Reference in-vitro dataset for inertial-sensor-to-bone alignment applied to the tibiofemoral joint

Skin-attached inertial sensors are increasingly used for kinematic analysis. However, their ability to measure outside-lab can only be exploited after correctly aligning the sensor axes with the underlying anatomical axes. Emerging model-based inertial-sensor-to-bone alignment methods relate inertial measurements with a model of the joint to overcome calibration movements and sensor placement assumptions. It is unclear how good such alignment methods can identify the anatomical axes. Any misalignment results in kinematic cross-talk errors, which makes model validation and the interpretation of the resulting kinematics measurements challenging. This study provides an anatomically correct ground-truth reference dataset from dynamic motions on a cadaver. In contrast with existing references, this enables a true model evaluation that overcomes influences from soft-tissue artifacts, orientation and manual palpation errors. This dataset comprises extensive dynamic movements that are recorded with multimodal measurements including trajectories of optical and virtual (via computed tomography) anatomical markers, reference kinematics, inertial measurements, transformation matrices and visualization tools. The dataset can be used either as a ground-truth reference or to advance research in inertial-sensor-to-bone-alignment.


Methods
Specimen overview. A complete fresh frozen cadaveric lower limb, disarticulated at the level of the hip was used for the experiment. The female specimen (age: 52, left leg) did not show any history in knee injuries, e.g., meniscal lesions, ligament ruptures or knee osteoarthritis, and was obtained from the licensed Institute for Orthopaedic Research and Training (IORT, Leuven, Belgium). The use of human specimen and all test procedures were approved by the local ethical committee UZ Leuven and registered at the Belgian National Council for Bioethics (number: NH019) prior to experimental testing.
Experimental work-flow. The specimen was kept in a freezer and removed twenty-four hours prior to experimentation, to allow sufficient time for thawing. First, the specimen was equipped with clusters of spherical infrared reflective markers that were rigidly attached via bone-pins at the medial side, mid-distance onto the femur and tibia segments as illustrated in Fig. 1a. A minimum of three non-collinear markers were necessary to establish a coordinate system, but four markers per cluster were used to reduce registration errors from occlusion in the optical motion tracking system. Second, a volumetric computed tomography scan (Siemens Somatom Force, Siemens Healthcare, Erlangen, Germany) was obtained from the frozen specimen, after placement of the bone-pins. Images were obtained with a slice thickness of 0.6 mm. The computed tomography scans were analyzed with Mimics (Materialise, Haasrode, Leuven, Belgium) to create three-dimensional (3D) reconstructions of both femur and tibia bones (Fig. 1b). Afterwards, the necessary anthropometric osseous anatomical landmarks were identified to construct joint coordinate systems for the femur and tibia from the 3D surface bone models, following Grood and Suntay 8 . The marker clusters were localized in both the CT-scan images and the optical motion capture system. This aids in the spatial alignment between the two reference systems and the registration of virtual anatomical landmarks. Before conduction of dynamic experiments, each bone-pin was equipped with a rigidly attached wireless inertial sensor (Mtw Awinda, Xsens, Enschede, the Netherlands) via zip ties (Fig. 1c). A hardware time synchronization was used to simultaneously capture optical marker trajectories by a six-camera OMC (MX + , Vicon, Oxford, UK) and inertial measurements, both with a sample rate of 100 Hz. Measurement protocol. Data of multiple dynamic experiments were collected by experienced physiotherapists. Prior to each trial, a pseudo-static time-period was introduced where the specimen was held still for approximately five seconds in the position described by the measurement protocol. For each trial, the specimen was then moved in an unloaded position by hand from full extension to a desired level of tibiofemoral flexion, following a predefined measurement protocol by altering the following protocol variables: 1. Movement plane -We differentiated between movements in a fixed vertical movement plane (horizontal femoral-fixed flexion-axis), fixed horizontal movement plane (vertical femoral-fixed flexion-axis) and a mixed movement plane that could change its orientation over time. This overcomes a fixed horizontal axis-setup on a mechanical knee rig 31 that may prevent identification of axis direction, (i.e., a problem of sign pairing may arise such that a femur-fixed flexion-axis that is pointing in medial direction, is estimated to point in lateral direction, but with the same orientation 32,33 ). 