Trunk posture monitoring with inertial sensors

Abstract

Measurement of human posture and movement is an important area of research in the bioengineering and rehabilitation fields. Various attempts have been initiated for different clinical application goals, such as diagnosis of pathological posture and movements, assessment of pre- and post-treatment efficacy and comparison of different treatment protocols. Image-based methods for measurements of human posture and movements have been developed, such as the radiography, photogrammetry, optoelectric technique and video analysis. However, it is found that these methods are complicated to set up, time-consuming to operate and could only be applied in laboratory environments. This study introduced a method of using a posture monitoring system in estimating the spinal curvature changes during trunk movements on the sagittal and coronal planes and providing trunk posture monitoring during daily activities. The system consisted of three sensor modules, each with one tri-axial accelerometer and three uni-axial gyroscopes orthogonally aligned, and a digital data acquisition and feedback system. The accuracy of this system was tested with a motion analysis system (Vicon 370) in calibration with experimental setup and in trunk posture measurement with nine human subjects, and the performance of the posture monitoring system during daily activities with two human subjects was reported. The averaged root mean squared differences between the measurements of the system and motion analysis system were found to be <1.5° in dynamic calibration, and <3.1° for the sagittal plane and ≤2.1° for the coronal plane in estimation of the trunk posture change during trunk movements. The measurements of the system and the motion analysis system was highly correlated (>0.999 for dynamic calibration and >0.829 for estimation of spinal curvature change in domain planes of movement during flexion and lateral bending). With the sensing modules located on the upper trunk, mid-trunk and the pelvic levels, the inclination of trunk segment and the change of spinal curvature in trunk movements could be estimated. The posture information of five subjects was recorded at 30 s intervals during daily activity over a period of 3 days and 2 h a day. The preliminary results demonstrated that the subjects could improve their posture when feedback signals were provided. The posture monitoring system could be used for the purpose of posture monitoring during daily activity.

Appendix

Mathematical section for auto-reset algorithm

$$ T_{{{\text{accX}}}} (t) = \left\{ {\begin{array}{*{20}c} {{\sin ^{{ - 1}} {\left( {\frac{{{\text{AccY}}(t)}} {{{\sqrt {{\text{AccY}}(t)^{2} + {\text{AccZ}}(t)^{2} } }}}} \right)},\;{\text{if}}\;{\text{AccZ}}(t) \ge 0}} \\ {{\sin ^{{ - 1}} {\left( {\frac{{ - {\text{AccY}}(t)}} {{{\sqrt {{\text{AccY}}(t)^{2} + {\text{AccZ}}(t)^{2} } }}}} \right)} + 180,\;{\text{if}}\;\left\{ {\begin{array}{*{20}c} {{{\text{AccZ}}(t) < 0}} \\ {{{\text{AccY}}(t) \ge 0}} \\ \end{array} } \right.}} \\ {{\sin ^{{ - 1}} {\left( {\frac{{ - {\text{Acc}}Y(t)}} {{{\sqrt {{\text{AccY}}(t)^{2} + {\text{AccZ}}(t)^{2} } }}}} \right)} - 180,\;{\text{if}}\;\left\{ {\begin{array}{*{20}c} {{{\text{AccZ}}(t) < 0}} \\ {{{\text{AccY}}(t) < 0}} \\ \end{array} } \right.}} \\ \end{array} } \right. $$

(1)

$$ T_{{{\text{accY}}}} (t) = \left\{ {\begin{array}{*{20}c} {{\tan ^{{ - 1}} {\left( {\frac{{ - {\text{AccX}}(t)}} {{{\sqrt {{\text{AccY}}(t)^{2} + {\text{AccZ}}(t)^{2} } }}}} \right)},\;{\text{if}}\;{\text{AccZ}}(t) \ge 0}} \\ {{\tan ^{{ - 1}} {\left( {\frac{{{\text{AccX}}(t)}} {{{\sqrt {{\text{AccY}}(t)^{2} + {\text{AccZ}}(t)^{2} } }}}} \right)},\;{\text{if}}\;{\text{AccZ}}(t) < 0}} \\ \end{array} } \right. $$

(2)

where AccX, AccY and AccZ are signals of accelerometer, and T_acc is tilting angle derived from the signals of accelerometer.

$$ \omega _{{{\text{gyroX}}}} (t) = \omega _{X} (t) $$

(3)

$$ \omega _{{{\text{gyroY}}}} (t) = \left\{ {\begin{array}{*{20}c} {\begin{aligned}{} & {\sqrt {\omega _{Y} (t)^{2} + \omega _{Z} (t)^{2} } },\;{\text{if}}\;\omega _{Y} (t) \ge 0 \\ & \\ \end{aligned} } \\ {{ - {\sqrt {\omega _{Y} (t)^{2} + \omega _{Z} (t)^{2} } },\;{\text{if}}\;\omega _{Y} (t) < 0}} \\ \end{array} } \right. $$

