- Email: [email protected]
Anteroposterior tibial translation during simulated isometric quadriceps contractions
The Knee Vol.
2, No. 2, pp. 85-91, 1995 Elsevier Science Ltd Printed in Great Britain 0968-0160195 $10.00 + 0.00
0968-0160(95)00015-1
Anteroposterior tibia1 translation simulated isometric quadriceps contractions A B Zavatsky,
during
-
J J O’Connor
University of Oxford, Oxford, UK
Oxford
Orthopaedic
Engineering
Centre,
Nuffield
Orthopaedic
Centre,
Summary
The anteroposterior tibia1 translations caused by simulated isometric quadriceps forces of up to 750 N were measured in vitro for two extension-restraining load placements at five flexion angles. Both quadriceps force and tibia1 translation were flexion-angle and loadplacement dependent. Quadriceps force was linearly dependent on restraining force; tibia1 displacement was either very small (
words:
The
Knee
Knee Vol.
model,
2, No.
tibia1
2, 85-91,
translation,
quadriceps
contraction
1995
Introduction Isometric quadriceps exercises are often prescribed after knee ligament surgery to prevent muscle atrophy’. They are performed with the knee at a fixed flexion angle and with a restraining load applied to the tibia to stop the knee from extending. Although knee flexion angle remains constant, small translations and rotations of the tibia and femur can occur due to stretching and compressing of the soft tissues’a3.Anterior tibia1 translation is assumed to be an indication of force in the anterior cruciate ligament (ACL)24. Posterior tibia1 translation is taken to be a sign of force in the posterior cruciate ligament (PCL). Zavarsky and O’Connor’ and Zavatsky, Beard and O’Conn.or6 used a theoretical model of the knee in the sagittal plane to study tibia1 translations and cruciate ligament forces during isometric quadriceps exercises. An elementary analysis in which the cruciate ligaments were assumed to be inextensible showed which ligament, the ACL or PCL, was loaded at a given flexion angle and known line of action of the extensionrestraining load (see Figure 1.) For the ‘critical’ load
Accepted: May 1995 Correspondence and reprint requests to: Amy B Zavatsky University of Oxford, Oxford Orthopaedic Engineering Nuffield Orthopaedic Centre, Windmill Road, Headington, OX3 7LI9, UK
DPHIL,
Centre, Oxford
placements and ‘critical’ flexion angles (those represented by the curve in Figure l), no ligament forces are needed to stabilize the tibia in the sagittal plane. For most distal load placements at flexion angles up to about 90”, an ACL force is needed, and the tibia is expected to translate anteriorly. For proximal load placements and for flexion angles greater than 90”, a PCL force is needed, and the tibia is expected to translate posteriorly. These model predictions agree with in vitro2.’ and in vivo3,4 experimental results reported in the literature and could be used as guidelines for the design of physiotherapy techniques for use after cruciate ligament reconstruction6. Modelling the cruciate ligaments as continuous arrays of extensible fibres showed that as a result of increasing isometric quadriceps forces, anteroposterior (AP) tibiofemoral translations and ligament forces increased non-linearly and approached asymptotic (limiting) values which, for a given load placement, depended on flexion angle5. The asymptotic values of tibiofemoral translation and ligament force were approached most rapidly when the flexion angle was near its critical value, as defined by the curve in Figure 1. No tibiofemoral translation or ligament force was expected at the critical flexion angle. The possibility of asymptotic values of ligament force may explain why, at certain flexion angles, large forces can be developed by the quadriceps without ligament rupture.
The Knee Vol. 2, No. 2, 1995
86
.
J
E .
0
30
60
90
120
Flexion Angle (degrees)
Figure 1. plateau of of the tibia Points A-J which AP measured
Model calculations: distance below the tibia1 the restraining force required for equilibrium with no ligament forces versus flexion angle. indicate flexion angles and load placements at tibia1 translation and quadriceps force were in the present experimental study.
stand, and equipment to measure AP translation of the tibia relative to the femur. Figure 2 shows a diagram of the experimental set-up, excluding the apparatus used to measure tibia1 translation. Force in the quadriceps was simulated by tensioning a wire connected to the quadriceps tendon of the specimen. The tension force in the wire was measured using a proving (strain) ring attached in series with the wire and quadriceps tendon. Relative AP tibiofemoral translation was measured using two linearly variable differential transformers (LVDTs; RDP Electronics, Wolverhampton, UK) rigidly connected to the femur, as shown in Figure 3. The LVDTs had a linear range of +12.5 mm. Their resistance to movement was less than 1 N. The movable tips of the LVDTs rested against two small plates located near the medial and lateral tibia1 plateau. The plates were connected via two ball-and-socket joints to an aluminum bar which was attached to the posterior aspect of the tibia. Protocol
This paper reports the results of in vitro experiments in which the AP tibia1 translations accompanying simulated isometric quadriceps forces up to approximately 7.50N were measured. The aim of the experiments was to quantify the effects of flexion angle and restraining-load placement on tibia1 translation by testing the predictions of the inextensible ligament mode15~6sat several flexion angles and extensionrestraining load placements (labelled A to J in Figure 1) and by investigating the possibility of asymptotic values of AP tibia1 translations, as suggested by the extensible ligament model’,‘.
The flexion angle of the specimen was set using a manual goniometer at either o”, 30”, 60”, 90” or 120” by applying an appropriate tension to the quadriceps wire. At each flexion angle, the LVDTs and their holding equipment were set up such that the LVDTs were perpendicular to their associated aluminum plates on the tibia. For the selected extension-restraining load placement (either 0.15 m or 0.3 m below the tibia1 plateau), the free-standing frame and attached pulley (labelled D2 and P in Figure 2) were positioned so that the extension-restraining load (R) could be applied
Materials and methods 2
Specimens Seven human knee specimens (1 amputation, 6 postautopsy), each including 0.15 m of both the distal femur and the proximal tibia and fibula, were used. The soft tissues of each specimen were dissected down to the joint capsule. A loop of canvas webbing to which a tension force could be applied was sutured to the quadriceps tendon. Threaded steel rods were cemented into the medullary canals of the tibia and femur along the anatomical axes of the bone shafts so that the specimens could be fixed in the testing rig. A visual check of the collateral ligaments was made, and each joint was examined manually to detect any abnormal AP laxity. The integrity of the cruciate ligaments was confirmed after the experiment. Experimental apparatus The experimental apparatus consisted of a main test rig for holding the knee specimens, a means of simulating quadriceps force, a device for applying an extensionrestraining load to the tibia, a flexion-angle reference
s
Dl
/ i=
‘1
Figure 2. Side view of the experimental set-up, excluding the apparatus used to measure AP tibia1 translation: S, flexion-angle reference stand; A, cable for applying restraining force; P, pulley; R, restraining load; T, tibia; F, femur; D2, free-standing frame; 0, quadriceps wire; G, guide for quadriceps wire; W, handle for tensioning quadriceps wire; Dl, Cl, C2, B, main testing rig.
