TECHNICAL

MODELLING

OF THE BIOMECHANICS

NOTE

OF POSTURE

AND BALANCE

PATRICK 0. RILEY,* ROBERT W. MANhit and W. ANDREW HODGE* ‘Biomotion Laboratory. Massachusetts General Hospital, Boston, MA 021 I4 U.S.A. and tNewman Laboratory. Massachusetts Institute of Technology. Cambridge. MA 02139. U.S.A. Abstract-A technique for studying the relationship of posture to balance has been developed. To investigate this relationship quantitatively, the human body was treated as consisting of II rigid body segments, each with six degrees of freedom. A bilateral Sclspot II@/TRACK@data acquisition system provides position and orientation kinematic data for estimation of the trajectories of the individual body segment centers of gravity. From these. the whole body center of gravity is estimated and compared to concurrent force plate center of force data. Center of gravity and center of force excursions agree where dynamics are not significant. The technique may be employed to study quiet stance, response to postural disturbances. or the initiation and coordination of complcx movements such as gait.

INTRODC;CTIoN Posture, the position and orientation of the body segments. and balance, the control of the center of gravity (CG) or center of force (COF) position, arc coupled: most postural adjustments change the CG location. During stance and movement. the central nervous system (CNS) presumably controls body segment alignment in order to control the CG location, i.c. the brain controls posture to maintain balance. Therefore. a model which quantifies the essential features of posture should be u.sefulin the study of balrncc and balance disorders. Most postural sway force plate and disturbrncv platform balance studies employ two-dimensional invcrtL4 pendulum or simple compound inverted pendulum models of posture (Barin and Stockwell. 1983; Kodde er al.. I982 Nash& and McCollum. 198% Peeters er al.. 1985). These models are useful for describing quasistatic stance and responrs to small disturbances of stance posture and balance. They are, however, too restrictive to represent the range of postural control strategies employed in complex activities such as walking, stair climbing. rising from a chair. or the precise coordination essential to skilled athletics. Since postural adjustments arc invariably associated with purposeful movements, we believe quantitative measures of posture and postural control are essential to the understandingofnormal and pathological human movement. In gait. for example. the CNS and neuromuscular system control the kinematics of the lower limb to generate propulsive thrust. Concurrently they must also control the kinematics of other body segments to balance the body dynamically. WC present here a technique which we have developed to address this need. LlETt1ODS Quantifying posture requires modelling the body with a sufiicient number of body xgmcnts and precise determination of the position and orientation of each body segment. The model presented here employs I I segments:the right and left feel.shanks, thighs and arms; and the pelvis. trunk and head. Ten joints exist between the segments but no holo-

Received

infinolform

IO Julp 1989. 503

nomic constraints are imposed. i.e. no linkage constraints are defined and therefore each segment is permitted six degreesof freedom. Thus the entire system has a total of 66 degrees of freedom (DOF). Although more scgmcnts, e.g. two-segment arms or a multi-segmented trunk, may bedcsirablc. technical constraints currently limit the number of segments. The information provided by the I I segment model is usefulper sr and as a precursor IO models of greater complexity. The modelling proc%!sinvolves four steps.First. TRACK@ software (Antonsson and Mann, 1989) detines the 6-DOF kinematics of arrays of infrared LEDs from raw bilateral kinematic data. The Selspot ll@system is conligured to sample up to 64 LEDs at I53 Hz. Second, array position and orientation data are converted to body segment positions and orientations. At this stage whole body three-dimensional computer graphics displays arc available for qualitative evaluation of the subject’s posture and postural control strategies. and parameters such as joint angles may be calculated. Third, the segment masses and CG locations are estimated based on data from the literature. The data of Jensen (1986) for normal males in the S-IS years age range are used for children, and the data compiled from a number ofsources by Contini (1972) are used for adults. Finally, using the segment massesand CG kinematics, the kinematics of the whole body CG is estimated. Since the placement of arrays on the body segments is unconstrained, the array-to-body segment transformation matrices required for the second step must be defined each time the arrays are donned or adjusted. The segment major axis and most of the terms of the transformation matrix arc defined by the line connecting the proximal and distal joint ccntcrs. lnstantancous axis of rotation methods are impractical for defining joint centers when observing quiet stance and movements preceded and/or followed by quiet stance. Two methods of defining the body segment position and orientation by locating nominal joint antcrs are used. One method uses average axes of rotation defined by kinematic data in combination with static data. The other is based on anatomical landmarks and usesstatic data only. The arrayto-body segment relationships thusestablished are presumed to remain valid for the whole text series. Only the segment-array relationship is specified:no intersegment relationships are determined, hence no constraints are imposed on the joints and the full 66 degrees of freedom arc maintained.

