Gait reaction reconstruction and a heel strike algorithm

Gait reaction reconstruction and a heel strike algorithm

GAIT REACTION RECONSTRUCTION ALGORITHM G. Department of Civil Engineering. W. University AND A HEEL STRIKE BRODLAND of Waterloo. Waterloo. On...

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GAIT REACTION

RECONSTRUCTION ALGORITHM G.

Department

of Civil Engineering.

W.

University

AND A HEEL STRIKE

BRODLAND of Waterloo.

Waterloo.

Ontario.

NZL 3G I.

Canada

and

A. Department

of Mechanical

B. THORNTON-TRUMP

Engineering.

University

of Manitoba.

Winnipeg.

Manitoba.

R3T 2Nz.

Canada Abstract-A

mathematical model of gait ground loading is presented. The model allows the ground reactions produced by any particular single- or multiple-footfall pattern to be constructed. given a sufficient variety of other measured ground reactions. An algorithm which uses center verticalpressure data on/~ lo determine the instants of successive heel strikes on a large force plate is then presented. Experiments shoa the high accuracy of the heel strike algorithm and show that reconstruclions of the vertical component of ground reactions are typically within 3 ‘;i. of corresponding measured reactions. The techniques presented allow certain broblems associated with small force Dlales and other problems associated with large force plates to be largely overcome.

of

ISTRODUCTION Gait

continues to be the subject of much experimental (Murray et al., 1964; Balakrishnan et al., 1982) and theoretical (King, 1984) research. The ground reactions produced by gait are of particular interest to both researchers and clinicians since they are highly sensitive to gait abnormalities and can be measured easily using a force plate (Cunningham, 1958; Jacobs et al., 1972).

Force plates which are only large enough to measure a single footfall have been popular for a number of years. Unfortunately, however, these plates can not measure the total reaction forces during double support, nor can they measure the motion of the center of vertical pressure from one foot to the other. Force plates which are large enough for both left and right feet to be supported simultaneously (see Fig. 1) are becoming more common (Yamashita and Katoh, 1976; Balakrishnan and Thornton-Trump, 1979). These large force plates reduce the tendency for the subject to disrupt his normal gait pattern in order to hit the plate. and increase the likelihood that useable force data will be obtained when the subject traverses the force plate area. These advantages are particularly important in studies of pathological gait. In addition, large force plates can provide accurate center of pressure data even during double support. A drawback of large force plates is that they make it more difficult to obtain single footfall forces. A long-standing problem in gait analysis is identification of the instants of heel strikes. Two main solutions have been used:cine;video methods (Murray Rewired 1985.

4 September

1984:

in reoised

form

14 Februor)

761

et al., 1964); and special shoes equipped with conductive tape (Yamashita and Katoh,1976), micro-switches (Winter er al., 1972) or pneumatic sensors (Nilsson et al., 1985). Both havedrawbacks in terms ofcost and/or interference with the subject’s gait. In this paper. a mathematical model of ground loading produced by locomotion is presented. The model accommodates locomotion using any number of supports; e.g. bipedal gait, cane-assisted gait, or quadripedal animal gait. However, to simplify the discussion, only bipedal human locomotion will be considered. The model allows the instants of successive heel strikes on a large force plate to be determined accurately from center of vertical pressure data only. It also makes it possible to reconstruct the ground forces produced by particular single or multiple footfalls from measured records of other footfall patterns. For example, the total ground reaction of one complete gait cycle can be constructed when separately measured left and right foot reactions only are available. Alternatively, the right foot reaction, for example, can be extracted from a measured record of combined right and left-foot reactions using a measured left foot reaction or any multiple footfall reaction record which begins with a left foot. Both the additive and extractive analyses outlined above provide powerful tools for the study of gait. Finally. the model allows the center of vertical pressure to be accurately reconstructed using single-footfall forces. Experiments done using a large force plate (Balakrishnan and Thornton-Trump, 1979) and a digital data acquisition system (Brodland, 1982) are then described. They show the high accuracy of the heel strike algorithm and show that both additive and subtractive reconstructions of vertical reactions are

768

G. W. BRODLAND and A. B. THORNTON-TRUMP

Force Sensitive Area

Fig. 1. Force platform.

typically curves.

