these cortical changes, deterioration can occur in the spinal and peripheral systems, including structural and physiological changes accompanied by muscle atrophy [46], denervation of muscle spindles [47], loss of neurons in the spinal cord [48], and lack of spinal reflex modulation [49].Owing to these alterations in the central nervous system, sensory integration and motor execution for postural control are more challenging, affecting inter-joint interactions.
Since there was no clear temporal delay between the elemental variables (Fig. 3A, C), predictive control might be required for local kinematics.We presume that the cerebellum is partly responsible for this interaction.In fact, it has been reported that the relation between muscle and interaction torques for angular acceleration is disrupted during reaching in a patient with cerebellar ataxia [50].Furthermore, we postulated that the spinal circuit, where the interaction torque could be generated is another candidate.It is proposed that intersegmental dynamics can be maintained without cortical contribution [51].If aging does not affect this function, the inter-joint interaction for local kinematics can be maintained in older adults.These neural mechanisms need to be further elucidated in an extended study of patients with neurological diseases, such as cerebellar ataxia or spinal cord injury.

D. Study Limitations
This study had some limitations.First, we did not investigate the contribution of mechanical factors.Passive elements, such Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
as ligaments and connective tissues can generate portion of joint torques because of their viscoelastic properties.Since the passive torque alone is not enough to maintain a standing posture [52], which additionally depends on muscle contraction level, we consider that a non-neural factor would not be separate from neural control.However, it might be possible that passive elements contribute to counteracting the interacted angular acceleration.
Second, the interpretation of the UCM ratio might be controversial.We evaluated the inter-joint interactions using the UCM ratio which was defined as a ratio of GEV and NGEV along the UCM subspaces.Since it may be affected by the relation between the ankle and hip joint kinematics (the slope of the long axis on data dispersion), we need to consider its validity when comparing the different postural strategies in which the relation varies markedly.If the task variable is changed depending on the postural strategy [37], it would be essential to capture the individual predominance in future studies.We expect that our findings have an impact on the evaluation of different strategies and can aid in the clinical assessment of postural disorders.

V. CONCLUSION
In the inter-joint interaction for global kinematics, the COM acceleration decreased with age, whereas for local kinematics, joint angular acceleration was not impaired.The components of the angular acceleration induced by the respective net torques in the ankle and hip joints were significantly increased in older adults, suggesting that increments in angular acceleration in the individual components rather than inter-joint interaction are the main cause of larger angular acceleration in older adults.

A. Definition of Upper and Lower Segments in the Double-Inverted Pendulum Model
The hip joint position in the double-inverted pendulum model was estimated with the length of the lower segment (l L ) and tilt angle (∅ L ) between the vertical line and line connecting the ankle position and COM of the lower segment.where period is the reciprocal of the sampling frequency.The angular acceleration is the second-order derivative of the joint angle.The same procedure was applied to the hip joint and the COM kinematics.

Fig. 1 .
Fig.1.Parameters for the double-inverted pendulum model.m U /m L , mass of each segment; l U /l L , length of each segment; h U /h L , distance from the COM of each segment to the distal end of each segment.θ ank, is the tilt angle which is formed by the vertical line and lower link, and θ hip is the difference between the tilt angle in the lower link and that in the upper link.θ ank, and θ hip were offset on average.
Thus, θ N E T ank ank and θ N E T hi p ank are elements of the inter-joint interaction for local kinematics.When the θank is zero, θ N E T ank ank is equal to the magnitude of θ N E T hi p ank and opposite in the sign ( θ N E T hi p ank = −1 * θ N E T ank ank

C
. Age-and Posture-Related Changes in Inter-Joint Interactions for Angular Acceleration in Ankle and Hip Joints (Local Kinematics) Figure 3A and 3C show a representative time series of angular acceleration induced by the net torque from the ankle and hip joints.It illustrates an antiphase relation entrained both on time and on magnitude between θ N E T ank ank

Fig. 2 .
Fig. 2. Inter-joint interaction between angular movement in ankle and hip joints and group comparison of COM movements.A. The relation between ankle and hip joint movements is depicted on the planar plane (a: displacement, b: velocity, c: acceleration in the QS condition).The black line represents the UCM for each parameter for which COM acceleration was zero.The grey lines indicate the longitudinal axes of the trajectories derived from the eigenvectors of the 1 st principal components.B. Group average UCM ratio for COM acceleration under the QS, EC, and Foam conditions.A UCM ratio of 1 indicates complete compensation (COM acceleration = 0) between the angular accelerations of the two joints.The thick and thin lines indicate the group averages and individual data for the three conditions, respectively.C. Time series of COM displacement (a), velocity (b) and acceleration (c) in the QS condition for a representative participant (upper panel).In the lower panels, the group averages of three parameters (d, e, and f) are depicted.* p<0.05, main effect of 2-way ANOVA, − p<0.05, post-hoc test.
θ N E T ank ank and θ N E T hi p ank for the ankle joint and θ N E T ank hi p and θ N E T hi p hi p for the hip joint.It indicates that every components of joint

Fig. 3 .
Fig. 3. Inter-joint interaction between components of angular acceleration induced by net torques, the reduction rate of angular acceleration, and angular acceleration in ankle and hip joints.A. A representative time course of ankle angular acceleration and its components from remote (hip) and homonymous (ankle) joints.The tight column shows the relation of their components on the planar plane (upper: older person, lower: younger person, QS condition).The black line indicates the zero angular acceleration as the net of both components ( θNETank ank

Fig. 4 .
Fig. 4. Torques in ankle and hip joints and the components of angular acceleration induced by net torques. A. a: time course of joint and gravitational torques for 20 seconds in a representative older participant in the Foam condition.T ank , ankle joint torque, G ank , ankle gravitational torque, T hip , hip joint torque, G hip , hip gravitational torque.b. time course of the net torque in ankle and hip joints.It is the same duration as a. c.Negative correlation between net torques in the ankle (NET ank ) and hip (NET hip ) joints for 50 seconds in the same trials as a. and b.B. Group average of components of angular acceleration induced in the ankle (a.ankle-to-ankle, b. hip-to-ankle) and hip joints (c.ankle-to-hip, b. hip-to-hip).Large and small dots indicate group average and individual data, respectively.* p < 0.05, main effect of 2-way ANOVA, − p < 0.05, post-hoc comparison.
, for θ N E T ank