correction of axis misalignment in the analysis of knee rotations

Human Movement Science 22 (2003) 285–296

www.elsevier.com/locate/humov

Correction of axis misalignment in the analysisof knee rotations

F. Marin *, H. Mannel, L. Claes, L. D€uurselen

Institute of Orthopaedic Research and Biomechanics, University of Ulm, Helmholtzstr. 14,

89081 Ulm, Germany

Abstract

The Cardanic or Eulerian description is the most commonly used method for the descrip-

tion of in vivo knee rotation. It is based on the determination of external anatomical land-

marks used for the decomposition of the position of the tibia relative to the femur by three

rotations about three pre-defined axes. However, the in vivo localisation of external anato-

mical landmarks is known to be difficult and subjective. Even a small mislocalisation may lead

to dramatic consequences: the Cardanic description may become irreproducible and angle val-

ues may be overestimated. This error is well documented in the literature and known as the

‘‘cross-talk effect’’. Therefore this study proposes an additional calibration step of the classic

Cardanic description by a reorientation procedure of rotation axes. The procedure is based on

biomechanical constraints of knee kinematics as they appear during a knee squat exercise

using the finite helical axis (FHA) method and is independent of anatomical landmark. The

method was validated with the help of a special set-up modelling a perfect knee. Furthermore,

an inter-session reliability study was performed involving tests on two healthy subjects during

knee squat exercises. We found that the reorientation procedure was more reproducible than

the classic Cardanic description. We observed a maximum inter-session difference of 37.1� forthe adduction angle obtained with the classic Cardanic description. In contrast, the maximum

angle difference obtained with the reorientation procedure was less than 10�.� 2003 Elsevier B.V. All rights reserved.

PsycINFO classification: 2330

Keywords: Knee kinematics; Knee axis; Cross-talk effect; Finite helical axis; Reorientation

* Corresponding author. Tel.: +49-90-731-502-3492; fax: +49-0-731-502-3498.

E-mail address: [email protected] (F. Marin).

0167-9457/$ - see front matter � 2003 Elsevier B.V. All rights reserved.

doi:10.1016/S0167-9457(03)00036-8

mail to: [email protected]

286 F. Marin et al. / Human Movement Science 22 (2003) 285–296

1. Introduction

The most commonly used method to describe rotations of the knee joint is the

Eulerian or Cardanic description, which decomposes the position of the tibia with

regard to the femur (or vice versa) into three sequential rotations along three pre-defined axes named flexion/extension, abduction/adduction and internal/external

axial rotation (Grood & Suntay, 1983). These three pre-defined axes are also

known as anatomical axes and are defined by palpation of external anatomical

landmarks (Cappozzo, Catani, Croce, & Leardini, 1995). The flexion/extension

angle is identified as the rotation about the transepicondylar axis of the femur,

the abduction/adduction as the rotation about the floating axis, and the internal/

external axial rotation as the rotation about the long axis of the tibia. Thus, from

an anatomical and clinical point of view the attention focuses on a description ofthe rotations of the human knee joint. The Cardanic convention, although criti-

cised for its biomechanical conception of knee rotations (Woltring, 1994), is

nevertheless the one supported by the International Society of Biomechanics

(Wu & Cavanagh, 1995) and thus became the standard for the knee rotation de-

scription.

Criticism arose because the localisation of the anatomical points is difficult

(Blankevoort, Huiskes, & de Lange, 1988). Della Croce, Cappozzo, and Kerrigan

(1999) reported precision errors with six examiners for two subjects from 13 to25 mm for anatomical landmarks localisation. The consequences are misorientation

of the anatomical axes from 5� up to 13� (Blankevoort et al., 1988; Della Croce

et al., 1999; Piazza & Cavanagh, 2000; Ramakrishnan & Kadaba, 1991). But the

effects of such misorientation are dramatic as they lead to overestimation of the

abduction/adduction angle and internal/external rotation angle (Baker, Finney, &

Orr, 1999; Blankevoort et al., 1988; Ramakrishnan & Kadaba, 1991; Woltring,

1994). They can even scramble the interpretation of the screw home mechanism

(Hollister, Jatana, Singh, Sullivan, & Lupichuk, 1993; Piazza & Cavanagh, 2000).The misorientation of the axes is defined as the cross-talk effect (Chao, 1980; Ram-

sey & Wretenberg, 1999). It affects the kinematical analysis of motions in joints

that articulate principally with only one major component of motion. In the case

of the knee joint this means that if the axis of flexion/extension is not accurate

(Hollister et al., 1993) or not the same for more than one examiner, a flexion/ex-

tension motion will be cross-talked into the ad/abduction and the internal/external

rotations.

