3D Tibial Acceleration and Consideration of 3D Angular Motion Using IMUs on Peak Tibial Acceleration and Impulse in Running

ABSTRACT

Purpose

Peak tibial acceleration (PTA) is defined as the peak acceleration occurring shortly after initial contact, often used as an indirect measure of tibial load. As the tibia is a rotating segment around the ankle, angular velocity and angular acceleration should be included in PTA. This study aimed to quantify three-dimensional tibial acceleration components over two different sensor locations and three running speeds, to get a better understanding of the influence of centripetal and tangential accelerations on PTA typically measured in running. Furthermore, it explores tibial impulse as an alternative surrogate measure for tibial load.

Methods

Fifteen participants ran 90 s on a treadmill at 2.8, 3.3, and 3.9 m·s⁻¹, with inertial measurement units (IMUs) located distally and proximally on the tibia.

Results

Without the inclusion of rotational accelerations and gravity, no significant difference was found between axial PTA between both IMU locations, whereas in the tangential sagittal plane axis, there was a significant difference. Inclusion of rotational accelerations and gravity resulted in similar PTA estimates at the ankle for both IMU locations and caused a significant difference between PTA based on the distal IMU and PTA at the ankle. The impulse showed more consistent results between the proximal and distal IMU locations compared with axial PTA.

Conclusions

Rotational acceleration of the tibia during stance differently impacted PTA measured proximally and distally at the tibia, indicating that rotational acceleration and gravity should be included in PTA estimates. Furthermore, peak acceleration values (such as PTA) are not always reliable when using IMUs because of inconsistent PTA proximally compared with distally on an individual level. Instead, impulse seems to be a more consistent surrogate measure for the tibial load.

Running 10 kilometers could comprise over several thousand ground contacts, resulting in significant repetitive impacts on the body while landing on the ground (1). Peak tibial acceleration (PTA) is often used as an indirect measure for the impact load at the tibia (2–6), and several studies link increased PTA to injuries retrospectively (7,8). PTA plays a role in the internal bone loading, even though there is no direct relation between externally measure PTA and the internal tibial bone loading (9,10). Other factors, for instance, the muscle forces acting on tibia and the bending of the tibia under impact, play an important role as well (11–13). Nevertheless, PTA is an easy to use and frequently measured parameter that can help better understand the load on the tibia during running. PTA is defined as the peak axial acceleration value at the tibia occurring shortly after initial contact (IC), commonly measured with an accelerometer (14). PTA typically varies between approximately 2g and 12g, but is highly dependent on factors such as foot strike pattern and orientation and movement of the tibia, stride frequency, and running surface, but also sensor location and running speed (14).

Even though the tibia is often considered a rigid body, the location of the sensor at the tibia influences PTA (14–17). Because the tibia is a rotating segment around the ankle joint during stance, acceleration measured by an accelerometer does not only consist of acceleration caused by impact with the ground (18). One needs to take into account gravitational acceleration, but also location-dependent rotational accelerations like centripetal and tangential accelerations. However, this is often not complied with because the typically used accelerometers cannot measure the kinematics needed to assess gravitational, centripetal, and tangential acceleration (14,15,17). The generally used assumption that PTA can be measured with an accelerometer anywhere on the tibia, because the tibia is a rigid body, is not correct because distal and proximal peak accelerations measured by an accelerometer differ significantly (6,14,16,17).

Centripetal and tangential acceleration are evaluated by the angular velocity and angular acceleration of the tibia, respectively, and the distance from the sensor to the ankle joint (18,19). As a consequence, centripetal and tangential accelerations are larger farther away from the ankle joint, which causes the accelerometer output to differ at different locations across the entire tibia (18). However, sensors are placed at various locations in running studies (14): ranging from 2 to 4 cm (20), 8 cm (21), or 12 cm (22) above the medial malleolus toward placing a sensor on the proximal anteromedial aspect of the tibia (2,5,23). Therefore, it can be expected that different sensor locations will result in different and incomparable PTA values due to the rotational motion of the tibia. To correctly evaluate the role of PTA in tibial bone loading and to compare PTA values measured at different locations, they need to be corrected for angular motion and gravitational aspects.

To get a better understanding of the effects of angular motion and gravitational aspects on PTA and its role in tibial bone loading, running speeds need to be evaluated because running speed affects peak accelerations (14), angular velocity, and angular acceleration during stance. Peak accelerations increase nonlinearly with higher running speed (14), approximately 34% to 42% per 1 m·s⁻¹ (24,25). Running speed will therefore have an influence on the angular velocity of the tibia during stance and consequently on the PTA values, due to faster movement of the leg at higher speeds, with consequently higher initial impact velocity and greater rates of dorsiflexion around the ankle. This likely increased angular velocity of the tibia segment. Hence, running speed is an important factor in peak impact acceleration, as well as in centripetal and tangential acceleration contributions (24,25). As a result, PTA based only on an accelerometer may not always be correctly interpreted or comparable over different running speeds while ignoring the centripetal and tangential accelerations. Corrections for these changing angular motions might allow PTA values to be compared at different running speeds.