Zavatsky
and O%onnorr
AP tibia1 translation
87
Table 1. Directions of measured displacements (anterior A and posterior P) of the medial and lateral sides of the tibia for a restraining load placed 0.15 m below the tibia1 plateau. The number of specimens giving each result also is tabulated. The average displacement is the mean of the medial and lateral displacements. The model predictions are from Figure 1. The letters in parentheses beside the flexion angles refer to points A-E in Figure 1. Experimental results that agree with the model are in bold type. Flexion angle (degrees1 0 30 60 90 120
Figure 3. Apparatus translation.
used
to
measure
AP
tibia1
parallel to the tibia1 plateau at an angle of approximately 82.5” to the shaft of the tibia’. Output readings of the proving ring (quadriceps force) and LVDTs (AP tibia1 displacement) were taken for extension-restraining masses of 0 kg, 0.5 kg, 0.5 kg, and then in 1 kg steps up to either 6.5 kg or 8.5 kg equivalent to 64 N or 83 N. The largest loads were applied for the 0.15 m restraining load placement. Two-sample, two-tailed t-testsi were used to compare the average tibia1 displacements and the quadriceps forces at the 64 N restraining load for each flexion angle at the two different restraining load placements. The same tests also were used to compare selected average tibia1 displacements and quadriceps forces at different flexion angles. Comparisons were done for the 83 N restraining load (maximum) at the 0.15 m load placement and for the 64 N restraining load (maximum) at the 0.30 m load placement. Results
Tables I and 2 summarize the directions of the measured displacements (anterior or posterior). The directions of movement of the medial and lateral sides of the tibia, along with the directions of their average or mean displacements, are shown, Also tabulated are the number of specimens giving each result and the model predictions based on Figure 1. The average values of the measured quadriceps forces and tibia1 displacements are plotted versus the
(A) (B) (C) KN {E)
Medial displacement IA, IA, 2A, 4A, 3A,
6P 6P 5P 3P 4P
Lateral dispiacement
Average displacement
7A, 7A, 5A, IA, OA,
74 74 2A, OA, OA,
OP OP 2P 6P 7P
OP OP 5P 7P 7P
Model predj~tion A A L P
Table 2. Directions of measured displacements (anterior A and posterior P) of the medial and lateral sides of the tibia for a restraining load placed 0.30 m below the tibia1 plateau. The number of specimens giving each result also is tabulated. The average displacement is the mean of the medial and lateral displacements. The model predictions are from Figure 1. The letters in parentheses beside the flexion angles refer to points F-J in Figure 1. Experimental results that agree with the model are in bold type. Nexion angle (degrees]
0 (I=) (G)
30 60 90 120
U-U (I) (J)
Medial displacement 2A, 2A, 3A, 4A, 2A,
5P 5P 4P 3P 5P
Lateral displacement
Average displacement
7A, 7A, 6A, 2A, OA,
7A, 7A, 74 OA, OA,
OP OP IP 5P 7P
OP OP OP 7P 7P
Model Prediction A A A P P
extension-restraining load in Figures 4 and 5. Statistical comparisons of the quadriceps forces and the tibia1 displacements at the maximum restraining loads also are shown. The standard deviations of the measured quadriceps forces ranged from 3 to 84 N and averaged 24 N (10.8% of the measured values). The standard deviations of the measured AP tibia1 displacements ranged from 0.05 to 1.13 mm and averaged 0.44 mm. Intra-observer errors and inter-observer errors were quantified and were well within these ranges. At all five flexion angles, there were significant differences (P < 0.01) between the quadriceps forces at the 64 N restraining load for the 0.15 m and 0.30 m restraining load placements. In all cases, the quadriceps forces were larger for the 0.30 m load placement. In addition, there were significant differences between the tibia1 displacements at the 64 N restraining load for the 0.15 m and 0.30 m load placements at 0” (P < O.OS), 30” (P < O.Ol), and 60” flexion (P < 0.01) but not at 90” or 120” flexion.
88
The Knee Vol. 2, No. 2, 1995 800 700 600
t t s= 9 z 400 L %300 a 200 3
100 0 0
10
20
30
40
80
60
70
80
90 I
.
0
a
10
20
30 Restraining
40
50
60
70
Force (N)
“f p
40
50
60
70
80
90
f2 5 e E ?I 20 .z P 25 z
1
ljco.01
-1
-2 -3
-41 b
-4 1 Restraining
Force
(N)
b
Restraining
Force
(N)
Figure 4. Measured force and translation plotted versus restraining force for the five flexion angles tested at the 0.15 m restraining load placement: W, 0”; q , 30”; +, 60”; force: statistical 0, 90”; A, 120”. a, Quadriceps comparisons at the maximum restraining forces are shown. b, Tibia1 translation (anterior postive and posterior negative): statistical comparisons at the maximum restraining forces are shown.
Figure 5. Measured force and translation plotted versus restraining force for the five flexion angles tested at the 0.30 m restraining load placement: W, 0”; Cl, 30”; +, 60”; 0, 90”; A, 120”. a, Quadriceps force: statistical comparisons at the maximum restraining forces are shown. b, Tibia1 translation (anterior positive, posterior negative): statistical comparisons at the maximum restraining forces are shown.