Knowing the clinical reality with different examiners and successive patient ex-aminations, this is a serious limitation for the use of the Cardanic representation,

Thus from a clinical point of view the use of this representation must be ques-

tioned because until now no effective solution has been proposed to counter this

error.

The aim of this study is to propose a procedure to obtain reliable knee axes with-

out anatomical landmarks by a reorientation of the anatomical coordinate system

based on biomechanical constraints.

F. Marin et al. / Human Movement Science 22 (2003) 285–296 287

2. Method

2.1. Reorientation procedure algorithm

For our method the reorientation was computed in three steps: first the compu-tation of the classic Cardanic representation with axes obtained from anatomical

landmarks, then the determination of the new flexion axis, and finally the reorienta-

tion.

2.1.1. Step 1: Cardanic representation with axes obtained from anatomical landmarks

As we wanted to find a method to counter the cross-talk effect, we first obtained a

Cardanic representation of the knee motions in order to have data to refer to. For

this in vivo knee movement investigation that we wanted to be non-invasive, we usedthe optoelectronic system Optotrak 3020 (Northern Digital, Toronto, Canada)

which permits markers comprising four LEDs to be tracked. One marker was at-

tached to the thigh permitting tracking of marker femur coordinate frame (mf). A

second marker on the shank was used to locate marker tibia coordinate frame (mt)

(Fig. 1).

Considering that for in vivo experiments in clinical environment, the hardest

constraint is time we consequently chose an ergonomic protocol. For this reason

Fig. 1. Marker localisation on the thigh (mf) and the shank (mt).


we used only three anatomical landmarks for defining the femur and the tibia

reference frame. Trochanter major, Epicondylus lateralis and medialis were used

to characterise the anatomical femur coordinate frame (af) and we defined the an-

atomical tibia reference co-ordinate (at) locally equal to the af at full knee exten-

sion (Marin, Allain, Diop, Maurel, & Lavaste, 1999). The orientation of the axesfollowed the recommendations of the ISB (Wu & Cavanagh, 1995), the Z-axis be-

ing the medio-lateral axis, the Y -axis the distal–proximal axis and the X -axis the

postero-anterior one. For the computing the hypothesis was as follows: Let Xfa,

Yfa and Zf

a be the axes of af . During the knee motion, af being supposed to be em-

bedded in the mf coordinate system, and at in mt. The relative position of at to af

was computed (Allard, Cappozzo, Lundberg, & Vaughan, 1998). The Cardanic

angle was deduced (Allard et al., 1998) and we obtained the angle ua for the

rotation about the Z-axis of af identified as flexion/extension, the angle wa forthe rotation about the X floating axis identified as ad/abduction, and the angle

ha for the rotation about the Y -axis of at identified as internal/external rotation.

2.1.2. Step 2: Determination of the new flexion axis

The reorientation procedure was performed using the method of the Finite Helical

Axes (FHA). Therefore with the relative position of at in af at each time, orientations

of the FHA of the displacement from the at in af were calculated. We used the pa-

rameters of Rodrigues (Bisshopp, 1969) extracted with the help of the Caley trans-formation (Mladenova, 1991). Then we determinated the mean orientation of the

FHAs between 40� and 80� while the subject was performing the squat movement

during its ascent phase and identified it as the mean flexion/extension axis (Mannel,

D€uurselen, Gillner, & Claes, 2000).

2.1.3. Step 3: Reorientation

Finally in step 3 we identified the precedent mean flexion/extension axis as the an-

atomical reoriented Z-axis of the femur (Zfr). For this purpose in a first step we de-

fined the anatomical initial reoriented reference coordinate of the femur (rf0) with

Xf0r ¼ ðYf

a � ZfrÞ=normðYf

a � ZfrÞ, Yf0

r ¼ Zfr � Xf0

r , and Zfr. Then rf0 was rotated with

an angle a along Zfr to define the intermediate reoriented reference coordinate of

the femur (rfa).