In previous work, Lafortune and Hennig (18) used high-speed video recording to estimate centripetal acceleration during running, and showed that this could be as high as 50 m·s⁻² proximally at the tibia. In other studies, significant differences between distal and proximal PTA estimates were found (6,16,17). However, only accelerometers were used in these studies, and therefore, it was not possible to take into account the contribution of the centripetal and tangential components. Lake and Greenhalgh (22) did assess the contribution of the centripetal component in PTA and concluded that centripetal acceleration needs to be taken into account when interpreting tibial impact. However, they did not investigate PTA at different speeds and used an optical motion capture system in a laboratory to estimate centripetal acceleration instead of inertial measurement units (IMUs). IMUs are convenient sensors for this application, as they measure acceleration and angular velocity simultaneously, are easy to use, and are not bound to a laboratory (26). As such, they can provide information about the impact acceleration solely caused by the impact from the ground by taking into account the rotational acceleration. When these rotational accelerations are taken into account, the measured acceleration is theoretically moved to the ankle joint (as the origin of the rotations during stance). Because the ankle joint axis is not obvious to locate from the exterior, the medial malleolus is a practical-to-use surrogate for the ankle joint, taking into account a slight translation. The recommendation to include centripetal and tangential accelerations in PTA estimates (18,22) is still not common practice, but it is needed to obtain a consistent PTA estimate at the ankle joint. The resulting PTA at the ankle joint is then independent of sensor location and valid over varying running speeds.

Investigating a single peak value, like PTA, is highly dependent on a sufficient sample frequency of the IMU in order not to miss the exact peak (27). Typically, the IMU sample frequency is lower compared with an accelerometer (14). The question rises if PTA based on a single sample obtained with an IMU is an appropriate measure or if a more robust method to obtain consistent and accurate estimates of the impact is needed. The mechanical impulse is used more often for impact evaluation with, for example, force plate (FP) data (28) or pressure insoles (29,30), but also the time integral of foot acceleration curves can be used as impulse (31). The impulse takes into account not only the magnitude but also the time duration of the impact and is therefore evaluating impact not only at the peak value but also during the entire impact wave. The impulse could therefore be a more appropriate surrogate measure for the external load on the tibia during the impact phase using IMUs, while still taking into account angular velocity and angular acceleration.

Assessment of three-dimensional (3D) PTA including centripetal, tangential, and gravitational acceleration over different sensor locations and speeds has not been considered yet, but may provide relevant information about the total contribution of the acceleration caused by ground impact at the tibia. Furthermore, the investigation of the single-valued PTA estimate versus the impulse could give insight into whether PTA estimates should still be used in biomechanics research, or other surrogate measures are more appropriate. This study aimed to quantify all 3D tibial acceleration components over two different sensor locations on the tibia and three running speeds (2.8, 3.3, and 3.9 m·s⁻¹), to explore the contribution of centripetal and tangential accelerations in PTA. Furthermore, the tibial acceleration was evaluated with the more robust estimate of the impulse while using an IMU.

It is hypothesized that PTA measured using an accelerometer at the tibia differs significantly from PTA values transferred to the ankle when taking into account the rotational components. In addition, it is expected that PTA at the ankle shows a greater increase with increasing running speeds compared with PTA measured using an accelerometer on a certain distance from the ankle, caused by the contributions of centripetal and tangential accelerations. Furthermore, it is expected that an impulse-based measure of tibial acceleration can give a more consistent measure of the external impact on the tibia compared with a single-valued PTA estimate. This underlines that PTA, measured by accelerometers, seems to have a doubtful future as a surrogate measure for tibial bone load.

METHODS

This study was part of a larger project, but only the relevant parts for this research are described here.

Participants

Fifteen recreational runners (male-to-female ratio, 10:5; 31.7 ± 9.9 yr; 182.1 ± 9.6 m; 76.3 ± 16.1 kg; 13 right dominant, 2 left dominant; distance of distal IMU from the ankle, 11.3 ± 2.3 cm; distance of proximal IMU from the ankle, 30.7 ± 3.2 cm; tibia length, 43.9 ± 2.9 cm) were included in this study. They ran recreationally (>15 km·wk⁻¹ on average, for at least 6 months) and had a self-reported habitual rearfoot strike (RFS) pattern. They were able to run 3.9 m·s⁻¹ for at least 5 min. They reported no major injuries in the past 6 months and had some experience with treadmill running. The local ethics committee (University of Twente, EEMCS EC-CIS; reference: RP2021-117) approved the experimental protocol of this study. All participants signed a written informed consent form. Eighteen participants volunteered to join this study. Three participants were excluded because of a clear forefoot strike, because of malfunction of IMUs, or because they were not able to finish the complete protocol.