Discussion
for the 0.30 m load placement. The linear relationship between quadriceps force and restraining force suggests that at the levels of load applied in this experiment, the length of the effective moment arm of the quadriceps is not significantly affected by soft-tissue deformations. The model with extensible ligaments5** also correctly predicts that the magnitude of tibia1 displacement is flexion-angle dependent, as shown in Figures 4b and 5b. In general, the smallest displacements occur for those loading situations closest to the curve in Figure 1. The largest anterior translations for both restraining load placements occur at 30” flexion. In this position with the knee unloaded, the ACL is relatively slack and poorly oriented to resist anteriorly-directed loads applied to the tibia I1 . Passive AP knee laxity also is greatest near 30” flexion12. The largest posterior tibia1 translations for both restraining load placements occur at 120” flexion, a knee position in which the PCL fibres are tight but are oriented nearly perpendicular to the
Comparisons with the sagittal-plane models The sagittal plane model with inextensible ligaments (Figure 1) correctly predicts the directions of the average tibia1 displacements (Tables 1 and 2). The experiment thus confirms that the direction of tibia1 displacement is a direct result of the geometry of the force system acting on the tibia (patellar tendon force, tibiofemoral contact force, restraining force, and if necessary, cruciate ligament force), as explained in detail by Zavatsky, Beard, and O’Connor6. The model with extensible ligaments’ correctly predicts the nearly linear variation of quadriceps force with increasing restraining force (Figures 4a and 5a). The extending moment of the quadriceps force balances the flexing effect of the restraining force. The restraining force has a larger moment arm when placed 0.30 m below the plateau than when placed 0.15 m below the plateau, and hence, the quadriceps forces are greatest
Zavatsky
tibia1 plateaui3, not a good position for resisting posteriorly-directed forces applied to the tibia. The non-linear dpendence of tibia1 displacement on restraining force (and, from Figures 4a and 5a, on quadriceps force) also is predicted correctly by the model with extensible ligaments5g8. This non-linear dependence is related to the non-linear relationship between AP force and AP tibia1 translation (e.g. reference 14), which is a combination of the non-linear relationships between tibia1 displacement and ligament fibre length, between fibre strain and fibre length, and between fibre strain and stressi’. It also reflects the recruitment of cruciate ligament fibres to resist AP forces applied to the tibia and the changing effective cross-sectional area and extensional stiffness of the ligament’l. It is difficult to judge whether or not all the measured tibia1 displacements shown in Figures 4b and 5b will approach asymptotic values, as predicted by the mode15.“. The very small tibia1 displacements for the 0.15 m load placement at 60” flexion, the non-linear increases in tibia1 displacement with increasing restraining force, and the variation of displacement with flexion angle suggest that asymptotic displacements may exist, but larger quadriceps forces must be applied and the experimental set-up altered before this can be confirmed. Comparisons with other experimental studies Hirokawa et aL2 used a radiographic method to measure AP tibia1 translation in cadaveric knee specimens subjected to isometric quadriceps forces up to 118 N. The restraining load, applied at a distance of over 0.4 m below the tibia1 plateau was not measured. There is little or no difference between the maximum posterior tibia1 translation measured by Hirokawa and that measured in the present experiment for a similar quadriceps load at 120” flexion; however, the magnitudes of the average anterior tibia1 translations measured in the present experiment at 30” flexion for the 0.3 m load placement are less than half those measured by Hirokawa. Part of this discrepancy is due to the difference in the locations of the restraining loads in the two studies, and part is due to the difference in the definition of the reference position for zero tibia1 displacement. Hirokawa defined his tibia1 displacement to be zero at zero quadriceps load. In the present study, zero tibia1 displacement is associated with the quadriceps force needed to balance the weight of the tibia and to hold the knee at a specified flexion position with no restraining force. Thus, the total measured tibia1 displacement in the present study does not include the anterior tibia1 translation caused by the initial application of quadriceps force, what Torzilli et aZ.‘5 have termed the ‘anterior neutral-position shift’. The quadriceps force needed in the present experiment to hold the knee at a fixed flexion angle with no restraining load ranged approximately from 15 to 60 N and depended on flexion angle. If the anterior tibia1
and O’Connor:
AP tibia/
translation
89
displacements resulting from such quadriceps forces (up to nearly 6 mm in Hirokawa’s experiment) were added to the displacements measured in the present experiment, the results of the two studies would be much closer. Jurist and Otis3 measured the tibiofemoral displacements associated with proximal, middle, and distal locations of the restraining force at flexion angles of 30”, 60” and 90” during isometric extension efforts performed in vivo at 33.9 Nm. In agreement with the present in vitro findings, they found that tibia1 displacements depended on both the location of the restraining force and the flexion angle, with anterior tibia1 displacements being associated with distal placement of the restraining load. The tibia1 displacements measured in the present experiment for the 0.3 m load placement are within the range of displacements reported by Jurist and Otis for the distal load placement at 60” and 90 flexion, but are a few millimeters larger at 30” flexion, even though Jurist and Otis were using a larger restraining load (calculated to be 96 N, if a representative tibia1 length16 is assumed). Using an arthrometer, Howell4 measured the tibia1 translation produced by a maximum isometric quadriceps contraction in normal knees at 15”, 30”, 45”, 60 and 75” flexion. The restraining force applied by a restraining pad placed 0.29 m distal from the joint line was not measured. Howell found that the tibia translated anteriorly at the four lower flexion angles and displaced a small amount posteriorly at 75” flexion. These results agree with the results of the present experiment for the 0.30 m load placement (Table 2 and Figure 4b). Beynnon et al.” used a Hall effect strain transducer in an arthroscopic technique to measure strain in the anteromedial band of the ACL during isometric quadriceps contractions in vivo. They found a significant increase from rest in ACL strain at 30” flexion, but no significant difference at 90” flexion. These results agree with those of the present experiment at 30” flexion, but not at 90” flexion. The 90” flexion angle, however, is very near to the critical flexion angle for the distal load placement in Beynnon’s experiment (assuming a representative tibia1 length16), where no tibia1 translation is expected (see Figure 1). Tibia1 rotation The fact that the measured displacements of the medial and lateral sides of the tibia are not equal in magnitude and not always in the same direction (Tables 1 and 2) indicates that the application of isometric quadriceps forces results not only in AP tibia1 translation, but also in internal or external tibia1 rotation. The directions of tibia1 rotation and the general locations of the axes of tibia1 rotation are summarized in Tables 3 and 4. The direction of tibia1 rotation reflects the alignment of the patellar tendon in the unloaded knee. In the neutral position of the joint, the patellar tendon runs inferiorly and laterally from femur to tibia”. Quadriceps contraction thus causesan internal rotation
90
The
Knee
Vol.
