Purpose: Measuring joint kinematics in the clinic is important for diagnosing injuries, tracking healing, and guiding treatments. Howe ver, c urrent methods for measuring joint kinematics are limited by accuracy and/or feasibility of widespread clinical adoption. Therefore, the purpose of this study was to develop and validate an ultrasound -based bone -tracking algorithm to track bone motion and assess kinematics during simulated clinical assessments. Methods: We mimicked four standard laxity assessments (i.e ., anterior, posterior, varus , valgus ) on five human cadaver knees using a robotic testing system . We simultaneously collected B -mode cine loops with an ultrasound transducer aligned to image in the plane of the applied load. We used the bone -tracking algorithm to estimate the change in knee kinematics throughout each laxity test to assess the potential of using ultrasound to estimat e dynamic knee kinematics . Additionally, we conducted additional studies to test the repeatability of measuring laxity with the transducer at the same position and the reproducibility of measuring laxity at different transducer positions. Results: Using the bone -tracking algorithm to estimate changes in knee kinematics, we computed the maximum root-mean -square errors of our bone -tracking algorithm to be 2.2 mm and 1.2° for the anterior -posterior and varus -valgus laxity assessments , respectively. Repeated laxity assessments proved to have good to excellent repeatability , while ICCs from repositioning the transducer varied more widely, ranging from poor to good reproducibility . Conclusions: Ultrasound is a n imaging modality capable of tracking knee kin ematics in both anterior -posterior and varus -valgus degrees -of-freedom . Since ultrasound is widely used in both clinical and research settings, our ultrasound -based bone -tracking algorithm has the potential to assess knee kinematics in a variety of applications, such as diagnosing disorders, monitoring healing, and informing rehabilitation. 3 Introduction Current techniques for assessing joint motion are limited by accuracy and/or feasibility of widespread clinical adoption. In the clinic , the most common assessment of joint motion is a qualitative assessment of range of motion or joint laxity to diagnose ligament injuries or disease severity [22]. However , because they are not quantitative, they are limited in their ability to (1) diagnose more subtle changes in kinematics due to partial injury, disease progression, or healing , and (2) inform treatment planning (e.g., pre -operative planning for knee arthro plasty) . Arthrometers, such as the commonly used KT -1000 or custom arthrometers (e.g., [33]), are also used in the clinic to measure joint motion. H owever, these devices are limited in their accuracy , in part due to soft -tissue compliance [10, 35] , and thus are used more so to distinguish between normal and abnormal knee states (e.g., ruptured and intact ligament states [32, 35] ) rather than to diagnose partial injuries or mild diseases , or to longitudinally track healing or disease progression . Stress radiographs [17] and other novel arthrometers [26] use x -rays to directly image changes in relative pose of the bones between loaded and unloaded states. However, while they overcome t he limitations of soft -tissue compliance , they expose the patient to ionizing radiation [21] and are limited to static poses. In a research setting, optical motion capture is common ly used to capture six degree -of- freedom kinematics . However, skin -motion artifacts can introduce large errors in measured joint motio n [3, 28] . Fluoroscopy (or dynamic x -ray) is the gold standard for measuring joint motion in the research setting , but it requires costly custom hardware , image -processing expertise, and exposes patients to ionizing radiation , which make large -scale clinical implementation, use in longitudinal studies, and/or use in sensitive populations (e.g., pediatric patients [4, 12] ) challenging . Thus, there is a critical need for a novel method to track joint motion that is both accurate and can be implemented for a broad range of applications in the clinic . To achieve the 4 latter requirement, t his method should utilize hardware that is already commonly available in both clinical and research environment s. Ultraso und may be a suitable alternative imaging modality to assess knee motion in clinical and research settings. It is advantageous over radiography and fluoroscopy because it does not expose patients to ionizing radiation and is already broadly familiar to both clinicians and researchers . Previous studies have shown that ultrasound has the potential to track increases in joint gaps , demonstrated in both the tibiofemoral joint during a valgus loading test [34] and the patellofemoral joint during a lateral patellar glide test [5]. However, both groups manually measured bone motion during post -processing , which limits the ability to track bone motion across a large -scale of activities and/or subjects . Constructing a method to automatically track bone motion and convert it to joint kinematics during dynamic testing would increase the feasibili ty of using ultrasound to assess bone motion , and thus measure kinematics, in both clinical and research applications. Therefore , the purpose of this stud y was to develop and validate an ultrasound -based bone -tracking algorithm to track bone motion during dynamic movement. Specifically, we used clinical laxity exams on the knee as an example use case. Accordingly, our two objectives for the present study were to (1) develop an ultrasound -based bone -tracking algorithm and determine the errors in using our algorithm to compute kinematics of the knee and (2) assess the repeatability and reproducibility of using our algorithm to measure kinematics of the knee . Methods Specimen Preparation We prepared five fresh -frozen cadaver ic knees (1F/4M, 66.2 ± 3.4 years, 178.3 ± 6.4 cm, 70.3 ± 11.0 kg) for robotic testing. We did not screen knees prior to testing, but following 5 dissection, we found two knees to have small to moderately small osteophyte formation (i.e., WORMS of 2-3 [27]) on the medial aspects of the femur and tibia . For each knee , we first fixed the fibula to the tibia using a transverse screw inserte d 12 cm distally from the joint line to maintain the rigidity of the proximal fibula r-tibial joint , and then transected the fibula just distal to this screw. Second, w e transected the femur and tibia 2 4 cm proximal and distal from the joint line, respectiv ely. Third , we removed all the tissue from the proximal and distal 10 cm of the femur and tibia, respectively . Fourth, we potted the femur and tibia within a luminum tubes (Bondo Body Filler, 3M) to enable rigid mount ing of each bone to our six-degree -of-freedom (DOF) robotic testing system (KR300 -R2700, KUKA Robotics) ( Figure 1a). Fifth, w e attached arrays of motion capture markers to the shafts of the femur and tibia using screws . Sixth , after mounting the specimen to the robot, we digitiz ed anatomical landmarks of the knee using an optical motion capture system (Optitrack Prime 13x, NaturalPoint, Inc.) to establish an initial joint coordinate system [13]. Seventh , we define d a functional coordinate system that minimized kinematic cross -talk [15] between the primary DOFs (i.e., flexion -extension and internal -external rotation) and secondary DOFs (i.e., varus -valgus rotation, and anterior -posterior, medial -lateral, and compression -distraction translation) during prescribed passive flexion -extension and internal -external rotation paths [25]. Robotic Testing Protocol We used a six-DOF robotic system controlled with simVITRO ® software (Cleveland Clinic) to perform clinical assessments of anterior , posterior, varus, and valgus laxity. We performed all