The role of vision, speed, and attention in overcoming directional biases during arm movements

Abstract

Previous research has revealed directional biases (preferences to select movements in specific directions) during horizontal arm movements with the use of a free-stroke drawing task. The biases were interpreted as a result of a tendency to generate motion at either the shoulder or elbow (leading joint) and move the other (subordinate) joint predominantly passively to avoid neural effort for control of interaction torque. Here, we examined influence of vision, movement speed, and attention on the directional biases. Participants performed the free-stroke drawing task, producing center-out strokes in randomly selected directions. Movements were performed with and without vision and at comfortable and fast pace. A secondary, cognitive task was used to distract attention. Preferred directions remained the same in all conditions. Bias strength mildly increased without vision, especially during fast movements. Striking increases in bias strength were caused by the secondary task, pointing to additional cognitive load associated with selection of movements in the non-preferred directions. Further analyses demonstrated that the tendency to minimize active interference with interaction torque at the subordinate joint matched directional biases in all conditions. This match supports the explanation of directional biases as a result of a tendency to minimize neural effort for interaction torque control. The cognitive load may enhance this tendency in two ways, directly, by reducing neural capacity for interaction torque control, and indirectly, by decreasing capacity of working memory that stores visited directions. The obtained results suggest strong directional biases during daily activities because natural arm movements usually subserve cognitive tasks.

Appendix

The four biomechanical cost functions are defined here as indexes varying between 0.0 and 1.0 with 1.0 being the optimal value.

Indexes of INT control at the shoulder and elbow (I_INTE and I_INTS)

These two cost functions represent the complexity of INT control at the subordinate joint predicted by the LJH (Dounskaia 2005, 2010). According to this factor, participants may exhibit a tendency to produce movements that require minimal intervention of MUS with elbow (shoulder) INT when the elbow (shoulder) is the subordinate joint and the shoulder (elbow) is the leading joint. Given that NET = MUS + INT, this tendency was quantified with the following indexes:

$$ I_{\text{INTE}} = {\frac{1}{{T_{1} - T_{0} }}}\sum\limits_{{t = T_{0} }}^{{T_{1} }} {{\frac{{\left| {{\text{INTE}}_{t} } \right|}}{{\left| {{\text{INTE}}_{t} } \right| + \left| {{\text{MUSE}}_{t} } \right|}}}} , $$

(A1)

$$ I_{\text{INTS}} = {\frac{1}{{T_{1} - T_{0} }}}\sum\limits_{{t = T_{0} }}^{{T_{1} }} {{\frac{{\left| {{\text{INTS}}_{t} } \right|}}{{\left| {{\text{INTS}}_{t} } \right| + \left| {{\text{MUSS}}_{t} } \right|}}}} , $$

(A2)

Strokes were considered quasi-optimal according to one of these indexes if I _INTE or I _INTS was greater than 0.5. This threshold indicated strokes performed with |INT| on average exceeding |MUS|, suggesting that INT served as the primary source of motion at the joint.

Even though strokes were produced with different speed in different conditions, the indexes can be compared across conditions because MUS and INT increase approximately in proportion with each other when movement speed increases (which can be seen, for example, in Dounskaia et al. 2002b), and therefore, the indexes are largely independent of movement speed.

Index of inertial resistance (I _IR)

Inertial resistance characterizes the translation of force applied at the hand into resultant hand acceleration (Gordon et al. 1994; Hogan 1985; Mussa-Ivaldi et al. 1985). Inertial resistance is expressed with the matrix $T_{IR} = (J')^{ - 1} MJ^{ - 1}$, where J is the 2 × 2 Jacobian matrix and M is the 2 × 2 matrix of the limb’s inertial properties. Both J and M were of the form used by previous authors (Lacquaniti et al. 1993; Sabes and Jordan 1997). They were computed for each stroke with the use of the initial joint angles and anthropometric properties of each participant. The major (minor) eigenvector of T _IR denotes the direction having the greatest (least) amount of inertial resistance. Here, the index of inertial resistance was defined as:

$$ I_{\text{IR}} = 1.0 - {\frac{{\left| {\beta_{s} - E_{{\min ,\,{\text{IR}}}} } \right|}}{\pi /2}}, $$

(A3)

where β _s is the angular orientation of the stroke and E _{min, IR} denotes the orientation of the minor eigenvector of T _IR. Movements during which inertial resistance was minimal were characterized by maximal values (near 1.0) of the index. We used a threshold of 0.875 to identify strokes that were quasi-optimal in terms of I _IR. Choice of this threshold was rather conservative as it included only 1/8 of the possible values for the index.

Index of kinematic manipulability (I _KM)

Kinematic manipulability represents a property of the kinematic structure of the arm according to which similar angular velocities at the shoulder and elbow can result in different hand velocities, depending on the combination of flexion and extension at the two joints and on the initial elbow angle. Kinematic manipulability has been quantified for multi-joint movements of robotic arms by Yoshikawa (1985, 1990), and discussed with respect to arm movements (Graham et al. 2003; Dounskaia 2007; Sabes and Jordan 1997). The matrix of kinematic manipulability quantifying this relationship is $T_{KM} = JJ'$. For shoulder-elbow movements, the major (minor) eigenvector of T _KM denotes the direction in which maximum (minimum) hand velocity is achieved. Here, the index of kinematic manipulability was represented as

$$ I_{\text{KM}} = 1.0 - {\frac{{\left| {\beta_{s} - E_{\text{maj, KM}} } \right|}}{\pi /2}}, $$

(A4)

where β _s is the angular orientation of the stroke and E _{maj, KM} denotes the orientation of the major eigenvector of T _KM. Movements during which kinematic manipulability was maximal were characterized by maximal values (near 1.0) of the index. Similar to I _IR, a threshold of 0.875 was used.