Measurement Devices

The protocol was performed on one side of a split-belt treadmill (custom Y-mill; Motek, Culemborg, the Netherlands) with an embedded 3D FP (sampling at 1024 or 2048 Hz). Three IMUs (dimensions, 36 × 24.5 × 10 mm; mass, 10 g; Xsens MVN Link (Movella Technologies BV, Enschede, the Netherlands) measured angular velocity (range, ±2000 deg·s⁻¹) and acceleration (range, ±16 g) with a sampling rate of 240 Hz. Two IMUs were placed on the tibia of the dominant leg, distally and anteromedially (11.3 ± 2.3 cm above the medial malleolus; Fig. 1) and proximally on the anteromedial surface of the tibia (30.7 ± 3.2 cm above the medial malleolus; Fig. 1), respectively. A third IMU was located proximally on the anteromedial surface of the nondominant tibia, used for time synchronization (see Data Processing). IMUs were attached to the skin with double-sided skin-friendly tape and were covered by a layer of strapping tape. The participant wore compressing socks over the tibia to minimize movement of the tibia IMUs following the method proposed by Scheltinga et al. (32). The lower extremity kinematics were recorded in the sagittal plane with a camera on a tripod (JVC GC-PX100BE, Yokohama, Japan).

FIGURE 1.

Distal (above ankle) and proximal (below knee) IMU on the tibia of the dominant leg. Left: frontal plane view, IMUs shown as originally attached to the tibia in Ψ_IMUp and Ψ_IMUd. Right: sagittal plane view, IMU CS shown as rotated based on principal component analysis (see “Data Processing”) into Ψ_IMUpfand Ψ_IMUdf.

Experimental Design

Foot strike pattern was recorded with the video camera during all trials. RFS was defined as the rear end of the shoe hitting the ground first. If the participant had a confirmed RFS on video, the participant was included in the study. Only rearfoot striking participants were included to eliminate the effect of foot strike pattern on PTA (33).

Anthropometric measurements of the foot and tibia were performed, and the dominant leg was determined by asking the participant with which leg they would kick a ball (34). Only the dominant leg was evaluated to avoid inclusion of any asymmetric behavior of the legs in the analysis (35). Before the measurement, participants performed a self-chosen warming-up. Participants ran for 90 s at three different speeds (2.8, 3.3, 3.9 m·s⁻¹) in randomized order on their preferred stride frequency, with at least a 3-min rest in between each trial to minimize fatigue.

Data Processing

Xsens software (Xsens MVN Analyze Pro 2021.0.1) was used to acquire data from the IMUs. Angular velocity and acceleration were directly obtained from the IMUs, without calibration or alignment with an anatomical coordinate system (CS). MATLAB (MathWorks Inc., Natick, MA; version 2021b) was used for data processing.

3D sensor accelerations and 3D sensor angular velocity were acquired from the IMUs (240 Hz). IMU data were obtained in a proximal (Ψ_IMUp) or distal (Ψ_IMUd) IMU-dependent CS, with z axis pointing upward, x axis frontally, and y axis to the left in the IMU frame to fit a right-handed CS (see both CS on the left in Fig. 1). Ψ_IMUpwas rotated with a time-independent rotation matrix based on principal component analysis of the 3D IMU angular velocity of the entire trial (36). This creates a functional axis perpendicular to the sagittal plane movement of the tibia, to have IMU data with the y axis always as main rotational axis. This allows movement of the IMU with the tibia mainly in the sagittal plane to form a functional IMU-dependent CS: Ψ_IMUpf. The same method was applied to Ψ_IMUd to obtain Ψ_IMUdf (see CS on the right in Fig. 1).

Vertical ground reaction force (vGRF) was obtained from the FP and was down-sampled toward 240 Hz from 1024 or 2048 Hz (depending on FP settings) to match IMU sample frequency. Time synchronization of both systems was done with three vertical jumps at the start and end of each trial. Axial acceleration (including gravity) of the left and right proximal tibia IMU during the first three jumps was used for normalized cross-correlation with the vGRF of the FP. Three jumps at the end of the trial were used to check this time synchronization, where FP data were interpolated to compensate for a potential mismatch of the internal clocks of the FP and IMU system.

Angular acceleration was obtained as the time derivative of angular velocity. Angular velocity and angular acceleration were filtered with a zero-phase second-order Butterworth filter. A cutoff frequency of 30 Hz was used for the angular velocity data, based on Falbriard et al. (37). Angular acceleration was filtered with a cutoff frequency of 15 Hz, based on Lafortune and Hennig (18). Sensor acceleration and FP data were filtered with a zero-phase second-order Butterworth filter with a cutoff frequency of 60 Hz according to Lafortune and Hennig (18).

Thirty strides were obtained halfway through the 90-s run at each speed, and these were used in further processing. IC and toe-off (TO) were determined when the vGRF measured by the FP exceeded or fell below 30 N, respectively. The distance from the medial malleolus toward the distal or proximal IMU origin was measured with measure tape, but if not available, the distance was estimated with the video recording where the participant was standing still. The shoe length (in centimeters) and height of the lateral malleolus to the floor (in centimeters) were measured with measure tape. These distances were used in the video recording to estimate the distance from the medial malleolus to IMU.

The determination of the gravitational acceleration and the alignment of Ψ_IMUpf and Ψ_IMUdf can be found in the Supplemental Digital Content (see text, Supplemental Digital Content, Gravitational acceleration determination and alignment of Ψ_IMUpf and Ψ_IMUdf, http://links.lww.com/MSS/C891). Ψ_IMUpf and Ψ_IMUdf are now assumed identical over time and defined as Ψ_IMUf in the remainder of this article.

