Fig. 1.
Overview of the three steps in the THA procedure.
Fig. 2.
Definitions of operative inclination θi, anteversion θa, and human body coordinate system {B}, and the illustration of cup axis and equivalent angles for θi and θa in system {B}.
Fig. 3.
Definitions of the IMU coordinate system {I} and the world coordinate system {W}.
Table 1.
Definitions of the three coordinate systems: world system{W}, IMU system {I}, and body system {B}.
| Name & notation | Definition |
|---|---|
| World | xW: pointing east |
| system | yW: pointing north |
| {W} | zW: pointing up, orthogonal to the local Earth surface |
| IMU | xI: pointing right (viewing from front-facing direction) |
| system | yI: pointing up (viewing from front-facing direction) |
| {I} | zI: pointing forward (front-facing direction) |
| Body | xB: pointing to the body’s right |
| system | yB: pointing forward |
| {B} | zB: pointing up along the spinal axis |
Fig. 4.
The full view image of the 3-axis tilt table used in experiments (left) and the close-up image of the single-axis tilt table (right), which is the constituent unit of the bottom two layers. The threaded rod simulates the axis of the acetabular cup.
Fig. 5.
Angle estimation accuracy of the IMU for single-axis rotation. The true values (blue line) and estimated values (orange line) are referenced to the left vertical axis, while their absolute errors (green line) are referenced to the right vertical axis.
Table 2.
Angle estimation accuracy (using RMSE and MAPE) of rotations in the three axes.
| Rotation axis | RMSE | MAPE |
|---|---|---|
| z-axis | 0.315° | 2.5 % |
| y-axis | 0.409° | 3.3 % |
| x-axis | 0.423° | 3.6 % |
Fig. 6.
Coordinates of rotation axis unit vector uW in {W} acquired during the registration phase using (17), recorded at four positions.
Table 3.
Part of the data (estimated coordinates of rotation axis vector at Position 1 & 2) and the corresponding test conditions (IMU pose & rotation angle).
| Tilt table position | IMU pose | Rotation angle | Estimated axis vector |
|---|---|---|---|
| Position 1 | Pose A | 10° | (−0.586, 0.810, −0.024) |
| Pose B | (−0.565, 0.819, 0.103) | ||
| Pose C | (−0.579, 0.808, −0.111) | ||
| Pose D | (−0.601, 0.799, −0.022) | ||
| Pose E | (−0.553, 0.812, −0.186) | ||
| Position 2 | Pose A | 3° | ( 0.993, 0.119, 0.020) |
| 6° | ( 0.993, 0.120, 0.006) | ||
| 9° | ( 0.993, 0.119, 0.006) | ||
| 12° | ( 0.993, 0.117, −0.004) | ||
| 15° | ( 0.994, 0.114, 0.007) |
Fig. 7.
Comparison of estimated (θi,θa) values vs. true values. A larger magnitude of the error vector indicates greater error.
Table 4.
Results of θi and θa measurement accuracy experiment.
| RMSE | ||||
|---|---|---|---|---|
| θi | θa | Min. | Mean | Max. |
| 0.278° | 0.296° | 0.073° | 0.373° | 0.714° |
Fig. 8.
Comparison of error vectors in different IMU poses.
Fig. 9.
Comparison of error vectors at different times.
Table 5.
Results of θi and θa measurement accuracy experiment.
| Test time | θi RMSE | θa RMSE | Average error vector magnitude |
|---|---|---|---|
| 0 min | 0.469° | 0.234° | 0.494° |
| 10 min | 0.618° | 1.085° | 1.199° |
| 20 min | 0.791° | 1.586° | 1.704° |
Table 6.
Performance comparison among different prosthesis pose estimation technologies for THA.
| This work | Chen et al. (2021) [16] | Tang et al. (2025) [17] | Computer-assisted system [11] | |
|---|---|---|---|---|
| Sensor type | IMU | IMU | IMU | camera |
| Angular error | RMSE: θi = 0.28° θa = 0.30° | RMSE: θi = 3.26° θa = 3.05° | MAE: θi = 2.3° θa = 2.2° | MAE: θi = 1.8° θa = 2.0° |
| Prosthesis adaptability | high | low | low | high |
| Invasiveness | non-invasive | non-invasive | non-invasive | invasive |
| Radiation exposure | no | no | no | yes |
| Experimental environment | 3-axis tilt table | customized measuring device | in vitro tests on sawbones | real cases (25 patients) |