Estimation of the knee joint load using plantar pressure data measured by smart socks: A feasibility study

2.1Smart socks and data acquisition module

The research used dAid smart socks and data acquisition modules, developed at Riga Technical University [29, 35]. The socks (Fig. 1a) have six knitted resistive sensors, positioned on the foot plantar surface when the socks are on (Fig. 2b). The sensors and conductive traces are knitted using conductive yarn and integrated into the sock directly during the manufacturing process. The conductivity of the sensors increases with applied pressure. The traces are connected to the originally designed data acquisition module (Fig. 1c) using the snap button-ended wires. The data acquisition module enables simultaneous connection of 8 resistive sensors (although only 6 of them were used). Sensor resistance is measured using the calibrated current injection method. The resulting voltage drop is converted using 10-bit ADC and converted to resistance; the resistance measurement range could be adjusted from 2 kOhms up to 1024 kOhms. Alongside this, the module is equipped with an embedded 6D IMU, that enables the measurement of linear and angular acceleration. The module data acquisition rate is about 160 s-1/channel. The module communicates acquired data via Bluetooth®-2.1 channel. Each data packet contains the time mark (module internal time in milliseconds), components of module acceleration (Ax,Ay,Az), measured in units of g, components of a quaternion (Qw,Qx,Qy,Qz), measured in the range [-1; +1], and eight measured in kiloohms sensor resistances R1-R8. The receiver is a laptop with Windows-based custom-made data acquisition software, enabling recording of the acceleration, quaternion component, and sensor resistance waveforms as well as real-time display of the acquired signals. The module enables measurements of acceleration up to 32 g, and resistances up to 1024 kΩ. The rechargeable battery of the module enables 8-hours of continuous operation.

Figure 1.

Pair of dAid smart socks with knitted sensors marked by numbers (a); typical position of sensors over the foot plantar surface (b); data acquisition module (c).

Figure 2.

Experimental setup: Position of the ankle (a) and tight (b) modules, initial position for measurements (c).

The experimental setup included a smart sock and two data acquisition modules (Fig. 2). Within the scope of the present paper, measurements were made on the subject’s left leg only. The first module was attached to the lateral surface of the subject’s ankle at the distance d1 from the bottom edge of the module to the ground (Fig. 2a), 10 cm above the lateral malleolus. This module was connected to the sock for plantar pressure measurements. The second accelerometer was connected to the lateral surface of the subject’s tight 10 cm above the superior edge of the patella at the distance d2 from the ground (Fig. 2b). In both cases, the modules were fastened using adhesive tape. Modules were positioned with IMU x-axis directed forward and y-axis directed downward. All measurements started from the same pre-defined starting position (Fig. 2c), straight posture with both feet shoulder-width apart. Each data recording began with a few seconds of rest, followed by exercise.

The modules did not have a synchronization option. To synchronize the tight and ankle modules, a sharp stomp was made at the beginning of each data recording. Then the acceleration waveforms, recorded by each module were used to check the synchronization of the modules and upon necessity align the waveforms manually, using the stomp-related spike as an alignment landmark. The inaccuracy of alignment was within one data point or 6 ms.

The recorded waveforms were digitally filtered using 2nd order Butterworth filter with a cut-off frequency 6 Hz for the squat exercises and 15 Hz for walking/running exercises. Such filters are often used in IMU applications [36, 37].

2.2The exercise

The research was conducted, involving only one volunteer subject – one of the authors of the research. The subject got into the starting position, then performed a series of 10 squats. The subject was instructed to perform squats as naturally as possible, trying to perform them at a similar depth, as well as perform squats steadily, without rapid acceleration. The exercise was performed barefoot. The series was repeated three times. In parallel to the data recording, all measurements were recorded on video – this visual information facilitated the process of result analysis.

