Knee Surg Sports Traumatol Arthrosc DOI 10.1007/s00167-014-3056-8


Quantitative pivot shift assessment using combined inertial and magnetic sensing David R. Labbe´ • Di Li • Guy Grimard • Jacques A. de Guise • Nicola Hagemeister

Received: 21 October 2013 / Accepted: 2 May 2014 Ó Springer-Verlag Berlin Heidelberg 2014

Abstract Purpose The purpose of the study was to demonstrate the feasibility of a new measurement system using microelectromechanical systems (MEMS)-based sensors for quantifying the pivot shift phenomenon. Methods The pivot shift test was performed on 13 consecutive anterior cruciate ligament-deficient subjects by an experienced examiner while femur and tibia kinematics were recorded using two inertial sensors each composed of an accelerometer, gyroscope and magnetometer. The gravitational component of the acquired data was removed using a novel method for estimating sensor orientations. Correlation between the clinical pivot shift grade and acceleration and velocity parameters was measured using Spearman’s rank correlation coefficients. Results The pivot shift phenomenon was best characterized as a drop in femoral acceleration observed at the time of reduction. The correlation between the femoral acceleration drop and the clinical grade was shown to be very strong (r = 0.84, p \ 0.0001).

Electronic supplementary material The online version of this article (doi:10.1007/s00167-014-3056-8) contains supplementary material, which is available to authorized users. D. R. Labbe´ (&)  D. Li  J. A. de Guise  N. Hagemeister Laboratoire de recherche en imagerie et orthope´die (LIO), Centre de recherche du Centre hospitalier de l’Universite´ de Montre´al (CHUM), Tour Viger, 900, rue Saint-Denis, Local R11.326, Montreal, QC H2X 0A9, Canada e-mail: [email protected] D. R. Labbe´  D. Li  J. A. de Guise  N. Hagemeister E´cole de technologie supe´rieure, Montreal, Canada G. Grimard Centre hospitalier universitaire Ste-Justine, Montreal, Canada

Conclusions The present study demonstrates the feasibility of quantifying the pivot shift using MEMS-based sensors and removing the gravitational component of acceleration using an estimation of sensor orientation for improved correlation to the clinical grade. Keywords Pivot shift  Anterior cruciate ligament  Objective measurement  Knee joint kinematics  Inertial sensors  Acceleration

Introduction The pivot shift test, which consists of flexing the knee under combined stresses, is used to reproduce the symptoms of dynamic instability following rupture of the anterior cruciate ligament. The manoeuver causes an anterior subluxation of the tibia followed by a sudden reduction [10]. The pivot shift test is more specific than other clinical tests in diagnosing anterior cruciate ligament (ACL) ruptures and its grade has been shown to correlate with subjective criteria of knee joint function [17, 24]. Moreover, the pivot shift test is widely used to evaluate the lingering postoperative dynamic instability of the knee. Despite its popularity, execution of the pivot shift test remains highly variable and its interpretation, highly subjective [4, 5, 16, 29]. Several studies have demonstrated that different clinicians attribute different pivot shift grades to a same knee, highlighting the need for and objective measure of the pivot shift phenomenon [20, 27]. A number of groups have attempted to quantify the pivot shift and develop a more objective way to grade it [2, 6, 13–15, 19–23, 28, 33, 34]. Most of these used electromagnetic devices to track the movement of the tibia and femur during the pivot shift test. Using this technology, a


Knee Surg Sports Traumatol Arthrosc

correlation was shown between the subjective pivot shift grade and different kinematic parameters. The parameter most reported to correlate strongly with the grade is linear acceleration [14, 19–21]. The use of electromagnetic sensors has a number of drawbacks such as their high cost, their low time resolution (usually 60 Hz) and the need for an anatomical calibration procedure for expressing the recordings into clinically relevant rotations and translations. In light of the demonstrated importance of acceleration in establishing the pivot shift grade and given the high cost and time-heavy protocol of using magnetic sensors, recent studies have attempted to quantify the pivot shift using only a triaxial accelerometer or a pair of accelerometers [1, 3, 25]. Such studies found significant differences between ACLdeficient and ACL-intact knees [18] and good correlation with rigidly fixed optical and electromagnetic sensors [3, 25] proving the feasibility of using accelerometers to quantify dynamic knee instability. However, the only study to find a correlation between these measures and the clinical grade was conducted on a single cadaveric knee [1]. The objectives of this study were as follows: (1) to develop a method to record the pivot shift using low-cost micro-electromechanical systems (MEMS) sensors that integrate an accelerometer, gyroscope and magnetometer and allow for the removal of the gravitational component of acceleration and therefore, a more accurate measure of acceleration of the bones, and (2) to identify a kinematic parameter which could be used to grade the pivot shift based on these recordings. A novel method is presented for improving accuracy of the measurements by periodically resetting the drift errors that MEMS sensors are prone to. It was hypothesized that the resulting pivot shift quantification has a very strong correlation with the subjective clinical grades.