laxity assessments with two different loading trajectories (Figure 2): (1) uni - directional loading to simulate an ideal laxity e xam wit h minimized off-axis loads , except a constant 50 N compressive load , and (2) multi -directional loading to simulate a manual laxity exam with small, representative off-axis loads , in addition to a constant 50 N compressive load . For the multi -directi onal loading simulations, we determined the load and flexion angle 6 trajectories by tracking joint kinematics and kinetics during manual laxity assessments on a knee surrogate mounted to the robotic system (Supplement A). Briefly, w e mounted the tibia of the surrogate to a universal force -torque sensor and then manually applied a load or torque to the femur to mimic a laxity exam performed by a clinician [1]. We recorded joint kinematics and kinetics using simVITRO® software (Cleveland Clinic) in the same functional coordinate system [25] that we use for cadaveric knees so these loading profiles could be directly applied to the cadaver knees . The maximum forces and torques for both trajectories were ±89 N (at a rate of 4.5 N/s) for anterior -posterior (A-P) assessments and ±15 Nm (at a rate of 0.75 Nm/s) for varus - valgus (V -V) assessments. We performed a ll assessments at 0°, 20°, and 45° of knee flexion. For each knee, w e randomized the order of the four loading directions, and then we randomized the order of the flexion angles and used this random order for each loading direction. Further details on the loading trajectories and robotic tracking errors for each assessment are shown in Supplement B . Tracking of Bone Motion To track bone motion d uring each laxity assessment, we collected ultrasound B-mode cine loops that were synchronized with the robotic testing system ’s data acquisition of knee kinematics and kinetics . We placed the ultrasound transducer (LF11 -5H60 -A3, ArtUS, TELEMED) in a custom holder that included four motion capture markers (Figure 1b). We used these markers to track th e transducer’s position and ori entation relative to the knee throughout testing. During testing, w e secured the transducer in the custom holder to t he knee using self- adherent wrap (Coban, 3M) , which mimics a fixation strategy that could be translated into the clinic. During A-P loading, we initially positioned the transducer over the patellar tendon, and then to avoid imaging over the patella, we moved the transducer laterally around the periphery of the knee until we obtained a quality image of both the femur and tibia without conta cting the patella or patellar tendon ( Figure 1c ). During V-V loading , we positioned the transducer over 7 the lateral collateral ligament for varus assessments and the medial collateral ligament for valgus assessments (Figure 1c ). We developed and implemented a custom algorithm to track bone motion in B -mode cine loops throughout each trial (MATLAB 2023a, Mathworks , Natick, MA ). In this algorithm , we used the first B -mode frame to define two rectangular regions of interest (ROI s) that we want ed to track over time: one ROI around the tibia and one ROI around the femur (Figure 3a). We conducted a supplemental study to determine the reproducibility of estimating kinematics when different users select the initial ROIs and found good reproducibility using our method (Supplement C). In the second B -mode frame, our custom algorithm performed a normalized cross -correlat ion to find the peak correlation between each bone ROI in the first and second B - mode frame s (Figure 3b ). The code repeat ed this cross -correlation between each successive pair of B -mode f rame s to track both ROIs throughout the trial . We convert ed the changes in ROI positions to distances using the resolution of the B-mode images , which was 0. 051 mm per pixel for all trials in this study. Finally, to eliminate high -frequency noise caused by small tracking errors from frame to frame , we filtered the distance changes using a second -order Butterworth low-pass filter with a cutoff frequency of 1 Hz. We also filtered the robot kin ematics using the same method. Evaluating tracking at clinically relevant movement speeds To obtain accurate tracking of the kinetics using the robotic system, we conducted each laxity assessment at a speed much slower than typical clinical assessments. Therefore , in addition to the speed at which we conducted the experiment (Case 1) , we also evaluated our bone -tracking algorithm with assessments conducted at faster velocities to mimic joint speeds during different clinically relevant movements. Specifica lly, we evaluated three additional cases: a standard laxity assessment of 0.5 seconds of loading followed by 0.5 seconds of unloading (Case 2) , the relative velocity between the femur and tibia during healthy gait (4.2 mm/s for A -P 8 motion [7] and 14.8 °/s for V -V motion [11], Case 3) , and the relative velocity between the femur and tibia in a pathologic state (e.g., 28.6 mm/s to mimic an ACL injury for A -P [7] and 32.2 °/s to mimic varus thrust for V-V [6], Case 4) . To mimic each of these additional cases , we downsampled the ultrasound data in Case 1 by different f actors to replicate the relative velocities reported in each of the other cases (Table 1 ). For example, for the uni-directional V -V trials during the experiment, we loaded the knee to 15 Nm over 20 seconds. Thus, to instead simulate 15 Nm over 0.5 seconds, we downsampled the ultrasound data by a factor of 40 (i.e., used every 40th frame of the Case 1 data as the Cas e 2 data). For Cases 3 and 4, we computed the experimental velocity for each knee by dividing the maximum motion from the experimental trials by the time elapsed to reach this maximum motion. Then, we divided reported velocities of the knee during healthy and pathologic gait, respectively, by these experimental velocities . Conversion of measured bone motion to joint kinematics To improve the interpretability of our measurements, w e convert ed the measured motion between the bones using our bone -tracking algorithm into either A-P or V-V kinematics . For each frame in each A-P assessment, we computed the angle between the face of the ultrasound transducer and the anterior -posterior axis of the tibial plateau , defined as the line orthogonal to the superior -inferior axis through the tibial shaft and the line between the most medial and lateral points on the tibial plateau [25]. Then, we divided the measured motion between the bones by the cosine of this angle to account for the oblique imaging plane necessary to avoid disrupting patellar motion ( Figure 4a ). For V-V assessments , we assumed the varus or valgus rotation occurred about an axis through the middle of the tibial plateau [8]. We calculated the medial -lateral width of each tibia as the distance between the most medial and lateral extremes of the tibial plateau . Using a small angle approximation, w e divided the measured motion using our algorithm by half the width of the tibial plateau to compute the 9 corresponding rotation . Finally, we calculated the angle between the face of the ultrasound transducer and the axis of the tibial plateau in the medial -lateral direction for each frame. We divided the corresponding rotation by the cosine of this angle to account for the potential oblique view from the transducer (Figure 4b). Repeatability and reproducibility studies We collected repeated trials on each knee to assess both the repeatability and reproducibility of our bone -tracking algorithm. First, w e conducted three additional uni - and multi-directional loading assessments at 20° of knee flexion for all DOFs. However, instead of prescribing kinetics like the first trial, we prescribed the resulting kinematics recorded during the first, kinetic -controlled trial for each of the three addit ional tests. For example, after we