As in step 1, at full knee extension the intermediate reoriented reference coordi-

nate of the tibia (rta) has the same orientation as rfa. During the knee motion, rfa

is supposed to be embedded in the mf coordinate system, and rta in mt. The relative

position of rta to rfa is computed. The Cardanic angles obtained are angle ua (rota-tion along the Z-axis of f a), angle wa (rotation along the X floating axis), and ha (ro-tation along the Y -axis of ta).

The reoriented reference coordinates of the femur (rf) was then set equal to rfa

with the amplitude of wa minimal in the interval ua 2 ½0� 40�� and a 2 ½�30� 30��.Thus, ua ¼ ur is assimilated to the reoriented flexion/extension angle, wa ¼ wr to

the reoriented abduction/adduction angle, and ha ¼ hr to the reoriented internal/ex-

ternal rotation.


2.2. Experiments

In order to validate our results and to find out the inter-session variabilities of the

classic Cardanic angle in comparison to the reoriented one we performed the follow-

ing two experiments:

2.2.1. Validation

To validate our method by verifying the two reorientation criteria, we used a spe-

cial set-up which produced an accurate and well defined motion which was consid-

ered as our reference knee motion (Fig. 2).

For this set-up the mechanical linkage consisted of two segments connected by a

joint with two rotational degrees of freedom. The orthogonal rotation axes could be

exactly located in space each with two oppositely drilled chamferings. A special gearensured a coupling of axial rotation and flexion with a ratio of 15:40 during the first

40� of flexion and then only a pure hinge motion between 40� and 90� of flexion. TheCardanic angle obtained with the reference frame by palpation of drilled chamfer-

ings reflects the real motion of this mechanism. The reoriented Cardanic angles were

then computed and we calculated the maximum differences with the Cardanic angles

obtained.

2.2.2. Inter-session reliabilities

For the investigation on the inter-session reliability we had data of two healthy

subjects A and B (aged 28 and 31 years respectively). Subject A performed four

Fig. 2. Special set-up to validate the reorientation procedure.


sessions spaced over three days, and subject B three sessions spaced over six months.

Motions of the right knee during the knee squat exercise were recorded. The position

feet were in neutral position.

The Cardanic angles obtained on one side with the anatomical reference frame

with anatomical landmarks and those with the reoriented reference frame were com-pared. The maximal differences were computed between the four curves for the sub-

ject A and three curves for the subject B. The range of motion (ROM) of abduction/

adduction, internal/external rotation, reoriented abduction/adduction and reoriented

internal/external rotation was determined from 0� to 90� of flexion and reoriented

flexion respectively.

3. Results

3.1. Validation

Due to the design of the set-up, the positions of the axes of rotation were easy to

locate. Thus the Cardanic angle obtained using the landmark procedure described

exactly the motion of the mechanism (Fig. 3). Here we found a difference of less than

1� between the classic Cardanic angles and reoriented Cardanic angles.

Fig. 3. Cardanic angles (in degree) for the set-up. Graphs (a) and (c) are angle rotations deduced from

axes defined with localisation of axes of rotation. Graphs (b) and (d) are angle rotations deduced from

axes after the reorientation procedure.


3.2. Inter-session reliability

Concerning the two series for the inter-session reliability we found that for all re-

sults the flexion/extension angle and reoriented flexion/extension angle presented a

difference of only 1� to 2�. This suggests that the reorientation has the least effectson the flexion/extension quantity.

For subject A (Fig. 4), we observed a maximum difference of 37.1� for the abduc-tion/adduction, 17.6� for the internal/external rotation, but only a difference of 2.9�for the reoriented abduction/adduction and 9.5� for reoriented internal/external ro-

tation. Between the four sessions, the ROM of the abduction/adduction varied from

7.5� to 23.4� and the ROM of the internal/external rotation from 3.3� to 16.5�. On

the contrary, ROM of the reoriented Cardanic angle was more homogeneous with

the ROM of the reoriented abduction/adduction from 1.3� to 2.9� and ROMof the reoriented internal/external rotation from 2.1� to 3.1� (Table 1).