2, No.
Table
3. Direction of external E) and location rotation (medial M and for the 0.15 m restraining specimens giving each Flexion angle (degrees) 0 30 60 90 120
Table
4. Direction of external E) and location rotation (medial M and for the 0.30 m restraining specimens giving each Flexion angle (degrees) 0 30 60 90 120
2, 1995
tibia1 rotation (internal I and of the intersection of the axis of lateral L) with the tibia1 plateau load placement. The number of result is tabulated.
Rotation direction 71, 71, 51, 21, 21,
OE OE 2E 5E 5E
Axis location 7M, 7M, 4M, 5M, 5M,
Acknowledgements OL OL 3L 2L 2L
tibia1 rotation (internal I and of the intersection of the axis of lateral L) with the tibia1 plateau load placement. The number of result is tabulated.
Rotation direction 71, 71, 61, 21, 21,
OE OE IE 5E 5E
reconstruction if appropriate flexion angles and restraining-load placements are chosen (Figure 1). It must be realized, however, that for a fixed restraining load, quadriceps forces are smallest for proximal load placements; thus, the quadriceps may not derive maximum benefit at this placement.
This research was supported by the Wellcome Trust (London, UK) and the Arthritis and Rheumatism Council (UK). Orthopaedic surgeons David Murray, Christopher Dodd, Russell Miller, and Tibor Gunther helped with the acquisition and preparation of the knee specimens. Research physiotherapist David Beard made valuable editorial comments on the manuscript. References 1
Axis location 7M, 7M, 5M, 5M, 5M,
Seto JL, Orofino AS, Morrissey MC et al. Assessment of quadriceps/hamstringsstrength, knee ligament stability, functional and sport activity levels five years after anterior cruciate ligament reconstruction. Am J Sports Med 1988;
OL OL 2L 2L 2L
2
3
4
of the tibia, as found in the present study for the majority of specimens at O”, 30” and 60” flexion. At 90” and 120” flexion, however, the patellar tendon presumably runs somewhat medially resulting in external rotation of the tibia when quadriceps force is applied. This change in patellar tendon alignment during knee flexion may be partly caused by the ‘automatic’ internal rotation’s of the tibia on the femur which occurs with increasing flexion angle. As part of their in vitro study of the tibia1 translations associated with isometric quadriceps forces, Hirokawa et al.’ quantified tibia1 rotations. With a restraining load place over 0.4 m below the tibia1 plateau, they found that the tibia rotated internally from 0” to 90” flexion and externally thereafter up to 120” flexion. Except at 90” flexion, which is near the critical flexion angle for Hirokawa’s load placement (see the curve in Figure l), these results agree with those for the present 0.3 m load placement, shown in Table 4. Clinical relevance Isometric quadriceps contractions are one type of exercise used after knee ligament surgery to prevent quadriceps atrophy and to minimize patellofemoral complications. The present experimental results, in conjunction with the knee model6 (Figure 1) and data from other studie?z7 show that it is possible for patients with newly reconstructed cruciate ligaments to perform isometric quadriceps exercises and protect the
5
6
7
8
9
16: 17G80
Hirokawa S, SolomonowM, Lu Y et al. Anteriorposterior and rotational displacementof the tibia elicited by quadricepscontraction. Am J Sports Med 1992;20: 229-306 Jurist KA, Otis JC. Anteroposterior tibiofemoral displacementsduring isometric extension efforts. Am J Sports Med 1985; 13: 254-8 Howell SM: Anterior tibia1 translation during a maximum quadricepscontraction: Is it clinically significant? Am J Sports Med 1990;18: 573-8 Zavatsky AB, O’Connor JJ. Ligament forces at the knee during isometric quadricepscontractions. J Eng Med 1993; 207: 7-18 Zavatsky AB, Beard DJ, O’Connor JJ. Cruciate ligament loading during isometric musclecontractions: A theoretical basisfor rehabilitation. Am J Sports Med 1994; 22: 418-23 Mandt PR, Daniel DM, Biden E et al. Tibia1translation with quadricepsforce: An in vitro study of the effect of load placement, flexion angle, and ACL sectioning. Tram Orthop Res Sot 1987; 12: 243 Zavatsky AB. The functional architecture of human knee ligaments.DPhil thesis, University of Oxford, 1993 Yoshioka Y, Siu DW. ScudamoreRA, et al: Tibia1 anatomy and functional axes. J Orthop Res 1989; 7: 132-7
10 11 12
Larson RJ, Marx ML. An Introduction to Mathematical Statistics and its Applications. Englewood Cliffs, NJ: Prentice-Hall, 1986 Zavatsky AB, O’Connor JJ. A model of human knee ligamentsin the sagittalplane. Part 2: fibre recruitment under load. J Eng Med 1992; 206: 13545 Grood ES, Noyes FR. Diagnosisof knee ligament injuries: biomechanicalprecepts. In: Feagin JA, ed. The Crucial Ligamentous
13 14
Ligaments: Diagnosis and Treatment of Injuries about the Knee. New York:
Churchill Livingstone, 1988: 245-85 Zavatsky AB, O’Connor JJ. A model of humanknee ligamentsin the sagittal plane. Part 1: responseto passiveflexion. J Eng Med 1992; 206: 125-34 Piziali RL, SeeringWP, Nagel DA et al. The function of the primary ligamentsof the knee in anterior-posterior and medial-lateral motions.J Biomech 1980; 13: 777-84
Zavatsky
1.5
16
Torzilli PA, Deng X, Warren RF. The effect of jointcompressive load and quadriceps muscle force on knee motion in the intact and anterior cruciate ligamentsectioned knee. Am J Sports Med 1994; 22: 105-12 Dempster W. Space Requirements of the Seated Operator. Wright Patterson Air Force Base, Technical report WADC-TR-55-159, 1955
17 18
and
O%onnor:
AP
tibia1
translation
91
Beynnon B, Howe JG, Pope MH et al. The measurement of anterior cruciate ligament strain in vivo. Int Orthop 1992; 66: 1-12 Kapandji IA. The Physiology of the Joints, Vol. 2, The Lower Limb, 5th edn. Edinburgh: Churchill Livingstone, 1987: 64-147
2, No. 2, pp. 85-91, 1995 Elsevier Science Ltd Printed in Great Britain 0968-0160195 $10.00 + 0.00
0968-0160(95)00015-1
Anteroposterior tibia1 translation simulated isometric quadriceps contractions A B Zavatsky,
during
-
J J O’Connor
University of Oxford, Oxford, UK
Oxford
Orthopaedic
Engineering
Centre,
Nuffield
Orthopaedic
Centre,
Summary
The anteroposterior tibia1 translations caused by simulated isometric quadriceps forces of up to 750 N were measured in vitro for two extension-restraining load placements at five flexion angles. Both quadriceps force and tibia1 translation were flexion-angle and loadplacement dependent. Quadriceps force was linearly dependent on restraining force; tibia1 displacement was either very small (
words:
The
Knee
Knee Vol.