Materials and methods To achieve 90 % statistical power with a a of 0.05 in demonstrating a very strong (r C 0.80) correlation, power analysis revealed that a minimum of 10 subjects would be required. A total of 13 consecutive ACL-deficient patients were recruited to participate in this study. Mean age of the patients was 15.5 ± 1.5 years old; 8 were females and 3 were males. All subjects were on a waiting list for reconstructive surgery of a chronic ACL injury (7 right knees and 6 left knees) that was confirmed by a magnetic resonance imaging (MRI) examination. Five subjects presented with concomitant meniscal tears and none of the subjects had other knee ligament injuries. None of the subjects had any self-reported pain or history of injury in the contralateral knee.


Fig. 1 A surgeon performing an instrumented pivot shift test with the developed MEMS measurement tool

Experimental protocol A single, experienced orthopaedic surgeon performed and graded the pivot shift test on each subject’s ACL-deficient and contralateral knees in a clinical setting, i.e. without anaesthesia, yielding a total of 26 pivot shifts (13 subjects 9 2 knees). He performed the pivot shift test as originally described by Galway et al. [10], and attributed a clinical grade following the IKDC-2000 scale. The kinematics of the tibia and femur during the pivot shift test were recorded individually at 150 Hz using two low-cost MEMS inertial sensor units (nIMUTM, 5 9 2 9 1 cm3, MEMSenseTM). Each device comprises one triaxial gyroscope, one triaxial accelerometer and one triaxial magnetometer. The sensitivity axes of the gyro, the accelerometer and the magnetometer are aligned to a sensor coordinate frame during the manufacturing process. The stated accuracy of the devices is ±0.03 g in linear acceleration and ±1° in angular velocity. The two devices were attached to the tibia and femur, respectively, using an attachment system designed to ensure the sensors follow the tibia and femur movement as precisely as possible. A single examiner, different from the evaluating surgeon, installed the attachment system on the subjects’ limbs. The two MEMS devices were connected to a laptop computer through USB ports. Prior to the examination, the MEMS devices were initialized with the initial values of the kinematic parameters such as angular orientation and velocity of the MEMS devices in the reference coordinate system, which takes approximately 10 s. The examination was recorded with a video camera that was synchronized with the MEMS devices through the aforementioned laptop computer. Due to initial guarding by some subjects, the knee was sometimes flexed a few times before the surgeon

Knee Surg Sports Traumatol Arthrosc

Fig. 2 The global coordinate frame and the kinematics of the tibia and the femur

felt that an unguarded pivot shift was properly induce, at which time he gave a vocal indication to that effect. The video and audio recording was later used to isolate the flexion where the pivot shift occurred, for data analysis. The surgeon was blinded to the recorded kinematics. (Fig. 1). Data analysis Tibia and femur kinematics were analysed individually for the knee flexion where the surgeon indicated a pivot shift was correctly induced. They are presented in the geographic coordinate reference, i.e. the global coordinate frame having its axes following the magnetic north, east and local vertical down. They are transformed from the inertial coordinate frames in which they are acquired to the global coordinate frame using the algorithm described by Farrell [9]. The total acceleration, total velocity, and the rotation angles of the tibia and the femur are therefore in the global frame, as shown in Fig. 2. The use of such a geographic coordinate frame has the advantage of simplifying the experimental protocol as it eliminates the need for identification of bony landmarks and functional calibration, which are used to build an anatomical coordinate system [11, 12]. Estimation of sensor orientation The orientation estimation was developed using an extended Kalman filter (EKF). The orientation of the MEMS device can be analytically represented by a 3 9 3 direction cosine matrix CG S , which is highly nonlinear. Kalman filtering is only able to estimate the values that are linear. Compared with the orientation, the errors of the orientation change slowly over time and first approximation (i.e. linearity) can be safely applied to it. Therefore, it is the orientation errors that are estimated in the developed Kalman filtering, and not the orientation itself. A state vector is defined to contain as its elements the orientation errors and inertial sensor errors, given as: x ¼ ½ qe