Parameters

PTA and its components (3D)

With Rigid Body Kinematics (RBK) one can obtain the acceleration on a specified location on a rigid body based on the kinematics measured by a body-mounted IMU (19,38), using equation 1:

$${\overrightarrow{\mathit{a}}}_2={\overrightarrow{\mathit{a}}}_1+\overrightarrow{\mathit{\alpha }}\times {\overrightarrow{\mathit{r}}}_{1\to 2}+\overrightarrow{\mathit{\omega }}\times \left(\overrightarrow{\mathit{\omega }}\times {\overrightarrow{\mathit{r}}}_{1\to 2}\right)$$ [1]

 where ${\overrightarrow{\mathit{a}}}_2$is the estimated acceleration (m·s⁻²) on a specified location and ${\overrightarrow{\mathit{a}}}_1$ is the IMU-measured acceleration (m·s⁻²). Angular acceleration, $\overrightarrow{\mathit{\alpha }}$ (rad·s⁻²), is the time derivative of the angular velocity measured by the IMU, $\overrightarrow{\mathit{\omega }}$ (rad·s⁻¹). ${\overrightarrow{\mathit{r}}}_{1\to 2}$ (m) is the 3D position vector from the IMU location toward a specified location.

Equation 1 forms the base to translate the acceleration measured with an IMU (i.e., ${\overrightarrow{\mathit{a}}}_1$) to the ankle joint (i.e., ${\overrightarrow{\mathit{a}}}_2$) for both IMUs. One can derive three distinctive equations for the acceleration estimate at the ankle joint for each axis in Ψ_IMUf: tangential in sagittal plane (x axis in Ψ_IMUf, equation 2), tangential in the frontal plane (y axis in Ψ_IMUf, equation 3), and axially (z axis in Ψ_IMUf, equation 4):

$${a_{\text{free},\text{ankle}}}_x\left(t\right)=\left(a_{\mathrm{IM}{\mathrm{U}}_x}\left(t\right)-g_x\left(t\right)\right)-{\alpha }_y\left(t\right)r_z$$ [2]

$${a_{\text{free},\text{ankle}}}_y\left(t\right)=\left(a_{\mathrm{IM}{\mathrm{U}}_y}\left(t\right)-g_y\left(t\right)\right)-{\alpha }_x\left(t\right)r_z$$ [3]

$${a_{\text{free},\text{ankle}}}_z\left(t\right)=\left(a_{\mathrm{IM}{\mathrm{U}}_z}\left(t\right)-g_z\left(t\right)\right)+{\omega }_y^2\left(t\right)r_z+{\omega }_x^2\left(t\right)r_z$$ [4]

 with $\overrightarrow{{\mathit{a}}_{\text{free},\text{ankle}}}$ (m·s⁻²) as the gravity-free acceleration at the ankle joint, $\overrightarrow{{\mathit{a}}_{\mathrm{IMU}}}$ (m·s⁻²) as IMU-measured acceleration, and $\overrightarrow{\mathit{r}}$ (m) as distance between the IMU and the medial malleolus. Centripetal acceleration is defined as $\overrightarrow{{\mathit{\omega }}^{\mathbf{2}}\mathit{r}}$ (m·s⁻²), tangential acceleration as $\overrightarrow{\mathit{\alpha r}}$ (m·s⁻²), and gravitational acceleration as $\overrightarrow{\mathit{g}}$ (m·s⁻²). Radius $\overrightarrow{\mathit{r}}$ was only evaluated in the axial direction (z axis in Ψ_IMUf), due to assumed negligible contributions of r_x and r_y.

PTA_anklez was taken as the peak value of the a_{free, anklez} estimate during each stance phase (IC to TO). PTA_anklex and PTA_ankleywere defined as a_{free, anklex} and a _{free, ankley} at the time instant of max(PTA_anklez), respectively. PTA_IMUz was taken as the peak value of a_IMUz during the stance phase (IC to TO), PTA_IMUx and PTA_IMUy were defined as a_IMUx and a_IMUy at the time instant of max(a_IMUz), respectively. All individual acceleration components on the right side of equations 2–4 were evaluated at the time instant of max(a_IMUz).

Area under curve: the impulse

The time integrals of a_IMUz and a_{free, anklez} were taken to obtain the area under the curve (impulse) of the axial tibial acceleration. The starting and end point of the integrals were defined as the sample closest to the zero-crossings during tibial impact. If there was no zero-crossing at the start, IC was taken as starting point of the impulse.

Statistical Analysis

All data were presented as mean ± SD. Statistical significance was set at α = 0.05, all statistical tests were performed in IBM SPSS Statistics (IBM, Armonk, NY; version 28.0.1.0).

A repeated-measures two-way ANOVA with Bonferroni post-hoc analysis was performed to test the differences between the distal and proximal IMU location, and type of measure ( $\overrightarrow{{\mathit{a}}_{\mathrm{IMU}}}$ or $\overrightarrow{{\mathit{a}}_{\text{free},\text{ankle}}}$) over three running speeds. The Greenhouse–Geisser correction was used for the correction on sphericity. Effect size was evaluated via the common ANOVA-related partial eta squared (η²), defined as small effect size for η² < 0.06, medium 0.06 ≤ η² < 0.14, and large for η² ≥ 0.14 (39).

