Model for static lifting: Relationship of loads on the spine and the knee

MODEL FOR STATIC LIFTING: RELATIONSHIP ON THE SPINE AND THE KNEE F. J. Division of Bioenginsering,

BEJJANI,

Hospital

C. M.

GROSS

and J. W.

for Joint Diseases. Orthopaedic

New York.

NY

OF LOADS

PUGH Institute.

301 East 17th Street.

lOW3. U.S.A.

Abstract-An experlmrntal study based on a trigonometric. anthropometric model. was conducted on thirty-five healthy subJccts 10 determine the relationship between knee and back forces during symmetric sagittal plane lifting. Total joint reaction forces for the knee and the back, along with their compressive and shear components, were calculated for each subject, as a function of the knee. back and ankle angles. The shear component was significantly higher in females than in males; the compressive component u’ab significantly higher in males. Strong inverse correlations were found between the back and the knee forces on all subjects. Strong correlations were also found between subject anthropometry and minimum and maximum joint reaction forces. The magnitudes of both back and knee joint reaction forces should be considered in recommending the lift type and position. based upon individual worker anthropometry. and Size and weight of the load-to be liftdd.

angle of flexion of the back . angle of flexion of the tup angle of Aexion of the knee angle between the foot and the leg angle between vertical and leg angle between Ihc thigh and the horizontal distance bctwcen acromion and third PIP joint. (ml distance bctwccn rl and the third coccygeal vertebra. <’ I

I II FE

FQ P

L, Lt.

LP I_;

2

L: L,, 11; II, % 111

CL3 SB JB CK SK JK

(m) distance between rl and vertex distance bcruecn greater rrochanter tip center of latcr;LI femoral condylc. (m) distance belwecn cenlcr oflutcral femoral condyla and heel. (m) height of the load. (m) erector spinac force, (N) quadriceps muscle force. IN) \reight of the load, (NI Icvcr arm of the arm about G, (m) lever arm of the erector spinae. (m) lever arm of the load about LCLS. (m) lever arm of the load about G, (m) lever arm of the quadriceps muscle, (m) leler arm of the head and torso about G, (m) lever arm of the rhigh about the center of rotation of the knee. G. (m) lever arm of It’1 about L4-LS. (m) uelght of the arms, (N) weight of the thighs. (NI uelght of the head and torso. (N) weight of the head, torso and arms (N) compression force on L-l-L% (N) shear force on L%LS. (XI total joint reaction force on L4-L.5, (N) compression force on the tibia-femoral joint, (N) shear force on the tibio-femoral joint. IN) lotal joint reaction force on the tibio-femoral joint, IN)

AJ

JB+ZJK 2 ISTRODC’CTION

The occurrence highest between

of low back pain in industry is the ages of 35 and 40 years (Calin er

al., 1980; Frymoyer rf rrl.. 1950). Knee joint arthritis usually appears later in life, with an age peak above 65. At this age, more than 2 ‘I(,of all men and 6.6 ‘I#,of all women in the United States suti-r from some degree of knee arthritis (U.S. Department of Health, 1971-75). Given that knee lifting is recommcndcd for back pain patients (Miller, 1980; Bendix and Eid. 1983: Swedish Back School), one would tend to think that ultimately there would be a greater incidence of knee arthritis among these patients. The purpose of the present study is to develop a model to predict loads at the knee as a function of relative participation of the back in lifting, and to evaluate the model using data taken from ths actual test subjects.

;\lODEL We used a simple. two-dimensional static model. based on trigonometry and anthropometry (Fig. I). The model represents the projection in a sagittal plane of the mechanical axes of the spine and the dominant upper and lower limbs of an individual. This position corresponds to the phase when weight is just about to leave the ground. The upper limb is vertical. The elbow is in full extension and slight pronation. The forearm is in contact with the patella. The proximal interphalangeal joints (PIP) are considered in contact with the handle. The foot is lying Rat on the ground. The angIes considered are the following (Fig. I):

ct = angle p = angle 0~- angle i i angle -angle of E = angle

of flexion of the back, of flexion of the hip. of Rexion of the knee. between the foot and the leg (= 90. dorsiflexion of the foot). between the thigh and the horizontal.

The anthropometric following (Fig. I): a = distance 281

measures

between acromion

considered

arc

the

and third PIP joint.

