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Standing Up From a Chair as a Dynamic Equilibrium Task

A Comparison Between Young and Elderly Subjects

^a Groupe d'Etude et de Recherche sur le Handicap (GERSH), Faculté de Médecine, Dijon, France
^b Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow
^c Service de Biostatistique et Informatique Médicale, CHRU, Dijon, France
^d Groupe d'Analyse du Mouvement (GAM), Université de Bourgogne, Dijon, France

France Mourey, Service de M\|[eacute]\|decine G\|[eacute]\|riatrique, Centre Hospitalier R\|[eacute]\|gional, Universit\|[eacute]\| de Dijon, 2, rue Jules Violle, 21034 Dijon C\|[eacute]\|dex, France E-mail: france.mourey{at}planetb.fr.

Decision Editor: Jay Roberts, PhD

	Abstract

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The purpose of this study was to analyze and compare the features of center of mass (CoM) control along anterior/posterior axis in young and elderly subjects during sit-to-stand (STS). From a sitting position, seven healthy young subjects and seven healthy elderly subjects were asked to stand up from a chair under different experimental conditions (visual conditions: normal and blindfolded; speed: normal and as fast as possible). Analysis of results was based upon the concept of a "dynamic equilibrium area" (DEA), which in turn identified the dynamic limits of balance. The results showed that both the maximal CoM velocity in the horizontal axis and the CoM velocity at the instant of seat-off were found to be lower in elderly compared with young subjects. Concerning the maximal CoM velocity, the difference was increased under blindfolded condition. The position of CoM in the phase plane (i.e., velocity according to displacement) at the instant of seat-off was found to be shifted backward in elderly subjects. From these results we can deduce that age-related modifications can be observed in the control of the horizontal CoM motion during STS in healthy elderly subjects.

THE transition of posture associated with sit-to-stand (STS) movements requires a large displacement of the body center of mass (CoM) toward a base of support (BoS) becoming smaller in size. To achieve this, it has been shown that both CoM displacement and velocity are controlled along anterior/posterior and vertical axes ⁽¹⁾. Following seat-off, such control must be achieved within limits of the BoS provided by the feet, in order to maintain a final static upright posture.

Using pattern analyses of CoM velocity along both anterior/posterior and vertical axes, several authors ⁽²⁾⁽³⁾ have described three phases during STS: (i) the acceleration phase, which is defined from the beginning of the movement until maximal CoM horizontal velocity; (ii) the transition phase, beginning at maximal CoM horizontal velocity and terminating at maximal vertical CoM velocity; and (iii) the deceleration phase, which is defined from peak vertical CoM velocity until the end of movement. In terms of equilibrium, the transition phase corresponds to reduction in BoS from three-point support to two-point support. Moreover, during this phase a coordinated control of CoM position during STS is necessary in two directions, CoM velocity decreases along the horizontal axis just before seat-off, but increases along the vertical axis at the instant of seat-off. The control of CoM horizontal motion has been well documented by Pai and colleagues in young subjects ⁽¹⁾⁽⁴⁾. Results from these studies showed that subjects deliberately limited peak horizontal momentum (product of the velocity of the CoM and the body mass) when faced with conditions of increasing speed. However, they were able to voluntarily increase CoM momentum above that required to rise from the chair when permitted to fall forward using the arms on a support bar to stop the fall, rather than maintaining upright stance. Such features of CoM motion were interpreted as deliberate strategies of dynamic balance during STS.

Age-related changes in balance control have previously been analyzed using a movable platform in order to test the automatic postural responses to support surface perturbations. The results showed both modifications in the temporal organization of motor response and in the amplitude ⁽⁵⁾. Links between posture and voluntary movement have also been studied in elderly subjects ⁽⁶⁾. These authors highlighted evidence for a slowing of postural responses related to arm movements. However, the effects of aging upon postural control during a task requiring large displacements of the CoM in both forward and upward directions, such as is common to STS, has until now been poorly documented in healthy elderly subjects.

Nevertheless, clinical studies have demonstrated a correlation between difficulties in performing STS movements and balance disorders in elderly persons ⁽⁷⁾. Kaya and colleagues ⁽⁸⁾ have demonstrated changes in dynamic parameters of STS motion and gait in elderly subjects with bilateral vestibular hypofunction. In these subjects the linear and angular momentum was decreased compared to healthy elderly subjects. This result showed modification in strategy aiming to decrease disequilibrium created by the locomotor activities. Moreover, Alexander and associates ⁽⁹⁾ have compared a group of young subjects to a group of elderly subjects including those able to rise without the use of armrests and those unable to rise without the use of armrests. Results of this study showed the importance of postural stability control in STS, particularly in the impaired group. In order to understand the mechanisms underlying an effect of age on strategies used during STS, postural or equilibrium control must be explored in greater depth.