within

3:;

of corresponding

THEORHICAL.

measured

BASIS

Consider a subject’s steady bipedal gait. His left foot will contact the Boor once every full gait cycle and will exert a particular time-varying force with each such contact. This force will have three components: vertical. medio-lateral and anterio-posterior. The vertical force component of the left foot of a subject with normal gait is shown with a solid line in Fig. 2a. We call this reaction force, F,(t,), and choose the time parameter t, to havea valueofzeroat theinstant SI of the first measured left-heel strike. Similarly, his right foot exerts a particular ground force which varies with time, as shown by the dashed line in Fig. 2a. We denote the right foot reaction by FR(12)where we set t2 to zero at the instant S2 of the first measured righr-heel strike. If only a left foot strikes the force plate, the reaction measured will be one cycle of F,(t,). If left, right and then left feet strike the plate in succession, the measured reaction will be the sum of two cycles of FL@,) and one cycle of F,(t,), as shown by the dotted line in Fig. 2a. It is possible and in fact likely that the subject was walking at slightly different rates when left and right force records F, and F, were taken. To scale the separate records to a particular gait period P, timescale factors Q, and Q2 are introduced. The time-scaled reactions are F,(Q,r,) and FR(Q2f2). If the subject walked with gait period P when both left and right reactions were measured, scale factors Q, and Q2 would be unnecessary. When Q is greater than one, the measured record is effectively speeded up. When Q is less than one, it is slowed down. Time scaling of this kind by up to 10% is shown to be valid by Brodland (1982). He also shows that significant changes do not occur in reaction force as a result of small changes in gait speed. The final consideration in combining records is the time between left and right heel strikes. This time, DLR shown in Fig. 2a, is measured in terms of the chosen gait period P. Suppose thegait period P, is 1.20 s when F,(t,) is measured and the time between left and right

heel strikes is D, = 0.65 s. Suppose also that the gait period P2 is 1.32 s when FR(t2) is measured. If we choose to combine the records using a gait period of P = 1.20 s, then

Q,++

1.10

D,, = DJQ, = 0.65.

(I)

Mathematically, the left-right reaction FL&) produced by successive left and right feet striking the force plate is F,,(r) = F,(Q,r)+F,(Q,(r-D,,)) (21 where F,,(t) is the calculated left-right reaction; F,(t) is the measured left reaction; F&) is the measured right reaction; D,, is the time between left and right heel strikes in terms of the gait period P; Q,, Q2 are reaction time scale factors and t is time measured in terms of the gait period P. The reaction F,,, of a left-righi-left combination can be reconstructed in a similar fashion F,,,(r)

= F,(Q,t)+F,(Q,(t-D,,))

+FAQ,O-PII.

(3)

A single-footfall reaction can be extracted from a measured multiple footfall reaction using a measured record which begins with the other foot. For example, a left record can be found from a left-right combination record FLR(tl) and right record F,(t,) using F,(r) = FLdQ,t)-FR(Q2(r - DJ).

(4)

Note that an RL or RLR force pattern could have been used instead to extract the L pattern from the measured LR pattern. Similar reconstructions of mediolateral and anterio-posterior forces are possible using the same methods. Indeed, forces such as F, can be thought ofas vector quantities rather than as scalars representing only one component (e.g. the vertical component) of the force. Reconstruction procedures are especially useful when a particular single or combination record is not

Gait

reaction

169

reconstruction

IX _ THIS

ii

Foot

-

Left

----

Right Foot

l

.. .

FORCE -

FR ($1

-

F, (1,)

-

FR 0,)

-

F,_b, 1

-

FR b,)

FOOT

STRIKES

SENSITIVE

AREA

z

FR(1,)

Left-Right-Left

/

2

FL($)

J

Sequence

FLRL(

t1 f

C

-I

.x .r,

2 F

0

a

THESE FOOT FALLS STRIKE FORCE PLATFORM

W > g W

a

\_

$ W v

3

s,

%

%

/

/

I I

THIS

+ SO

s4

f A

5

s,

s,

FORCE AREA

FOOT

STRIKES

SENSITIVE

s,

TIME

TIME Fig. 2. (a.

b) Typical center of vertical pressure record.