282

F. J.

BEJJANI. C. M. GROSS and J. W. PUGH

Fig I. Trigonometric and anthropometric model; IL = back Rexion angle; fi = hip flexion angle; y = knee flexion angle; E = angle between thigh and horizontal; 6 = angle between foot and leg; p = angle between vertical and leg; B = center of rotation of the hip; G = center of rotation of the knee; a = distance between acromion and 3rd PIP joint; b = distance between TI and 3rd coccygeal vertebra; c = distance between Tl and vertex: I = distance between greater trochanter and lateral femoral condyle; I = distance between lateral femoral condyle and heck It = height of the load.

between 7Y and third coccygeal vertebra, t = distance between greater trochanter tip and center of lateral femoral condyle, 1= distance between center of lateral femoral condyle and heel, c = distance between 7’l and vertex. h = distance

Considering the triangles CDL. QBG and WBQ (Fig. 1). we have the following trigonometric equation: lsinb+rsins+bcosa

= a+11

(1)

where h is the height of the load and the other variables are described above. A value for E can be obtained: & = 90’-(P-r). In the quadrilateral

ABGD

(9O+ca)+~+(180”-6)+(180’-‘J)=360”. Equations

(2)

(3)

(2) and (3) give us the following E = 180-y-6.

Equations (1) and (4) give us the following relationship coso! = (a+h)--Isin6-fsin(y+6) b

(4) angular

(5)

A free-body analysis was done on both the back and the knee (Frankel, 1980). For the back, we used the free-body above the L4-L5 joint, including the head, torso and arms (Fig. 2a). We obtained the erector spinae force, FE, by applying the moment balance

Ezb

Cb)

Ip

Fig. 2.(a) Free-body diagram above L4-L5: FE = erector spinae force; LE = lever arm of the erector spinae about L4-LS; VVJ= weight of the head, torso and arms; L, = lever arm of IV? about L4-LS; P = weight of the load; L, = lever arm of the load about L4-L5; JB = joint reaction force; C’B = compression force; SB = shear force. (b) Free-body diagram above the knee: N;. = weight of the head and torso; L, = lever arm of ‘.Vt,. about G (center of rotation of the knee); tVr = weight of the thigh; Lr = lever arm of W, about G: W’ = weight of the arm; FQ = quadriceps force; LQ = Lb = L, = lever arms of FQ, P,, and IV’ about G; JK = joint reaction force; CK = compression force; SK = shear force. equation

(all forces and weights are in Newtons) (WI x &.)+(P

x IL,)--(FE

x L,)

= 0

(6)

FEJ~xL,v)+(PxL,) L&

where 1%= WC (weight of head and torso)+ it> (weight of arms). According to Barter, W,. = 0.47 x total body weight + 54, WA= 0.13 x total body weight + 14, L,.= lever arm of WI about L4-LS, assumed to be = b/2sinz (Fig. Za), P = weight of load, L, = lever arm of load about L4-L5 assumed to be = absin z, L, = lever arm of erector spinae = 0.05 m. By projecting all the forces on two axes. one along the spine mechanical axis (compression axis) and one perpendicular to it (shear axis), and by applying the force balance equation, we then have (Fig. 2a) CB=

CMxcosz+FE

where CL? is the compression SE=

(7)

force on the back (L4- L5)

Wlxsina+Pxsinz

(8)

where SJ3 is the shear force on the back (L4-L5) JB = ,,‘CB’ f SB2

(9)

283

Mode! for static hftmg

H herr JB is the total Joint reaction force on the back (L4-L5). For the knee, we used the free-body above the knee. including the ipsilateral thigh and arm and half the sum of the head and torso. The moment equilibrium equation gives us the value of FQ. the quadriceps muscle force (Fig. 2b): I

FQ=jx

(-PxL,+lt;

xLc-w;+tt;x&l

LQ

-

(101

bt; and P have been defined above. itT = weight of the thighs = 0.18 x total body u-eipht + 15 (according to Barter, 1957) Lr = lever arm of the thigh about the center of rotation of the knee. G. Barter’s tables show the centerof-mass of the thigh at 56.7”,, of the thigh length (r) from G. The value of 4. is therefore: 4,. = 0.567 x I x cosE(Figs 1 and 2b); and if we solve for E in equation (4) L, = 0.567 x t x cos( 180 - y - 6), L, = (lever arm of the quadriceps muscle) = Lb = lever arm of the load, about G) = L,, (lever arm of the arm, about G) = 0.05 m. (approximate distance between the pat&r surface and G) (Fig. 2b). L, = lever arm of the head and torso, about G. Barter’s tables show the center-ofmass of the head and torso at 39.6”,, of h (defined above)+c (distance between 7l and the vertex). from the distal end of the spine. This and equation (41 give us:

where It;.

