The Protraction and Retraction Angles of Horse Limbs: An Estimation during Trotting Using Inertial Sensors

Abstract

The protraction and retraction angles of horse limbs are important in the analysis of horse locomotion. This study explored two methods from an IMU positioned on the canon bone of eight horses to estimate these angles. Each method was based on a hypothesis in order to define the moment corresponding with the verticality of the canon bone: (i) the canon bone is in a vertical position at 50% of the stance phase or (ii) the verticality of the canon bone corresponds with the moment when the horse's withers reach their lowest point. The measurements were carried out on a treadmill at a trot and compared with a standard gold method based on motion capture. For the measurement of the maximum protraction and retraction angles, method (i) had average biases (0.7° and 1.7°) less than method (ii) (-1.3° and 3.7°). For the measurement of the protraction and retraction angles during the stance phase, method (i) had average biases (4.1° and -3.3°) higher to method (ii) (2.1° and -1.3°). This study investigated the pros and cons of a generic method (i) vs. a specific method (ii) to determine the protraction and retraction angles of horse limbs by a single IMU.

Keywords: biomechanics; horse; inertial measurement units; limb angles; locomotion; method comparison; protraction; retraction.

Figure 1

Representation of (A) the angle α of protraction of the whole limb measured from the orientation of the segment connecting the tuber spinae scapulae and the hoof with respect to the vertical and (B) of the angle α’ of protraction measured from the orientation of the canon bone (third metacarpal bone) relative to the vertical.

Figure 2

Positioning of the IMU (in red) and kinematic markers on the right front limb and orientation of the laboratory coordinate system ($\overrightarrow{\mathrm{x}},\overrightarrow{\mathrm{y}},\overrightarrow{\mathrm{z}})$. The markers were positioned on specific anatomical landmarks (lateral styloid process of the radius for the carpal joint (Carpus), lateral condyle for the metacarpophalangeal joint (MCP), hoof (toe, heel, front coronary band, lateral coronary band)) and on the IMU (center, up lateral part, down lateral part). The orientation of the canon bone (in yellow) was defined by the coordinates of the Carpus and MCP markers (in blue).

Figure 3

Graphic representation of the moments of the stride at which the angular values α’ of protraction and retraction were measured. (Adapted from the illustration by [42]).

Figure 4

Representation of the canon bone orientation obtained from the MOCAP data for the 26 normalized strides of a trial of one horse trotting at a 4 m/s speed. The maximum and minimum points at each stride, corresponding, respectively, with the ProtractionSwingMOCAP and RetractionSwingMOCAP of the right forelimb, are circled in grey on the Figure. The angles of protraction and retraction at the stance correspond, respectively, with the angles of the canon bone at Foot On and Foot Off, represented by blue circles in the Figure.

Figure 5

Example of dorso-ventral (DV) displacement curves obtained from the IMU of the withers at a 4 m/s trot (26 standardized strides shown) for one of the eight horses that participated in the experimental protocol. For each stride, the first minimum point is obtained during the first oscillation corresponding with the stance of the right front limb (RF) and named minWithersIMU(i). It is followed by a suspension phase before reaching a second minimum point during the second oscillation corresponding with the stance of the left front limb (LF).

Figure 6

Protraction/retraction angles (PR) normalized by the stance phase obtained by calculating the cumulative trapezoidal integral without resetting, named AngleCanonIMU_temps(i) (A), with resetting at the index 50% Stance(i), named AngleCanonIMU_50%S(i) (B) and with resetting to the index minWithersIMU(i), named AngleCanonIMU_minW(i) (C) of the gyroscope signal on the Y axis on the 26 strides recorded during a trial at a 4 m/s trot of one horse (i ranging from 1 to 26).

Figure 7

Bland–Altman graphs for the comparison of the protraction angles at a stance obtained using the indices 50%Stance (A) and minWithers (B) and of the angles of maximal protraction obtained using the indices 50%Stance (C) and minWithers (D) with the protraction angles, respectively, at a stance and at a swing obtained from the MOCAP data. The results for the 4 m/s trot are shown in gray (o) and the results for the 6 m/s trot are shown in blue (Δ). The accuracy (bias between the developed method and the MOCAP) and the limits of the confidence interval (95% of values) are shown for each graph.

Figure 8

Bland–Altman graphs for the comparison of the retraction angles at a stance obtained using the indices 50%Stance (A) and minWithers (B) and of the angles of maximal retraction obtained using the indices 50%Stance (C) and minWithers (D) with the retraction angles, respectively, at a stance and at a swing obtained from the MOCAP data. The results for the 4 m/s trot are shown in gray (o) and the results for the 6 m/s trot are shown in blue (Δ). The accuracy (bias between the developed method and the MOCAP) and the limits of the confidence interval (95% of values) are shown for each graph.