Intrinsic Coordinate Frame Research Articles

Diverse coordinate frames on sensorimotor areas in visuomotor transformation

The visuomotor transformation during a goal-directed movement may involve a coordinate transformation from visual ‘extrinsic’ to muscle-like ‘intrinsic’ coordinate frames, which might be processed via a multilayer network architecture composed of neural basis functions. This theory suggests that the postural change during a goal-directed movement task alters activity patterns of the neurons in the intermediate layer of the visuomotor transformation that recieves both visual and proprioceptive inputs, and thus influence the multi-voxel pattern of the blood oxygenation level dependent signal. Using a recently developed multi-voxel pattern decoding method, we found extrinsic, intrinsic and intermediate coordinate frames along the visuomotor cortical pathways during a visuomotor control task. The presented results support the hypothesis that, in human, the extrinsic coordinate frame was transformed to the muscle-like frame over the dorsal pathway from the posterior parietal cortex and the dorsal premotor cortex to the primary motor cortex.

Dissociable neural representations of wrist motor coordinate frames in human motor cortices

There is a growing interest in how the brain transforms body part positioning in the extrinsic environment into an intrinsic coordinate frame during motor control. To explore the human brain areas representing intrinsic and extrinsic coordinate frames, this fMRI study examined neural representation of motor cortices while human participants performed isometric wrist flexions and extensions in different forearm postures, thereby applying the same wrist actions (representing the intrinsic coordinate frame) to different movement directions (representing the extrinsic coordinate frame). Using sparse logistic regression, critical voxels involving pattern information that specifically discriminates wrist action (flexion vs. extension) and movement direction (upward vs. downward) were identified within the primary motor and premotor cortices. Analyses of classifier weights further identified contributions of the primary motor cortex to the intrinsic coordinate frame and the ventral and dorsal premotor cortex and supplementary motor area proper to the extrinsic coordinate frame. These results are consistent with existing findings using non-human primates and demonstrate the distributed representations of independent coordinate frames in the human brain.

The effects of healthy aging on mental imagery as revealed by egocentric and allocentric mental spatial transformations

Previous studies suggest that mental rotation can be accomplished by using different mental spatial transformations. When adopting the allocentric transformation, individuals imagine the stimulus rotation referring to its intrinsic coordinate frame, while when adopting the egocentric transformation they rely on multisensory and sensory-motor mechanisms. However, how these mental transformations evolve during healthy aging has received little attention. Here we investigated how visual, multisensory, and sensory-motor components of mental imagery change with normal aging. Fifteen elderly and 15 young participants were asked to perform two different laterality tasks within either an allocentric or an egocentric frame of reference. Participants had to judge either the handedness of a visual hand (egocentric task) or the location of a marker placed on the left or right side of the same visual hand (allocentric task). Both left and right hands were presented at various angular departures to the left, the right, or to the center of the screen. When performing the egocentric task, elderly participants were less accurate and slower for biomechanically awkward hand postures (i.e., lateral hand orientations). Their performance also decreased when stimuli were presented laterally. The findings revealed that healthy aging is associated with a specific degradation of sensory-motor mechanisms necessary to accomplish complex effector-centered mental transformations. Moreover, failure to find a difference in judging left or right hand laterality suggests that aging does not necessarily impair non-dominant hand sensory-motor programs.

Sleep consolidates the effector-independent representation of a motor skill

During off-line consolidation a motor skill becomes less vulnerable to interference (stabilisation) and improves in performance (enhancement). Here we examined whether off-line consolidation contributes to the process of generalisation in the extrinsic and intrinsic coordinate frame in the motor domain. Participants trained with the left hand a sequential finger tapping task that has proved sensitive to off-line consolidation. Generalisation was tested by the ability to transfer the original sequence (extrinsic transformation) or the mirror sequence (intrinsic transformation) to the right hand, and this was compared with performance on a new sequence not learned before. To determine acute effects on generalisation, transfer was assessed immediately after training of the left hand. To study the effects of off-line consolidation participants were tested after an interval of daytime (training at 8 am and retrieval test on the transfer sequences at 8 pm) or after an interval of night-time sleep (training at 8 pm and retrieval test on the transfer sequences at 8 am). Acutely, training of the left hand induced significant transfer effects to the right hand for the extrinsic transformation of the sequence, but there was no advantage for the intrinsic transformation. After a period of daytime wakefulness the transfer from the left to the right hand for the extrinsic sequence transformation had vanished and, again, there was no transfer effect for the intrinsic transformation of the sequence. By contrast, nocturnal sleep saved the initial transfer effect for the extrinsic sequence transformation. The intrinsic sequence transformation was not affected by sleep. Our results show that an effector-independent representation in an extrinsic co-ordinate frame of a skill develops soon after initial training. Sleep has the capacity to consolidate this transfer and, in this way, contributes to the generalisation of a motor skill.