2. Movement duration -15 seconds, 30 seconds or 120 seconds, to allow for both quick processing as well as the introduction of drift-effects 4,34 . 3. Movement excitation -We instructed different movement excitation levels as slow, fast and mixed, and later quantified it as slow (norm angular velocity 0.85 ± 0.63 rad/s (femur-attached inertial sensor) and 0.72 ± 0.60 rad/s (tibia-attached inertial sensor)), fast (norm angular velocity 1.63 ± 1.05 rad/s (femur-attached inertial sensor) 1.60 ± 1.20 rad/s (tibia-attached inertial sensor)) and mixed (a random sequence of slow and fast movement periods) to mimic a wide range of movement dynamics. 4. Tibiofemoral flexion range of motion (RoM) -We differentiated between tibiofemoral flexion RoM of 60 degrees, in line with expected RoM during normal gait and 110 degrees to simulate functional squat movements 13 .
The measurement protocol included every possible combination of these four protocol variables and a custom script gave real-time feedback on the RoM to guide the physiotherapists in actuating the specimen. Experiments were executed with care to ensure that the limb was supported in the same way for all runs. Additionally, functional limb poses and movements were recorded and are described as: Although not in line with the intuition of model-based alignment methods that aim to be independent from calibration movements. These additional functional movements enrich the dataset with a debugging purpose on simple functional limb motions. Spatial alignment. We differentiate between the following Cartesian coordinate systems in which measurements can be expressed: 1) the global reference coordinate system M, in which the anatomical landmarks from the 3D surface bone models are defined, 2) the global reference coordinate system G of the OMC in which marker trajectories are expressed, 3) the sensor coordinate system S in which the inertial measurements and estimated biomechanical parameters are expressed, 4) the navigation coordinate system N that serves as a reference for the sensor orientation q NS . Since the optical markers on femur and tibia are identified in both the CT-scan (M) and in the optical motion capture system (G), a common intermediate coordinate system O can be defined on the basis of three non-collinear optical markers O1, O2 and O3 with normalized base vectors; This allows us to describe virtual anatomical marker trajectories within G after the necessary rotations from reference coordinate frame M to reference coordinate frame G via intermediate coordinate frame O.
Furthermore, the sensor's internal on-chip sensing axes are not perfectly aligned with the IMU-case, nor with a coordinate system on the basis of three surrounding rigidly attached optical markers O F , O T . A constant misalignment that describes the rotation from inertial sensor coordinate system to the optical marker-based coordinate system was identified for each sensor (q O S F F , q O S T T ) with the closed-form solution in Theorem 4.1 from J. D. Hol 25 by using measured (from the inertial measurements) and approximated (from the optical cluster markers) angular velocities as an input 25 , from all experimental data points (excluding the pseudo-static time-period) of all trials, to cover most of the rotation space 35 .

Data Records
The data records and a dataset summary spreadsheet (Data_Summary.xlsx) are available through the Figshare repository 36  www.nature.com/scientificdata www.nature.com/scientificdata/ of recorded samples (including the pseudo-static period at the start of each trial). Raw and derived data from different modalities (optical marker trajectories, inertial measurements, reference kinematics, alignment matrices) were structured into separate.mat datafiles (structure arrays data-type) per trial with a custom Matlab (R2019b, Mathworks, Natick, USA) script. Each datafile has the following naming convention "MovementPlane"_"Duration"_"Excitation"_"RoM" and is structured as illustrated in Fig. 2a. The naming convention for the functional movements is provided in the dataset summary spreadsheet. Table 1 provides a detailed explanation on the abbreviations used in the data structure, including the unit and the reference coordinate system in which the data are expressed. The following sections further describe the raw and derived data that are available within each datafile.