Pearson’s correlation coefficient (r) was used for the relationship between peak acceleration and impulse. Here, ±(r ≥ 0.8) is a strong correlation, ±(0.5 ≤ r < 0.8) as a moderate correlation, ±(0.3 ≤ r < 0.5) as a weak correlation, and ±(r < 0.3) as a negligible correlation (40). An a priori power calculation (G*Power 3.1.9.7) (41) showed for an expected large effect size of η² = 0.14 (Cohen f = 0.40) and a power of 0.95 to include at least nine participants.

RESULTS

PTA and Its Components (3D)

Figure 2 shows all tibial acceleration components over the complete stance phase, for the x and z axes in Ψ_IMUf at the proximal IMU location. Tables 1 and 2 show the acceleration values at both IMU locations and over all speeds for the x and z axes in Ψ_IMUf, respectively. Contribution of the y axis in Ψ_IMUf was limited and therefore not shown here (see Supplemental Table 1, Supplemental Digital Content, Data of y axis in Ψ_IMUf, http://links.lww.com/MSS/C891).

FIGURE 2.

All tibial acceleration components from equations 2 and 4 visualized in the complete stance phase for one participant at 3.3 m·s⁻¹ at the proximal IMU location. Axes shown in the Ψ_IMUf CS. Mean over 30 strides visualized with a shaded SD. Impulse window also visible.

TABLE 1.

Acceleration components as mentioned in equation 4, based on both IMU locations.

Axial Axis (z Axis in ΨIMUf)
	Proximal IMU			Distal IMU
	2.8 m·s−1	3.3 m·s−1	3.9 m·s−1	2.8 m·s−1	3.3 m·s−1	3.9 m·s−1
PTAIMUz, m·s−2	60.92a,b ± 9.05	72.01a,b,c ± 10.98	85.74a,b ± 16.63	63.07a,b,c, ± 10.86	75.74a,b,c ± 12.21	89.69a,b,c ± 16.15
${\omega }_y^2{r}_z$, m·s−2	7.69 ± 2.75	10.24 ± 3.92	12.69 ± 4.87	3.96 ± 1.02	5.05 ± 1.19	6.29 ± 1.75
${\omega }_x^2{r}_z$, m·s−2	0.96 ± 0.76	1.29 ± 0.97	1.55 ± 1.19	0.24 ± 0.13	0.33 ± 0.24	0.40 ± 0.23
gz, m·s−2	9.73 ± 0.09	9.71 ± 0.11	9.71 ± 0.11	9.73 ± 0.10	9.71 ± 0.11	9.71 ± 0.11
PTAanklez, m·s−2	59.89a,b ± 9.58	73.91a,b ± 12.38	90.38a,b ± 17.89	58.29a,b,c ± 11.29	72.43a,b,c ± 13.11	87.89a,b,c ± 17.22

Values are reported as mean ± SD. PTA_IMUz and PTA_anklez are the values of max(a_IMUz) and max(a_{free, anklez}), respectively.

^aSignificant difference over speed.

^bSignificant interaction measure–speed.

^cSignificant difference between measures PTA_IMUz and PTA_anklez.

TABLE 2.

Acceleration components as mentioned in equation 2, based on both IMU locations.

Tangential Sagittal Plane axis (x Axis in ΨIMUf)
	Proximal IMU			Distal IMU
	2.8 m·s−1	3.3 m·s−1	3.9 m·s−1	2.8 m·s−1	3.3 m·s−1	3.9 m·s−1
PTAIMUx, m·s−2	−0.45a,b.c,d ± 21.30	−0.61a,b.c,d ± 24.75	0.73a,b.c,d ± 23.73	−9.30a,b.c,d ± 25.75	−16.32a,b.c,d ± 26.81	−23.11a,b.c,d ± 31.70
${\alpha }_y^2{r}_z$, m·s−2	17.94 ± 7.38	22.35 ± 8.86	24.93 ± 10.58	8.34 ± 2.51	9.40 ± 2.33	10.26 ± 2.84
gx, m·s−2	−0.09 ± 1.14	0.14 ± 1.19	0.38 ± 1.05	−0.14 ± 1.16	0.10 ± 1.21	0.33 ± 1.10
PTAanklex, m·s−2	−19.45c,d ± 20.35	−24.60c,d ± 24.80	−26.36c,d ± 28.41	−17.97c,d ± 25.65	−26.49c,d ± 25.71	−34.26c,d ± 30.32

Values are reported as mean ± SD. PTA_IMUx is the value of a_IMUx at the time instant of max(a_IMUz), PTA_anklex is the value of a_{free, anklex} at time instant of max(a_{free, anklez}).

^aSignificant difference between IMU locations.

^bSignificant interaction location–speed.

^cSignificant difference between measure PTA_IMUx and PTA_anklex

^dSignificant interaction measure–speed.

Axial axis (z axis in Ψ_IMUf)

.Table 1 shows all accelerations components in the z axis in Ψ_IMUf. PTA_IMUz only increases over speed (P < 0.001, F = 67.62, η² = 0.83) for both IMU locations. Centripetal acceleration around the y axis increases over speed, whereas centripetal acceleration around the x axis has a relatively small contribution. Distal and proximal PTA_anklez values only show a significance difference over speed (P < 0.001, F = 90.92, η² = 0.87).