Fig. 4. Cardanic angles (in degree) for the subject A during knee squat exercise obtained from four ses-

sions. Graphs (a) and (c) are knee angle rotations deduced from axes defined themselves with anatomical

landmarks. Graphs (b) and (d) are knee angle rotations deduced from axes after the reorientation proce-

dure.

Table 1

Comparison between the Cardanic angles obtained with anatomical landmark and reoriented Cardanic

angles for the subject A and B

Subject A Subject B

Cardanic angle

with anatomical

landmarks

Reoriented

Cardanic

angle

Cardanic

angle with

anatomical

landmarks

Reoriented

Cardanic

angle

Maximal difference Ad/adduction 37.1� 2.9� 15.7� 3.3�Maximal difference internal/

external rotation

17.6� 9.5� 14� 4.3�

Maximum ROM Ad/adduction 23.4� 2.9� 9.5� 6.2�Minimum ROM Ad/adduction 7.5� 1.3� 2.3� 4.5�Maximum ROM internal/exter-

nal rotation

16.5� 3.1� 26.8� 2.2�

Minimum ROM internal/external

rotation

3.3� 2.1� 11.1� 1.6�


Moreover, the waveforms of the Cardanic angle curves obtained with the anato-

mical landmarks were radically different in between the four sessions. In contrast to

these results, the reoriented Cardanic angle curves showed the same characteristic for

all four sessions.

For subject B (Fig. 5), similar observations were made. We found that the max-

imal difference for the abduction/adduction angle is 15.7�, and 14� for the internal/

external rotation.

Differences for Cardanic angles obtained with the reoriented anatomical axis weresmaller with only 3.3� for the reoriented abduction/adduction angle and 4.3� for thereoriented internal/external rotation. Maximum and minimum ROM of abduction/

adduction was 9.5� and 2.3� respectively, and 26.8� and 11.1� for the ROM internal/

external rotation. The ROM of the reoriented Cardanic angles presented once again

less variation: between 4.5� and 6.2� for the reoriented abduction/adduction angle

and 1.6� and 2.2� for the reoriented internal/external rotation (Table 1).

4. Discussion

We found that the Cardanic angle obtained with anatomical landmarks was not

reproducible. Moreover, the value of ROM of the classical Cardanic angle obtained

using the landmark procedure gave data that were out of range from what can be

considered physiological values for healthy subjects (Woltring, 1994). These two ob-

servations are due to the misorientation of anatomical axes (cross-talk effect) which

may occur when there is more than one examiner or more than one examination.In contrast, the reorientation of the anatomical axes was more reproducible and

the values of the ROM of abduction/adduction or internal/external rotation never

exceeded 6.5� during the knee squat exercise. This result was the desired one

and was obtained by implementing of the reorientation procedure which relocates

Fig. 5. Cardanic angles for the subject B during a knee squat exercise obtained from three sessions.

Graphs (a) and (c) are knee angle rotations deduced from axes defined themselves with anatomical land-

marks. Graphs (b) and (d) are knee angle rotations deduced from axes after the reorientation procedure.


the position of the knee rotation axes. This method removes the errors introduced by

the mislocalisation of anatomical landmarks.

The idea of a reorientation of the anatomical reference coordinate has been pro-

posed by Woltring (1994), but it was only motivated by numerical considerations.Our reorientation method was motivated by biomechanical considerations resulting

from recent studies. We used our reorientation method during the ascent phase of

the squat exercise. We chose this motion as knee kinematics depend on the load con-

ditions (Asano, Akagi, Tanaka, Tamura, & Nakamura, 2001; Blankevoort, Huiskes,

& de Lange, 1990). In order to have a reproducible localisation of FHA, load con-

ditions must be reproducible. Therefore the knee squat is an excellent motion to

choose because of its ease and safety (Escamilla, 2001). It assures stability of the knee

(Jonsson & Karrholm, 1994) and reflects the active mechanisms of the knee joint.Moreover the ascent phase bounded the mechanical condition because the sub-

ject performed a motion against the gravity force, which can be considered as a con-

stant.