model,
2, No.
tibia1
2, 85-91,
translation,
quadriceps
contraction
1995
Introduction Isometric quadriceps exercises are often prescribed after knee ligament surgery to prevent muscle atrophy’. They are performed with the knee at a fixed flexion angle and with a restraining load applied to the tibia to stop the knee from extending. Although knee flexion angle remains constant, small translations and rotations of the tibia and femur can occur due to stretching and compressing of the soft tissues’a3.Anterior tibia1 translation is assumed to be an indication of force in the anterior cruciate ligament (ACL)24. Posterior tibia1 translation is taken to be a sign of force in the posterior cruciate ligament (PCL). Zavarsky and O’Connor’ and Zavatsky, Beard and O’Conn.or6 used a theoretical model of the knee in the sagittal plane to study tibia1 translations and cruciate ligament forces during isometric quadriceps exercises. An elementary analysis in which the cruciate ligaments were assumed to be inextensible showed which ligament, the ACL or PCL, was loaded at a given flexion angle and known line of action of the extensionrestraining load (see Figure 1.) For the ‘critical’ load
Accepted: May 1995 Correspondence and reprint requests to: Amy B Zavatsky University of Oxford, Oxford Orthopaedic Engineering Nuffield Orthopaedic Centre, Windmill Road, Headington, OX3 7LI9, UK
DPHIL,
Centre, Oxford
placements and ‘critical’ flexion angles (those represented by the curve in Figure l), no ligament forces are needed to stabilize the tibia in the sagittal plane. For most distal load placements at flexion angles up to about 90”, an ACL force is needed, and the tibia is expected to translate anteriorly. For proximal load placements and for flexion angles greater than 90”, a PCL force is needed, and the tibia is expected to translate posteriorly. These model predictions agree with in vitro2.’ and in vivo3,4 experimental results reported in the literature and could be used as guidelines for the design of physiotherapy techniques for use after cruciate ligament reconstruction6. Modelling the cruciate ligaments as continuous arrays of extensible fibres showed that as a result of increasing isometric quadriceps forces, anteroposterior (AP) tibiofemoral translations and ligament forces increased non-linearly and approached asymptotic (limiting) values which, for a given load placement, depended on flexion angle5. The asymptotic values of tibiofemoral translation and ligament force were approached most rapidly when the flexion angle was near its critical value, as defined by the curve in Figure 1. No tibiofemoral translation or ligament force was expected at the critical flexion angle. The possibility of asymptotic values of ligament force may explain why, at certain flexion angles, large forces can be developed by the quadriceps without ligament rupture.
The Knee Vol. 2, No. 2, 1995
86
.
J
E .
0
30
60
90
120
Flexion Angle (degrees)
Figure 1. plateau of of the tibia Points A-J which AP measured
Model calculations: distance below the tibia1 the restraining force required for equilibrium with no ligament forces versus flexion angle. indicate flexion angles and load placements at tibia1 translation and quadriceps force were in the present experimental study.
stand, and equipment to measure AP translation of the tibia relative to the femur. Figure 2 shows a diagram of the experimental set-up, excluding the apparatus used to measure tibia1 translation. Force in the quadriceps was simulated by tensioning a wire connected to the quadriceps tendon of the specimen. The tension force in the wire was measured using a proving (strain) ring attached in series with the wire and quadriceps tendon. Relative AP tibiofemoral translation was measured using two linearly variable differential transformers (LVDTs; RDP Electronics, Wolverhampton, UK) rigidly connected to the femur, as shown in Figure 3. The LVDTs had a linear range of +12.5 mm. Their resistance to movement was less than 1 N. The movable tips of the LVDTs rested against two small plates located near the medial and lateral tibia1 plateau. The plates were connected via two ball-and-socket joints to an aluminum bar which was attached to the posterior aspect of the tibia. Protocol
This paper reports the results of in vitro experiments in which the AP tibia1 translations accompanying simulated isometric quadriceps forces up to approximately 7.50N were measured. The aim of the experiments was to quantify the effects of flexion angle and restraining-load placement on tibia1 translation by testing the predictions of the inextensible ligament mode15~6sat several flexion angles and extensionrestraining load placements (labelled A to J in Figure 1) and by investigating the possibility of asymptotic values of AP tibia1 translations, as suggested by the extensible ligament model’,‘.
The flexion angle of the specimen was set using a manual goniometer at either o”, 30”, 60”, 90” or 120” by applying an appropriate tension to the quadriceps wire. At each flexion angle, the LVDTs and their holding equipment were set up such that the LVDTs were perpendicular to their associated aluminum plates on the tibia. For the selected extension-restraining load placement (either 0.15 m or 0.3 m below the tibia1 plateau), the free-standing frame and attached pulley (labelled D2 and P in Figure 2) were positioned so that the extension-restraining load (R) could be applied
Materials and methods 2
Specimens Seven human knee specimens (1 amputation, 6 postautopsy), each including 0.15 m of both the distal femur and the proximal tibia and fibula, were used. The soft tissues of each specimen were dissected down to the joint capsule. A loop of canvas webbing to which a tension force could be applied was sutured to the quadriceps tendon. Threaded steel rods were cemented into the medullary canals of the tibia and femur along the anatomical axes of the bone shafts so that the specimens could be fixed in the testing rig. A visual check of the collateral ligaments was made, and each joint was examined manually to detect any abnormal AP laxity. The integrity of the cruciate ligaments was confirmed after the experiment. Experimental apparatus The experimental apparatus consisted of a main test rig for holding the knee specimens, a means of simulating quadriceps force, a device for applying an extensionrestraining load to the tibia, a flexion-angle reference
s
Dl
/ i=
‘1
Figure 2. Side view of the experimental set-up, excluding the apparatus used to measure AP tibia1 translation: S, flexion-angle reference stand; A, cable for applying restraining force; P, pulley; R, restraining load; T, tibia; F, femur; D2, free-standing frame; 0, quadriceps wire; G, guide for quadriceps wire; W, handle for tensioning quadriceps wire; Dl, Cl, C2, B, main testing rig.