completed a uni -directional varus loading assessment in kinetic control, we used the resulting kinematics from that assessment to prescribe the kinematics for the three repeatability tests of varus loading. Second, we rep ositioned the transducer to conduct additional tests. For A -P trials, we repositioned the transducer once more: instead of initially placing the transducer anterior to the knee and moving laterally, we instead moved the transducer medially until a quality image of the femur and tibia appeared. For V -V assessments, we repositioned the transducer twice more: one anteri or to the original position (~ 2 cm) and one posterior to the original position ( ~2 cm). For each position, we conducted three repeatability tes ts. Thus, we conducted six tests per A -P assessment (two positions for A -P, each with three trials) and nine tests per V -V assessment (three positions for V -V, each with three trials) for each specimen . For the repeatability study, we analyzed the data wi thin each transducer position to assess the repeatability of our algorithm when neither the transducer placement nor the true knee kinematics changed. For the reproducibility study, we analyzed the data between transducer placements to characterize the err ors introduced by repositio ning the ultrasound 10 transducer. For each of these additional laxity assessments, we used our US -based bone - tracking algorithm to measure kinematics. Statistical Analysis To address the first objective, w e computed the errors in the US-measured kinematics by taking the difference between the US - and the robot -measured kinematics at each ultrasound frame. Following processing, we excluded one trial ( a varus, multi -directional loading assessment at 45° of knee flexion) because the femur dropped out of the ultrasound frames . Additionally, we computed the errors in the maximum excursions (i.e., laxity) measured with ultrasound compared with the maximum exc ursions measured with the robot . We pooled the errors across specimens and flexion angles to compute the bias (mean) , precision (standard deviation) , and root-mean -square error ( RMSE ) for each DOF [2]. We repeated this process for all four cases of the different loading rate s. To address the second objective, w e performed two different analyses on (1) the repeatability of measuring joint laxity in the same position and (2) the reproducibility of measuring joint laxity after repositioning the ultrasound transducer. First, we computed the repeatability and reproducibility variance s of our ultrasound -based bone -tracking algorithm using ISO 5725 [16] (equations found in Supplement D). Then, t o put these variances into context of the measured kinematics, we computed the coefficient of variation for each repeatability and reproducibility variance using Equation 1 : 𝐶𝑉=√𝜎2 𝜇 Equation 1 Where 𝐶𝑉 is the repeatability or reproducibility coefficient of variation , 𝜎2 is the repeatability or reproducibility variance, and 𝜇 is the mean of the measured kinematics over all the trials for that specimen’s laxity assessment . Finally, we computed the median coefficient of variation for each laxity assessment to summarize the coefficients of variation across the specimens. 11 For the second analysis, we computed the intra -class correlation coefficients (ICC) to assess the repeata bility and reproducibility of measuring laxity. We computed ICCs using two - way random effects models for absolute agreement a mong measurements [24]. To compute ICCs for the repeatability study, we treated each position as independent, so we had 10 (for A - P) or 15 (for V -V) positions, each with three measurements. To compute ICCs for the reproducibility study , we treated each measurement within a specimen as independent, so we had five specimens, each with six ( for A-P) or nine (for V -V) measurements. We interpreted ICC values according to Koo et al. [20] where ICC values less than 0.5, between 0.5 and 0.75, between 0.75 and 0.9, and greater than 0.9 are indicative of poor, moderate, good, and excellent repeatability/reproducibility , respectively. Due to data collection or post -processing challenges (e.g., femur dropped out of the ultrasound frames) , we excluded two positions of the multi-directional -loading anterior test, and one position each for a multi -directional -loading varus test, uni-directional -loading anterior test, and uni- and multi -directional -loading posterior test . Results When using all of the ultrasound frames (Case 1), t he largest RMSEs for translations and rotations were 2.2 mm and 1.2°, respectively, for uni -directional loading and 2.1 mm and 1.3°, respectively, for multi -directional loading ( Figure 5). Our algorithm tended to under estimate kinematics in each degree of freedom, e xcept for the varus assessments . When downsampling to simulate different clinically relevant joint speed s (Cases 2 -4), the errors largely remained unchanged when simul ating a one -second laxity exam , but increased , more in A -P than in V -V, when simulating relative velocity of the knee during he althy and pat hological gait . We reported e rrors in tabular format in Supplement E. When computing joint laxity, the largest RMSEs for translations and rotations were 2.6 mm and 1.6°, respectively, for uni -directional 12 loading and 2.1 mm and 1. 3°, respectively, for multi -directional loading ( Figure 6). The errors largely remained unchanged when downsampling to simulate different joint speeds. To assess the repeatability of measuring laxity with the transducer in the same position , we computed the median coefficients of variation to be between 2.6 and 21.1 % (Figure 7). In terms of I CC values, ICCs ranged from 0.81 to 0.99 ( Table 2 ). To assess the reproducibility of measuring laxity with the transducer at different positions, we computed the median c oefficients of variation to be between 8.9 and 47.3 % (Figure 7). In terms of ICC values, ICCs ranged from 0.21 to 0.89 (Table 2). Discussion Current techniques for assessing joint motion are limited by accuracy and/or feasibility of widespread clinical adoption. Thus, o ur objectives in the present study were to (1) develop an ultrasound -based bone -tracking algorithm and determine the errors in using our algorithm to compute kinematics of the knee and (2) assess the repeatability and reproducibility of us ing our algorithm to compute kinematics of the knee. Our first key finding was that the RMSEs for measuring A-P and V-V kinematics using our bone -tracking algorithm were less than 2.2 mm and 1.3°, respectively , for the experimental and the one -second loadi ng rates . The second key finding was that our bone -tracking algorithm was highly repeatable when the transducer was in approximately the same position ( median coefficients of variation between 2.6 and 21.1%, ICC = 0.81 to 0.99), but not as reproducible when the transducer was placed in different positions (median coefficient of variation between 8.9 and 47.3%, ICC = 0.21 to 0.89). Regarding the first key finding that RMSEs for measuring A -P and V -V kinematics using our bone -tracking algorithm were less than 2. 