Fig 1.
A) Four-link 2D model. Reference frame defined with origin at O, with the positive X axis directed anteriorly coincident with the ground (grey line), the positive Y axis directed superiorly, and positive rotation defined in the counterclockwise direction. Link 0 is formed by a rigid, perpendicular connection between lines CT and OA. Link 1 is defined by line AK. Link 2 is defined by line KH. Link 3 is a lumped representation of the head, arms, and torso (HAT) defined by the line from H to the center of mass of the HAT. Generalized coordinates: θ0, θ1, θ2, and θ3. Variables Li, ri, and mi define the lengths, center of mass location relative to the proximal joint, and mass, respectively, of segment i. θc defines the angle between CT and the vector from O to the center of mass of Link 0. B) Musculoskeletal (MSK) model.
Table 1.
Range of joint angles analyzed.
Fig 2.
Dimensions for foot position and pelvis height calculations.
Xkh and Ykh are the horizontal and vertical distances, respectively, between K and H. Xak and Yak are the horizontal and vertical distances, respectively, between A and K. Foot position is the sum of Xkh and Xak and defined relative to H. Pelvis height is the sum of Ykh and Yak and defined relative to A. Foot position and pelvis height are normalized to leg length (L1 + L2). In this figure, θhip is defined assuming a neutral pelvis tilt angle (θpelvis = 0°).
Fig 3.
Experimental kinematics of YA and patients with KOA for key parameters during the momentum transfer phase of the STS transfer.
Positive (negative) values indicate posterior (anterior) pelvic tilt, lumbar flexion (extension), and a more anterior (posterior) foot position. The line represents the population mean and the shaded area represents ± one standard deviation.
Fig 4.
Muscle support potentials during the momentum transfer phase of the STS.
For each muscle, the top plot expresses support potential as a function of pelvic tilt angle such that each data point represents the average muscle potential for a given pelvic tilt angle accounting for the range of kinematic states observed by the population with the respective pelvic tilt. Error bars represent ± one standard deviation from the average. Positive angles indicate posterior pelvic tilt. The bottom plot provides the time curve of the muscle’s support potential during the momentum transfer phase (30–40% of the STS cycle) estimated using a musculoskeletal model scaled to each subject’s anthropometrics in OpenSim. The line represents the population mean and the shaded area represents ± one standard deviation.
Fig 5.
Muscle progression potentials during the momentum transfer phase of the STS.
For each muscle, the top plot expresses progression potential as a function of pelvic tilt angle such that each data point represents the average muscle potential for a given pelvic tilt angle accounting for the range of kinematic states observed by the population with the respective pelvic tilt. Error bars represent ± one standard deviation from the average. Positive angles indicate posterior pelvic tilt. The bottom plot provides the time curve of the muscle’s progression potential during the momentum transfer phase (30–40% of the STS cycle) estimated using a musculoskeletal model scaled to each subject’s anthropometrics in OpenSim. The line represents the population mean and the shaded area represents ± one standard deviation.
Fig 6.
Muscle potentials to contribute to A) support and B) progression during the momentum transfer phase of the STS as a function of foot position. Each data point represents the average muscle potential for a given foot position accounting for the range of kinematic states with the respective foot position and a neutral pelvis position. Error bars represent ± one standard deviation from the average.
Fig 7.
Muscle potentials to contribute to A) support and B) progression during the momentum transfer phase of the STS as a function of pelvis height. Each data point represents the average muscle potential for a given pelvis height accounting for the range of kinematic states with the respective pelvis height and a neutral pelvis position. Error bars represent ± one standard deviation from the average.
Fig 8.
Muscle potentials to contribute to A) support and B) progression during the momentum transfer phase of the STS as a function of lumbar flexion angle. Each data point represents the average muscle potential for a given lumbar flexion angle accounting for the range of kinematic states with the respective lumbar angle and a neutral pelvis position. Error bars represent ± one standard deviation from the average. Positive angles indicate lumbar flexion.
Fig 9.
Muscle potentials to contribute to A) support and B) progression during the momentum transfer phase of the STS as a function of pelvic tilt angle. Each data point represents the average muscle potential for a given pelvic tilt angle accounting for the range of kinematic states. Error bars represent ± one standard deviation from the average. Positive angles indicate posterior pelvic tilt.
Table 2.
Correlation coefficients for Pearson correlation between muscle potentials during the momentum transfer phase and kinematic modifications*.
Fig 10.
Select kinematic states and associated muscle potentials.
Foot position and pelvis height were normalized to leg length.
Fig 11.
Relationship between foot position, pelvis height, and support potentials.
A) Influence of foot position and pelvis height on muscle support potentials for 30° of anterior pelvic tilt and 15° of lumbar flexion (average KOA kinematics at the start of the momentum transfer phase). B) Graphical depiction of selected pelvis heights and foot positions associated with muscle potentials in (A). Foot position and pelvis height were normalized to leg length.
Fig 12.
Relationship between foot position, pelvis height, and progression potentials.
A) Influence of foot position and pelvis height on muscle progression potentials for 40° of anterior pelvic tilt and 10° of lumbar flexion (average KOA kinematics in the middle of the momentum transfer phase). B) Graphical depiction of selected pelvis heights and foot positions associated with muscle potentials in (A). Foot position and pelvis height were normalized to leg length.