Zavatsky
and O%onnorr
AP tibia1 translation
87
Table 1. Directions of measured displacements (anterior A and posterior P) of the medial and lateral sides of the tibia for a restraining load placed 0.15 m below the tibia1 plateau. The number of specimens giving each result also is tabulated. The average displacement is the mean of the medial and lateral displacements. The model predictions are from Figure 1. The letters in parentheses beside the flexion angles refer to points A-E in Figure 1. Experimental results that agree with the model are in bold type. Flexion angle (degrees1 0 30 60 90 120
Figure 3. Apparatus translation.
used
to
measure
AP
tibia1
parallel to the tibia1 plateau at an angle of approximately 82.5” to the shaft of the tibia’. Output readings of the proving ring (quadriceps force) and LVDTs (AP tibia1 displacement) were taken for extension-restraining masses of 0 kg, 0.5 kg, 0.5 kg, and then in 1 kg steps up to either 6.5 kg or 8.5 kg equivalent to 64 N or 83 N. The largest loads were applied for the 0.15 m restraining load placement. Two-sample, two-tailed t-testsi were used to compare the average tibia1 displacements and the quadriceps forces at the 64 N restraining load for each flexion angle at the two different restraining load placements. The same tests also were used to compare selected average tibia1 displacements and quadriceps forces at different flexion angles. Comparisons were done for the 83 N restraining load (maximum) at the 0.15 m load placement and for the 64 N restraining load (maximum) at the 0.30 m load placement. Results
Tables I and 2 summarize the directions of the measured displacements (anterior or posterior). The directions of movement of the medial and lateral sides of the tibia, along with the directions of their average or mean displacements, are shown, Also tabulated are the number of specimens giving each result and the model predictions based on Figure 1. The average values of the measured quadriceps forces and tibia1 displacements are plotted versus the
(A) (B) (C) KN {E)
Medial displacement IA, IA, 2A, 4A, 3A,
6P 6P 5P 3P 4P
Lateral dispiacement
Average displacement
7A, 7A, 5A, IA, OA,
74 74 2A, OA, OA,
OP OP 2P 6P 7P
OP OP 5P 7P 7P
Model predj~tion A A L P
Table 2. Directions of measured displacements (anterior A and posterior P) of the medial and lateral sides of the tibia for a restraining load placed 0.30 m below the tibia1 plateau. The number of specimens giving each result also is tabulated. The average displacement is the mean of the medial and lateral displacements. The model predictions are from Figure 1. The letters in parentheses beside the flexion angles refer to points F-J in Figure 1. Experimental results that agree with the model are in bold type. Nexion angle (degrees]
0 (I=) (G)
30 60 90 120
U-U (I) (J)
Medial displacement 2A, 2A, 3A, 4A, 2A,
5P 5P 4P 3P 5P
Lateral displacement
Average displacement
7A, 7A, 6A, 2A, OA,
7A, 7A, 74 OA, OA,
OP OP IP 5P 7P
OP OP OP 7P 7P
Model Prediction A A A P P
extension-restraining load in Figures 4 and 5. Statistical comparisons of the quadriceps forces and the tibia1 displacements at the maximum restraining loads also are shown. The standard deviations of the measured quadriceps forces ranged from 3 to 84 N and averaged 24 N (10.8% of the measured values). The standard deviations of the measured AP tibia1 displacements ranged from 0.05 to 1.13 mm and averaged 0.44 mm. Intra-observer errors and inter-observer errors were quantified and were well within these ranges. At all five flexion angles, there were significant differences (P < 0.01) between the quadriceps forces at the 64 N restraining load for the 0.15 m and 0.30 m restraining load placements. In all cases, the quadriceps forces were larger for the 0.30 m load placement. In addition, there were significant differences between the tibia1 displacements at the 64 N restraining load for the 0.15 m and 0.30 m load placements at 0” (P < O.OS), 30” (P < O.Ol), and 60” flexion (P < 0.01) but not at 90” or 120” flexion.
88
The Knee Vol. 2, No. 2, 1995 800 700 600
t t s= 9 z 400 L %300 a 200 3
100 0 0
10
20
30
40
80
60
70
80
90 I
.
0
a
10
20
30 Restraining
40
50
60
70
Force (N)
“f p
40
50
60
70
80
90
f2 5 e E ?I 20 .z P 25 z
1
ljco.01
-1
-2 -3
-41 b
-4 1 Restraining
Force
(N)
b
Restraining
Force
(N)
Figure 4. Measured force and translation plotted versus restraining force for the five flexion angles tested at the 0.15 m restraining load placement: W, 0”; q , 30”; +, 60”; force: statistical 0, 90”; A, 120”. a, Quadriceps comparisons at the maximum restraining forces are shown. b, Tibia1 translation (anterior postive and posterior negative): statistical comparisons at the maximum restraining forces are shown.
Figure 5. Measured force and translation plotted versus restraining force for the five flexion angles tested at the 0.30 m restraining load placement: W, 0”; Cl, 30”; +, 60”; 0, 90”; A, 120”. a, Quadriceps force: statistical comparisons at the maximum restraining forces are shown. b, Tibia1 translation (anterior positive, posterior negative): statistical comparisons at the maximum restraining forces are shown.
