Biomechanics, motor control and dynamic models of the soft limbs of the octopus and other cephalopods.

Muscular hydrostats are organs composed entirely of packed arrays of incompressible muscles and lacking any skeletal support. Found in both vertebrates and invertebrates, they are of great interest for comparative biomechanics from engineering and evolutionary perspectives. The arms of cephalopods (e.g. octopus and squid) are particularly interesting muscular hydrostats because of their flexibility and ability to generate complex behaviors exploiting elaborate nervous systems. Several lines of evidence from octopus studies point to the use of both brain and arm-embedded motor control strategies that have evolved to simplify the complexities associated with the control of flexible and hyper-redundant limbs and bodies. Here, we review earlier and more recent experimental studies on octopus arm biomechanics and neural motor control. We review several dynamic models used to predict the kinematic characteristics of several basic motion primitives, noting the shortcomings of the current models in accounting for behavioral observations. We also discuss the significance of impedance (stiffness and viscosity) in controlling the octopus's motor behavior. These factors are considered in light of several new models of muscle biomechanics that could be used in future research to gain a better understanding of motor control in the octopus. There is also a need for updated models that encompass stiffness and viscosity for designing and controlling soft robotic arms. The field of soft robotics has boomed over the past 15 years and would benefit significantly from further progress in biomechanical and motor control studies on octopus and other muscular hydrostats.

A Whole-Body Sensory-Motor Gradient is Revealed in the Medial Wall of the Parietal Lobe.

In 1954, Penfield and Jasper's findings based on electric stimulation of epileptic patients led them to hypothesize that a sensory representation of the body should be found in the precuneus. They termed this representation the "supplementary sensory" area and emphasized that the exact form of this homunculus could not be specified on the basis of their results. In the decades that followed, their prediction was neglected. The precuneus was found to be involved in numerous motor, cognitive and visual processes, but no work was done on its somatotopic organization. Here, we used a periodic experimental design in which 16 human subjects (eight women) moved 20 body parts to investigate the possible body part topography of the precuneus. We found an anterior-to-posterior, dorsal-to-ventral, toes-to-tongue gradient in a mirror orientation to the SMA. When inspecting body-part-specific functional connectivity, we found differential connectivity patterns for the different body parts to the primary and secondary motor areas and parietal and visual areas, and a shared connectivity to the extrastriate body area, another topographically organized area. We suggest that a whole-body gradient can be found in the precuneus and is connected to multiple brain areas with different connectivity for different body parts. Its exact role and relations to the other known functions of the precuneus such as self-processing, motor imagery, reaching, visuomotor and other body-mind functions should be investigated.SIGNIFICANCE STATEMENT Using fMRI, as well as sensitive spectral analysis, we found a new homunculus in the precuneus: an anterior-to-posterior, dorsal-to-ventral, toes-to-tongue somatotopic gradient in a mirror orientation to the SMA. When inspecting body-part-specific functional connectivity, we found differential connectivity patterns for the different body parts to the primary and secondary motor areas, parietal and visual areas, and a shared connectivity to the extrastriate body area, another topographically organized area. We suggest that a whole-body gradient can be found in the precuneus and is connected to multiple brain areas in a body-part-specific manner.

Does the Cerebellum Implement or Select Geometries? A Speculative Note.

During evolution, living systems, actively interacting with their environment, developed the ability, through sensorimotor contingencies, to construct functional spaces shaping their perception and their movements. These geometries were modularly embedded in specific functional neuro-architectures. In particular, human movements were shown to obey several empirical laws, such as the 2/3 power law, isochrony, or jerk minimization principles, which constrain and adapt motor planning and execution. Outstandingly, such laws can be deduced from a combination of Euclidean, affine, and equi-affine geometries, whose neural correlates have been partly detected in several brain areas including the cerebellum and the basal ganglia. Reviving Pellionisz and Llinas general hypothesis regarding the cerebrum and the cerebellum as geometric machines, we speculate that the cerebellum should be involved in implementing and/or selecting task-specific geometries for motor and cognitive skills. More precisely, the cerebellum is assumed to compute forward internal models to help specific cortical and subcortical regions to select appropriate geometries among, at least, Euclidean and affine geometries. We emphasize that the geometrical role of the cerebellum deserves a renewal of interest, which may provide a better understanding of its specific contributions to motor and associative (cognitive) functions.