taken or cannot be easily taken. The procedures apply equally well to both normal and abnormal gait. Consider the motion of the center of pressure across the force plate if left, right and then left feet strike the plate. When only the left foot bears on the force plate, starting at S, (see Fig. 2), the center of vertical pressure coincides with A, the point of application of the left foot reaction FL(t). When the right foot begins to carry weight, double support begins, and the center of pressure moves out from under the left foot and moves toward the right foot (point B) where it remains during single support by the right foot. When the left foot again begins to carry weight on the plateat point C, the center of pressure suddenly begins to move forward towards point C, where it remains until the left foot leaves the plate. Since a single foot reaction begins suddenly at heel strike and increases quickly, the instant of heel strike can be accurately determined simply by noting when the center of vertical pressure begins to move at a high rate in the direction of walking. By making the areas adjacent to the force plate force sensitive using microswitches as shown in Fig. 1, the heel strike S, of the last footfall before striking the force plate and the heel strike S, of the first footfall striking off the force pIate can be determined. These additional strike times allow more accurate determination of the speed of gait when less than three footfalls strike the force plate. The heel strike algorithm then, monitors the microswitches on the force sensitive areas adjacent to the force plate. The first measured heel strike is identified by closure of the switch associated with either area. If desired, the direction of walking can be determined automatically by noting which force sensitive area switch closed first. The next heel strike occurs on the force plate and is determined by the total vertical plate

reaction exceeding some small threshold value. In practice, it is more accurate to use a threshold value 01 approximately 25 y0 of the peak force so the algorithm is not triggered by signal noise, and to extrapolate back to zero force based on the initial slope of the measured portion of the vertical reaction force. Alternatively, plate reactions could be measured and stored continuously, with readings, say, I sold being overwritten with current ones. When the 25”,/, threshold is reached, actual plate loads for the full previous second have been recorded and can be used to determine the actual instant of heel strike. Successive heel strikes on the force plate are determined by monitoring the motion of the component of the center of vertical force in the direction of walking. When the center of force begins to move forward at a rate in excess of approximately 0.4 m s-’ another heel strike has occurred. Since a single foot reaction such as F,(r) begins very suddenly and increases rapidly, this test prosides surprisingly good results. The last heel strike determined by the algorithm is that of the first step off the force plate onto the force-sensitive area adjacent to the plate. This heel strike is determined simply by closure of the area microswitch. If the subject traverses the force plate near its long side (see Fig. 1). the forces of up to three footfalls will be measured, e.g. F,,,_(I). and a total of five heel strikes identified. If the subject walks along the other side of the walkway, he will cross the apex of the force plate and the forces of one footfall, e.g. F,(r), will be measured and a total of three heel strikes identified. Finally, walking down the center of the walkway usually produces a double footfall on the plate and identification of four heel strikes. Application of properly-time-scaled measured or reconstructed single-foot reactions F‘,(t) and F,(r) at corresponding contact positions X,and X,allows the

770

G. W.

BRODUND~~~A. B. THORNTON-TRUMP

motion of the center of pressure x to be reconstructed; i.e..

X(f) =

B -

F’,(l)x,-+ F,(r)X,

2 i?

It also permits accurate analysis of the double support phase. EXPERI.MESTALRESULTS

800 600

2 2

400

k u >

200

%?tl TIME

Run number

of heel

Meosurad right-left sequence ---Reconstructed from left ond right records

2 5

1000

;

800

i

600

F

400

6 >

200

0 TIME

Second heel

Third heel

Fourth heel

in run

strike

strike

strike

strike

0.560 (0.568)

1

1

PO,

2

2

(00)

(0.528)

3

1 S)

0.568 (0.568)

PO)

0.560 (0.568)

1.048 (1.048)

1.568 (1.576)

(“0)

0.584 (0.592)

1.112 (1.120)

1.656t

PO,

0.576 (0.576)

1.120 (1.120)

1.688 (1.696)

.0.528

5

3

6

(sec.)

strikes (s)*

heel

3

2

I

Meosured s ---3 Reconstructed from right ond left records

strikes

4

(sec.)