Secondly we defined the mean flexion axis the FHA between 40� and 80�. Recent

studies on the in vivo estimation of the contact point localisation between the femur

and the tibia during weight-bearing exercises (Asano et al., 2001; Hill et al., 2000)

showed that during 45� to 90� flexion the contact point on the tibia remains un-

changed. As the postural femoral condyles can be approximated with spheres ofthe same radius (Kurosawa, Walker, Abe, Garg, & Hunter, 1985), it can be assumed

that between 45� and 90� the in vivo loaded knee can be approximated as a hinge

joint. Consequently the motion is a pure flexion/extension. Moreover, an in vitro

study (Blankevoort et al., 1990; Wilson, Feikes, Zavatsky, & O�Connor, 2000) andthe in vivo study (Jonsson & Karrholm, 1994) using the FHA to characterise knee

kinematics have shown that FHAs are stable between 40� and 80�. In this range, ori-

entations of FHA are almost perpendicular to the sagittal plane. This was observed

in vivo for 13 subjects in the study of Jonsson and Karrholm (1994), in vitro for fourspecimens in the study of Blankevoort et al. (1990) and for 15 specimens in the pub-

lication of Wilson et al. (2000).

Finally we assumed that abduction/adduction quantity must be minimal during

the first 40� of flexion. Studies of Blankevoort et al. (1990) and Jonsson and Karrholm

(1994) have shown that between 0� and 40� of flexion the FHA tilts only in the frontal

plane and stays stable in the transverse plane of the femur. This indicates that the axis

of rotation has only components about the sagittal and the vertical axes of the femur

which can be interpreted as a flexion/extension and an internal/external rotation(Jonsson & Karrholm, 1994). This fact has indirectly been measured with the help

of the contact point investigation between the tibia and the femur obtained with

MRI (Hill et al., 2000) and with the biplanar image-matching technique (Asano et al.,

2001) under weightbearing conditions. Both studies showed that the contact point

in the lateral condyle moves backwards and in the medial condyle moves forwards

during the first 45� of flexion. The authors interpreted these motions as the combina-

tion of external rotation of the tibia and flexion. Indeed, if abduction/adduction was

present the contact point in the condyle could move laterally or medially as well.However, the reorientation method still presents two limitations due to practical

considerations. The first limitation concerns the problem of soft tissue movement

that we are always confronted with in the field of non invasive in vivo studies. We

must assume that the thigh marker and the shank marker provide an accurate image

of the motion of the tibia and the femur. We minimised the soft tissue error by put-

ting the thigh markers onto a large neoprene band which reduced the motion of the

soft tissues. The thigh markers are the most susceptible to affect the reliability of the

measurement. Moreover the subject was told to perform the knee squats withouthigh acceleration or deceleration.

The second limitation concerns the application of the reorientation concept on

pathological patients. The FHA stability and minimum abduction/adduction are cri-

teria based on analysis of healthy subjects only. Moreover, they are only useful to

describe a kinematical model of the squatting knee motion of a healthy subject.

To avoid a falsely adjusted application of the reorientation when dealing with patho-

logical subjects, we proposed to control two parameters: the mean deviation of

orientation of FHA between 40� and 80� and the existence of a minimum amplitude


of wa when a 2 ½�30� 30��. If the mean deviation of FHA is high, it indicates that the

motion between 40� and 80� of flexion is not pure flexion but coupled with other ro-

tation. If no minimum amplitude of wa is found, it suggests that the abduction/ad-

duction motion is not an artefact of the cross talk effect. In this case, we suggest

that specific criteria should be found to perform the reorientation on pathologicknees.

5. Conclusion

The reorientation of knee axes has been developed using a kinematical model of a

knee squat motion in order to correct axis misalignment (cross-talk effect) arising

with the classical landmarks method for obtaining the Cardanic angles. The reorien-tation criteria assume that the abduction/adduction is minimal during the first 40� offlexion, and that the flexion axis is identified between 40� and 80� of flexion during

the knee squat ascent phase. Thus the reorientation is independent of anatomical

landmarks. Inter-examiner and inter-session results confirm clearly that knee rota-

tion angles are reliable after reorientation.

Being independent of the examiner, the reorientation procedure offers the oppor-

tunity of objective knee kinematics follow-up measurements of patients with conser-

vative therapy or post-operative procedures with previous verification of two controlparameters. In the future specific reorientation criteria will be developed for specific

pathologies.

Acknowledgement

This work was supported by the German Research Council (Deutsche Fors-

chungsgemeinschaft, DFG DU254/2-2).

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correction of axis misalignment in the analysis of knee rotations

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