Discussion
for the 0.30 m load placement. The linear relationship between quadriceps force and restraining force suggests that at the levels of load applied in this experiment, the length of the effective moment arm of the quadriceps is not significantly affected by soft-tissue deformations. The model with extensible ligaments5** also correctly predicts that the magnitude of tibia1 displacement is flexion-angle dependent, as shown in Figures 4b and 5b. In general, the smallest displacements occur for those loading situations closest to the curve in Figure 1. The largest anterior translations for both restraining load placements occur at 30” flexion. In this position with the knee unloaded, the ACL is relatively slack and poorly oriented to resist anteriorly-directed loads applied to the tibia I1 . Passive AP knee laxity also is greatest near 30” flexion12. The largest posterior tibia1 translations for both restraining load placements occur at 120” flexion, a knee position in which the PCL fibres are tight but are oriented nearly perpendicular to the
Comparisons with the sagittal-plane models The sagittal plane model with inextensible ligaments (Figure 1) correctly predicts the directions of the average tibia1 displacements (Tables 1 and 2). The experiment thus confirms that the direction of tibia1 displacement is a direct result of the geometry of the force system acting on the tibia (patellar tendon force, tibiofemoral contact force, restraining force, and if necessary, cruciate ligament force), as explained in detail by Zavatsky, Beard, and O’Connor6. The model with extensible ligaments’ correctly predicts the nearly linear variation of quadriceps force with increasing restraining force (Figures 4a and 5a). The extending moment of the quadriceps force balances the flexing effect of the restraining force. The restraining force has a larger moment arm when placed 0.30 m below the plateau than when placed 0.15 m below the plateau, and hence, the quadriceps forces are greatest
Zavatsky
tibia1 plateaui3, not a good position for resisting posteriorly-directed forces applied to the tibia. The non-linear dpendence of tibia1 displacement on restraining force (and, from Figures 4a and 5a, on quadriceps force) also is predicted correctly by the model with extensible ligaments5g8. This non-linear dependence is related to the non-linear relationship between AP force and AP tibia1 translation (e.g. reference 14), which is a combination of the non-linear relationships between tibia1 displacement and ligament fibre length, between fibre strain and fibre length, and between fibre strain and stressi’. It also reflects the recruitment of cruciate ligament fibres to resist AP forces applied to the tibia and the changing effective cross-sectional area and extensional stiffness of the ligament’l. It is difficult to judge whether or not all the measured tibia1 displacements shown in Figures 4b and 5b will approach asymptotic values, as predicted by the mode15.“. The very small tibia1 displacements for the 0.15 m load placement at 60” flexion, the non-linear increases in tibia1 displacement with increasing restraining force, and the variation of displacement with flexion angle suggest that asymptotic displacements may exist, but larger quadriceps forces must be applied and the experimental set-up altered before this can be confirmed. Comparisons with other experimental studies Hirokawa et aL2 used a radiographic method to measure AP tibia1 translation in cadaveric knee specimens subjected to isometric quadriceps forces up to 118 N. The restraining load, applied at a distance of over 0.4 m below the tibia1 plateau was not measured. There is little or no difference between the maximum posterior tibia1 translation measured by Hirokawa and that measured in the present experiment for a similar quadriceps load at 120” flexion; however, the magnitudes of the average anterior tibia1 translations measured in the present experiment at 30” flexion for the 0.3 m load placement are less than half those measured by Hirokawa. Part of this discrepancy is due to the difference in the locations of the restraining loads in the two studies, and part is due to the difference in the definition of the reference position for zero tibia1 displacement. Hirokawa defined his tibia1 displacement to be zero at zero quadriceps load. In the present study, zero tibia1 displacement is associated with the quadriceps force needed to balance the weight of the tibia and to hold the knee at a specified flexion position with no restraining force. Thus, the total measured tibia1 displacement in the present study does not include the anterior tibia1 translation caused by the initial application of quadriceps force, what Torzilli et aZ.‘5 have termed the ‘anterior neutral-position shift’. The quadriceps force needed in the present experiment to hold the knee at a fixed flexion angle with no restraining load ranged approximately from 15 to 60 N and depended on flexion angle. If the anterior tibia1
and O’Connor:
AP tibia/
translation
89
displacements resulting from such quadriceps forces (up to nearly 6 mm in Hirokawa’s experiment) were added to the displacements measured in the present experiment, the results of the two studies would be much closer. Jurist and Otis3 measured the tibiofemoral displacements associated with proximal, middle, and distal locations of the restraining force at flexion angles of 30”, 60” and 90” during isometric extension efforts performed in vivo at 33.9 Nm. In agreement with the present in vitro findings, they found that tibia1 displacements depended on both the location of the restraining force and the flexion angle, with anterior tibia1 displacements being associated with distal placement of the restraining load. The tibia1 displacements measured in the present experiment for the 0.3 m load placement are within the range of displacements reported by Jurist and Otis for the distal load placement at 60” and 90 flexion, but are a few millimeters larger at 30” flexion, even though Jurist and Otis were using a larger restraining load (calculated to be 96 N, if a representative tibia1 length16 is assumed). Using an arthrometer, Howell4 measured the tibia1 translation produced by a maximum isometric quadriceps contraction in normal knees at 15”, 30”, 45”, 60 and 75” flexion. The restraining force applied by a restraining pad placed 0.29 m distal from the joint line was not measured. Howell found that the tibia translated anteriorly at the four lower flexion angles and displaced a small amount posteriorly at 75” flexion. These results agree with the results of the present experiment for the 0.30 m load placement (Table 2 and Figure 4b). Beynnon et al.” used a Hall effect strain transducer in an arthroscopic technique to measure strain in the anteromedial band of the ACL during isometric quadriceps contractions in vivo. They found a significant increase from rest in ACL strain at 30” flexion, but no significant difference at 90” flexion. These results agree with those of the present experiment at 30” flexion, but not at 90” flexion. The 90” flexion angle, however, is very near to the critical flexion angle for the distal load placement in Beynnon’s experiment (assuming a representative tibia1 length16), where no tibia1 translation is expected (see Figure 1). Tibia1 rotation The fact that the measured displacements of the medial and lateral sides of the tibia are not equal in magnitude and not always in the same direction (Tables 1 and 2) indicates that the application of isometric quadriceps forces results not only in AP tibia1 translation, but also in internal or external tibia1 rotation. The directions of tibia1 rotation and the general locations of the axes of tibia1 rotation are summarized in Tables 3 and 4. The direction of tibia1 rotation reflects the alignment of the patellar tendon in the unloaded knee. In the neutral position of the joint, the patellar tendon runs inferiorly and laterally from femur to tibia”. Quadriceps contraction thus causesan internal rotation
90
The
Knee
Vol.