Movement Decomposition in the Primary Motor Cortex.

A complex action can be described as the composition of a set of elementary movements. While both kinematic and dynamic elements have been proposed to compose complex actions, the structure of movement decomposition and its neural representation remain unknown. Here, we examined movement decomposition by modeling the temporal dynamics of neural populations in the primary motor cortex of macaque monkeys performing forelimb reaching movements. Using a hidden Markov model, we found that global transitions in the neural population activity are associated with a consistent segmentation of the behavioral output into acceleration and deceleration epochs with directional selectivity. Single cells exhibited modulation of firing rates between the kinematic epochs, with abrupt changes in spiking activity timed with the identified transitions. These results reveal distinct encoding of acceleration and deceleration phases at the level of M1, and point to a specific pattern of movement decomposition that arises from the underlying neural activity. A similar approach can be used to probe the structure of movement decomposition in different brain regions, possibly controlling different temporal scales, to reveal the hierarchical structure of movement composition.

Intersegmental coordination patterns are differently affected in Parkinson's disease and cerebellar ataxia.

The law of intersegmental coordination (Borghese et al. 1996) may be altered in pathological conditions. Here we investigated the contribution of the basal ganglia (BG) and the cerebellum to lower limb intersegmental coordination by inspecting the plane's orientation and other parameters pertinent to this law in patients with idiopathic Parkinson's disease (PD) or cerebellar ataxia (CA). We also applied a mathematical model that successfully accounts for the intersegmental law of coordination observed in control subjects (Barliya et al. 2009). In the present study, we compared the planarity index (PI), covariation plane (CVP) orientation, and CVP orientation predicted by the model in 11 PD patients, 8 CA patients, and two groups of healthy subjects matched for age, height, weight, and gender to each patient group (Ctrl_PD and Ctrl_CA). Controls were instructed to alter their gait speed to match those of their respective patient group. PD patients were examined after overnight withdrawal of anti-parkinsonian medications (PD-off-med) and then on medication (PD-on-med). PI was above 96% in all gait conditions in all groups suggesting that the law of intersegmental coordination is preserved in both BG and cerebellar pathology. However, the measured and predicted CVP orientations rotated in PD-on-med and PD-off-med compared with Ctrl_PD and in CA vs. Ctrl_CA. These rotations caused by PD and CA were in opposite directions suggesting differences in the roles of the BG and cerebellum in intersegmental coordination during human locomotion. NEW & NOTEWORTHY Kinematic and muscular synergies may have a role in overcoming motor redundancies, which may be reflected in intersegmental covariation. Basal ganglia and cerebellar networks were suggested to be involved in crafting and modulating synergies. We thus compared intersegmental coordination in Parkinson's disease and cerebellar disease patients and found opposite effects in some aspects. Further research integrating muscle activities as well as biomechanical and neural control modeling are needed to account for these findings.

The speed-curvature power law of movements: a reappraisal.

Several types of curvilinear movements obey approximately the so called 2/3 power law, according to which the angular speed varies proportionally to the 2/3 power of the curvature. The origin of the law is debated but it is generally thought to depend on physiological mechanisms. However, a recent paper (Marken and Shaffer, Exp Brain Res 88:685-690, 2017) claims that this power law is simply a statistical artifact, being a mathematical consequence of the way speed and curvature are calculated. Here we reject this hypothesis by showing that the speed-curvature power law of biological movements is non-trivial. First, we confirm that the power exponent varies with the shape of human drawing movements and with environmental factors. Second, we report experimental data from Drosophila larvae demonstrating that the power law does not depend on how curvature is calculated. Third, we prove that the law can be violated by means of several mathematical and physical examples. Finally, we discuss biological constraints that may underlie speed-curvature power laws discovered in empirical studies.

The Default Mode Network Differentiates Biological From Non-Biological Motion.