On the State Space Geometry of the Kuramoto–Sivashinsky Flow in a Periodic Domain

The continuous and discrete symmetries of the Kuramoto-Sivashinsky system restricted to a spatially periodic domain play a prominent role in shaping the invariant sets of its chaotic dynamics. The continuous spatial translation symmetry leads to relative equilibrium (traveling wave) and relative periodic orbit (modulated traveling wave) solutions. The discrete symmetries lead to existence of equilibrium and periodic orbit solutions, induce decomposition of state space into invariant subspaces, and enforce certain structurally stable heteroclinic connections between equilibria. We show, on the example of a particular small-cell Kuramoto-Sivashinsky system, how the geometry of its dynamical state space is organized by a rigid `cage' built by heteroclinic connections between equilibria, and demonstrate the preponderance of unstable relative periodic orbits and their likely role as the skeleton underpinning spatiotemporal turbulence in systems with continuous symmetries. We also offer novel visualizations of the high-dimensional Kuramoto-Sivashinsky state space flow through projections onto low-dimensional, PDE representation independent, dynamically invariant intrinsic coordinate frames, as well as in terms of the physical, symmetry invariant energy transfer rates.

Sensorimotor transformations in cortical motor areas

A central problem in motor research has been to understand how sensory signals are transformed to generate a goal-directed movement. This problem has been formulated as a set of coordinate transformations that begins with an extrinsic coordinate frame representing the spatial location of a target and ends with an intrinsic coordinate frame describing muscle activation patterns. Insight into this process of sensorimotor transformation can be gained by examining the coordinate frames of neuronal activity in interconnected regions of the brain. We recorded the activity of neurons in primary motor cortex (M1) and ventral premotor cortex (PMv) in a monkey trained to perform a task which dissociates three major coordinate frames of wrist movement: muscle, wrist joint, and an extrinsic coordinate frame. We found three major types of neurons in M1 and PMv. The first type was termed ‘extrinsic-like’. The activity of these neurons appeared to encode the direction of movement in space independent of the patterns of wrist muscle activity or joint movement that produced the movements. The second type was termed ‘extrinsic-like with gain modulation’. The activity of these neurons appeared to encode the direction of movement in space, but the magnitude (gain) of neuronal activity depended on the posture of the forearm. The third type was termed ‘muscle-like’ since their activity co-varied with muscle activity. The great majority of the directionally-tuned neurons in the PMv were classified as ‘extrinsic-like’ (48/59, 81%). A smaller group was classified as ‘extrinsic-like with gain modulation’ (7/59, 12%). In M1, the three types of neurons were more equally represented. Our results raise the possibility that cortical processing between M1 and PMv may contribute to a sensorimotor transformation between extrinsic and intrinsic coordinate frames. Recent modeling studies have demonstrated the computational plausibility of such a process.

Direction of action is represented in the ventral premotor cortex.

The ventral premotor area (PMv) is a major source of input to the primary motor cortex (M1). To examine the potential hierarchical processing between these motor areas, we recorded the activity of PMv neurons in a monkey trained to perform wrist movements in different directions with the wrist in three different postures. The task dissociated three major variables of wrist movement: muscle activity, direction of joint movement and direction of movement in space. Many PMv neurons were directionally tuned. Nearly all of these neurons (61/65, 94%) were 'extrinsic-like'; they seemed to encode the direction of movement in space independent of forearm posture. These results are strikingly different from results from M1 of the same animal, and suggest that intracortical processing between PMv and M1 may contribute to a sensorimotor transformation between extrinsic and intrinsic coordinate frames.

Splines as embeddings for generalized cylinders

Generalized cylinders are an attractive representation for three-dimensional objects. One of their principal features is that the representation contains an intrinsic coordinate frame. The intrinsic (object-centered) frame computed from image data facilitates the matching of an object with a similarly represented stored prototype. The definitions of generalized cylinders are loose and do not specify how a generalized cylinder is to be represented digitally. Previous digital representations have tended to be either nonparametric renditions, which makes them computationally cumbersome, or parametric simplifications, which limit the class of objects that can be represented. It is shown that splines provide an attractive representation technique for generalized cylinders. In fact splines provide a parametric representation for the full generalization of the generalized cylinders concept.

Splines as embeddings for generalized cylinders

Generalized cylinders are an attractive representation for three-dimensional objects. One of their principal features is that the representation contains an intrinsic coordinate frame. The intrinsic (object-centered) frame computed from image data facilitates the matching of an object with a similarly represented stored prototype. The definitions of generalized cylinders are loose and do not specify how a generalized cylinder is to be represented digitally. Previous digital representations have tended to be either nonparametric renditions, which makes them computationally cumbersome, or parametric simplifications, which limit the class of objects that can be represented. It is shown that splines provide an attractive representation technique for generalized cylinders. In fact splines provide a parametric representation for the full generalization of the generalized cylinders concept.