dm  T


where qe contains orientation errors, bx contains gyroscope sensor errors, ba contains accelerometer errors and dm contains the three magnetic disturbances, which can be

caused by the vicinity of the ferromagnetic materials, for example. The orientation errors are parameterized using quaternions to avoid calculation singularities while keeping the computing load low for real-time or embedded solutions. Detailed development of orientation errors is given by Creamer [7]. The acceleration errors ba and the magnetic disturbances dm can be described by a 1st order Markov random process [31]. Low-cost gyroscopes have significant stochastic errors that Kalman filters can effectively estimate and compensate for. In this study, the gyro errors bx are approximated as a random walk process due to the short duration of the pivot shift: b_ x ¼ nx


where nx is Gaussian white noise, which values are based on the specific type of the sensor used. The estimated orientation errors are transformed into an equivalent form that can be directly applied to the orientation estimation, i.e. DCG S (qe). CSG ðþÞ ¼ CSG ðÞDCSG ðqe Þ


where, (?) and (-) represent the orientation parameter after and before the correction. Assessment of orientation estimation The accuracy of the aforementioned orientation estimation was assessed by comparing it to a 6-camera 3D optical motion capturing system (Vicon 460, Oxford MetricsTM). Such a system is often used as gold standard in motion analysis and it has been shown to be both accurate (63 ± 5 lm) and precise (15 lm) [32]. To compare the systems, a rigid body was mounted with both the MEMS sensor unit and a set of four 10 mm-diameter reflective markers. Following calibration of the acquisition volume, a 300 s recording was taken with both systems while the rigid body was manually rotated about all three rotation axes. Orientations were compared in Euler angles, i.e. heading (W), pitch (H) and roll (/) to facilitate the interpretation of results. Acceleration and velocity Once the orientation CG S is obtained, it can be used to remove the gravitational component of the measured acceleration with Eq. 4: v_ ¼ CSG  a þ g  ðxE


þ 2xI



where g is gravity, which can be approximated by ½ 0 0 9:81 T , ðxE G þ 2xI E Þ  v is the Coriolis acceleration generated by the sensor movement and the Earth’s self-rotation, which is negligible compared with the amount of errors of a low-cost accelerometer, i.e.


Knee Surg Sports Traumatol Arthrosc

ðxE G þ 2xI E Þ  v ¼ 0 and a is the output of the accelerometer. Velocity is then obtained by integrating the acceleration v_ over the time interval of the pivot shifts. The study was approved by the ethics committee of Sainte-Justine University Hospital. All subjects gave their informed consent prior to their inclusion in the study.

the orientation errors are reduced gradually and average errors at the end of estimation are smaller than those at the beginning. This is due to the iterative process that is Kalman filtering. After sufficient iterations, the orientation estimation converges to the actual value, within the system’s noise limits.

Statistical analysis

Clinical evaluation

Correlations of the tibial and femoral acceleration and velocity values to the clinical grades were calculated using the Spearman’s rank correlation coefficients [30]. Correlation coefficients were interpreted as weak (r \ 0.4), moderate (0.4 B r \ 0.6), strong (0.6 B r \ 0.8) and very strong (0.8 B r). The values for the individual clinical grades were compared to each other using one-way analysis of variance (ANOVA). Statistical significance level set to p \ 0.05.