-

Table 1. Comparison of heel strike times Instants

foot record foot record

0

A test was first devised to determine the accuracy of the heel strike algorithm since it would play a critical role in the reaction reconstructions. A special pair of shoes having heel and toe contact switches was available. Heel strikes as determined from the shoeswitch record and as determined by the heel strike algorithm are shown in Table 1: The extremely good correlation between the two shows that the algorithm is extremely accurate. Indeed, the data in Table 1 shows that measurement accuracy was in this case limited to -t_4 ms by the sampling frequency. The accuracy of the algorithm is further verified by the accuracy of the force reconstructions of several different patients, including some with abnormal gait, which are discussed in this section and which rely on the heel strike algorithm for time scaling and offsets. The heel strike algorithm makes it possible to reconstruct the vertical reactions of particular footfall patterns from the reactions of other footfall patterns. For example, Fig. 3a shows the separate left and right vertical reactions of a subject who has an abnormal gait. The subject was recovering from a fracture of his right femur. His right foot reaction is easily identified

Number of heel First

1

1000

IIJ

(5)

.

-Right --- Left

3

1.016 (1.024)

20

I

2

TIME (sec.)

‘Non-bracketed times determined from shoes equipped with tape switches. Bracketed times determined using heel strike algorithm. Sampling rate was 0.008 s. *tFoot struck edge of force plate.

Fig. 3. (a-c)

Additive

reconstruction

of a right-left

record.

by the missing first hump which is normally produced by a firm heel strike. For comparison, the reaction of a subject with normal gait is shown in Fig. 4. The left foot reaction shown in Fig. 3a is more normal. These records are time scaled using the calculated heel strike points. Jn this case, they are scaled to match the gait period of the composite record shown with a solid line in Fig. 3b. The left record is then time shifted

Gait

-Left

I

reaction

foot record

left-right-left records

5

;

771

reconstruction

000

record

As a final example, 600

right

record

obtained 2

400

G E >

200

normal

left

subject

by subtracting Both

tremely

good

of

these

final

correlation

n 0

potential

2

I

TIME

same

type.

multiple

also

maximum

examples

of a gait

a right-left show

ex-

error)

be-

record and a measured

The

record

demonstrate

and subtraction

footfall

reactions

to

reconstruct

footfall

reaction.

As a further

the accuracy of a two-footfall

record constructed

records, we consider

the

of single

They also show its accuracy. two single-footfall

800

the

normal

from

almost any desired single or multiple

-Measured left-right-left record --Reconstructed from left and right records

‘;

having

examples (31,

of using addition

and/or

(sec.)

right

Exactly

were used here.

a left record

tween the reconstructed the

and

gait.

Fig. 5 shows the reconstruction

of another

record.

of

8

separate

with

same time scaling and offset technique

0

E

from

for a subject

indicator

of

from

the reconstruc-

tion of the center of pressure. The present model treats the foot as an unmoving

time-varying

hence does not account

-

the heel to the toe (Grundy during

single support.

include

this second-order

in equation

point

for the weight

et al., 1975) which

A more

refined

from occurs

model

effect by making

(5) functions

load and

transfer

would

XL and X,

of time, e.g. X,(t).

Figure 3c shows as a solid line the center of pressure

0

calculated line

shown

reconstructed

from

reactions.

2 TIME

motion dashed

to the measured weight

-Measured

the force-plate

is the

center

the separate

figure

shows

center of force is, during

(sec.)

between

---

The

from

left

that

double

force

The

motion

and right

foot

the reconstructed

support,

very similar

one. It is also clear that the difference

the two curves is almost transfer

reactions.

of

from

entirely

a result

the heel to the toe during

?

X Reconstructed from left and right records

5

000

8

600

r

-Right-left record ----Left record

E LL 400

G 0 200 k W >

0

TIME

TIME

Fig. 4. (a-c)

Additive

by the right-left

(sec.)

reconstruction record.

heel strike period

D,,

This

shows that the reconstructed

right-left

by the dashed

the measured

line) matches

record with less than 3 ‘A maximum good

agreement,

successive

as variations

records

record

(sec.)

-Measured right record --Reconstructed from left and right-left records

of a left-right-left

figure (shown

right-left

error. This is very of

this

of the same subject

amount

in

are not

un-

of

a

TIME

(sec.)

common. Figure

4

shows

the

reconstruction

Fig. 5. (a, b) Subtractive

reconstruction

of

single

of a right record.

