Computation of the kinematics and the minimum peak joint moments of sit-to-stand movements

Abstract

Background: A sit-to-stand (STS) movement requires muscle strength higher than that of other daily activities. There are many elderly people, who experience difficulty when standing up from a chair. The muscle strength required (or the load on the joints) during a STS task is determined by the kinematics (movement pattern). The purpose of this study was to evaluate the kinematics and resultant joint moments of people standing up from a chair in order to determine the minimum peak joint moments required for a STS task.

Methods: This study consisted of three steps. In the first step, kinematic data of lower extremity joint angles (hip, knee and ankle) during STS movements were experimentally collected from human subjects. Eighty-five sets of STS kinematic data were obtained. In the second step, the experimentally collected kinematic data and a link segment model of the human body were used to generate more than 5,000,000 computed STS movements. In the third step, using inverse dynamics method, joint moments of the lower extremity were calculated for all movements obtained through the preceding steps. From the outputs of the third step, the optimal kinematics (movement pattern) in terms of minimized peak joint moment for the hip, knee and ankle was determined.

Results: The peak hip joint moment ranged from 0.24 to 1.92 N.m/kg. The peak knee joint moment ranged from 0.51 to 1.97 N.m/kg, and the peak ankle joint moment ranged from -0.11 to 1.32 N.m/kg. The optimal movement patterns differed depending on which minimized joint moment index was selected (hip, knee or ankle). However, the sum of the peak hip joint moment and peak knee joint moment was always approximately 1.53 N.m/kg regardless of which minimized joint moment index was selected.

Conclusion: The most important finding of this study was that the relation between the peak joint moments at the hip and knee joints was complementary and the sum of those moments needed to be greater than 1.53 N.m/kg in order to perform a successful STS. A combined hip-knee value of 1.5 N.m/kg or lower may indicate the need for physical rehabilitation and/or exercise to increase muscular force.

Figure 1

The joint kinematics normalization, joint definition and the foot segment definition. (a) The translation process from the raw movement data to the normalized format suitable for the computer model. (b) Hip, knee and ankle joint definitions. A counterclockwise angle has a positive value. (c) Details of the foot segment size. L1 indicates the horizontal length between the heel and the ankle joint. L2 indicates the horizontal length between the ankle joint and the tip toe.

Figure 2

The adjustment process for the parameters influencing the initial posture. The adjustment process for the three parameters influencing the initial posture (hip joint height, initial knee joint angle and initial ankle joint angle). Initial ankle joint angles in Posture-A and Posture-B were calculated from the hip joint height and initial knee joint angle. In Posture-C, initial knee joint angle was calculated from the hip joint height and initial ankle joint angle.

Figure 3

Normalized joint angle time series data. Normalized hip (a), knee (b), and ankle (c) joint angle time series data obtained from the experimental trials (n = 17 × 5).

Figure 4

Initial postures of the experimental and computed movements. Stick figures of the initial postures of the experimental and computed movements drawn with a fixed hip joint center position. Blue figures are the initial postures of the experimental movements. Black figures are the initial postures of the computed movements.

Figure 5

Peak joint moments of each movement. (Top row) The relation between the peak joint moments of each movement. Plotted data include: the relation between peak joint moments at the ankle and knee joints (a); the relation between peak joint moments at the ankle and hip joints (b); and the relation between peak joint moments at the knee and hip joints (c). (Bottom row) The relation between peak knee and hip joint moments with 3 different ranges ankle joint moments. The peak ankle joint moments ranged from -0.11 to 0.4 N.m/kg (d); 0.4 to 0.8 N.m/kg (e); and 0.8 to 1.32 N.m/kg (f). The plots ((d), (e) and (f)) show the relation between the peak ankle joint moment and other two joint moments. Plots (d), (e), and (f) all show similar distribution profiles. The value of the peak ankle joint moment did not influence the distribution pattern of other two joint moments. Joint moments are the values for one leg. The cross mark plots indicated the data of the original experimental data.

Figure 6

Movement pattern, peak joint moments, and movement time. Movement pattern, peak joint moments, and movement time for each joint moment index. M_H, M_K and M_A are peak joint moment at the hip, knee and ankle joints during the movement, respectively. |M_H|, |M_K| and |M_A| are the absolute values. The index value of each movement was the smallest among the values of all computed movements. Circle mark indicates the total body center of gravity.

Figure 7

The profile of the joint angles and angular velocities. Time = 0 indicates the instance when the buttocks lost contact with the chair. All graphs are drawn to the end of each STS movement. The left and right axes are the scale of the joint angle and angular velocity, respectively. The solid and dotted lines show the joint angle and angular velocity of each joint, respectively.

Figure 8

The profile of the anterior-posterior COP position and joint moments. Time = 0 indicates the instance when the buttocks lost contact with the chair. All graphs are drawn until the end of each STS movement. The upper end of the graph indicates tip toe position (line-1). The lower limit of the same graph indicates the heel position (line-3). The intermediate line indicates ankle joint position (line-2). Joint moments are the values for one leg. Peak hip and knee joint moments reached their maximum near the initial position. At the ankle, joint moments tended to increase or decrease in synchrony with the changes in the anterior-posterior position of the COP. At the early stage of the movement, the hip joint moment exhibited the highest value when the joint moment index was |M_K|. The magnitude of the hip joint moments decreased in order from |M_A|, |M_H + M_K + M_A| and |M_H|, respectively. In the case of the knee joint moment, the order was the opposite.