L, = I cos ( 1SO - ;’ - 3) - 0.396 (h + (‘1sinz (Figs 1 and 2b). By projecting all the forces mvolvcd on two axes. one along the thigh mechanical axis (compression axis)and one perpendicular to it (shear axis), and by applying the force equilibrium equation, we then have (Fig. 2b)

=!&

cK

+lt:,+&+P) 2

-sm(y+6)+FQ

(11)

where CK is the compression force on the knee (tibiofemoral joint). In equation (1 I), sin (y - b) = cos (;’ - 14) because /i = 90’ -d (Fig. I) sK

_

( 4 + Lb;+ y+ 2

PI

x (-cos(y+8))

(12)

where SK is thr shear force on the knee JK = ,‘CK=

-+sK2

(13)

where JK is the total joint reaction force on the knee*.

>lATERIALS

AZD

.\lETHODS

The anthropometric data were collected from 35 subjects, IS females and 17 males. Age range for the females was from 15.5 to 30, with a mean of I8 + 3.0.

* The patello-femoral joint reaction force bears a determinate relationship to geometry and extension force. and has not been addressed in this srudy.

Ape ranpr for the males was from 16 to ill. with a mean of 232 5. After recording Height and height. the subjects were positioned against a vertical gradicule for the folloaing measurements on the dominant side: distance between acromion and third PIP jotnt. distance between tip of the greater trochanter to the center of the lateral femoral condyls. distance between the center of the lateral femoral condyle to the floor. Then, using an anthropometric tape. the distance between Tl and the third coccygeal vertebra and between 71 and the vertex were measured. A computerprogram was urirten to solve the cquations previously derived. The knee angle (;) was allowed to vary from 0 to I20 by steps of 5 The ankle angle (6) was allowed to kary in 2 increments from 65 to 90 The back angle (z) was obtained from equation (5) and was allowed a maximum of 60 . because pelvic tilt would occur after that. The anthropometric measurements of each subject were entered and several sets of data were obtained. In the first set, weight and height of the load were constant for all the subjects: P = 5kg; h = 0.2 m. In the second set. height of the load was a constant (II = 0.2 m) and its weight took three diKerent values: lo”,,, 3X33”,,. and 50”,, of the total body weight of each subject. In the third set. weight of the load was a constant (P = 5 kg) and its height took three different values: IO”,,, 20”,, and 35”,, of the height of each subject. Each of these seven sets of data was tabulated for each subject under dlfrerent loading conditions. A *Table for Joint Forces’ (see Appendix) showed all the possible combinations of back. knee and ankle angles (60-80 combinations. dcpcnding on the subject) and corresponding values for all the forces involved. A new coefficient was added to help describe the global forces on the body:

JB + ZJK AJ = p-. 2 The program wasalso set to pick minimal and maximal values for each of these variables and print them separately with the corresponding combination ot’ angles and forces. All data collected were analyzed statistically, using the SPSS package (Version 8). Two major studies were performed: a comparison between back and knee forces for each subject and a comparison between males and females.

RESULTS AhD

DISCLSSIOS

A very high inverse correlation was found between knee and back forces for all subjects (Table I). The graph of knee joint reaction force as a function of lumbar spine joint reaction force displays an inverse quasi-linear relationship (Fig. 3). As the knee takes an increased amount of load. spinal load is decreased. Another strong correlation was found between the anthropometric measurements and the minimal and

284

C. M. GROSS and J. W.

F. J. BUJANI.

PLGH

Table I. Pearson Correlation Table between the forces on the back and the knee for subject no. 32: age = 28; sex = M; dominant = R; weight = 83 kg; height = 1.68 m; b = 0.54 m: a = 0.69 m: t = 0.38m; I = 0.5 m; c = 0.26 m Total joint reaction

Knee Back

Shear

Compression

Shear

0.866 p < 0.001 0.864 p
- 0.980 p
Compression Total joint reaction

maximal

values

anthropometry

of

JK

JB.

and

was summarized

AJ

- 0.987 p
p
(Table

2). The 903

in three major com-

I 3000 Back jomt reaction

25CO

ponents for this purpose: distance between the vertex

fwce

.

I 3500 IN

1

and the distal end of the spine, upper limb Length, and lower limb length. This correlation and corroborates

was accounted for

the work of Tichauer

(1968), Mital

PI al. (1980), and others in the prediction capability,

of lifting

Fig. 3. Graph of the knee joint reaction force as a function of the back reaction force (p < 0.001) for subject no. 32 (see Table I). when lifting position isallowed to vary. This pattern was consistent among al! subjects.

based on somatotype.