2 mm and 1.3 °, these errors fall between those reported for optical motion capture and fluoroscopy during walking. We used kinematic tracking 13 errors during walking for comparison to our results because we are not aware of comparable kinematic tracki ng errors for laxity assessments. Reinschmidt et al. compared rotational kinematics from optical motion capture to intracortical bone pins during walking [29]. In three subjects, the range of root -mean -square errors in V -V were 2.1 to 2.8°. Similarly, Benoit et al. quantified the errors in motion capture to bone pins in eight subjects during walking [3]. Absolute error values during foot -strike, mid -stance, and toe -off ranged between 2.5 to 4.4° in V -V. Other studies have quantified the errors of using biplane fluoroscopy to track kinematics, which is the current gold standard method. For example, Guan et al. measured the accuracy of a mobile biplane fluoroscopy syste m in one healthy subject during walking [14]. Root -mean -square errors resulted in 0.77° for V -V. Therefore, errors in V-V are lower than values previously reported with optical motion capture and slightly larger th an values previously reported with biplane fluoroscopy. When computing joint laxity, the largest RMSEs for translations and rotations were 2.6 mm and 1.6°, respectively, for the experimental and the one -second loading rates. To put these errors into better context, we can compare them to other studies that have used different modalities to estimate joint laxity. For instance, a previous study [10] compared KT -1000 measurements of total A -P laxity to the gold -standard, Roentgen Steroephotogrammetric Analysis, in 15 patient s following anterior cruciate ligament reconstruction. They reported an RMSE of 5.0 mm, which is larger than the RMSEs of the total A -P laxity from our ultrasound measurements (2.8 and 2.3 mm for the uni - and multi -directional loading assessments, respecti vely). For V -V measurements, we are not aware of any studies that have reported the errors in V -V laxity compared to a gold -standard method. We were encourage d that the trials were similar when the data was downsampled to replicate a one -second laxity exam , with the only notable change in RMSE being an improvement from 2.1 to 1.5 mm in the anterior, multi -directional loading assessments . When 14 simulating joint motion velocities reported in healthy and pathologic gait, all but valgus uni - and multi-directional -loading and varus multi -directional -loading assessments increased in errors, up to 141% for the posterior, uni -directional -loading assessments during healthy gait. These res ults suggest that to obtain more accurate tracking of bone motion during functional activities, a faster frame rate than used in the current study (~40 Hz) is needed , but can be realistically obtained . The second key finding was that our bone -tracking algorithm was highly repeatable when the transducer was in approximately the same position (median coefficients of variation between 2.6 and 21.1%, ICC = 0.81 to 0.99). These ICC values were comparable to values previously reported when using devices durin g clinical assessments, such as the KT -1000 for A - P laxity (0.47 -0.94 [19, 31, 36] ), or an instrumented V -V laxity device (0.84 -0.93 [9]) or stress radiographs (0.97 -1.0 [18]) for V -V laxity. In terms of the reproducibility study , we found measuring kinematics when the transd ucer is in different positions to not be reproducible, with median coefficients of variation between 8.9 and 47.3% and ICC values ranging from 0.21 t o 0.89. These ICC values were comparable, but slightly lower than values previously reported when using devices during clinical assessments (KT -1000: 0.14 -0.75 [30–32, 36] , V-V instrumented laxity device: 0.65 -0.88 [9], stress radiographs: 0.98 -0.99 [18]). These results suggest repositioning the transducer could lead to high variability in results, which is troublesome for studies consisting of repeated measurements over time. However, because we used anatomical landmarks to initially position the transducer before the reproducibility study, and repeated measurements in approximately the sa me location produce d excellent repeatability , we suggest positioning the transducer over anatomical landmarks (LCL for varus, MCL for valgus, and the first quality image of the femur and tibia laterally to the patellar tendon) to obtain repeatable measurem ents. This is easily achievable because these structures are visible on the US images. 15 Three limitations should be considered when interpreting our findings. First, our sample size of five knees is relatively small. However, the focus of this paper was to demonstrate the ultrasound -based bone -tracking algorithm and its use on a subset of knees. Because we were not drawing statistical comparisons from these data, our sample size was not a limiting factor in our conclusions. Second , our cross -correlation algorithm is a relatively easy motion -tracking method, but artifacts found within the bone ROIs (e.g., shape of the bones changing or surrounding soft tissue that is in close proximity to the bones) can lead to poor tracking. For further details on how these artifacts can cause poor tracking of the bones, see Supplement F. Our ongoing work is focused on more robust tracking approaches to mitigate these artifacts . Third , discrepancies between the assumed planes of motion and the actual planes of motion could lead to errors during the conver sion of bone motion to joint kinematics . For A -P assessments, tracking bone motion at an oblique angle to the A -P axis could increase the errors in A-P kinematics. However, we wanted to place the trans ducer in a position that could track bone motion during dynamic, functional activities, which caused us to place the transducer lateral of the patella. For V -V trials, we assumed a rotation axis about the center of the joint [8]. In reality , the rotation axis likely changes with different V -V angles [8], and potentially different knee geometries (e.g., cartilage wear in one compartment). As a supplement, we processed the A-P and V -V data while varying the transducer angle and location of the V -V axis, respectively, to show their effect s on predicting kinematics (Supplement G). In conclusion, this study showed that our ultrasound -based bone -tracking algorithm can track bone motion with RMSEs between 0.6 and 2.2 mm of A -P translation and 0.4 ° and 1.3° of V-V rotation during a range of loading scenarios from experimental speeds to clinical laxity assessments. Overall, this study is a promising first step in showing our ultrasound -based bone - tracking algorithm can measure joint kinematics in the clinic , which could enhanc e a variety of 16 clinical applications including diagnosing joint dysfunction, monitoring healing, and informing rehabilitation. 17 Tables Table 1: Downsampling factors used to mimic different velocities of joint motion during different movements. For example, to mimic Case 2 velocities (a standard laxity exam of 0.5 seconds of loading followed by 0.5 seconds of unloading), the anterior -posterior uni -directional loading trials were downsampled by a factor of 40 (i.e., we used the 1st, 41st, 81st, etc. frames). Cases 3 and 4 are reported as ranges as the downsampling factor was adjusted for each knee because the maximum excursion of each trial differed from knee to knee . Uni = uni -directional -loading assessments and Multi = multi -directional loading assessments. Case 1 (Experiment) Case 2 (Laxity Exam) Case 3 (Healthy Gait) Case 4 (Pathologic Gait) Anterior -Posterior Uni 1 40 14-30 95-204 Multi 1 54 21-33 144-224 Varus -Valgus Uni 1 40 81-113 177-245 Multi 1 58 167-227 364-494 Table 2: Intra-class correlation coefficients (ICCs) to determine the repeatability in measuring laxity in the same transducer position (ICC Repeatability ) and the reproducibility when the ultrasound transducer is in a new position (ICC Reproducibility ). Also reported are 95% confidence intervals (95% CI). Uni = uni -directional -loading assessments and Multi = multi -directional loading assessments. Note: due to data collection or post -processing challenges (e.g., femur dropped out of the ultrasound frames), we excluded two positions of the multi -directional -loading anterior test, and one position each for a multi -directional -loading varus test, uni -directional -loading anterior test, and uni - and multi -directional -loading posterior test. ICC Repeatability (95% CI) ICC Reproducibility (95% CI) Anterior Uni 0.99 (0.96 -1.00) 0.89 (0.67 -0.99) Multi 0.97 (0.90 -0.99) 0.19 ( -0.09-0.94) Posterior Uni 0.99 (0.95 -1.00) 0.81 (0.49 -0.98) Multi 0.99 (0.96 -1.00) 0.73 (0.29 -0.98) Varus Uni 0.92 (0.83 -0.97) 0.55 (0.24 -0.92) Multi 0.81 (0.62 -0.93) 0.55 (0.22 -0.95) Valgus Uni 0.89 (0.77 -0.96) 0.34 (0.10 -0.83) Multi 0.91 (0.81 -0.97) 0.21 ( -0.01-0.76) 18 Figures Figure 1: (a) We used a six -degree -of-freedom robotic testing system to perform laxity assessments in human cadaver knees . (b) We placed an ultrasound transducer over the joint line of the knee to track relative motion of the femur and tibia during each assessment . (c) We placed the transducer over the lateral collateral ligament during varus loading, over the medial collateral ligament during valgus loading, and lateral to the patellar tendon during anterior and posterior loading. 