Raw data. 3D surface bone models. The surface bone models of both femur (tibia.stl) and tibia (femur.stl) segments provide additional insight and allow for the identification of other custom landmarks. We also provided a reduced vertex version of both surface bone models (indicated by'_red' suffix) that can be used for rapid plotting. From these models, anatomical landmarks and optical markers were identified on the 3D surface bone models and structured in (ct.mat) as depicted in Fig. 2b. Table 2 provides a full explanation of the identified points, spheres and circles. Note that coordinates are expressed in the reference coordinate system of the CT-image.
Optical marker trajectories. Six (MX + , Vicon) infrared cameras positioned in a half-sphere around the specimen recorded the trajectories of the optical marker clusters that were rigidly attached at the femur and tibia segments. The raw marker trajectories were processed in Vicon Nexus (Vicon, Motion Systems, Oxford, UK) using the processing pipelines for the labeling and gap filling. Gap-filling was done with a cubic spline interpolation. For each trial, the processed, unfiltered optical marker trajectories of the four markers per cluster (O 1 -O 4 ) (both for femur and tibia) were included in the datafiles.
Inertial measurements. Each inertial sensor that was attached on the specimen consisted of a gyroscope, an accelerometer and a magnetometer that measured the sensor's angular velocity, external specific force (comprised of the sensor's acceleration and gravity component) and magnetic field strength, in three orthogonal directions.
The sample rate f s of the inertial sensors and an estimate of its orientation expressed in terms of a unit quaternion q t NS with respect to a sensor navigation coordinate system N (typically aligned with the Earth's gravity and the local magnetic field) is provided in each datafile. The subscript t explicitly denotes the time-dependency. The sensor fusion algorithm that was used to obtain these orientation estimates (Xsens Kalman filter) is proprietary of the sensor 37 , but any custom or available 38  Anatomical landmarks in bold represent spheres and circles. The first three coordinates define the coordinates of the center and a fourth coordinate was used for the radius where appropriate. N denotes the amount of samples. An explanation of each individual abbreviation in the data structure can be found in Table 1 for the structure in (a) and in Table 2 for the structure in (b).
www.nature.com/scientificdata www.nature.com/scientificdata/ inertial measurements. Also, an accurate orientation of the sensor can be obtained from the available marker trajectories after the necessary spatial alignment 25 .
Additionally, regular measurements for gyroscope bias estimation and magnetometer calibration were included and annotated in the dataset summary spreadsheet. The gyroscope bias can be estimated from measurements where the sensor-equipped specimen was kept stationary for approximately ten seconds 4 . If magnetometer readings are a desired input of the inertial-sensor-based alignment algorithm subject to validation, possible magnetic disturbance (due to mounting of the sensor on magnetic objects or the presence of magnetic equipment in the lab) can be compensated for 26 using these associated recordings of slow movements in all directions of the data acquisition.
Derived data. Virtual anatomical marker trajectories and sensor alignment rotations. A spatial alignment was used to describe the trajectory of virtual anatomical landmarks within the OMC reference coordinate frame G. Figure 2a describes the data structure used for all trials, including the virtual anatomical landmarks. Furthermore, the constant misalignments rotations q O S F F and q O S T T are provided (align.mat) for each sensor and describe the rotation from the inertial sensor coordinate frame to the optical marker-based coordinate frame.
