Patients Knee to Know: Evaluating the robustness of IMU-derived Knee Angle measurements

By Jae Min Seo (He/Him)

Over 2.5 million people around the world turn to knee replacement surgery (also called total knee arthroplasty) to treat conditions such as osteoarthritis [1], and other degenerative joint diseases, which cause pain during gait and often prevent them from walking effectively [2]. The road to post-operative recovery and walking independently is a long and arduous process. The result of such invasive surgery is that patients’ rotational range of motion about their knee is severely attenuated, and most patients can only extend their legs up to 80 degrees in their first two weeks post-operation, if at all [3]. In order to track patients’ rehabilitation and to check for any abnormalities, it is important to measure how their range of motion about the knee improves over time [4-6]. How then, do we measure the joint angles about the knee?

Anatomical Considerations

One may think that the knee joint only has a single axis of rotation, but this is actually not the case; The knee joint has 6 degrees of freedom¹: 3 rotational (flexion/extension, varus/-valgus, axial), and 3 translational (superior/inferior, anterior/posterior, medial/lateral) [7]. Try it! You can find the axial rotation of your knee by holding your knee still and moving your heel inwards and outwards. During knee flexion, the motion is caused by a combination of translation and rotation between the contacting tibia and femoral condyle surfaces [8]. Excess sliding or rolling about the joint is prevented by soft tissue structures, such as the menisci, the muscular connections via the tendons, and the ligaments between the femur and tibia [8]. The combinations of these muscle contractions and physical structures allow us to observe from a macroscopic scale what we know as knee flexion and its characteristic range of motion [7].

However, the knee-joint is often regarded as a perfect hinge-joint for modelling purposes. This is because the flexion-extension angle (~140°) of the knee joint is much larger than the varus/valgus angle (~10°), and the axial angle (~5°) [7-8], and in everyday movements such as walking and squatting, clinicians are primarily concerned about the restoring the flexion-extension angle of the knee [5,9,10].

Figure 1: The knee has 6 degrees of freedom [7]

Current Methods & Technologies

One may think that measuring the angle about the knee is quite trivial – you simply use a protractor and measure the angle between the thigh and shank when the leg is fully flexed and fully extended. And you thought right! There are in fact clinical tools that do just that, called goniometers [11].

However, clinicians often place the goniometers on different parts of the knee joint each time, and do not actually align them in line with biomechanical landmarks and bones [11]. This has shown to cause large inter-clinician (and in some cases, intra-clinician) variability in repeated measurements, causing large errors compared to ground-truth data measurements calculated using body scans [13-14]. There is also the added disadvantage of not being able to capture dynamic data, which is oftentimes more useful for biomechanists and orthopaedics [15].

Figure 2: Long arm goniometers are a common tool by orthopaedics and biomechanists to determine the knee angle of patients undergoing rehabilitation [12]

The gold standard for calculating biomechanical measurements is to use Optical Motion Capture (OMC) [16]. This is where reflective markers are placed on the patient, and the movement of the markers is tracked in a room surrounded by high-rate, high-accuracy cameras [16]. You may have seen these being used in high-performance athletes or other fields where human movement is tracked, like in video game animation captures [17].

Figure 3: Motion Capture is used in a myriad of different applications [18]

The data collected from these cameras are processed by an open source software called OpenSim [19]. This software uses the marker information to calculate biomechanical variables using inverse kinematic techniques, which uses each time frame of marker positions and positions the model in a pose that "best matches" experimental marker and coordinates data for that time step [20]. This "best match" is the pose that minimises a sum of weighted squared errors of marker coordinates. OpenSim assumes that the marker position relative to the bones does not change over time. These Optical Motion Capture and optimisation techniques are the most accurate non-invasive methods for capturing knee angle data [18]. This method typically has a root mean square error (RMSE)2 of less than 5 degrees and is used most widely as a ground-truth measurement for other prediction algorithms [19-20], [21-23]. We do not consider this RMSE to be significant as it is of a similar scale to the measurement errors that occur during data capture [22].

Optical Motion Capture is not perfect, however. This is due to the non-invasive nature of the markers; Reflective markers are placed on the skin, and oftentimes on top of other soft tissue such as muscle and fat. These soft tissues have large deformations for small changes in position, which can cause variation over time in the distance between the markers and the anatomical landmarks/bones they are meant to represent over time [24]. These introduce noise called soft-tissue artefact into the data acquired, and can result in large inaccuracies if markers are not placed on landmarks with a lower proportion of soft tissue/fat/muscles such as the ankle (where soft-tissue movement is minimal) [25]. This is particularly of interest as we know that knee movements cause these soft tissues to jiggle, and we know that the knee joint doesn’t jiggle-jiggle, it folds.

Figure 4: Markers on my leg as I do a range of motion exercise, visualised in OpenSim

There exists an even more accurate form of data acquisition, and this is through bone pins. These pins are directly attached to the bones, which prevents any form of relative movement between the bones of interest and the markers, minimising soft-tissue artefact [26]. However, this method is typically for purely research purposes, and the bone pins can have a confounding effect on the gait of participants, which can render the data useless from a gait rehabilitation standpoint.

The three aforementioned methods come in varying degrees of accessibility, accuracy, and invasiveness. Whilst goniometers may be more accessible and non-invasive, they are not the most precise. Bone pins are extremely accurate, but are invasive and not very accessible for patients who have undergone surgery. Optical Motion Capture provides a nice middle ground, but these are typically only found in Biomechanics research institutes and require very expensive equipment. None of these options are favourable for patients who need accessible, accurate, and dynamic measurements of their knee angle during their rehabilitation.