A previous study, comparing young and elderly subjects during standing and sitting movements, described angular velocity adjustments of trunk and knee in the elderly group, particularly following seat-off ⁽¹⁰⁾. Such results could be interpreted in terms of an alteration of CoM control during the critical transition phase. The present study attempted to explore the nature of these alterations by examining the parameters of dynamic equilibrium under different experimental conditions of light and speed. Analysis of results was based upon the concept of a "dynamic equilibrium area" (DEA). CoM position and velocity were used to define this area, which in turn identified the dynamic limits of balance. A similar approach has been used for postural control during bipedal robot locomotion ⁽¹¹⁾. This method allows the comparison of strategies used for the control of CoM motion between young and healthy elderly subjects. It was hypothesized that consistent differences between the two groups would be found in the position and velocity of the CoM at the instant of seat-off. This in turn would reflect changes with age in the equilibrium control system during STS. Implications of this method in clinical studies are also discussed.

	Materials and Methods

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Subjects
Data were obtained from 7 healthy young subjects (3 women and 4 men), aged between 20 and 25 years (mean age 22.8 ± 1.5 years) and 7 healthy older subjects (6 women and 1 man) aged between 71 and 82 years (mean age 75.1 ± 4.4 years) (Table 1 ). Young subjects were physiotherapy students. Older subjects were recruited from a senior citizens' club. Potential elderly subjects were screened by a geriatrician in order to exclude any neurological diseases, peripheral neuropathologies, or musculoskeletal conditions that could have limited their movements. All subjects volunteered and gave their informed consent prior to participation.

Recording system..-- Movements of specific anatomical sites of the body were measured using a 100 Hz optoelectronic movement ELITE analyzer (BTS, Milan, Italy) that computed the spatial coordinates of small reflective markers (0.5 cm in diameter) glued to the skin. Two cameras (sampling frequency 100 Hz) placed 3 m from the subject's sagittal axis (left side), one on top of the other, 1 m and 2 m from the ground, recorded movements of eight markers fixed on the left side of the body at the following sites:

• the head: external canthus of the eye; auditory meatus.
  
• the trunk: acromion; side of the trunk (at the level of the seventh rib).
  
• the lower limb: hip (trochanter); knee (interstitial joint space); ankle (external malleolus); foot (fifth metatarsophalangeal).
  

During the experiments, both the chair and the subject's feet were placed on the 6-component dynamometric force platform (AMTI, Watertown, MA) allowing the measurement of three components (horizontal, vertical, and mediolateral) of applied force, and horizontal and mediolateral coordinates of the center of foot pressure (CP).

Data Analysis
Timing..-- Recorded data were filtered using a Butterworth fourth order low-pass filter (cutoff frequency 6 Hz). In order to determine the beginning and the end of the motion, an angle (₁) between the trunk (the link between the acromion and the trochanter marker) and the vertical was calculated. The onset of intentional movement was defined as the first 10-millisecond frame at which values of forward angular velocity of the trunk exceeded a threshold of 10% of peak angular velocity during the entire STS movement. In the same way, the end of the movement was defined as this value decreased below a threshold of 10% of the peak. The threshold of 10% of peak of vertical linear displacement of the trochanter marker was used to identify the instant of seat-off.

CoM positions..-- Sagittal CoM positions were calculated using a five-segment, rigid mathematical model (Fig. 1), consisting of the following appendicular and axial segments: head, thorax, lower trunk, thigh, and shank. The arms were included in the thorax segment, and the leg segments comprised both the thigh and the shank. Only six of the eight markers were used: auditory meatus, acromion, side of the trunk, hip, knee, and ankle. Only motions of the CoM in the sagittal plane were explored in the present study. The coordinate system was defined as illustrated in Fig. 1: = , with the origin being placed at the center of the ankle joint. The coordinates X_i, Y_i of the center of mass of a segment number i were calculated using the following formulae:

(1)

where X_1i, Y_1i, X_2i, Y_2i are coordinates of the end markers of the i-th limb; l_i is the ratio between the distance of the proximal marker to the segments CoM, and its length. Coordinates X, Y of the common CoM were thus calculated using the formulae:

(2)

with m_i being the mass of the i-th segment. Anthropometric parameters m_i, l_i were assumed to be equal to average ones, and thus were taken from the literature ⁽¹²⁾. The coordinates of the position of the CoM were corrected using force platform data, and assuming that before the movement the position of the CP corresponded to that of the CoM. Thus, a constant value was added to X in order that calculated CoM position equalled the CP during quiet sitting. The velocity of the CoM was calculated by numeric derivation of position (displacement) values.