Reference kinematics. Reference kinematics consisting of tibiofemoral flexion, tibia external rotation and tibiofemoral abduction were calculated from the virtual anatomical marker trajectories following the standards for reporting clinical rotations of the knee 8 and are provided as a reference for each trial. The motions in the measurement protocol contained tibiofemoral flexion angles >90° and in hyper-extension (<0°). This would lead to clipping in the TF flexion kinematics when calculated following Grood and Suntay 8 . We therefore used the adaptation from Dabirrahmani and Hogg 40 to provide a kinematic reference for all ranges of tibiofemoral flexion. The provided kinematics allow in-depth assessment of inertial-sensor-to-bone alignment methods by feeding the algorithm with samples that are measured during specific ranges of clinical rotations. We also provide the time-dependent base vectors for the femoral (I t , J t , K t ) and tibial (i t , j t , k t ) Cartesian coordinate systems as a reference. These vectors can for example be used to visualize the movement from a static tibia or femur anatomical coordinate frame perspective or to rotate estimated joint axes into anatomical coordinate systems for validation purposes.
Visualization tools. All Matlab scripts for visualization and assessment of the data are provided. An example plot of the raw and processed data for one datafile is given in Fig. 3. The script to reproduce this visualization includes the transformation of coordinates starting from a global CT-scan frame M to a global optical motion capture frame G, and the identification procedure to obtain the rotations q OS that align the optical marker frames O with the inertial frames S.
Missing data. After data acquisition, we found trials of inertial sensor measurements that had a significant data-length mis-match with the optical marker trajectories. Also, we occasionally found trials with optical marker trajectories, where occlusion of the markers prevented a correct processing (with a minimum of three visible  www.nature.com/scientificdata www.nature.com/scientificdata/ optical markers per segment). These particular datasets were dropped as annotated in the dataset summary spreadsheet 36 . Furthermore, slight deviations from the protocol as described in this study can be seen in certain trials that either started in 90° tibiofemoral flexion, instead of in a full extended pose or exceeded the desired measurement duration or RoM. All deviations of the protocol are described in the dataset summary spreadsheet. In general, the missing data does not result in any significant loss or limitation. For any combination of measurement protocol variables, there is a sufficient amount of usable data-points to infer the relation between sensor axes and anatomical axes. Additionally, depending on the IMU-based algorithm of interest, random samples from different experiments can be combined if a time-dependency is not assumed 14,33 .

technical Validation
The multimodal dataset of size (53 trials, 321,073 samples) is sufficient for the purpose of validating inertial-sensor-to-bone alignment strategies and inferred biomechanical parameters from inertial sensor data. The measurements of both the marker trajectories and inertial measurements needed to be temporally synchronized to be of use. The temporal synchronization was established by using a custom analog signal routed between the base stations (Lock Sync box, Vicon and Awinda Station, Xsens). A length mismatch of 2 samples (3 out of 53 trials) and one sample (24 out of 53 trials) was found. The corresponding potential time mismatch of 0.01 to 0.02 seconds should not pose a problem for the validation in most use-cases.
The raw measurement data were checked semi-automatically and manually on anomalies. We provided the constant misalignment orientations q OS F and q OS T for each inertial sensor and its surrounded optical cluster markers. These mis-alignment orientations were obtained from all experimental data points. To prove a rigid placement of the inertial sensor with respect to its cluster of optical markers and a correct data-match between the inertial data and optical marker trajectories, the constant misalignments were re-calculated for each trial separately. The per-file calculated misalignments deviated from the provided misalignment in the range of the expected accuracy of such sensor alignment methods 41 with angular distances 42 of . ± . 0 98 055 for the femur-attached inertial sensor and 0.99° ± 0.78° for the tibia-attached inertial sensor.
Unloaded motions on cadavers are often used to describe the relative movement of the bones 28,43,44 . The tibiofemoral flexion was set by the measurement protocol. It is known that secondary rotations are coupled to Visual and annotated representation of the multimodal data content. Reference kinematics, inertial measurements, virtual anatomical/opical marker trajectories and a representation of the relevant anatomical landmarks on the three-dimensional bone surface models (in this example: V_15_f_110.mat). Here, the specimen is in a vertical position (horizontal femoral-fixed flexion-axis). The full explanation of all abbreviations can be found in Table 1. The code for reproducing the plots for any trial is available via the public GitHub repository (https://github.com/IveW/IS2B).