19 Figure 2: Example uni -directional and multi -directional loading trajectories for posterior assessments. For all uni -directional loading trajectories, the load of interest was ramped to maximum force/torque, held for five seconds, and then ramped back to zero. For al l multi - directional loading trajectories, we manually applied loads/torques to a knee surrogate to mimic a laxity exam performed by a clinician [1]. In addition to these forces/torques, we also prescribed the knee flexion angle for each trajectory. 20 Figure 3: (a) We defined a rectangular region of interest (ROI) around both the tibia and the femur in t he first B -mode frame. Our bone -tracking algorithm finds the maximum correlation of these ROIs in subsequent frames to track bone motion over time. (b) For anterior -posterior assessments, we computed distance changes (Δ distance) as the changes in the ROI position s that are perpendicular to the transducer plane. For varus-valgus assessments, we computed distance changes (Δ distance) as the changes in the ROI positions that are parallel to the transducer plane. 21 Figure 4: We converted the bone motion measured using ultrasound to anterior -posterior ( A- P) or varus -valgus ( V-V) kinematics using the equations above. For A -P assessments, we account ed for the oblique placement of the ultrasound transducer relative to the A-P axis of the tibia. For V -V assessments, we account ed for the V -V rotation axis, as well as the placement of the transducer relative to the medial -lateral axis of the tibia. Abbreviations : dA-P = A-P translation measured by the robot , yUS = bone displaceme nt measured by ultrasound (A-P), θTran, A-P = angle between the transducer and the A-P axis of the tibia, d A-P, pred = ultrasound prediction of A-P displacement, θV-V = V-V rotation measured by the robot, r Tib = half the medial -lateral width of the tibial plateau, z US = bone displacement measured by ultrasound (V -V), θV-V, obs = ultrasound prediction of V -V angular displacement at oblique angle , θTran, V -V = angle between transducer and medial -lateral axis of t he tibia, θV-V, pred = ultrasound prediction of V -V angular displacement. 22 Figure 5: We computed the errors in kinematics at each frame when using our ultrasound kinematics compared to the gold -standard robot kinematics. We measured kinematics using each frame (Case 1), as well as downsampling the data to mimic a one-second laxity exam (Case 2), the relative velocity between the femur and tibia during healthy gait (Case 3), and the relative velocity between the femur and tibia in a pathologic state (C ase 4). The bar plots represent root -mean -square errors, the scatter points represent the bias errors , and the error bars represent the precision errors . Uni = uni -directional -loading assessments and Multi = multi-directional loading assessments. Note: we excluded one trial (varus, multi -directional loading assessment at 45° of knee flexion) because the femur dropped out of the ultrasound frames during this trial . 23 Figure 6: We computed the errors in measuring laxity using our ultrasound -based tracking by comparing values to the gold -standard robot meas urements during the experiment. We measured laxity as the maximum excursion of the kinematics when using each frame (Case 1), as well as downsampling the data to mimic a one -second laxity exam (Case 2), th e relative velocity between the femur and tibia during healthy gait (Case 3), and the relative velocity between the femur and tibia in a pathologic state (Case 4). The bar plots represent root-mean -square errors, the scatter points represent the bias error s, and the error bars represent the precision errors. Uni = uni -directional -loading assessments and Multi = multi - directional loading assessments. Note: we excluded one trial (varus, specimen 3, multi - directional loading assessment at 45° of knee flexion) because the femur dropped out of the ultrasound frames during this trial. 24 Figure 7: We computed the coefficients of v ariation of measuring laxity with the transducer at the same position ( Repeatability ) and at different positions ( Reproducibility ). The CVs of each specimen are plotted as scatter points, and box plots are created to obtain the medians and the 25% and 75% percentiles. Uni = uni -directional -loading assessments and Multi = multi -directional loading assessments. Note: due to data colle ction or post - processing challenges (e.g., femur dropped out of the ultrasound frames), we excluded two positions of the multi -directional -loading anterior test, and one position each for a multi - directional -loading varus test, uni -directional -loading ante rior test, and uni - and multi - directional -loading posterior test. 25 Supplemental Sections Supplement A: Knee Surrogate We used a surrogate knee model to obtain joint kinematics and kinetics during a manual laxity assessment, similar to a laxity assessment performed by a clinician. Our knee surrogate consists of t wo rigid bodies connected by compression springs to provide comparable stiffness to a typical knee (Figure S.1 ). Each rigid body consists of a combination of aluminum and 3D printed mater ial (PLA material). The compression springs allowed for six -degree -of-freedom movement between the two rigid bodies, mimicking movement of a knee. Figure S.1: We used a surrogate knee model to mimic a laxity assessment performed by a clinician. The surr ogate consisted of a femur, tibia, and compression springs between the two rigid bodies to allow for six -degree -of-freedom movement. 26 Supplement B: Loading Trajectories and Load Tracking Errors We performed all laxity assessments with two different loading trajectories: (1) uni - directional loading to simulate an ideal laxity exam with minimized off -axis loads, except a constant 50 N compressive load, and (2) multi -directional loading to simulate a manual laxity exam with small, representative off -axis loads, in addition to a constant 50 N compressive load. For the multi -directional loading simulations, we determined the load and flexion angle trajectories by tracking joint kinematics and kinetics during manual laxity assessments on a knee surrogate mo unted to the robotic system ( Supplement A ). The loading trajectories that we prescribed for the anterior and posterior laxity assessments are shown in Figure S.2, and the varus and valgus laxity assessments are shown in Figure S. 3. 27 Figure S.2: We prescribed these forces and torques for the uni -directional and multi - directional loading trajectories for anterior and posterior laxity assessments. For all uni - directional loading trajectories, one load of interest was ramped to maximum force/torque, held for five seconds, and then ramped back to zero. For all multi -directional loading trajectories, we manually applied loads/torques to a knee surrogate to mimic a laxity exam performed by a clinician [1]. In add ition to the forces/torques, we also prescribed knee flexion angle for each trajectory. 