2, No.
Table
3. Direction of external E) and location rotation (medial M and for the 0.15 m restraining specimens giving each Flexion angle (degrees) 0 30 60 90 120
Table
4. Direction of external E) and location rotation (medial M and for the 0.30 m restraining specimens giving each Flexion angle (degrees) 0 30 60 90 120
2, 1995
tibia1 rotation (internal I and of the intersection of the axis of lateral L) with the tibia1 plateau load placement. The number of result is tabulated.
Rotation direction 71, 71, 51, 21, 21,
OE OE 2E 5E 5E
Axis location 7M, 7M, 4M, 5M, 5M,
Acknowledgements OL OL 3L 2L 2L
tibia1 rotation (internal I and of the intersection of the axis of lateral L) with the tibia1 plateau load placement. The number of result is tabulated.
Rotation direction 71, 71, 61, 21, 21,
OE OE IE 5E 5E
reconstruction if appropriate flexion angles and restraining-load placements are chosen (Figure 1). It must be realized, however, that for a fixed restraining load, quadriceps forces are smallest for proximal load placements; thus, the quadriceps may not derive maximum benefit at this placement.
This research was supported by the Wellcome Trust (London, UK) and the Arthritis and Rheumatism Council (UK). Orthopaedic surgeons David Murray, Christopher Dodd, Russell Miller, and Tibor Gunther helped with the acquisition and preparation of the knee specimens. Research physiotherapist David Beard made valuable editorial comments on the manuscript. References 1
Axis location 7M, 7M, 5M, 5M, 5M,
Seto JL, Orofino AS, Morrissey MC et al. Assessment of quadriceps/hamstringsstrength, knee ligament stability, functional and sport activity levels five years after anterior cruciate ligament reconstruction. Am J Sports Med 1988;
OL OL 2L 2L 2L
2
3
4
of the tibia, as found in the present study for the majority of specimens at O”, 30” and 60” flexion. At 90” and 120” flexion, however, the patellar tendon presumably runs somewhat medially resulting in external rotation of the tibia when quadriceps force is applied. This change in patellar tendon alignment during knee flexion may be partly caused by the ‘automatic’ internal rotation’s of the tibia on the femur which occurs with increasing flexion angle. As part of their in vitro study of the tibia1 translations associated with isometric quadriceps forces, Hirokawa et al.’ quantified tibia1 rotations. With a restraining load place over 0.4 m below the tibia1 plateau, they found that the tibia rotated internally from 0” to 90” flexion and externally thereafter up to 120” flexion. Except at 90” flexion, which is near the critical flexion angle for Hirokawa’s load placement (see the curve in Figure l), these results agree with those for the present 0.3 m load placement, shown in Table 4. Clinical relevance Isometric quadriceps contractions are one type of exercise used after knee ligament surgery to prevent quadriceps atrophy and to minimize patellofemoral complications. The present experimental results, in conjunction with the knee model6 (Figure 1) and data from other studie?z7 show that it is possible for patients with newly reconstructed cruciate ligaments to perform isometric quadriceps exercises and protect the
5
6
7
8
9
16: 17G80
Hirokawa S, SolomonowM, Lu Y et al. Anteriorposterior and rotational displacementof the tibia elicited by quadricepscontraction. Am J Sports Med 1992;20: 229-306 Jurist KA, Otis JC. Anteroposterior tibiofemoral displacementsduring isometric extension efforts. Am J Sports Med 1985; 13: 254-8 Howell SM: Anterior tibia1 translation during a maximum quadricepscontraction: Is it clinically significant? Am J Sports Med 1990;18: 573-8 Zavatsky AB, O’Connor JJ. Ligament forces at the knee during isometric quadricepscontractions. J Eng Med 1993; 207: 7-18 Zavatsky AB, Beard DJ, O’Connor JJ. Cruciate ligament loading during isometric musclecontractions: A theoretical basisfor rehabilitation. Am J Sports Med 1994; 22: 418-23 Mandt PR, Daniel DM, Biden E et al. Tibia1translation with quadricepsforce: An in vitro study of the effect of load placement, flexion angle, and ACL sectioning. Tram Orthop Res Sot 1987; 12: 243 Zavatsky AB. The functional architecture of human knee ligaments.DPhil thesis, University of Oxford, 1993 Yoshioka Y, Siu DW. ScudamoreRA, et al: Tibia1 anatomy and functional axes. J Orthop Res 1989; 7: 132-7
10 11 12
Larson RJ, Marx ML. An Introduction to Mathematical Statistics and its Applications. Englewood Cliffs, NJ: Prentice-Hall, 1986 Zavatsky AB, O’Connor JJ. A model of human knee ligamentsin the sagittalplane. Part 2: fibre recruitment under load. J Eng Med 1992; 206: 13545 Grood ES, Noyes FR. Diagnosisof knee ligament injuries: biomechanicalprecepts. In: Feagin JA, ed. The Crucial Ligamentous
13 14
Ligaments: Diagnosis and Treatment of Injuries about the Knee. New York:
Churchill Livingstone, 1988: 245-85 Zavatsky AB, O’Connor JJ. A model of humanknee ligamentsin the sagittal plane. Part 1: responseto passiveflexion. J Eng Med 1992; 206: 125-34 Piziali RL, SeeringWP, Nagel DA et al. The function of the primary ligamentsof the knee in anterior-posterior and medial-lateral motions.J Biomech 1980; 13: 777-84
Zavatsky
1.5
16
Torzilli PA, Deng X, Warren RF. The effect of jointcompressive load and quadriceps muscle force on knee motion in the intact and anterior cruciate ligamentsectioned knee. Am J Sports Med 1994; 22: 105-12 Dempster W. Space Requirements of the Seated Operator. Wright Patterson Air Force Base, Technical report WADC-TR-55-159, 1955
17 18
and
O%onnor:
AP
tibia1
translation
91
Beynnon B, Howe JG, Pope MH et al. The measurement of anterior cruciate ligament strain in vivo. Int Orthop 1992; 66: 1-12 Kapandji IA. The Physiology of the Joints, Vol. 2, The Lower Limb, 5th edn. Edinburgh: Churchill Livingstone, 1987: 64-147