3D spinal motion analysis during staircase walking using an ambulatory inertial and magnetic sensing system

Abstract

Previous research on spinal motion during walking has been restricted to the level walking condition in a gait lab although staircase walking (i.e., stair ascent and descent) exhibits unique biomechanical characteristics. A major difficulty in spinal motion capture during staircase walking is the in-the-lab limitation of measurement techniques. The purpose of this article is twofold: (i) to present an ambulatory spinal motion measurement system based on inertial and magnetic sensors (IMSs) to overcome this limitation and (ii) to demonstrate its application to 3D spinal motion analysis during staircase walking to fill a gap in the spinal kinematics literature. The proposed system is comprised of three tri-axial IMSs on the pelvis/spine measuring 3D angular motions of the pelvis, lumbar spine and thoracic spine and two uni-axial gyroscopes on the shanks providing gait cycle information. The proposed system was employed in comparing the spinal motion during the staircase walking to that of the level walking with respect to the motion pattern, variability, and range of motion (ROM). The test results showed clear differences in spinal motion between the level walking and staircase walking conditions, particularly in regards to the motion pattern and ROM of the flexion/extension and lateral bending of the spine.

Appendix: initial coordinate reset

The rotation matrix $_{B}^{G} {\bf{R}}$, expressed in the body frame B with respect to the global frame G, can be written as follows:

$$ _{B}^{G} {\bf{R}} = [^{B} {\bf x}_{G} \,^{B} {\bf y}_{G} \,^{B} {\bf z}_{G} ]^{T} $$

(7)

where, ${}^{B}{\bf x}_{G}$, ${}^{B}{\bf y}_{G}$, and ${}^{B}{\bf z}_{G}$ are three unit vectors denoting the principal axes of G, expressed in B. If the authors set the gravitational pointing-up direction to the z-axis of G, ${\bf{z}}_{G}$ can be expressed by using the gravity information, i.e., ${}^{G}{\bf z}_{G} = {}^{G}{\bf g}/\left\| {{}^{G}{\bf g}}\right\|$ where ${}^{G}{\bf g} = \left[ {\begin{array}{*{20}c} 0 & 0 &{9.81}\\ \end{array} } \right]^{T} \,(m/s^{2} )$ and ${}^{B}{\bf{z}}_{G} = {}^{B}{\bf{g}}/\left\| {{}^{B}{\bf{g}}} \right\|$. Note that, since the tri-axial accelerometer detects only the gravity without any body acceleration in the static conditions, ${}^{B}{\bf z}_{G}$ can be obtained by

$$ {}^{B}{\bf z}_{G} = {}^{B}{\bf s}_{A} /\left\| {{}^{B}{\bf s}_{A} } \right\| $$

(8)

where ${}^{B}{\bf s}_{A}$ is the accelerometer signal with respect to B, which can be obtained by a simple coordinate transformation from the raw accelerometer signal ${}^{S}{\bf s}_{A}$, i.e., ${}^{B}{\bf s}_{A} = {}_{S}^{B} {\bf{R}}\,{}^{S}{\bf s}_{A}$. Using the conventional Z–Y–X Euler angles, $_{B}^{G} {\bf{R}}$ is expressed as:

$$ _{B}^{G} R = R_{{z^{\prime}y^{\prime}x^{\prime}}} (\alpha ,\beta ,\gamma ) = \left[ {\begin{array}{*{20}c} {c\alpha c\beta } & {c\alpha c\beta s\gamma - s\alpha c\gamma } & {c\alpha s\beta c\gamma + s\alpha s\gamma } \\ {s\alpha c\beta } & {s\alpha s\beta s\gamma + c\alpha c\gamma } & {s\alpha s\beta c\gamma - c\alpha c\gamma } \\ { - s\beta } & {c\beta s\gamma } & {c\beta c\gamma } \\ \end{array} } \right] $$

(9)

where $\alpha$, $\beta$, and $\gamma$ are rotation angles about Z, Y, and X axes, respectively. Note that the last row of the matrix ${}_{B}^{G} {\mathbf{R}}$ of Eq. 9 is expressed in terms of only $\gamma$ and $\beta$, without $\alpha$. Therefore, considering Eqs. 8 and 9, $\gamma$ and $\beta$ can be obtained as follows:

$$ \gamma = \tan^{ - 1} \left( {{\frac{{{}^{B}s_{A,y} }}{{{}^{B}s_{A,z} }}}} \right){\text{ and }}\beta = \tan^{ - 1} \left( {{\frac{{ - {}^{B}s_{A,x} }}{{{}^{B}s_{A,y} /\sin \gamma }}}} \right) $$

(10)

In the calibration procedure, the direction of ${\mathbf{x}}_{B}$ projected to the horizontal plane (i.e., the transverse plane) is set to the x-axis of G, ${\bf x}_{G}$. Therefore, there is no rotation about the z-axis (i.e., $\alpha = 0$). Then, the final $_{B}^{G} R$ is given by:

$$ _{B}^{G} R = \left[ {\begin{array}{*{20}c} {c\beta } & {s\beta s\gamma } & {s\beta c\gamma } \\ 0 & {c\gamma } & { - s\gamma } \\ { - s\beta } & {c\beta s\gamma } & {c\beta c\gamma } \\ \end{array} } \right] $$

(11)

Once ${\mathbf{z}}_{G}$ and ${\mathbf{x}}_{G}$ are determined, ${\mathbf{y}}_{G}$ can also determined using the right-hand coordinate rule. See the right figure (after the reset) of Fig. 5 compared with the left figure (before the reset).

Fig. 5

Illustration of the global (G) and body (B) reference frames before (left) and after (right) the initial coordinate reset has been performed