28 Figure S. 3: We prescribed these forces and torques for the uni -directional and multi - directional loading trajectories for varus and valgus laxity assessments. For all uni -directional loading trajectories, one load of interest was ramped to maximum force/torque, held for five seconds, and then ramped back to zero. For all multi -directional loading trajectories, we manually applied loads/torques to a knee surrogate to mimic a laxity exam performed by a clinician [1]. In additio n to the forces/torques, we also prescribed the knee flexion angle for each trajectory. 29 We also computed the errors in prescribing forces/torques during the experiment by taking the difference between the prescribed loads and the actual applied loads at each time point ( Figure S. 4). We pooled the errors across specimens and flexion angles to compu te the root-mean -square error (RMSE) for each load in each laxity assessment [2] (Table S.1 ). Figure S.4: Example plots of the prescribed loads (solid lines) versus the actual (i.e., experimental) loads (dashed lines) during a posterior, uni -directional loading assessment. 30 Table S.1: Root -mean -square errors (RMSE) for prescribing loads compared to the actual loads applied for each laxity assessment. Abbreviations: A -P = anterior -posterior force, C -D = compression -distraction force, M -L = medial -lateral force, V -V = varus -valgus torque , I-E = internal -external rotation torque, F -E = flexion -extension angle , Uni = uni -directional -loading assessments, Multi = multi -directional loading assessments. A-P (N) C-D (N) M-L (N) V-V (Nm) I-E (Nm) F-E (°) Anterior Uni 7.4 13.3 2.4 0.7 0.1 0.2 Multi 7.9 21.5 3.4 0.8 0.4 0.2 Posterior Uni 6.7 12.3 2.0 0.7 0.2 0.2 Multi 6.2 21.7 5.0 0.5 0.3 0.2 Varus Uni 1.8 26.6 2.6 3.0 0.3 0.2 Multi 3.0 29.7 4.5 2.1 0.4 0.3 Valgus Uni 2.8 28.3 3.5 2.6 0.3 0.2 Multi 3.6 32.9 6.1 2.3 0.5 0.2 We computed RMSEs in tracking loads to be under 8 N in both anterior -posterior and medial -lateral loads. However, errors in compression -distraction (C -D) tracking were larger, with RMSEs up to 32.9 N. This is likely due to the much larger sensitivity of C -D, as even translations of less than a millimeter can cause increases/decreases of hundreds of newtons. For torques, we computed RMSEs to be under 3 Nm for varus -valgus and 0.5 Nm for internal - external rotation. Interestingly, errors in V -V were larger for the V-V uni-directional loading assessments compared to the multi -directional loading assessments , whereas this relationship was opposite for all of the other forces/torques for the V -V assessments . Our hypothesis is the multi-directional loading case is the more natural path for the knee to go into V -V torque, with small off -axis loads, rather than the pure V -V angular rotation. This more natural trajectory could be less stiff than the pure V -V angular rotation, allowing for better tracking of the prescri bed loads. Finally, errors in prescribing flexion -extension were low, with maximum RMSEs reaching only 0.3° for all assessments. 31 Supplement C: Reproducibility of ROI Selection To determine the repeatability and reproducibility variance s of the within -user and between -user variance , respectively, of selecting the bone ROIs, we used the uni - and multi - directional -loading assessments at 20° of knee flexion for all DOF s (eight assessments per specimen) . The lead author (MBB) gave high -level directio ns on the method to select the ROIs to three users (Figure S. 5). Each user had up to three practice trials of selecting ROIs in a random assessment to ensure they could correctly identify the bones. We duplicated the eight assessments two more times to obt ain three trials per assessment. We put the 24 trials per specimen in a random order and each user independently selected the initial ROIs for the bone - tracking algorithm. For each of these additional trials, we used our US -based bone -tracking algorithm to estimate kinematics . 32 Figure S. 5: We showed the following directions and example ROI selections to each user before the user selected the bone ROIs for each assessment. Then, w e ran our ultrasound - based bone -tracking algorithm to compute the laxity in each assessment. 33 We chose to create ROIs that split the bones in the middle in the left -right direction in case a trial had a large V -V movement that would cause the ROI to leave the total frame. Additionally, in order to capture the contrast of the edge s of the bones, we increased the ROIs in the top (superficial), bottom (deep), and inside (towards the joint line) directions by 10, 20, and 20 pixels, respectively. As a reminder, the pixel resolution in both directions was 0.051 mm/pixel for each trial. We chose these values during pilot testing to give a balance of capturing the bright/dark contrast while minimizing the amount of soft tissue around the bones that were captured in the ROIs ( Figure S.6). Figure S. 6: After selecting the regions of interest (ROIs) around the bones, we expanded them by 10, 20, and 20 pixels in the top (superficial), bottom (deep), and inside (towards the joint line) directions to capture the bright/dark contrast of the frame while minimizing the amount of soft tissue around the bones in the ROIs. We computed the repeatability variance and reproducibility variance for each assessment to assess repeatability of measuring joint laxity when selecting bone ROIs within a user and between users , respectively. To compute the repeatability variance, we used Equation S.1 from the ISO 5725 standard: 𝑠𝑟𝑗2=∑(𝑛𝑖𝑗−1)𝑠𝑖𝑗2 𝑝 𝑖=1 ∑(𝑛𝑖𝑗−1)𝑝 𝑖=1 Equation S.1 34 Where 𝑠𝑟𝑗2 is the repeatability variance for each laxity assessment ( 𝑗), 𝑝 is the number of users (i.e., 3), 𝑛𝑖 is the number of repeated trials per laxity assessment (i.e., 3), and 𝑠𝑖𝑗2 is the variance in laxity measurements of the three repeated trials in a laxity assessment . To compute the between -user variance, we used Equation S.2 from the ISO 5725 standard: 𝑠𝐿𝑗2=𝑠𝑑𝑗2−𝑠𝑟𝑗2 𝑛𝑗̿ Equation S.2 Where 𝑠𝐿𝑗2 is the between -user variance for each laxity assessment ( 𝑗), 𝑠𝑟𝑗2 is the repeatability variance for each laxity assessment ( Equation S.1), and 𝑠𝑑𝑗2 and 𝑛𝑗̿ are calculated in Equation S.3 and Equation 4 : 𝑠𝑑𝑗2=1 𝑝−1∑𝑛𝑖𝑗(𝑦𝑖𝑗̅̅̅̅−𝑦𝑗̿)2𝑝 𝑖=1 Equation S.3 𝑛𝑗̿=1 𝑝−1[∑𝑛𝑖𝑗𝑝 𝑖=1−∑𝑛𝑖𝑗2𝑝 𝑖=1 ∑𝑛𝑖𝑗𝑝 𝑖=1] Equation S.4 Where 𝑦𝑖𝑗̅̅̅̅ is the mean of the measured kinematics over the three repeated trials in a laxity assessment and 𝑦𝑗̿ is the mean of the measured kinematics over all the trials (i.e., for all three users) for that laxity assessment. Next, we computed the reproducibility variance for each assessment to assess the reproducibility of m easuring joint laxity between different users (Equation S.5): 𝑠𝑅𝑗2=𝑠𝑟𝑗2+𝑠𝐿𝑗2 Equation S.5 Finally, to put these variances into context of the measured kinematics, we computed the coefficient of variation for each repeatability and reproducibility variance using Equation S.6: 35 𝐶𝑉𝑟𝑒𝑝𝑒𝑎𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ,𝑗=√𝑠𝑟𝑗2 𝑦𝑗̿̿̿ and 𝐶𝑉𝑟𝑒𝑝𝑟𝑜𝑑𝑢 𝑐𝑖𝑏𝑖𝑙𝑖𝑡𝑦,𝑗=√𝑠𝑅𝑗2 𝑦𝑗̿̿̿ Equation S.6 Where 𝐶𝑉𝑟𝑒𝑝𝑒𝑎𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ,𝑗 is the coefficient of variation within a user for each laxity assessment, 𝑠𝑟𝑗2 is the repeatability variance for each laxity assessment, 𝐶𝑉𝑟𝑒𝑝𝑟𝑜𝑑𝑢𝑐𝑖𝑏𝑖𝑙𝑖𝑡𝑦 ,𝑗 is the coefficient of variation between users for each laxity assessment, and 𝑠𝑅𝑗2 is the reproducibility variance for each laxity assessment. The results are shown in Figure S. 7 below: Figure S. 7: We computed the coefficients of variances (CV) of measuring laxity when selecting regions of interest within a user ( Within -User) and between different users (Between -User). The CVs of each specimen and each assessment are plotted as scatter points, and box plots are crea ted to obtain the medians and the 25% and 75% percentiles . Uni = uni -directional -loading assessments and Multi = multi -directional