772

G. W. BRODLAND and A. B. THORNTON-TRUMP

support and which is not accounted for in the present model. The center of force reconstruction of a left-right-left sequence is shown in Fig. 4c. Here again, the center of force reconstruction is almost indistinguishable from the measured one during most of double support. The difference between the two curves close to and during single support is again caused by the fact that the model does not account for the heelto-toe weight transfer which occurs during single support. CONCLUSIONS

The mathematical model of ground loading presented herein makes it possible to identify the instants of successive heel strikes on a large force plate using center of vertical pressure measurements only. By making the approach adjacent to the force plate force sensitive, two additional heel strikes can be identified. Comparison with measurements taken simultaneously from shoes equipped with heel contact switches demonstrated the extremely good accuracy of the algorithm. Specially equipped shoes and tine/video methods are no longer needed to determine the instants of successive heel strikes on a large force plate. The model also allows the vertical reactions of particular footfall patterns such as left foot followed by right foot striking the force plate to be reconstructed from the reactions of other footfall patterns, such as left foot only and right foot only. Additive as well as subtractive reconstructions are possible. Comparison with measured force records of the same types demonstrates that the reconstructions are typically accurate within 3 %. The centre of pressure can be reconstructed using a method similar to that used for force reconstruction. The reconstruction is often indistinguishable from and usually within 5% of corresponding measured center of pressure records during double support. The error is due almost entirely to motion of the center of pressure from heel to toe during single support. The reconstruction could, thus, be made more accurate by incorporating the center of pressure motion during single support into the model. The reconstruction procedures developed here can be used to construct the reaction of any particular footfall pattern desired by the clinician. They are especially useful in cases where force plates large enough for multiple successive foot strikes on the plate

are not available. as they allow any multiple-step reaction to be constructed and make accurate studies of double support possible. Subtractive reconstructions are particularly useful for extracting infficiduol foot forces when large force plates are used and singlestrike reactions seldom occur. Also. gait time asymmetries can be accurately determined using only a large force plate. The model can easily be extended to accommodate gait modes using more than two supports such as a person walking with a cane or other prosthetic support, or an animal walking on four legs. Ackna~Iedl/emenr-The authors are grateful for the financial support of the Natural Sciences and Engineering Research Council of Canada.

REFERESCES

Balakrishnan. S. and Thornton-Trump, A. B. (1979) Measurements of reaction forces between foot and ground using a modified force plate. CANCAM 79. Universite de Sherbrooke, Sherbrooke, Quebec, Canada. Balakrishnan. S., Thornton-Trump, A. B. and Brodland. G. W. (1982) Moments about body centered coordinate axes at limb joints from force plate and biplane photography measurements. Biostereometrics ‘82, Vol. 361. Proceedings o/SPIE-7%e Inrernarional Sociery of Oprical Engineering, pp. 293-301. Brodland. G. W. (1982) Vertical reaction force reconstruction in human locomotion by developing a digital da:a acquisition system and a heel strike algorithm. MSc Thesis, University of Manitoba. Cunningham. D. M. (1958) Components of floor reactions during walking. University of California. Berkeley. Grundy, M.,Tosh, P.A., McLeish, R. D.and Smidt, L. (1975) An investigation of the centres of pressure under the foot while walking. J. Bone Jr Surg. 57B, 98-103. Jacobs. N. A., Skorecki, J. and Charnley, J. (1972) Analysis of the vertical component of force in normal and pathological gait. J. Biomechonics5. 1 l-34. King. A. 1. (1984) A review of biomechanical models. J. biomech.

Engng

106,

97-104.

Murray, P. M., Drought, A. B. and Kory, R. C. (1964) Walking patterns of normal men. J. Bone Jt Surg. 46-A, 335-360. Nilsson, J., Stokes, V. P. and Thorstensson, A. (1985) A new method to measure foot contact. J. Biomechanics 18. 625-627. Winter, D., Greenlaw, R. K. and Hobson. D. A. (1972) A microswitch shoe for use in locomotion studies. J. Biomeckanics 5, 553-554. Yamashita. T. and R. Katoh (1976) Moving pattern of point of application of vertical resultant force during level walking. J. Biomechonics9, 93-99.