Affine differential geometry analysis of human arm movements

Humans interact with their environment through sensory information and motor actions. These interactions may be understood via the underlying geometry of both perception and action. While the motor space is typically considered by default to be Euclidean, persistent behavioral observations point to a different underlying geometric structure. These observed regularities include the “two-thirds power law” which connects path curvature with velocity, and “local isochrony” which prescribes the relation between movement time and its extent. Starting with these empirical observations, we have developed a mathematical framework based on differential geometry, Lie group theory and Cartan’s moving frame method for the analysis of human hand trajectories. We also use this method to identify possible motion primitives, i.e., elementary building blocks from which more complicated movements are constructed. We show that a natural geometric description of continuous repetitive hand trajectories is not Euclidean but equi-affine. Specifically, equi-affine velocity is piecewise constant along movement segments, and movement execution time for a given segment is proportional to its equi-affine arc-length. Using this mathematical framework, we then analyze experimentally recorded drawing movements. To examine movement segmentation and classification, the two fundamental equi-affine differential invariants—equi-affine arc-length and curvature are calculated for the recorded movements. We also discuss the possible role of conic sections, i.e., curves with constant equi-affine curvature, as motor primitives and focus in more detail on parabolas, the equi-affine geodesics. Finally, we explore possible schemes for the internal neural coding of motor commands by showing that the equi-affine framework is compatible with the common model of population coding of the hand velocity vector when combined with a simple assumption on its dynamics. We then discuss several alternative explanations for the role that the equi-affine metric may play in internal representations of motion perception and production

Covert Tracking: A Combined ERP and Fixational Eye Movement Study

Attention can be directed to particular spatial locations, or to objects that appear at anticipated points in time. While most work has focused on spatial or temporal attention in isolation, we investigated covert tracking of smoothly moving objects, which requires continuous coordination of both. We tested two propositions about the neural and cognitive basis of this operation: first that covert tracking is a right hemisphere function, and second that pre-motor components of the oculomotor system are responsible for driving covert spatial attention during tracking. We simultaneously recorded event related potentials (ERPs) and eye position while participants covertly tracked dots that moved leftward or rightward at 12 or 20°/s. ERPs were sensitive to the direction of target motion. Topographic development in the leftward motion was a mirror image of the rightward motion, suggesting that both hemispheres contribute equally to covert tracking. Small shifts in eye position were also lateralized according to the direction of target motion, implying covert activation of the oculomotor system. The data addresses two outstanding questions about the nature of visuospatial tracking. First, covert tracking is reliant upon a symmetrical frontoparietal attentional system, rather than being right lateralized. Second, this same system controls both pursuit eye movements and covert tracking

Who Has Done It? Exploring Gaze Agency in Obsessive-Compulsive Checkers

The sense of agency (SoA) is a multifaceted construct, which can be defined as the ability to understand the causal relationships between our actions and sensory events. Obsessive-Compulsive Disorder (OCD) patients with checking compulsions often report a “lack of action completion” sensations, which has been conceptualized in the so-called “Not Just Right Experiences” construct. An intriguing explanation of this phenomenon comes from Belayachi and Van der Linden (2009, 2010), who suggest that OCD-checking patients are more prone to specify their action in a relatively molecular and inflexible way. Currently, there are no studies in literature which address this issue in OCD patients, except for the one of Gentsch et al. (2012), who suggested an altered SoA in these patients. Here we exploited a novel construct, gaze agency, to evaluate causal attribution capabilities in a group of 21 OCD patients (checkers) and matched healthy controls (HCs). Basically, two tasks targeted observers’ capability to identify their own eye movements as the cause of concurrently presented beeps, which allowed us to measure agency sensitivity as well as subtle agency alterations in an ecological setting. We found a poorer performance in OCD patients as compared to HCs in many parameters of our tasks, suggesting a difficulty with causal attribution possibly due to both a reduced cognitive flexibility and a less functional gaze agency in OCD patients