(4)

where ω_X, ω _Y and ω _Z are signals of gyroscopes, ω_gyro are angular velocity.

$$ T_{{{\text{angle}}}} (t) = \left\{ {\begin{array}{*{20}c} {\begin{aligned}{} & T_{{{\text{acc}}}} (t),\;{\text{if}}\;S(t - N:t) \le {\text{Threshold,}}\;{\text{else}} \\ & \\ \end{aligned} } \\ {{\frac{{{\left( {\omega _{{{\text{gyro}}}} (t) + \omega _{{{\text{gyro}}}} (t - 1)} \right)}}} {{{\text{sr}}}} + T_{{{\text{angle}}}} (t - 1)}} \\ \end{array} } \right. $$

(5)

where T_angle is angle calculated with auto-reset algorithm (Fig. 10), S(t) is the rectified signals derived from the variation of the T_acc, t is the index of time, the value of N is 5 and the threshold is 1 which are derived from the experimental results.

Fig. 10

a An auto-reset algorithm with b “quasi-static and dynamic moment detector” for calculation of the sensor orientation. Rectified signals S(t), which derived from the variation of the inclination derived from the accelerometer’s signals (T_acc), compared with the threshold to identify the condition is quasi-static or dynamic. The orientation of the sensor along the x and y axes (T_angle) was calculated from the integration of the gyroscope’s signals (ω_gyro) at dynamic moment (condition) and the inclination derived from the accelerometer’s signals at quasi-static moment (condition)

Calculation of the trunk posture change (motion analysis system)

The parameters of the trunk posture measurement were calculated based on several axis systems, including thoracic axis system (X _ut, Y _ut and Z _ut), lumbar axis system (X _lt, Y _lt and Z _lt), and spinal axis system (X _s, Y _s and Z _s). The X, Y and Z axes constructed a right-handed Cartesian coordinate system and point to the anatomical directions:

X to anatomical right side, Y to anatomical anterior direction, Z to anatomical superior.

The regional trunk posture change of thoracic and lumbar spine was calculated based on the thoracic and lumbar axis system. The sign of angle was adopted as flexion and lateral bending to right were considered to be positive, and movement in opposite directions were represented by negative value for all data. Kinematic parameters, including the peak value and angular velocity of the trunk movements and, were calculated from the data of the motion analysis system and were documented for reference. The angular velocity of the trunk movements was defined as the angular velocity of the projection of the line formed by C7 and the sacrum (S2) on the sagittal and coronal planes of the pelvic axis system.

Inter-segmental angles (θ _i ) is formed with three consecutive retro-reflective markers, where α _j is the projection angle relative to y-axis and x-axis of the thoracic axis system for thoracic region and lumbar axis system for lumbar region on the sagittal plane and coronal plane, respectively (Figs. 11, 12).

Fig. 11

Calculation of the trunk posture changes on (a, c) sagittal and (b, d) coronal planes during trunk movement

Fig. 12

Calculation of the inter-segmental angles on a sagittal and b coronal planes during trunk movement

For sagittal plane,

$$ \alpha _{{y(j)}} = \cos ^{{ - 1}} {\left( {\frac{{y_{{(j)}} }} {{r_{{(j)}} }}} \right)} $$

(6)

where y and r are y-coordinate and magnitude of the vector which formed with 2 consecutive markers respectively

$$ \theta _{{y(i)}} = \alpha _{{y(j)}} - \alpha _{{y(j + 1)}} \quad {\text{for}}\;i = \;{\left\{ {0:\;N - 3} \right\}},\;j = {\left\{ {0:\;N - 2} \right\}} $$

(7)

where θ and N is an inter-segmental angle and number of reflective markers at the subject’s back in the specific trunk region respectively

For coronal plane,

$$ \alpha _{{x(j)}} = \cos ^{{ - 1}} {\left( {\frac{{x_{{(j)}} }} {{r_{{(j)}} }}} \right)}$$

(8)

where x and r are x-coordinate and magnitude of the vector which formed with 2 consecutive markers respectively

$$ \theta _{{x(i)}} = \alpha _{{x(j)}} - \alpha _{{x(j + 1)}} \quad for\;i = \;{\left\{ {0:\;N - 3} \right\}},\;j = {\left\{ {0:\;N - 2} \right\}}$$

(9)

where θ and N is an inter-segmental angle and number of reflective markers at the subject’s back in the specific trunk region respectively

Trunk angle (β) is a sum of total inter-segmental angles.

$$\beta = {\sum\limits_{i = 0}^{N - 3} {\theta _{{(i)}} } }\;\;{\text{for}}\;i = \;{\left\{ {0:\;N - 3} \right\}}$$

(10)

where θ and N is an inter - segmental angle and number of reflective markers at the subject’s back in the specific trunk region respectively

The trunk posture changes (δ) during trunk movements on the sagittal and coronal planes were estimated by subtraction of the trunk angle at initial time (β₀) from those at the spontaneous time (β _T ).

$$ \delta = \beta _{T} - \beta _{0} $$

(11)