loading assessments. Generally, the coeffic ients of variation (CVs) within a user were very similar to those between users , as a majority of the CVs were very low with the median coefficients of variation 36 to be between 0.04 and 7.3% within a user and 0.04 and 9.1% between users. These results indicate selecting ROIs are largely robust to the user selecting the ROI, even after the user has a very brief training on how to select the ROIs. Supplement D: Equations to Compute Reproducibility We computed the repeatability variance and reproducibility variance for each assessment to assess repeatability of measuring joint laxity in t he same position and to assess the reproducibility of measuring joint laxity when the transducer position changes, respectively. To compute the repeatability variance, we used Equation S.7 from the ISO 5725 standard: 𝑠𝑟𝑗2=∑(𝑛𝑖𝑗−1)𝑠𝑖𝑗2 𝑝 𝑖=1 ∑(𝑛𝑖𝑗−1)𝑝 𝑖=1 Equation S.7 Where 𝑠𝑟𝑗2 is the repeatability variance for each laxity assessment ( 𝑗), 𝑝 is the number of positions (i.e., 3 for V -V and 2 for A -P), 𝑛𝑖 is the number of trials per position (i.e., 3), and 𝑠𝑖𝑗2 is the variance in laxity measurements of the three trials at the same position for each combination of loading trajectory -loading direction combination. To compute the between -position variance, we used Equation S.8 from the ISO 5725 standard: 𝑠𝐿𝑗2=𝑠𝑑𝑗2−𝑠𝑟𝑗2 𝑛𝑗̿ Equation S.8 Where 𝑠𝐿𝑗2 is the between -position variance for each laxity assessment ( 𝑗), 𝑠𝑟𝑗2 is the repeatability variance for each laxity assessment ( Equation S.7), and 𝑠𝑑𝑗2 and 𝑛𝑗̿ are calculated in Equation S.9 and Equation S.10: 37 𝑠𝑑𝑗2=1 𝑝−1∑𝑛𝑖𝑗(𝑦𝑖𝑗̅̅̅̅−𝑦𝑗̿)2𝑝 𝑖=1 Equation S.9 𝑛𝑗̿=1 𝑝−1[∑𝑛𝑖𝑗𝑝 𝑖=1−∑𝑛𝑖𝑗2𝑝 𝑖=1 ∑𝑛𝑖𝑗𝑝 𝑖=1] Equation S.10 Where 𝑦𝑖𝑗̅̅̅̅ is the mean of the measured kinematics over the three trials at the same position and 𝑦𝑗̿ is the mean of the measured kinematics over all the trials for that laxity assessment. Next, we computed the reproducibility variance for each assessment to assess the reproducibility of measuring joint laxity when repositioning the ultrasound transducer (Equation S.11): 𝑠𝑅𝑗2=𝑠𝑟𝑗2+𝑠𝐿𝑗2 Equation S.11 Finally, to put these variances into context of the measured kinematics, we computed the coefficient of variation for each repeatability and reproducibility variance using Equation S.12: 𝐶𝑉𝑟𝑒𝑝𝑒𝑎𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ,𝑗=√𝑠𝑟𝑗2 𝑦𝑗̿̿̿ and 𝐶𝑉𝑟𝑒𝑝𝑟𝑜𝑑𝑢𝑐𝑖𝑏𝑖𝑙𝑖𝑡𝑦 ,𝑗=√𝑠𝑅𝑗2 𝑦𝑗̿̿̿ Equation S.12 Where 𝐶𝑉𝑟𝑒𝑝𝑒𝑎𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ,𝑗 is the coefficient of variation within a position for laxity assessment , 𝑠𝑟𝑗2 is the repeatability variance for each laxity assessment , 𝐶𝑉𝑟𝑒𝑝𝑟𝑜𝑑𝑢𝑐𝑖𝑏𝑖𝑙𝑖𝑡𝑦 ,𝑗 is the coefficient of variation between positions for each laxity assessment , and 𝑠𝑅𝑗2 is the reproducibility variance for each laxity assessment. Suppleme nt E: Bias, Precision, and Root -Mean -Square Errors for Predicting Kinematics We c omputed values of using our ultrasound -based bone -tracking algorithm to estimate kinematics of laxity assessments at different joint velocities. Specifically, we evaluated at the experimental speed (Case 1; Table S. 2), the relative velocity during a standard, one -second 38 laxity assessment (Case 2, Table S. 3), the relative velocity between the femur and tibia during healthy gait (Case 3, Table S. 4), and the relative velocity betw een the femur and tibia in a pathologic state (Case 4, Table S. 5). Table S. 2: Bias, precision, and root -mean -square errors (RMSE) for estimating kinematics for each loading trajectory during loading velocities at the experimental speed. The last column contains the maximum translations/rotations measured by the robot (mean ± standa rd deviation) for each loading trajectory. Uni = uni -directional -loading assessments and Multi = multi - directional loading assessments. Bias Precision RMSE Maximum Motion Anterior Uni -0.46 mm 2.10 mm 2.15 mm 4.4 ± 2.3 mm Multi -1.00 mm 1.84 mm 2.10 mm 5.6 ± 1.9 mm Posterior Uni -0.58 mm 0.94 mm 1.10 mm 3.4 ± 1.6 mm Multi -0.06 mm 0.63 mm 0.64 mm 3.0 ± 1.2 mm Varus Uni 0.79° 0.88° 1.18° 3.3 ± 1.3° Multi 0.33° 0.68° 0.76° 1.9 ± 0.6° Valgus Uni -0.07° 0.39° 0.40° 2.9 ± 0.7° Multi -0.32° 1.21° 1.25° 2.3 ± 1.2° Table S. 3: Bias, precision, and root -mean -square errors (RMSE) for estimating kinematics for each loading trajectory during loading velocities mimicking a one -second laxity assessment. The last column contains the maximum translations/rotations measured by the robot (mean ± standard deviation) for each loading trajectory. Uni = uni -directional -loading assessments and Multi = multi -directional loading assessments. Bias Precision RMSE Maximum Motion Anterior Uni -0.46 mm 2.09 mm 2.14 mm 4.4 ± 2.3 mm Multi -0.82 mm 1.27 mm 1.51 mm 5.6 ± 1.9 mm Posterior Uni -0.57 mm 0.94 mm 1.09 mm 3.4 ± 1.6 mm Multi -0.05 mm 0.64 mm 0.64 mm 3.0 ± 1.2 mm Varus Uni 0.79° 0.88° 1.18° 3.3 ± 1.3° Multi 0.32° 0.67° 0.74° 1.9 ± 0.6° Valgus Uni -0.06° 0.39° 0.39° 2.9 ± 0.7° Multi -0.31° 1.21° 1.25° 2.3 ± 1.2° 39 Table S. 4: Bias, precision, and root -mean -square errors (RMSE) for estimating kinematics for each loading trajectory during loading velocities mimicking relative motion of the knee during healthy gait. The last column contains the maximum translations/rotations meas ured by the robot (mean ± standard deviation) for each loading trajectory. Uni = uni -directional -loading assessments and Multi = multi -directional loading assessments. Bias Precision RMSE Maximum Motion Anterior Uni -1.13 mm 2.44 mm 2.68 mm 4.4 ± 2.3 mm Multi -1.12 mm 2.16 mm 2.43 mm 5.6 ± 1.9 mm Posterior Uni -1.27 mm 2.33 mm 2.65 mm 3.4 ± 1.6 mm Multi -0.12 mm 0.93 mm 0.94 mm 3.0 ± 1.2 mm Varus Uni 0.87° 1.31° 1.57° 3.3 ± 1.3° Multi 0.39° 0.82° 0.91° 1.9 ± 0.6° Valgus Uni -0.06° 0.38° 0.39° 2.9 ± 0.7° Multi -0.13° 1.28° 1.29° 2.3 ± 1.2° Table S. 5: Bias, precision, and root -mean -square errors (RMSE) for estimating kinematics for each loading trajectory during loading velocities mimicking relative motion of the knee during pathologic gait. The last column contains the maximum translations/rotations m easured by the robot (mean ± standard deviation) for each loading trajectory. Uni = uni -directional -loading assessments and Multi = multi -directional loading assessments. Bias Precision RMSE Maximum Motion Anterior Uni -1.05 mm 2.35 mm 2.57 mm 4.4 ± 2.3 mm Multi -1.09 mm 2.09 mm 2.35 mm 5.6 ± 1.9 mm Posterior Uni -1.19 mm 2.26 mm 2.55 mm 3.4 ± 1.6 mm Multi -0.28 mm 0.88 mm 0.92 mm 3.0 ± 1.2 mm Varus Uni 0.83° 1.30° 1.54° 3.3 ± 1.3° Multi 0.30° 0.60° 0.67° 1.9 ± 0.6° Valgus Uni -0.05° 0.38° 0.38° 2.9 ± 0.7° Multi -0.32° 1.24° 1.27° 2.3 ± 1.2° Supplement F: Further Detai ls into Trials with High Errors We took a more detailed look into the trials with higher errors in order to help us understand what could be the cause of the high errors. As mentioned in the limitations of the Discussion , some trials results in high errors potentially due to artifacts wi thin the bone ROIs that led to poor cross -correlation tracking. Below is a more detailed analysis of three trials , with plots of robot and ultrasound kinematics, along with images of some ultrasound frame s at specific time points. 