2.3The biomechanical model and calculation of moments and forces

The present study is limited to the analysis of motion in the plane, which coincides with the x-y plane of IMU. Any motion in the lateral, or z-axis direction, as well as rotation of tight and calf around their longitudinal axes, are ignored. All exercises were designed in a manner that the subject moved only along a straight line, with the movement of each segment being tracked along the x-y plane. For the squat motion, the tight and calf were considered as being coplanar all squat time. Figure 3a presents the geometry of the lower limb, where the height of the ankle la was measured from the ground to the lateral malleolus, the length of the calf lc was measured from the lateral malleolus to the lateral femoral condyle, and the length of the tight lt was measured from the lateral femoral condyle to the greater trochanter.

Figure 3.

Geometry of the leg model for the squat exercise (a); the relation between IMU and global coordinate systems (b). The segments of the leg are the height of the ankle la, length of the calf lc, and length of the tight lt. The loading mass is concentrated in point m.

The angular position of the calf and tight were described by declination from the plumb line, measured by the angles α and β. In the starting position, both angles were taken equal to zero. Angles were calculated from the quaternion data: the Euler’s yaw angle was calculated first, the angles α and β were calculated as a difference between the current yaw angle and the angle, calculated for the starting position. The angles were used further to recalculate the acceleration vector from the IMU-related coordinate system to the global coordinate system (Fig. 3b).

The calculation of forces was made using the model (Fig. 3a), based on the simplified inverse dynamic approach [14]. As the subject made squats slowly, the tight was considered as being in quasi-equilibrium. The loading mass m, being 1/2 of the total body mass, was concentrated at the proximal end of the tight. In such a setup, the torque of the gravity force Ng=𝑚𝑔𝑙t⋅sin⁡β is equal to the torque, provided by quadriceps muscular force Nm=Fm⁢r, where the lever arm r is the distance between the knee rotation axis and the quadriceps tendon attachment point. In this work, the arm r was taken equal to 1/2 of the subject knee joint anterior-posterior thickness, or 4.5 cm. The force F, applied to the knee joint, was evaluated as being equal to the quadriceps muscle force:

Using this model, the knee torque and force were calculated for all squat duration.

The parameters of the subject, involved in the research were: body mass 86 kg, the height of the ankle la= 11 cm, the length of the calf lc= 41 cm, and the length of the tight lt= 44 cm.

2.4The plantar pressure estimation

In the scope of the present research, the plantar pressure was not calculated. Instead, the values of reciprocal readouts of the sock sensors were used. These reciprocal values, measured in kOhm-1, are directly proportional to the plantar pressure. Such an approach is adequate, and even preferable, for the purpose of future application of the smart socks for the development of knee joint overload application: exploring the relationship between knee joint load and reciprocal sensor readout, one could use the latter as an input value for the alert algorithm directly, without additional recalculation from sock data to the plantar pressure data.

The research used data from metatarsal sensors, middle sensor, and heel sensors (sensors 1, 2, 4, 5, 6, Fig. 1a). Sensor 3, placed under the foot ark, was excluded, as it was not loaded during barefoot exercises. The sum of the reciprocal readouts from all five sensors was used to detect foot contact instances in walking/running tasks and separate stance phase waveforms.

3.1Correlation between knee joint force and sock sensor data

Figure 4.

The typical waveforms of the estimated knee joint force (top) and average reciprocal sock sensors readout (bottom) for a series of squats.