Figure 3 shows the difference between PTA_IMUz and PTA_anklez. Proximally, a significant difference over speed (P < 0.001, F = 6.86, η² = 0.83) and their interaction (P < 0.001, F = 57.31, η² = 0.80) are observed. Distally, changes are observed over speed (P < 0.001, F = 66.72, η² = 0.83), measure (P < 0.001, F = 57.87, η² = 0.81), and their interaction (P < 0.001, F = 73.43, η² = 0.84).

FIGURE 3.

Difference of PTA_anklez versus PT_AIMUz based on the proximal and distal IMU locations.

Tangential sagittal plane axis (x axis in Ψ_IMUf)

Table 2 shows all acceleration components in the x axis in Ψ_IMUf. PTA_IMUx differs significantly proximally versus distally (P = 0.028, F = 6.00, η² = 0.30) and their interaction (P = 0.045, F = 4.41, η² = 0.24). The tangential acceleration increases over running speed, resulting in no difference in estimation of PTA_anklex from either IMU location, where PTA_anklex only decreases over running speed (P = 0.027, F = 5.58, η² = 0.29, no post-hoc pairwise significance).

PTA_anklex shows a significant difference with PTA_IMUx proximally (P < 0.001, F = 112.04, η² = 0.89) and their interaction speed–measure (P = 0.001, F = 13.29, η² = 0.49). Distally, the same changes are observed between PTA_anklex and PTA_IMUx (P < 0.001, F = 129.75, η² = 0.90), and their interaction (P = 0.001, F = 9.22, η² = 0.40), but also a relatively small change in speed (P = 0.047, F = 4.62, η² = 0.25, no post-hoc pairwise significance).

Area under Curve: The Impulse

Table 3 shows the impulse of a_IMUz and a_{free, anklez} for both distal and proximal IMU. Based on a_IMUz, the impulse is significantly different between the distal and proximal IMU location (P < 0.001, F = 236.18, η² = 0.94), over speed (P < 0.001, F = 63.64, η² = 0.82) and their interaction (P < 0.001, F = 27.27, η² = 0.66). The impulse of a_{free, anklez} is only significant over speed (P < 0.001, F = 199.76, η² = 0.94).

TABLE 3.

Area under the curve (impulse) of a_IMUz and a_{free, anklez}, based on both IMU locations.

	Proximal IMU			Distal IMU
	2.8 m·s−1	3.3 m·s−1	3.9 m·s−1	2.8 m·s−1	3.3 m·s−1	3.9 m·s−1
Impulse aIMUz, m·s−1	1.16a,b,c,d ± 0.20	1.30a,b,c,d ± 0.18	1.43a,b,c,d ± 0.21	1.40a,b,c,d,e ± 0.20	1.59a,b,c,d,e ± 0.18	1.78a,b,c,d,e ± 0.22
Impulse afree, anklez, m·s−1	1.08a,d ± 0.21	1.31a,d ± 0.22	1.54a,d ± 0.26	1.13a,d,e ± 0.19	1.36a,d,e ± 0.17	1.60a,d,e ± 0.21

Values are reported as mean ± SD.

^aSignificant difference over speed,

^bSignificant difference between IMU locations.

^cSignificant interaction location–speed.

^dSignificant interaction measure–speed.

^eSignificant difference between measure a_IMUz and a_{free, anklez}.

Between a_IMUzand a_{free, anklez} proximally, there is a significant difference over speed (P < 0.001, F = 106.36, η² = 0.88) and their interaction measure–speed (P < 0.001, F = 75.12, η² = 0.84). Distally, there is a difference over speed (P < 0.001, F = 113.40, η² = 0.89), measure (P < 0.001, F = 194.80, η² = 0.93), and their interaction (P < 0.001, F = 48.67 η² = 0.78).

Figure 4 shows the mean impulse (from a_{free, anklez}) and mean PTA_anklez for every participant, based on the proximal and distal IMU, including the Pearson correlation coefficient at each speed. Based on the distal IMU, PTA and impulse showed a moderate correlation: r = 0.64 at 2.8 ms⁻¹, r = 0.52 at 3.3 ms⁻¹, and r = 0.64 at 3.9 ms⁻¹. A moderate to strong correlation was found based on the proximal IMU, with r = 0.84 at 2.8 ms⁻¹, r = 0.73 at 3.3 ms⁻¹, and r = 0.79 at 3.9 ms⁻¹.

FIGURE 4.

PTA estimates versus the impulse, as a mean of over 30 strides of each participant. Data shown for 2.8, 3.3, and 3.9 m·s⁻¹ including Pearson correlation (r) for each speed.

DISCUSSION

The aim of this study was to evaluate all 3D tibial acceleration components over two different sensor locations and three running speeds (2.8, 3.3, 3.9 m·s⁻¹), to show the contribution of angular velocity and angular acceleration in the 3D PTA estimate during running. Furthermore, the impulse of the tibial acceleration was evaluated as a more robust surrogate measure for impact load while using an IMU.