The default mode network (DMN) has been implicated in an array of social-cognitive functions, including self-referential processing, theory of mind, and mentalizing. Yet, the properties of the external stimuli that elicit DMN activity in relation to these domains remain unknown. Previous studies suggested that motion kinematics is utilized by the brain for social-cognitive processing. Here, we used functional MRI to examine whether the DMN is sensitive to parametric manipulations of observed motion kinematics. Preferential responses within core DMN structures differentiating non-biological from biological kinematics were observed for the motion of a realistically looking, human-like avatar, but not for an abstract object devoid of human form. Differences in connectivity patterns during the observation of biological versus non-biological kinematics were additionally observed. Finally, the results additionally suggest that the DMN is coupled more strongly with key nodes in the action observation network, namely the STS and the SMA, when the observed motion depicts human rather than abstract form. These findings are the first to implicate the DMN in the perception of biological motion. They may reflect the type of information used by the DMN in social-cognitive processing.

New whole-body sensory-motor gradients revealed using phase-locked analysis and verified using multivoxel pattern analysis and functional connectivity.

Topographic organization is one of the main principles of organization in the human brain. Specifically, whole-brain topographic mapping using spectral analysis is responsible for one of the greatest advances in vision research. Thus, it is intriguing that although topography is a key feature also in the motor system, whole-body somatosensory-motor mapping using spectral analysis has not been conducted in humans outside M1/SMA. Here, using this method, we were able to map a homunculus in the globus pallidus, a key target area for deep brain stimulation, which has not been mapped noninvasively or in healthy subjects. The analysis clarifies contradictory and partial results regarding somatotopy in the caudal-cingulate zone and rostral-cingulate zone in the medial wall and in the putamen. Most of the results were confirmed at the single-subject level and were found to be compatible with results from animal studies. Using multivoxel pattern analysis, we could predict movements of individual body parts in these homunculi, thus confirming that they contain somatotopic information. Using functional connectivity, we demonstrate interhemispheric functional somatotopic connectivity of these homunculi, such that the somatotopy in one hemisphere could have been found given the connectivity pattern of the corresponding regions of interest in the other hemisphere. When inspecting the somatotopic and nonsomatotopic connectivity patterns, a similarity index indicated that the pattern of connected and nonconnected regions of interest across different homunculi is similar for different body parts and hemispheres. The results show that topographical gradients are even more widespread than previously assumed in the somatosensory-motor system. Spectral analysis can thus potentially serve as a gold standard for defining somatosensory-motor system areas for basic research and clinical applications.

Alpha and beta band event-related desynchronization reflects kinematic regularities.

The short-lasting attenuation of brain oscillations is termed event-related desynchronization (ERD). It is frequently found in the alpha and beta bands in humans during generation, observation, and imagery of movement and is considered to reflect cortical motor activity and action-perception coupling. The shared information driving ERD in all these motor-related behaviors is unknown. We investigated whether particular laws governing production and perception of curved movement may account for the attenuation of alpha and beta rhythms. Human movement appears to be governed by relatively few kinematic laws of motion. One dominant law in biological motion kinematics is the 2/3 power law (PL), which imposes a strong dependency of movement speed on curvature and is prominent in action-perception coupling. Here we directly examined whether the 2/3 PL elicits ERD during motion observation by characterizing the spatiotemporal signature of ERD. ERDs were measured while human subjects observed a cloud of dots moving along elliptical trajectories either complying with or violating the 2/3 PL. We found that ERD within both frequency bands was consistently stronger, arose faster, and was more widespread while observing motion obeying the 2/3 PL. An activity pattern showing clear 2/3 PL preference and lying within the alpha band was observed exclusively above central motor areas, whereas 2/3 PL preference in the beta band was observed in additional prefrontal-central cortical sites. Our findings reveal that compliance with the 2/3 PL is sufficient to elicit a selective ERD response in the human brain.

Brain activity correlates with emotional perception induced by dynamic avatars.

An accurate judgment of the emotional state of others is a prerequisite for successful social interaction and hence survival. Thus, it is not surprising that we are highly skilled at recognizing the emotions of others. Here we aimed to examine the neuronal correlates of emotion recognition from gait. To this end we created highly controlled dynamic body-movement stimuli based on real human motion-capture data (Roether et al., 2009). These animated avatars displayed gait in four emotional (happy, angry, fearful, and sad) and speed-matched neutral styles. For each emotional gait and its equivalent neutral gait, avatars were displayed at five morphing levels between the two. Subjects underwent fMRI scanning while classifying the emotions and the emotional intensity levels expressed by the avatars. Our results revealed robust brain selectivity to emotional compared to neutral gait stimuli in brain regions which are involved in emotion and biological motion processing, such as the extrastriate body area (EBA), fusiform body area (FBA), superior temporal sulcus (STS), and the amygdala (AMG). Brain activity in the amygdala reflected emotional awareness: for visually identical stimuli it showed amplified stronger response when the stimulus was perceived as emotional. Notably, in avatars gradually morphed along an emotional expression axis there was a parametric correlation between amygdala activity and emotional intensity. This study extends the mapping of emotional decoding in the human brain to the domain of highly controlled dynamic biological motion. Our results highlight an extensive level of brain processing of emotional information related to body language, which relies mostly on body kinematics.