504

Technical Note

In the first method, subject movements wherein the joints undergo sufficiently large angular displacements are used to define mean axes of rotation using a finite displacement method (Roth, 1967). Tbe preferred maneuver is a sit-tostand. with control of foot position, yielding axes of rotation for the ankles, knees and hips. Each joint Center is defined as the intersection of an axis of rotation with the joint midsagittal planedefined manually using a pointer TRACK array in a static data set (Fig. 1). Sina the finite displacement method produces an average rather than an instantaneous axis, the smallest useful range of motion as the normal stance position is being approached is used. Fijan (1985) found this method to be repeatable to within 8 mm at the hip, 5 mm at the knee and 3 mm at the ankle under conditions similar to ours. In the second method, the pointer TRACK array indicates the location of anatomical landmarks from which the joint center locations an inferred. The choice of method depends on reproducibility: the axis of rotation method is reproducible when applied to the lower extremity joints, but not with the lower back, shoulders and neck because of their complex kinematics and multi-segmented structure. The body segment internal and external rotation angles are not defined by the line connecting proximal and distal joint centers. These angles must be specified either by orientation of the pointer array during a static data set or by the relative positions of anatomical landmarks indicated by the pointer array.

RESOLTS The CG estimation technique was tested using a ‘body’ comprised of two parallelpiped segments whose masseswere measured to &2%, and whose stgrnent CGs were located to f4 mm. relative to their associated TRACK arrays. Estimates of the combined CG for diRerent juxtapositions of the two segments agreed with force plate COF location to within &4 mm for both horizontal axes. To assessuncertainties in estimating body segment parameten. results produced by using the two body segment parameter sources were compared. The body segment parameters of one female subject were estimated using the Contini data for adult females and the Jensen data for a I S-year-old male. The horizontal plane coordinates of the combined CG differed by 3 mm. Since the Jensendata attributes more of the body mass to the lower extremity, the body CG was 3 cm lower than that obtained with the Contini parameters. Such ditTerenccstypify expected discrepancies when standard litcrature reference data an used in lieu of subject-specific parameters. Figure 2 is a three-dimensional representation of the quiet stana posture of a typical subject. Frontal and right side views are shown along with a third view looking down on the force plates. A number of biomechanically significant, quantitative parameters may be derived from this kinematic data including angles at all IO joints and net joint forces and

AXIS OF ROTAT 106 S-O VECTOR FROll TRACK KIREtlATtC

SECTIOW

THROUGH

Fig. 1. Joint anter determination using the axis of rotation method. The axis of rotation is determined by a separate movement study while the joint midsagittal plane is indicated by the TRACK pointer array in a static data set as shown. The joint center is defined as the intersection of the joint midsagittal plane and the axis of rotation.

,... ’

---I)

i,i

:...

(b)

(a)

Fig. ?. Three-dimensional I I segment representation of quiet slunce posture. Right side (3) and front (b) views show ground rcnction force vectors (GRF) ;Ind the location or the center of gravity (CG). The force plate view (c) shows the base of support (~WI positions). left and ripht centers of force (Meld I cop, r cop). and the comb&d center ol force (lab&d COP). Right side and axial body segments are drlwn with solid lines. I& side scpmcnts with dashed lines. Lat

AP

+ 0

i

5

0

5

La1

AP

T

b

0 ::

-6( 0

5

0

5

AP

Lat 4

-1

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Time(s)

3

6

I

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3 Time (3)

Fig. 3. Time histories of the antcrior/posmrior and lateral displacrmcms of the center of gravity and center of lorce (labeled CG/COP) during stance oTa quadriplegic cerebral palsied subject (3-l and 3-Z). an arm raise maneuver by the same subjcrt (3-3 and 3-4) and a chair rise by a 3?-year-old fcmalc subject (3-5 and 3-6). Vertical CG displacemen& were also calculated but arc not shown here. Nok the scale change for the AP displacements during the chair rise. Because the chair support force is not included in the determination of the COP when the subject is seated Ihc CG/COP separation is large. but the CC and COP come together rapidly as the subject rises and quasistatic conditions are quickly established. The close agreement of the CG and COP trajectories in the stance and arm raise studies indicate that quasistatic conditions arc maintained and conlirm the adequacy of the model even with relatively large displacements as long as such conditions are mainuuned.