All ACL-deficient knees showed a positive pivot shift during the clinical evaluation (5 grade 1; 7 grade 2, 3 grade 3) and all ACL-intact knees were evaluated as grade 0. In this study, in accordance with previous ones, the angular rotation of the tibia and the femur were found to be highly variable between individuals presenting a pivot shift and in some cases, no angular rotation was present at all. Therefore, linear acceleration and velocity will be the focus of subsequent analysis. Acceleration

Results Assessment of orientation estimation Over a period of 300 ms, the mean heading error of the inertial sensor was 2.57 ± 1.08° compared with the optical-camera reference (Fig. 3). The estimation converged within a few seconds. The pitch and roll angles showed average errors of 0.78 ± 0.05° and 0.72 ± 0.06°. Note that

Fig. 3 Estimated orientation of the inertial sensor (EKF) compared with the optical reference (Vicon)


Figure 4 shows the total acceleration of a typical pivot shift. The reduction phase of the pivot shift is characterized as a sudden drop of the acceleration. The duration of the entire manoeuver is approximately 100 ms, whereas the sudden drop indicating the pivot shift phenomenon (the tibial reduction) lasts approximately 30 ms. Such a sudden drop was observed in all the acceleration data associated with a positive pivot shift immediately preceding the time

Knee Surg Sports Traumatol Arthrosc Fig. 4 The total linear acceleration of a typical pivot shift (grade 2), for the tibia and femur

Table 1 Mean acceleration drop and standard deviation of the femur and tibia, for each pivot shift grade Clinical grades

Tibial acceleration (m/s2)

Grade 0

1.3 ± 3.2

Grade 1

2.9 ± 3.2

Table 2 Statistical analysis of linear acceleration and velocity data per clinical grade, for the tibia and femur

Femoral acceleration (m/s2)

Clinical grades

0.6 ± 1.6

Grade 0 versus 1









1.4 ± 1.3

Grade 0 versus 2





Acceleration p value

Velocity p value









Grade 2

5.2 ± 3.0

7.0 ± 3.4

Grade 0 versus 3

11.7 ± 7.3

7.8 ± 2.2




Grade 3

Grade 1 versus 2


Grade 1 versus 3





Grade 2 versus 3





when the surgeon indicated having induced a pivot shift, for both the tibia and the femur. Statistical analysis was conducted on the acceleration drop rather than on the maximum acceleration because maximum acceleration can be affected by factors such as the dynamics introduced by the surgeon’s movement while performing the pivot shift test and muscular guarding by the subject due to apprehension. Mean and standard deviation of the acceleration drop are given in Table 1 and shown in Fig. 5. The femoral acceleration drop is very strongly correlated to the clinical grade (r = 0.84, p \ 0.0001) while the tibial acceleration drop is strongly correlated to it (r = 0.69, p \ 0.001). Femoral acceleration drop is significantly different for each pair of pivot shift grades except for grades 0 versus 1 and grades 2 versus 3 as shown in Table 2.


0.0002 0.006 0.002


0.004 0.026 0.012

* Statistically significant (p \ 0.05)

Velocity Figure 6 shows the total linear velocity of a typical pivot shift, which presents a spike-shaped variation. Such a spike of the velocity was observed in all the subjects presenting a positive pivot shift although this characteristic appeared more variable than was the acceleration drop. Similar to the analysis of acceleration data, the amplitude of the linear velocity spike was preferred to the total linear velocity as it is less dependent on the clinician and the subject’s guarding. Figure 7 shows the mean and standard deviation of the variation in velocity for each pivot shift grade. The spikes in femoral and tibial velocity both display a


Knee Surg Sports Traumatol Arthrosc Fig. 5 Mean and the standard deviation of the acceleration drop for each grade of pivot shift

Fig. 6 The total linear velocity of a typical pivot shift (grade 2)


Knee Surg Sports Traumatol Arthrosc Fig. 7 Mean and the standard deviation for the values of acceleration drop according to the attributed grade

strong correlation with the clinical grade (r = 0.71, p \ 0.001 and r = 0.70, p \ 0.001, respectively). Intergrade differences are similar to those obtained using the acceleration data (Table 2). Again, the differences between the grades are more significant on the femur than on the tibia.

