How visual information links to multijoint coordination during quiet standing

Abstract

The link between visual information and postural control was investigated based on a multi-degree-of-freedom model using the framework of the uncontrolled manifold (UCM) hypothesis. The hypothesis was that because visual information specifies the position of the body in space, it would couple preferentially into those combinations of degrees of freedom (DOFs) that move the body in space and not into combinations of DOFs that do not move the body in space. Subjects stood quietly in a virtual reality cave for 4-min trials with or without a 0.2, 2.0 Hz, or combined 0.2 and 2.0 Hz visual field perturbation that was below perceptual threshold. Motion analysis was used to compute six sagittal plane joint angles. Variance across time of the angular motion was partitioned into (1) variance associated with motion of the body and (2) variance reflecting the use of flexible joint combinations that keep the anterior–posterior positions of the head (HD_POS) and center of mass (CM_POS) invariant. UCM analysis was performed in the frequency domain in order to link the sensory perturbation to each variance component at different frequencies. As predicted, variance related to motion of the body was selectively increased at the 0.2-Hz drive frequency but not at other frequencies of sway for both CM_POS and HD_POS. The dominant effect with the 2.0-Hz visual drive also was limited largely to variance related to motion of the body.

Appendix

The geometric model of the standing configuration related to the AP center of mass position (CM_POS) in the sagittal plane was formulated in terms of four joint angles (θ _i ), where i = [ankle, knee, hip, and L5-S1], and four limb segment lengths (l _j ), the proportion of mass each contributes to the total body mass (m _j ), and the distance of the individual segment masses from the distal end of the segment (d _j ), where for all j = [shank (SH), thigh (TH), pelvis (PV), head–arms–trunk (HAT)] (Winter 2009).

The geometric model for CM motion in the AP dimension is:

$$ \begin{aligned} d_{\text{CM}} =\, & m_{\text{SH}} *d_{\text{SH}} *l_{\text{SH}} *\cos (\theta_{\text{ANKLE}} ) \, \\ & + \cdots m_{\text{TH}} *(l_{\text{SH}} *\cos (\theta_{\text{ANKLE}} ) + l_{\text{TH}} *d_{\text{TH}} *\cos (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} )) \\ & + \cdots m_{\text{PV}} *(l_{\text{SH}} *\cos (\theta_{\text{ANKLE}} ) + l_{\text{TH}} *\cos (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} ) + l_{\text{PV}} *d_{\text{PV}} *\cos (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} + \theta_{\text{HIP}} )) \\ & + \cdots m_{\text{HAT}} *(l_{\text{SH}} *\cos (\theta_{\text{ANKLE}} ) + l_{\text{TH}} *\cos (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} ) + l_{\text{PV}} *\cos (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} + \theta_{\text{HIP}} ) \\ & + l_{\text{HAT}} *d_{\text{HAT}} *\cos (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} + \theta_{\text{HIP}} + \theta_{{{\text{L}}5/{\text{S}}1}} )). \\ \end{aligned} $$

The geometric model for head motion in the AP dimension is:

$$ \begin{aligned} d_{\text{HD}} = \, & l_{\text{SH}} *\cos (\theta_{\text{ANKLE}} ) \\ & + \cdots l_{\text{TH}} *\cos (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} ) \\ & + \cdots l_{\text{PV}} *\cos (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} + \theta_{\text{HIP}} ) \\ & + \cdots l_{\text{TRUNK}} *\cos (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} + \theta_{\text{HIP}} + \theta_{{{\text{L}}5/{\text{S}}1}} ) \, \\ & + \cdots l_{\text{NECK}} *\cos (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} + \theta_{\text{HIP}} + \theta_{{{\text{L}}5/{\text{S}}1}} + \theta_{{{\text{C}}7/{\text{T}}1}} ) \, \\ & + \cdots l_{\text{HEAD}} *\cos (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} + \theta_{\text{HIP}} + \theta_{{{\text{L}}5/{\text{S}}1}} + \theta_{{{\text{C}}7/{\text{T}}1}} + \theta_{\text{AO}} ). \\ \end{aligned} $$

Jacobian matrices were obtained by computing analytically for each equation the partial derivative with respect to each joint angle, for example,

$$ \begin{aligned} \partial_{\text{CM}} /\partial_{{\theta {\text{ankle}}}} = & - m_{\text{SH}} *d_{\text{SH}} *l_{\text{SH}} *\sin (\theta_{\text{ANKLE}} ) - m_{\text{TH}} *l_{\text{SH}} *\sin (\theta_{\text{ANKLE}} ) - m_{\text{TH}} *l_{\text{TH}} *d_{\text{TH}} *\sin (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} ) \\ & - \, m_{\text{PV}} *l_{\text{SH}} *\sin (\theta_{\text{ANKLE}} ) - m_{\text{PV}} *l_{\text{TH}} *\sin (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} ) - m_{\text{PV}} *l_{\text{PV}} *d_{\text{PV}} *\sin (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} + \theta_{\text{HIP}} ) \\ & - m_{\text{HAT}} *l_{\text{SH}} *\sin (\theta_{\text{ANKLE}} ) - m_{\text{HAT}} *l_{\text{TH}} *\sin (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} ) - m_{\text{HAT}} *l_{\text{PV}} *\sin (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} + \theta_{\text{HIP}} ) \\ & - m_{\text{HAT}} *l_{\text{HAT}} *d_{\text{HAT}} *\sin (\theta_{\text{ANKLE}} + \theta_{\text{KNEE}} + \theta_{\text{HIP}} + \theta_{{{\text{L}}5/{\text{S}}1}} ). \\ \end{aligned} $$