Figure 4 represents the typical waveforms of the estimated knee joint forces and reciprocal sock sensor readouts in a series of squats. The calculated knee joint force ranged from about 0.5 kN at the beginning of the squat (i.e. in the start position) to 4 kN at the maximal squat depth. These values correspond to the range of 0.58 to 4.6 body weights (BW) and, generally are close to data, reported in the literature for squatting [10]and high-risk dynamic tasks [38], and are reasonably higher, than forces, reported for walking/running [15]. The force maximums generally coincided with the sensor readouts, and hence, with plantar pressure maximums. The readout, presented in Fig. 4. is an average of five sensors waveforms. Analysis of the recordings of each individual sensor revealed that not all sensor waveforms exhibit clear congruence with the force waveform, as the averaged data do. The best coincidence was found for the lateral toe sensor (sensor 2, Fig. 1b). The coincidence between waveforms was evaluated both graphically and numerically. Figure 5 shows correlation diagrams between knee joint force and readouts of some sensors. The diagrams reveal a moderate knee joint force association with averaged sensors data and data from the lateral toe sensor (sensor 2), but poor correlation with, e.g., medial and heel sensors (sensors 4 and 6). The correlation coefficients, summarized in Table 1, endorse this observation. These (Pearson) correlation coefficients were calculated for each sensor and for each squat series. The P-value, associated with the t-test was lower than 0.001 for each coefficient. This indicates a high level of significance, but such low P-values may be related just to the big number of points (more than 3000 for each measurement). A strong correlation with correlation coefficients exceeding 0.7 is observed for the lateral toe sensor and averaged data only. Note that for the heel sensor, the correlation coefficient is negative, and its value, being about -0.65, suggests a moderate correlation. This result, generally, could be expected, as it just indicates the lift of the heel during deep squats. As the averaged sensor data provided the highest correlation coefficients, these data were used for further analysis.

Figure 5.

The correlation diagram for the estimated knee joint force and reciprocal data of the selected sensors: a) averaged data; b) toe lateral sensor (Sensor 2); c) middle lateral sensor (Sensor 4); d) heel lateral sensor (Sensor 6).

3.2Linear regression model

A simple mathematical model for the prediction of knee joint force was built using linear regression. Two models were considered: one with non-zero intercept, and another with zero intercept. The model was constructed for each squat series separately and for the merged together data from all series. Table 2 summarizes the parameters of the models. For all models, either with zero or non-zero intercept, the model coefficients are significant at the level of 0.05: the ± 1.96σ confidence intervals do not include zero. On the other hand, the R2 values are greater for the models with zero intercept (0.87–0.91), as compared with models with non-zero intercept (0.56–0.72). In addition, the ± 1.96σ confidence intervals of both slopes and intercepts are overlapping for different measurement series. Taking the above into account, the predictive model was built using all series data, with zero intercept. The resulting model is:

where F is a knee joint force, but X is an average of the reciprocals of readouts of the sock sensors, measured in kOhms. In this model, the slope coefficient is determined with an uncertainty of 1.1%. The standard deviation of the force estimate is 0.9 kN, that, considering the range of the estimated force from 0.5 to 4 kN, corresponds to the fiducial uncertainty 22%.

Figure 6.

Linear regression approximation for the estimated knee joint force (a) and corresponding Bland-Altman plot (b).

Figure 6a shows the linear model in comparison with the scattering diagram knee joint force – sensor readouts. Despite the rather high R2 value, the experimental data demonstrates a high degree of variability. To compare the model prediction with the experimental data, the Bland-Altman plot was constructed (Fig. 6b). The plot shows rather poor agreement between the model and experiment. The uncertainty of the force estimation could reach 2 kN in the middle of the knee force variation range. Still, for the forces that fall in the interval from about 0.9 from maximal force and above, the uncertainty remains within 20%. Since the potential application of the model is a prediction of extremely high forces and overloads, such accuracy at the highest force values could be satisfactory.

3.3The overload detection

To simulate the detection of the extremely high forces, the developed linear model (Eq. (2)) was used to design an overload test. The force equal to the 0.9 of the maximal observed force 4.1 kN was chosen as a threshold. If the force, calculated from Eq. (2), exceeded the threshold, the test was considered as positive – overload was detected. The prediction of the linear model was compared with actual knee joint force values, classified using the same principle. The 2x2 contingency table of the test is presented in Table 3. The resulting parameters of the tests are sensitivity 0.31, and specificity 1.00. The total accuracy of the test, measured as the ratio of the total number of correct predictions (either positive or negative) to the total number of cases, was 0.82. Such parameters mean that the test could detect about 31% of all overload cases, but never generates false alert. Bearing in mind the nature of physical exercises that are repeated for a long time, such a low sensitivity still is acceptable. As the potential purpose of the perspective alert system is to prevent long-term overload, even with low sensitivity, the athlete will be sooner or later alerted about excessive training. For instance, during running, the alert comes at each third step, on average.