In order to compare

males and females. the mean

There

was also a significant

pression

dividing

to

Females appear to respond more in shear and males in

minimize factor.

total

the role of the individual

The

test (Table

ratios were compared 3). There

body

was a significant

ratios

being greater

difference

ratios

greater

for

the

be-

The coefficient AJ = (JB + 2JK)/2

back and knee for females.

an acceptable body. Under

representation the different

was considered

of average force on the

load conditions

above. this coefficient was computed

mentioned

for each subject

Table 2. Pearson Correlation Table for all subjects, between the anthropometric measurements and the minimal and maximal values for the joint reaction forces on the back and the knee, and the coefficient AJ = (JB + 2JK)/2 JB minimum

Forces anthropometry Vertex to coccyx Acromion to 3rd PIP joint Great trochanter to floor

JB

JK

JK

AJ

AJ

maximum

minimum

maximum

minimum

maximum

0.92

0.89

p < 0.005

p < 0.005

0.57

0.54

p < 0.005

0.65

0.71

p < 0.005

p < 0.005

0.47

p < 0.005

0.76

p < 0.005

0.83

p < 0.05

0.62

p < 0.005

0.53

p < 0.005

0.15

p < 0.005

0.72 p < 0.005

0.34 NS

p < 0.005 0.75

p < 0.005

Table 3. Student’s t-test table between male and female subjects for the ratios of the mean forces over the body weight (Ii’) Mean force/ Body weight

Sex

N

Mean

S.D.

SB,W

F M

17 16

SKJW

F M

17 16

CB/W

F M

CK/W

F M F M

17 16 17 16 17 16

F M F M

17 16 17 16

0.62 0.59 0.19 0.17 3.8 4.07 1.66 1.58 3.85 4.11 I .68 1.60 6.83 6.94

0.041 0.033 0.017 0.005 0.39 0.451 0.187 0.202 0.389 0.449 0.185 0.202 0.585 0.421

JB/W JKjW AJjW

males.

compression.

anthropomorphic

with a Student’s I-

tween males and females for normalized

shear forces, with

weight

with

in back com-

by

it by the subject’s

force

difference

was taken for each one of the forces and normalized

f

P

2.356

< 0.05

4.642

< 0.005

- 1.834 1.178 - 1.773 1.184 -0.623

< 0.05 NS < 0.05 NS NS

0.18 p < 0.005 0.78 p < 0.005 0.73 p < 0.005

285

Model for static hfting

and

the set of angles

responding

to optimal

These optimal weight

(knee.

back

(minimal)

angles were plotted

(Fig. 4) and as a function

and .&I

optimization

in either

was IO”,, of body flexion

(56

minimize

weight.

cor-

as a function

of load

of load height (Fig. 5).

The ankle angle did not significantly force

ankle)

was retained.

influence

case. When

optimize similar

33 “,,_ both

,-I./. At

angles

total force on the body varies significantly

as a function

of

load weight

characteristics,

and does not follow

) and the back. in extreme tlenion 159‘) to

bending Bejjani.

the anthropometry

and

an optimal

the knees to save the back’

(Miller.

1983).

(I 10

for the knee and 76 for the back). When height of the

This study is staticand

load was IO”,, of body

height

to shed light on the interrelatedness

moderately

and the back extremely

bent

(59‘) to optimize

(91’)

(Fig. 5). the knees were bent

AJ. At 20”,,. the back angle stayed the

the knee angle

decreased

significantly

to

quantitative:

of the knees and the spine during particular.

that for lifting

representing

its main purpose between

lifting.

minimize Forces’

We shovved. in

IO”,, of total body weight, one must bend

A-

) in order to

I 33 33

Body

weqht

I 50 I%)

Fig. 4. Graph of the optimal back knee and ankle angles as a function of the weight of the load (estimated in “,, body height). for a constant height of the load. Mean and standard deviation for all subjects. are considered for each joint angle.

I x7

IG i3oay

be produced

demands

Knee Bock

I

should

a ‘Table

as an aid

for Joint

in reducing

on the musculoskeletal

system.

A(.~nowl~d!/cmmrs-Mr. Keith losephson for his tine programming. Ms. Rirgitta Nilsson and \fr. Gillcs Demculenacrc for thctr excellent graphic work. Jnd to Ms. Toby Z. Licdcrman for her careful editing and t!p)ng

-‘\‘-IO

the average force. Ideally.

cumulative

is

function

a load of 0.2 m hetght and

both back (about 60 )and knees (about 90

0

of

1980;

.4J. At 50”,,.

the angles did not change much for either joint

:

the load

the princtple

PI./. At 33.33 l’l). the knees had to bend more

and the back less to maintain

same and

m a

This last phase of the study shows that the best way to minimize

average

the knee was in moderate

decreased

manner.

height

I 35 I%1

Fig. 5. Graph of the optimal back. knee and ankle angles as a function of the height of the load (estimated in ‘I0 body height). for a constant weight of the load. Mean and standard deviation for all subjects. are considered for each joint angle.