Timing of continuous motor imagery: the two-thirds power law originates in trajectory planning.

The two-thirds power law, v = γκ(-1/3), expresses a robust local relationship between the geometrical and temporal aspects of human movement, represented by curvature κ and speed v, with a piecewise constant γ. This law is equivalent to moving at a constant equi-affine speed and thus constitutes an important example of motor invariance. Whether this kinematic regularity reflects central planning or peripheral biomechanical effects has been strongly debated. Motor imagery, i.e., forming mental images of a motor action, allows unique access to the temporal structure of motor planning. Earlier studies have shown that imagined discrete movements obey Fitts's law and their durations are well correlated with those of actual movements. Hence, it is natural to examine whether the temporal properties of continuous imagined movements comply with the two-thirds power law. A novel experimental paradigm for recording sparse imagery data from a continuous cyclic tracing task was developed. Using the likelihood ratio test, we concluded that for most subjects the distributions of the marked positions describing the imagined trajectory were significantly better explained by the two-thirds power law than by a constant Euclidean speed or by two other power law models. With nonlinear regression, the ß parameter values in a generalized power law, v = γκ(-ß), were inferred from the marked position records. This resulted in highly variable yet mostly positive ß values. Our results imply that imagined trajectories do follow the two-thirds power law. Our findings therefore support the conclusion that the coupling between velocity and curvature originates in centrally represented motion planning.

Stopping is not an option: the evolution of unstoppable motion elements (primitives).

Stopping performance is known to depend on low-level motion features, such as movement velocity. It is not known, however, whether it is also subject to high-level motion constraints. Here, we report results of 15 subjects instructed to connect four target points depicted on a digitizing tablet and stop "as rapidly as possible" upon hearing a "stop" cue (tone). Four subjects connected target points with straight paths, whereas 11 subjects generated movements corresponding to coarticulation between adjacent movement components. For the noncoarticulating and coarticulating subjects, stopping performance was not correlated or only weakly correlated with motion velocity, respectively. The generation of a straight, point-to-point movement or a smooth, curved trajectory was not disturbed by the occurrence of a stop cue. Overall, the results indicate that stopping performance is subject to high-level motion constraints, such as the completion of a geometrical plan, and that globally planned movements, once started, must run to completion, providing evidence for the definition of a motion primitive as an unstoppable motion element.

Negative blood oxygenation level dependent homunculus and somatotopic information in primary motor cortex and supplementary motor area.

A crucial attribute in movement encoding is an adequate balance between suppression of unwanted muscles and activation of required ones. We studied movement encoding across the primary motor cortex (M1) and supplementary motor area (SMA) by inspecting the positive and negative blood oxygenation level-dependent (BOLD) signals in these regions. Using periodic and event-related experiments incorporating the bilateral/axial movements of 20 body parts, we report detailed mototopic imaging maps in M1 and SMA. These maps were obtained using phase-locked analysis. In addition to the positive BOLD, significant negative BOLD was detected in M1 but not in the SMA. The negative BOLD spatial pattern was neither located at the ipsilateral somatotopic location nor randomly distributed. Rather, it was organized somatotopically across the entire homunculus and inversely to the positive BOLD, creating a negative BOLD homunculus. The neuronal source of negative BOLD is unclear. M1 provides a unique system to test whether the origin of negative BOLD is neuronal, because different arteries supply blood to different regions in the homunculus, ruling out blood-stealing explanations. Finally, multivoxel pattern analysis showed that positive BOLD in M1 and SMA and negative BOLD in M1 contain somatotopic information, enabling prediction of the moving body part from inside and outside its somatotopic location. We suggest that the neuronal processes underlying negative BOLD participate in somatotopic encoding in M1 but not in the SMA. This dissociation may emerge because of differences in the activity of these motor areas associated with movement suppression.