View larger version (11K): [in this window] [in a new window]   Figure 1. Stick diagram of the five-limb model including the head, thorax, lower trunk, thigh, and shank used in the calculation of the CoM position. l correspond to the spatial angle between the trunk and the vertical.

View larger version (9K): [in this window] [in a new window]   Figure 2. The pendulum consists of weightless "leg" with a point mass m comprising the whole mass of the body. The leg stands on a foot. A torque M can be applied in the ankle joint, but this torque is limited by foot length.

(3)

where time constant equals where l is the height of the CoM, g is the acceleration due to gravity, and points denote time derivation. After multiplying both parts of the equation by l and replacing l with X (abscissa of the CoM) and with P (abscissa of a center of pressure of ground reaction force [CP]), the following formula can be obtained:

(4)

The CP must lie between bounds: X_t P X_h, where X_t, X_h are abscissas of the toe and the heel, respectively. There are two lines in the phase plane X,X separating phase trajectories of 4 when the value of P is constant and equals to one of the two limiting values. These two lines bound the region:

(5)

where X_t and X_h are coordinates of the toe and heel, respectively. This condition describes a zone inside of the phase plane bounded by two parallel lines, which cross the X axis at the points X_t X_h (heel) (Fig. 3). For zero velocity, 5 yields the well known condition of static equilibrium, that the projection of the CoM lies within the supporting area. Thus, 5 can be regarded as a generalization of static equilibrium conditions, where CoM velocity exceeds zero. We named this zone, defined by 5, as the dynamic equilibrium area (DEA).

View larger version (14K): [in this window] [in a new window]   Figure 3. The zone described by 5, dynamic equilibrium area. If the starting position is outside the region between the dashed lines, it is impossible to cross the boundary of the region and to bring the CoM into area of support with zero velocity. Thus, the system will fall backward (curve 2) or forward (curve 3). So, only motion of CoM represented by points from the region, 5, can be executed within an equilibrium state.

where , are normalized CoM position and velocity, and _{f h t} is foot length.

Statistical Analysis
The different periods corresponding to the different combinations of vision and speed conditions were not randomized over periods owing to the complexity of the measurement: all the periods were of four types: normal speed/normal vision; as fast as possible/normal vision; normal speed/blindfolded; and as fast as possible/blindfolded. Data were then studied with an analysis of variance considering as a block the four successive combinations of vision and speed of each subject and taking into account:

• the age effect (variation between young and elderly);
  
• the period effect (variation between the 4 different periods);
  
• the Age x Period interaction.
  

When a period effect was found to be significant, vision and speed effects were studied separately by linear contrasts between the corresponding means for normal speed versus as fast as possible, and normal vision versus blindfolded. If the Age x Period interaction was significant, these means were compared separately in the young subjects and in the elderly subjects.

A result was considered significant at the p < .05 level.

	Results

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General Movement Characteristics in Young Subjects
A description of the general characteristics of STS has been achieved on the basis of both dynamic and kinematic analyses. Fig. 4 shows, from top to bottom, angular velocity relative to the vertical of trunk, the vertical displacement of hip marker, the CoM and CP displacement along the anterior/posterior axis, and CoM velocity in the forward direction for one typical young subject. Preceding seat-off, the trunk demonstrated forward flexion. Following seat-off, the direction of trunk movement was inverted (moving in extension). There was a backward displacement of the CP preceding seat-off, indicating that CP and CoM moved in opposite directions. The maximal value of CoM velocity was attained before seat-off. The delay between time to maximal CoM velocity and seat-off was small (0.03 ± 0.02 s).

View larger version (15K): [in this window] [in a new window]   Figure 4. Kinetic and kinematic analysis of a young subject. Top: angular velocities of trunk (l ). Middle: displacement of center of mass (CoMD in bold) and displacement of center of pressure of ground force (CP), both along the anterior/posterior axis, vertical displacement of hip marker (HIP). Bottom: horizontal projection of center of mass velocity (CoMV). The following instants were identified: beginning (T1); CoM maximal horizontal velocity (T2); seat-off (T3); end of motion (T4). The complete motion is represented by the sequence of stick figures, and displacement of CoM is shown as filled black dots.

For max there was a significant Period by Age interaction ( p < .05) that may be interpreted in different ways (Table 3 ):

• The absolute means were significantly lower in elderly subjects, the difference being greater in blindfolded condition (mean elderly–mean , 0.175 for fast speed) than under normal vision (mean elderly–, 0.133 for fast speed).
  