506

Technical Note

moments. In addition the placement and stability of theCOF in the base of the support may be characterized. Figure 3 shows the body CG and COF displacement time histories for three studies: (a) normal stance for a cerebral palsied subject. (b) a rapid arm raise maneuver by the same subject and (c) a chair rise for a control subject. General overall agreement of the CG and COF patterns is readily apparent differences are discussed below.

DISCUSSION Deviations between the CG and COF positions are due to several factors. First. the COF reflects the foot-floor force vector which is a reaction to body dynamics. whereas the CG is a function of static body segment position. Therefore, when dynamics are present the COF cannot be expected to correspond exactly to the model CG. As a consequence the CG displacements show a damped form of the COF displacements. Second, in the chair rise maneuver the full body weight is not applied initially to the force plates; the CG approaches the COF as the subject risesotTthe chair. Finally, model errors. primarily those due to body segment parameter estimation error. produce static offsets with minimal etfect on the estimation of displacements. The tests with the mechanical model and comparisons of the parameter estimation algorithms indicated these otTsetswould be of the order of I cm; subject testing indicates that this also holds true for subjects of reasonably normal body type. A technique has been dcvclopcd which quantiftcs and compares posture and balance. Body segment kinematic data with force plate data provide quantitative measures of the coordination of movement in achieving balance. Using this technique, it is possible to determine how spccitic COF/CG changes arc brought about by postural adjustments. Preliminary data also indicate that the method is suBicicntly sensitive to reword accurately the small postural adjustments associated with postural sway. However. analysis of the correlation between postural adjustments and COFcxcursions in postural sway, as in theattempt of Pceters et ul. (1985). requires tens of seconds of data to observe the low frequency components of such movements. With our current system we are limited to data sets of 5-7 s duration, oreventina us from undertakinu this tvne of studv.

New opportunities now exist for studying disorders which affect posture and for evaluating clinical methods, orthopaedic. orthotic and pharmacological. for correcting or ameliorating postural defects. Research prospects include applying the method to the study of normal postural maintenance strategies, a central issue in the coordination of movement. Since the control of CG location can be readily evaluated over a broad range of maneuvers from quiet stance to stair climbing, the study of such movements both in normal individuals and in those with neuromuscular or musculoskeletal pathology will illuminate the CNS control of muscles for movement and thereby advance clinical practice. Acknowledgement-This work was supported in part by NIDRR grant number Hl33E80024-89.

REFERENCES

Antonsson. E. and Mann, R. (1989) Automatic 6-D.O.F. kinematic trajectory acquisition and analysis. ASbfE J. Dynam. Syst. izIea.vmrControl I I I, 3 l-39. Barin. K. and Stockwell. C. W. (1983) A computer simulation of human postural control. Pm 36th ACE.\fB. p. 198. Contini. R. (1972) Body segment parameters, part ii. Arri/iriul Limbs 1% I-19. Fijan. R. S. (1985) Axes of rotation of the joints of the human luwcr cxtrcmity. S.M. Thesis. M.I.T.. February. Jensen. R. (1986) Body segment mass. radius and radius of gyration proportions of children. J. Biomrchunicx 19, 359-368. __. .~ Koddc. L.. Cabcrg, J. B., Mol. J. M. F. and Massen. C. H. (1982) An application of mathematical models in --.-nosturography. J. /%med. Enyng 4. 4448. Nashncr, L. M. and McCullum. G. (1985) The organixation of human postural movements: a formal basis and expcrimental synthesis. fkhuu. Bruin Sri. II, 135~ 172. Peeters. tl. P. M.. Caberg, H. B. and Mol. J. M. F. (19X5) Evaluation of biomechanical models in posturography. Mrd. Viol. Engng Comput. 23, 469473. Ruth, B. (1967) Finite-position theory applied IO mechanism synthesis. J. uppl. Mech.. ASME Truns.. Sept.. 599-605.