Discussion The most important finding of the present study was that inertial sensor data, when processed to remove the gravitational component, correlate very strongly to the pivot shift grade. The strongest correlation was found when considering the amplitude of the acceleration drop of the femur at the time of reduction. Previous studies using position sensors, i.e. optical or electromagnetic systems, have found kinematic parameters that correlate with the clinical grade of the pivot shift. Bull et al. [6] found a moderate correlation (r = 0.498) between the pivot grade given by a single examiner on 10 subjects and the tibial rotation during the reduction phase of the pivot shift. On 25 subjects evaluated by a single examiner, Kubo et al. [19] found low correlation between the clinical pivot shift grades and the maximum velocity of the tibia. Lane et al. [23] found a very strong correlation (r = 0.97) between the pivot shift grade and what they call the ‘‘angle of P’’. Their study

involved 12 subjects under anaesthesia with percutaneous bone markers for motion capture. Thus far, results from studies using inertial sensors have not reached such strong correlations to the grade. Recently, studies have demonstrated the feasibility of quantifying the pivot shift using accelerometers and/or gyroscopes on a porcine knee [8, 26], on a cadaveric knee [1, 3] and on anesthetized subjects [18, 25]. Such studies have generally focused on the sum of linear acceleration and/or the sum of angular rate during the pivot shift test. Using this measure, Ahlden et al. [1] found a moderate correlation (r = 0.58) between the pivot shift grade and the maximal acceleration of the tibia. Their results were obtained from 12 surgeons performing the pivot shift test on a single cadaveric knee. In an in vivo setting, Kopf et al. [18] showed a significant difference between the healthy and injured knees of 20 subjects but found no correlation to the pivot shift grades. Their system, similar to ours, employed accelerometers, gyroscopes and magnetometers and accounted for gravity but the parameters they used were ratios between the ACLdeficient and ACL-intact knees of each subject. Lopomo et al. [25] showed a strong correlation of r = 0.72 between the acceleration range of an accelerometer and the anteroposterior acceleration measured by a reference bonemounted optical navigation system but no correlation to the actual clinical grades. The aforementioned systems, with the exception of Kopf et al. [18], do not account for gravity and therefore suffer


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from diminished precision in measuring the acceleration of the tibia and femur. To address this drawback, we have proposed a system that uses MEMS sensors comprised of an accelerometer, a gyroscope and a magnetometer. Lowcost MEMS are low-performance sensors with large drift errors. This study proposed a closed-loop iterative process using the EKF to perform the online estimation of the angular orientation of knee movements. This orientation estimation was shown to be stable and to be accurate relative to an optical reference. With this method, a very strong correlation (r = 0.84, p \ 0.0001) was found between the clinical grade and the amplitude of the drop in femoral acceleration, at the time of reduction. Using this parameter, the different grades were significantly different from one another except for between grades 0 and 1 and for between grades 2 and 3. The correlation was also strong between the grade and the amplitude of the femoral linear velocity spike at reduction (r = 0.71, p \ 0.001). Although the same parameters on the tibia also correlated to the clinical grades, in our study these correlations were weaker. This is, to our knowledge, the first study to show a correlation between inertial sensor data and the pivot shift grade. These results show the strong potential of the proposed method to be used as a quick, non-invasive method to quantitatively measure the pivot shift phenomenon on live (non-anesthetized) patients in a clinical evaluation setting, using a single inertial sensor. Our study has some important limitations. Foremost, a single surgeon performed and graded the pivot shift test on every knee. Clinical validation of the proposed methodology will require validation of interobserver reliability. This is especially important as inter-clinician variability is known to be high for the pivot shift test. Also, the inertial sensors that were used were applied over the skin. This has the potential to introduce skin-motion artifacts caused by the relative movement between the skin and underlying bones.

Conclusion In conclusion, the results of this study are similar to those obtained using more expensive, cumbersome and timeconsuming motion capture technologies. The study demonstrates the feasibility of a method that improves upon other accelerometer-based solutions by incorporating a novel method to remove the gravitational component of acceleration and by measuring the drop in acceleration rather than its sum. Acknowledgments The authors would like to thank the Canada Research Chair in 3D Imaging and Biomedical Engineering, Prompt Inc., and Emovi Inc. for funding. We would also like to thank Gerard


Parent for his invaluable help in operating the Vicon optical reference system during the validation process. Conflict of interest of interest.

The authors declare that they have no conflict

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Quantitative pivot shift assessment using combined inertial and magnetic sensing.

The purpose of the study was to demonstrate the feasibility of a new measurement system using micro-electromechanical systems (MEMS)-based sensors for...
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