Bandi. W. (1972) Chondromalcia patellae and femoropatellarc arthrosc. H&. c&r. rlcrcl 1. 3. Barter. J. T. (1957) Estimation of Mass of Body Segments WADC Technical Reports: 57--X0. Wright- PJttrrson. OH. Bejjani. F. J.. Gross. C. M. and Pugh J. W. (1953) Stress relationship bctucrn the knee and the back. Proi &itt
286

F. J. BEJJAX C. M. GROSS and J. W. PUGH

APPE\DIS.

TABLE FOR JOINT FORCES

Subject: JR. Age = 28 years. 5 months. Sex = male. Dominant side = right. Height = 1.68 m. Wetght = 93 kg. Somatotype factor = 0.0625162. Distance between rl and third coccygeal vert’bra = 54 cm. Distance between rl and top of head = 26 cm. Distance between third coccygeal vertebra and top of head = SO cm. Distance between acromion and third PIP joint = 69 cm. Distance between greater trochanter and femoral condyle = 38 cm. Distance between heel and lateral remora1 condyle = 48 cm. Distance between greater trochanter and heel = 86 cm. Box height = 20cm.

x”

i.0

60

FE (N)

FE/W

59 5s 57 56 56

85 85 85 S5 90

69 71 73 75 65

3259 3233 3202 3167 3176

4.00 3.97 3.93 3.89 3.90

56 55 54 53 52

90 90 90 90 90

67 69 71 73 75

3152 3123 3090 3052 3010

52 52 51 50 49

95 95 95 95 95

65 67 69 71 73

48 48 47 46 45

95 100 100 100 loo

44 43 43 42 41

FQ (N)

Box weight = 10 kg

FQjM’

SE (N)

SK (N)

CB (N)

503 542 5SI 619 54s

0.61 0.66 0.71 0.76 0.67

561 556 551 545 547

365 371 377 382 368

3592 3573 3551 3525 3532

681 70s 733 755 720

3636 3616 3593 3567 3574

773 799 a24 819 sG9

3.87 3.S4 3.79 3.75 3.70

556 622 65S 693 728

0.72 0.76 0.8 O.S5 0.89

542 538 532 525 51s

374 379 3S-l 389 393

3514 3492 3439 3406

745 769 791 812 834

3555 3534 350s 3479 3445

a34 857 579 901 922

3026 2995 2959 2919 ‘873

3.72 3.6S 3.63 3.58 3.53

670 704 737 770 802

0.82 0.86 0.9 0.94 0.98

521 515 509 502 495

382 386 391 349 398

341s 3395 3367 3335 3299

809 830 849 868 887

345s 3434 3405 3373 3336

595 915 935 954 972

75 65 67 69 71

282 I 2845 2807 2764 2714

3.46 3.49 3.45 3.39 3.33

834 7SS 819 849 879

I .02 0.96 1.00 1.04 1.OS

486 490 483 476 467

400 393 396 399 401

3257 3276 3245 3210 3170

905 894 910 927 943

3293 3312 3281 3245 3204

990 976 993 109 103

100 loo 105 105 IO5

73 75 65 67 69

2659 2596 2628 25s I 252S

3.26 3.19 3.23 3. I7 3.10

909 939 905 933 961

1.1 I 1.15 1.1 I 1.14 I.18

458 447 452 444 435

403 405 400 402 404

3124 3072 3098 3059 3014

959 975 976 989 1003

3157 3104 3131 3091 3@46

IMO 1056 1055 106S iOS7

40 39 37 38 37

105 105 105 110 110

71 73 75 65 67

2468 2401 2325 2365 230S

3.03 2.95 2.85 2.90 2.83

988 1017 1046 1023 1049

1.21 1.25

425 413 400 407 397

405 406 406 405 406

2964 2906 2840 2875 2825

LO17 1031 1046 1059 1070

2994 2935 2868 2904 2553

1095 IIOS 1122 1134 1115

36 34 33 31

110 110 110 110

69 71 73 75

2242 2169 2085 1990

2.75 2.66 2.56 2.44

1075 1102 1130 1160

1.32 1.35 1.38

386 373 359 342

406 406 406 405

2768 2704 2630 2546

1082 1095 1109 II24

2795 2729 2654 2569

II56 1168 IlSI 1195

I.28 1.25 1.29

1.42

CK (NI

JB (N)

JK IN)