40 (1) Example Trial 1 Below is an example trial of a valgus, multi -directional -loading assessment in specimen 3 (Figure S. 8). This trial had a root -mean -square error of 2.26°, and likely did not track the bones well throughout the trial due to the contours of the bone changing shape as well as the close proximity of surro unding tissue around the bones. Figure S. 8: (Top) Ultrasound vs robot kinematics for a trial that had poor tracking due to shape changes of the bones. (Bottom) We extracted specific frames (Frames A -D) from the 41 ultrasound cine loop to identify potential reasons that the errors in estimating kinematics were high. In frame A, we create the ROIs. By frame B, the tibia (left ROI) and femur (right ROI) are starting to change shape. At frame C, the femur ROI shifts i nward (you may notice the larger black space in the inside of the right ROI), leading to a sharp decrease in estimated V -V rotation. Additionally, the tibia’s ROI is obscured with the superficial tissue in close proximity to the tibia, which also shifts the tibia ROI inward. These ROIs never get back to looking like they did in frame A, as frame D stil l predicts a negative rotation. (2) Example Trial 2 Below is another ex ample trial of a valgus, multi -directional -loading assessment in specimen 3 ( Figure S. 9). This trial had a root -mean -square error of 1.70°, and likely did not track the bones well throughout the trial due to the contours of the bone changing shape as well as close proximity of surrounding tissue around the bones. 42 Figure S. 9: (Top) Ultrasound vs robot kinematics for a trial that had poor tracking due to surrounding soft tissue around the bones. (Bottom) We extracted specific frames (Frames A - D) from the ultrasound cine loop to identify potential reasons that the errors in estimating kinematics were high. In frame A, we create the ROIs. By frame B, the tibia (left ROI) is starting to shift downward, potentially due to the close proximity of the superficial tissue. By frame C, the tibia ROI shifts inward (you may notice the larger black space in the inside of the left ROI), leading to a sharp decrease in estimated V -V rotation. The ROIs never get back to surrounding the bones 43 as they do in frame A, and the tibia ROI shifts entirely to the superficial tissue by frame D, leading to po or estimates of V -V kinematics. (3) Example Trial 3 Finally, some trials resulted in high errors even though the cross -correlation method tracked the bones well. A potential source of this error may be in converting distance changes in the B -mode ultrasound frames to kinematics of the joint. For A -P assessm ents, we needed to account for the oblique angle of the transducer relative to the A-P axis since we had to move the transducer to the side of the patella to image the femur and the tibia. Therefore, to convert the distance changes measured from ultrasound to A-P kinematics, we divided by the angle between the transducer and the anterior -posterior axis of the tibia. Likely, tracking bone motion at an oblique angle to the A -P axis increases the errors in A -P kinematics. For V -V trials, we assumed a rotation axis about the center of the joint [8]. In reality, though, the rotation axis likely changes with different V -V angles [8], and potentially different knee geometries (e.g., cartilage wear in one compartment). Below is an anterior assessment with a root -mean -square er ror of 2.68° that tracked the bones well throughout the trial, but still had larger errors ( Figure S. 10). 44 Figure S. 10: (Top) Ultrasound vs robot kinematics for a trial that had good tracking, but high errors in kinematics. (Bottom) We extracted specific frames (Frames A -D) from the ultrasound cine loop to identify potential reasons that the errors in estimating kinematics were high. In frame A, we create the ROIs. In frames B and C, the shape of the bone are similar to the first frame, and the ROIs arou nd the bone are still surrounding the same portion of the bone. Thus, this is a trial that tracked the bone well, but still under -predicted the A -P kinematics. 45 Supplement G: Effects of Altering Planes of Motion A potential source of error in our ultrasound -based bone -tracking algorithm is the conversion of distance changes to kinematics. For A -P assessments, we needed to account for the oblique angle of the transducer relative to the A-P axis since we had to move the transducer to the side of the patella to image the femur and the tibia. Therefore, to convert the distance changes measured from ultrasound to A -P kinematics, we divided by the angle between the transducer and the anteri or-posterior axis of the tibia. However, we wanted to explore processing the data at varying angles from the transducer angle to observe if a trend could be obtained that would lower the errors . Thus, we reprocessed the data, but when accounting for the angle of the transducer and the A -P axis of the tibia, we added an o ffset angle. We plotted the root -mean -square errors as a function of this angle deviation, both when all angles and specimens were pooled within an assessment ( Figure S. 11) and for each individual trial ( Figure S.12). Figure S. 11: We plotted root -mean -square errors as a function of the angle deviation from the current transducer axis. Data was pooled by assessment, so fifteen different trials are combined for each curve (three angles and five specimens per assessment). Black scatte r 46 points represent the minimum values of each curve. Uni = uni -directional -loading assessments and Multi = multi -directional loading assessments. Figure S. 12: We plotted root -mean -square errors as a function of the angle deviation from the current transducer axis for each trial. Each row represents a different specimen, and each column represents a different flexion angle. Black scatter points represent the minimum values of each curve. Uni = uni -directional -loading assessments and Multi = multi -directional loading assessments. 47 Although the minimum RMSE of each assessment differed slightly from the 0° angle deviation used previously, the difference s were negligible . Additionally, no trends were observed between different flexion angles and differen t specimens. For V -V trials, we assumed a rotation axis about the center of the joint [8]. In reality, though, the rotation axis likely changes with different V -V angles [8], and potentially different knee geometries (e.g., cartilage wear in one compartment). Thus, we conducted a supplemental study to show the effect of using different locations of the V-V axis on estimating V -V kinematics. To do this, we reprocessed the data and altered the rotation axis about the joint as a function of the percent distance across the tibia joint. A value of 50 represents the midpoint of the tibial plateau and a value above 50 represents a rotation axis about the opposite compartment that is opening (i.e ., medial compartment for varus and lateral compartment for valgus). We plotted the root -mean -square errors as a function of this rotation axis, both when all angles and specimens were pooled within an assessment ( Figure S. 13) and for each individual trial ( Figure S. 14). 48 Figure S. 13: We plotted root -mean -square errors as a function of the V -V rotation axis for each trial. Data was pooled by assessment, so fifteen different trials are combined for each curve (three angles and five specimens per assessment). Black scatter points represent the minimum values of each curve. Uni = uni -directional -loading assessments and Multi = multi - directional loading assessments. Figure S. 14: We plotted root -mean -square errors as a function of the V -V rotation axis for each trial. Each row represents a different specimen, and each column represents a different flexion angle. Black scatter points represent the minimum values of each curve. Uni = uni - directional -loading assessments and Multi = multi -directional loading assessments. 49 When pooling the data within each laxity assessment, RMSEs generally decreased as the rotation axis across the tibia width increased. Therefore, a ro tation axis around 75% (i.e., approximately in the center of the medial compartment during varus loading and approximately in the center of the lateral compartment during valgus loading) would give lower errors than the 50% location in all assessments exce pt for the valgus uni -directional loading assessments. However, as previously stated, the rotation axis likely changes based on many factors (e.g., specimen, V -V angle), as seen in Figure S. 14. 50