Figure 4: IMeasureU is one of the leaders in wearable motion tracking (and was founded by research at the University of Auckland) [27]

Inertial Measurement Units

In the past decade there has been a surge in research regarding capturing joint measurement angles using portable and lightweight devices called Inertial Measurement Units (IMUs). IMUs capture linear acceleration, angular acceleration, and magnetic field strength through on-board accelerometers, gyroscopes,and magnetometers respectively. Research has been done by strapping one IMU on each segment about the joint (one IMU on the thigh, one IMU on the shank), and running the rate information through a data processing pipeline that can predict the angle using these different measurements.

IMUs by nature do not have an absolute frame of reference. If you have two IMUs in motion, you cannot directly determine the distance or angle between them without using some analytical or computational tools. Research has been done by placing IMU markers as parallel as possible to anatomical coordinate systems, but depending on the algorithm used, this may not be the optimal method for capturing the angle of the knee, or having participants perform simple calibration movements.

Angle Prediction Algorithms

Initial research on IMU-derived angle-calculations was done in 2001 by simply integrating the rate data at each capture to get from the angular acceleration to absolute angle measurements, from some known calibration pose (eg. full extension or full flexion) [28]. Any offsets were removed by subtracting the average angle from a static pose, and the initial angle was found by taking the inverse tangent of the acceleration in the first few seconds of each trial. The calibration procedures were done at the beginning of each trial to zero the effects of any accumulated drift on the next trial. Some studies have tried running calibrations by assuming IMUs are mounted exactly parallel to anatomical reference frames/axis, but have found that results are quite heavily corrupted by kinematic crosstalk3.

A new approach was taken by Seel [29] where kinematic constraints were applied to the joint axis algorithms. This works under the assumption that the joint axis is a perfect hinge, whereby the only degree of freedom is the flexion-extension angle. This is done by projecting all knee motion vectors onto a shared plane that is defined by the range of motion of the thigh and shank. The angle was found by integration using the Gauss-Newton algorithm4. However, the problem of drift and measurement bias were not addressed in this paper.

Seel extended upon his work in 2014 to find the flexion/extension angle of the knee, by estimating local joint positions using data from the gyroscope and accelerometer [4]. This allows a data-fusion approach to find the real-time angle without any drift, as no integration is involved. However, only information about the flexion/extension angle is found, with no mention of abduction/adduction or internal/external rotation.

An extension is offered by Laidig et al., where knee flexion/extension angles are accurately estimated by exploiting the knee’s hinge axis to control misalignment about the vertical axis due to drift and/or magnetic field interference. Vitali [30] provided yet another approach similar to the above, but was able to extract abduction/adduction and internal/external rotation angles, though they did not mention the extent of kinematic crosstalk. Baudet used Principal Component Analysis5 to minimise kinematic crosstalk, and has been very successful in minimising crosstalk, especially in the abduction/adduction and internal/external rotation angles [31] .

Research Objectives

Lots of measurements have been made by researchers that know exactly where and at what orientation to place their IMUs for optimal results. There is a plethora of research in this field that claim to have the best results for IMU-derived predictions, but do not disclose their robustness to different dynamic movements and slight variations in IMU placement. In order to make IMU-derived clinical measurements more accessible, we must assess the robustness of different prediction algorithms, as well as at which IMU positions and orientations the error in the predictions are minimised. My research will determine just that, by comparing the error associated with different combinations of IMU positions, orientations, prediction algorithms, and movements, to find the optimal conditions in which the error is minimised. Through this research, clinicians can better advise their patients on how to get the optimal readings from IMU-derived knee-angle measurements. This should vastly improve the accessibility of current postoperative total knee arthroplasty patients undergoing rehabilitation, ultimately improving patient outcomes.

Footnotes

1 Degree of freedom is the number of independent parameters that can define another parameter within a system. In this case of knee joint biomechanics, the degrees of freedom are the different possible movements, which superimpose together to give what we define as the ‘range of movement’.

2 Root Mean Square Error (RMSE) is the difference between two parameters. This is often used in scientific research and statistical analysis as a means of comparing one or multiple measurements to an expected value. The RMSE is calculated by taking the absolute value of the difference between the two parameters squared, and taking the square root of the result. One may see parallels between the RMSE, Euclidean norm and the Pythagorean theorem.

3 Crosstalk is the phenomenon whereby one parameter’s output is incorrectly recognised as another parameter. In biomechanics this is called Kinematic Crosstalk, and in the context of the knee, an example could be the some part of the internal/external rotation being recognised as an abduction/adduction movement.

4 The Gauss-Newton Algorithm is an iterative algorithm that is used to solve nonlinear least squares (overdetermined) problems. This allows us to make the best possible approximation to overspecified systems (where the amount of degrees of freedom is negative) by minimising the squared sums of the residual errors. This is used in scenarios such as this, where there are more known parameters than the number of equations.

5 Principal Component Analysis is one of the key cornerstones of feature extraction and statistical analysis. The vector which best explains the variation in data is considered the principal component, and the next best vector that is orthogonal to this principal component is the next principal component and so on. In this context, the largest principal component of the three rotations is assumed to be the flexion/extension angle of the knee.

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