Axial peak accelerations measured by the distal IMU accelerometer (a_IMUz) were slightly higher compared with the proximal IMU accelerometer on a group level; however, there was no significant difference found between both IMU locations over all speeds (Table 1). This indicates that it did not matter here where the IMU was attached, but this is in contrast with previous literature (6,16,17). Lucas-Cuevas et al. (6) did find a significant difference between a distal and proximal location at 2.2, 2.8, and 3.3 m·s⁻¹. Accelerometers were attached close to the distal end and to the anteromedial aspect of the tibial; however, no clear participant-specific clarification was given (6). The results of (6,16,17) show the importance of the location of the accelerometer in PTA estimates. The nonsignificant difference between peak proximal and distal accelerations found here can be explained by the fact that the IMUs could be located closer to each other at the tibia, resulting in a smaller difference between the distal and proximal IMU accelerations. Another reason for a small distal versus proximal a_IMUz difference is that four participants showed a higher proximal peak value compared with the distal peak value (see Supplemental Table 2, Supplemental Digital Content, Differences between distal and proximal subject-specific PTA and impulse values, http://links.lww.com/MSS/C891). Tissue artifacts or muscle contractions could influence the measurements. However, the IMUs were tightly fitted and did not get loose from the tibia during the measurements; still, external factors can influence the peak acceleration values distally and proximally as shown here. A majority of PTA studies do only use one sensor on the tibia (e.g., [2]), therefore not directly evaluating external factors as there is no reference sensor on the same segment. Therefore, it is unknown how reliable PTA measurements with IMUs are in previous literature because of the influence of these external factors. Furthermore, the generally lower sample frequency of an IMU compared with high-sampling accelerometers could result in missing the actual PTA value; however, this should occur on both IMU locations. The result of this study indicates that peak accelerations taken at the tibia could not always be trustworthy, and PTA based on a single sample could be highly influenced by external and sensor-related factors, providing evidence for shifting interest toward more robust measurement, like the impulse.

Centripetal acceleration around the y axis in Ψ_IMUf showed a difference between IMU locations and over speed (Table 1), confirming the importance of the inclusion of centripetal acceleration over different speeds. Lafortune and Hennig (18) found a centripetal acceleration of approximately 50 m·s⁻² for runners, five times higher than found here. Their rotation arm of 0.42 m, on average, was almost 1.5 times the rotation arm in this study. However, this does not explain the big difference. Lake and Greenhalgh (22) corrected the impact peak by +1.5g to +3g for their two participants because of gravitational and centripetal acceleration, which implies a centripetal acceleration of approximately 25 to 40 m·s⁻². In this study, the angular velocity measured here was in the same range of similar joint angular velocities (42). Running overground compared with running on a treadmill, specific running technique of the participants or the use of optical motion capture for estimation of angular velocity in these studies could be factors for this difference, but this remains not fully understood.

The increment of centripetal acceleration over increasing speed causes that the PTA_anklez does differ from the PTA_IMUz over different speeds, as hypothesized. At the proximal IMU location, the PTA_anklez and PTA_IMUz are approximately the same (Table 1), as the centripetal acceleration value is similar to the gravitational acceleration. Although differences are small, PTA seems to show a steeper slope of increment over different running speeds as centripetal acceleration increases over speed compared with the constant gravitational acceleration. The significant interaction speed–measure (P < 0.001) underlines this behavior at the proximal IMU location. The distal IMU location showed a bigger systematic offset between PTA_anklez and PTA_IMUz, caused by a smaller centripetal acceleration (between 3.96 and 6.29 m·s⁻²) compared with the proximal IMU location. These results suggest that measuring on a proximal IMU location is closer toward the actual impact PTA compared with a distal IMU location because of this larger offset. Overall, the difference between PTA_anklez and PTA_IMUz was found but expected to be greater, as described by Lafortune and Hennig (18).

To the author’s knowledge, tangential acceleration has not been evaluated in previous PTA studies but does have a relevant contribution in the x axis in Ψ_IMUf for the acceleration during running (Table 2). Inclusion of tangential acceleration makes PTA in the x axis in Ψ_IMUf more negative for both IMU locations, which can be expected during the braking phase at impact, where the forward-directed tangential acceleration of the tibia cancels out this braking acceleration, especially in studies investigating the 3D vector norm of tibial acceleration that take this tangential acceleration factor into account and are therefore likely to misinterpret the PTA. Thus, the braking impact acceleration is actually strongly negative compared with what an accelerometer actually measures.

The inclusion of angular velocity and angular acceleration is needed to accurately estimate PTA by impact with the ground only. This is substantiated by the slightly different slopes of PTA_anklez compared with PTA_IMUz over different speeds, and the difference in PTA_anklez versus PTA_IMUz distally. Still, accelerometers are often placed distally (20–22), which results in an offset between PTA_IMUz and PTA_anklez. Furthermore, for both the proximal and distal IMU locations, the PTA_anklez showed a steeper increment over different running speed compared with PTA_IMUz. This makes inclusion of centripetal and tangential accelerations an interesting finding for more accurate PTA estimates over different speeds, although the contributions are smaller compared with previous findings (18,22).