• The absolute means were significantly lower in blindfolded condition in elderly subjects only.
  
• The absolute means were significantly higher in fast condition than in normal condition for both the elderly subjects and the younger subjects.
  

View larger version (14K): [in this window] [in a new window]   Figure 5. The normalized velocity of CoM was plotted relevant to displacement of CoM at the instant of seat-off in young () and elderly (•) subjects for normal condition. Dashed lines indicate the boundary of the dynamic equilibrium area (DEA).

where seatoff and seatoff are normalized CoM position and velocity at the seat-off instant. This formula gives a length of a line segment parallel to the X axis drawn along the phase plane from the representative point up to the heel boundary of the DEA (the distance from this point to the heel boundary of DEA is equal to _DEA/).

This length (_DEA) was found to be significantly smaller in elderly subjects than in young ones ( p < .05) (Table 5 ). In other words, the position of CoM in the phase plane was located nearer to the limits of a fall backward in elderly than in young subjects. Neither effect of vision nor speed effect was found significant.

View this table: [in this window] [in a new window]   Table 5. Statistical Analysis for the Distance From Center of Mass Positioning to the Hill Boundary of the Dynamic Equilibrium Area: DEA

	Discussion

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In agreement with a previous study ⁽³⁾, the analysis of kinematic data indicated that the CoM reached maximal horizontal velocity before seat-off. The comparison between the two groups showed that the maximal CoM velocity in the horizontal axis and the CoM velocity at the instant of seat-off were lower in elderly compared to young subjects. Thus, elderly subjects began vertical motion (at the instant of seat-off) with a lower horizontal velocity compared to young subjects. This result can appear as expected if we consider that elderly subjects achieved STS more slowly than young subjects. The elderly subjects were able to increase motion speed, but under all experimental conditions the movement time remained greater than in young subjects. If we consider the movement time, no vision effect was found, and we can think that STS is a very automatized task mainly dependent upon somatosensory information ⁽¹⁰⁾.

However, the analysis of vision revealed a greater difference between elderly and young subjects under blindfolded condition for the maximal CoM velocity along the horizontal axis. This finding shows that the visual feedback is necessary to elderly subjects when the CoM velocity reaches the peak value. In this case, the movement control needs visual information and cannot be based on feedforward process only. This inability to adapt to vision privation suggests a difficulty in integration within the central nervous system ^(14)(15). Moreover, this finding shows that the maximal CoM velocity allows a pertinent approach of movement control in the aging process.

The analysis of horizontal CoM velocity as a function of displacement allowed the definition of DEA, which determined the mechanical limits of motion. Assuming that CoM motion following seat-off depended upon ankle torque only, movement termination at a state of equilibrium was found to be impossible outside the DEA. A similar zone has been constructed by Pai and Patton ⁽¹³⁾, using computer analysis of the human whole body model. Here it has been constructed analytically.

Our results showed a difference in the control of the CoM within the DEA between healthy young and elderly subjects. The position of CoM in the phase plane at the instant of seat-off was found to be shifted backward in elderly subjects. This decreased a risk of falling forward but simultaneously increased the risk of a backward fall. This modification of equilibrium conditions in elderly subjects can be interpreted as a protective attitude against the risk of forward falling. A change in the perceived stability limits with aging could explain such a protective attitude, which can be interpreted as a compensatory process with regards to a decrease in postural stability ⁽¹⁶⁾. It is also interesting to note that clinical observations often show a trend toward backward disequilibrium in elderly patients who present a history of falls.

According to the method, the whole body weight cannot influence the results, but an effect of mass distribution should be found. We think that the difference between mass distribution in the young and elderly subjects in our population would have a minor impact. However, in future studies the influence of this parameter could be analyzed in other groups. Moreover, further research will be required to fully elucidate the relationship between the decrease of muscular strength with age and the strategy modification. An obvious relationship between muscle weakness and functional loss in elderly subjects presenting functional limitations has been reported ⁽¹⁷⁾. On the contrary, this relationship has not been found in healthy elderly subjects.

Finally, we suggest that the present analysis might be used in clinical practice in order to identify the strategies adopted and to assess results of rehabilitation in pathological elderly subjects.

	Acknowledgments

 
This research was supported by a grant from the Institut National de la Santé et de la Recherche Médicale (INSERM/CRE n°92107). The authors gratefully acknowledge the contribution of the Centre National d'Etudes Spatiales for providing a part of the equipment needed for this research.

Received August 11, 1998

Accepted February 17, 2000

	References

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