The application of RBK to take into account centripetal and tangential accelerations depends on angular velocities and therefore on IMUs: the question rises if such a sensor can measure accurately enough because they generally have a lower sample frequency. A lower sampling frequency allows for prolonged measurement of multiple parameters (e.g., sensor acceleration, angular velocity, and sensor orientation) indoors and outdoors (2), but might have limitations for the assessment of the exact peak in PTA. The inclusion of angular velocity and angular accelerations seems necessary to estimate tibial acceleration by impact only, however. An option to counteract this is to look at the impulse: the impulse has already its applications in force impact estimates of GRF (28) or pressure insoles (29) as mechanical impulse. The impulse used here, the time integral of tibial acceleration, ignores the effective mass that is accelerated. However, the time integral includes not only magnitude but also the time interval over which it acts. The impulse seems therefore more robust against external factors and less dependent on sampling frequency. The impulse under a_IMUzcurve showed a significant difference over speed (P < 0.001, F = 63.64, η² = 0.82), location (P < 0.001, F = 236.18, η² = 0.94), and their interaction speed–location (P < 0.001, F = 27.27, η² = 0.66) between the proximal and distal locations. The four participants showing higher proximal peak acceleration values compared with the distal IMU did show a larger impulse distally (see Supplemental Table 2, Supplemental Digital Content, Differences between distal and proximal subject-specific PTA and impulse values, http://links.lww.com/MSS/C891) as one would expect: a larger peak acceleration is expected distally as there is less influence of centripetal accelerations. Because the PTA values obtained here do not always show this behavior, while impulse does, for all participants, underlie that a single peak value can probably be trusted less compared with the impulse.

The impulse based on a_IMUz does show a significant difference between IMU locations: this relates to the findings of Lucas-Cuevas et al. (6) based on distal and proximal PTA. The impulse of a_{free, anklez} did not show a significant difference between IMU locations, as expected, as they both are translated toward the ankle based on RBK. Pearson correlation coefficients showed moderate to strong correlations between impulse and PTA, indicating that impulse gives relatable results compared with PTA. Including the impulse instead of only one peak value seems, as hypothesized, a more robust estimate of tibial impact load as surrogate measure and should be investigated in further research.

The sample frequency used here with IMUs (240 Hz) can, as a result, be seen as a limitation, as articles investigating (peak) impact acceleration frequently usually use accelerometers with a high sample frequency of 1000 Hz or higher (14). This high frequency is, based on the articles mentioned in the review of Sheerin et al. (14), chosen to detect the peak value accurately. However, Reenalda et al. (2) found that 96.3% of the impact acceleration signal is less than 50 Hz, measured with a 1200-Hz accelerometer. This indicates that a sample frequency of 240 Hz can theoretically detect frequencies up to 120 Hz. Furthermore, Mitschke et al. (27) defined that at least a sample frequency of 200 Hz is needed to identify PTA values. Although the sample frequency is lower in IMUs compared with single accelerometers, the need for angular velocity in PTA estimates makes the use of IMUs more suited to find the impact PTA. Still, peak values are not always correctly detected for both IMU locations, creating doubt about the minimal sample frequency needed (27) and the use of single peak acceleration values in surrogate tibial load estimates versus the use of the impulse.

Future research could focus on using more advanced IMUs with higher sample frequencies and less disturbance from external factors (e.g., tissue artifact, muscle contraction). Furthermore, the impulse outcome could include the effective mass to obtain a better estimate of mechanical impulse during running (28). Impulse could also be directly compared with, for example, the average loading rate of a, FP, or in relation to tibial bone load estimate including muscle and external forces (40). Externally measured parameters only provide information about one part of the tibial bone loading estimates. Other factors like muscle forces acting on the tibia and the bending and deformation of the tibia under impact should also be investigated to get a better insight into the etiology of running related injuries of the tibia (9–13). This could eventually contribute to injury prevention. The proposed method could potentially be used in real-time feedback application based on IMUs. For this, the orientation estimation as used in this study (based on Zandbergen et al. [36]) needs to be updated for quasi–real-time orientation estimation. This means that the time-invariant functional axis used for the tibia IMUs needs to be updated and validated to a time-variant functional axis, as this functional axis can vary for every stride when not running on a treadmill or can vary even within a stride. Future research should investigate and validate the use of a time-variant functional axis between and within strides. Furthermore, estimates of the internal forces need to be included.

CONCLUSIONS

The importance of centripetal and tangential accelerations in the estimation of PTA was shown here during treadmill running at different speeds, where significant differences were found between PTA_anklez and PTA_IMUz at two IMU locations. However, the impulse seems to be a more robust parameter to obtain knowledge about the tibial load during running, as the peak IMU-accelerometer values are not always detected correctly. It is suggested to use an accelerometer with high sampling frequency at the medial or lateral malleolus to avoid centripetal and tangential accelerations, or to use an IMU with high sampling frequency at a known location on the tibia to be able to accurately correct for centripetal and tangential accelerations. Concluding, tibial acceleration should be corrected by centripetal, tangential, and gravitational accelerations. It is suggested to use the impulse of a_{free, anklez} to obtain a surrogate measure for tibial bone load. As such, the future might lie in adding centripetal and tangential components when the sampling frequency is sufficient and in evaluating at the impulse.