Spatial constant equi-affine speed and motion perception.

The two-thirds power law, postulating an inverse local relation between the velocity and cubed root of curvature of planar trajectories, is a long-established simplifying principle of human hand movements. In perception, the motion of a dot along a planar elliptical path appears most uniform for speed profiles closer to those predicted by the power law than to constant Euclidean speed, a kinetic-visual illusion. Mathematically, complying with this law is equivalent to moving at constant planar equi-affine speed, while unconstrained three-dimensional drawing movements generally follow constant spatial equi-affine speed. Here we test the generalization of this illusion to visual perception of spatial motion for a dot moving along five differently shaped paths, using stereoscopic projection. The movements appeared most uniform for speed profiles closer to constant spatial equi-affine speed than to constant Euclidean speed, with path torsion (i.e., local deviation from planarity) directly affecting the speed profiles perceived as most uniform, as predicted for constant spatial equi-affine speed. This demonstrates the dominance of equi-affine geometry in spatial motion perception. However, constant equi-affine speed did not fully account for the variability among the speed profiles selected as most uniform for different shapes. Moreover, in a followup experiment, we found that viewing distance affected the speed profile reported as most uniform for the extensively studied planar elliptical motion paths. These findings provide evidence for the critical role of equi-affine geometry in spatial motion perception and contribute to the mounting evidence for the role of non-Euclidean geometries in motion perception and production.

Human arm redundancy: a new approach for the inverse kinematics problem.

The inverse kinematics (IK) problem addresses how both humans and robotic systems coordinate movement to resolve redundancy, as in the case of arm reaching where more degrees of freedom are available at the joint versus hand level. This work focuses on which coordinate frames best represent human movements, enabling the motor system to solve the IK problem in the presence of kinematic redundancies. We used a multi-dimensional sparse source separation method to derive sets of basis (or source) functions for both the task and joint spaces, with joint space represented by either absolute or anatomical joint angles. We assessed the similarities between joint and task sources in each of these joint representations, finding that the time-dependent profiles of the absolute reference frame's sources show greater similarity to corresponding sources in the task space. This result was found to be statistically significant. Our analysis suggests that the nervous system represents multi-joint arm movements using a limited number of basis functions, allowing for simple transformations between task and joint spaces. Additionally, joint space seems to be represented in an absolute reference frame to simplify the IK transformations, given redundancies. Further studies will assess this finding's generalizability and implications for neural control of movement.

Dopamine improves defective cortical and muscular connectivity during bilateral control of gait in Parkinson's disease.

Parkinson's Disease (PD)-typical declines in gait coordination are possibly explained by weakness in bilateral cortical and muscular connectivity. Here, we seek to determine whether this weakness and consequent decline in gait coordination is affected by dopamine levels. To this end, we compare cortico-cortical, cortico-muscular, and intermuscular connectivity and gait outcomes between body sides in people with PD under ON and OFF medication states, and in older adults. In our study, participants walked back and forth along a 12 m corridor. Gait events (heel strikes and toe-offs) and electrical cortical and muscular activities were measured and used to compute cortico-cortical, cortico-muscular, and intermuscular connectivity (i.e., coherences in the alpha, beta, and gamma bands), as well as features characterizing gait performance (e.g., the step-timing coordination, length, and speed). We observe that people with PD, mainly during the OFF medication, walk with reduced step-timing coordination. Additionally, our results suggest that dopamine intake in PD increases the overall cortico-muscular connectivity during the stance and swing phases of gait. We thus conclude that dopamine corrects defective feedback caused by impaired sensory-information processing and sensory-motor integration, thus increasing cortico-muscular coherences in the alpha bands and improving gait.

Expression of emotion in the kinematics of locomotion.

Here, we examine how different emotions-happiness, fear, sadness and anger-affect the kinematics of locomotion. We focus on a compact representation of locomotion properties using the intersegmental law of coordination (Borghese et al. in J Physiol 494(3):863-879, 1996), which states that, during the gait cycle of human locomotion, the elevation angles of the thigh, shank and foot do not evolve independently of each other but form a planar pattern of co-variation. This phenomenon is highly robust and has been extensively studied. The orientation of the plane has been correlated with changes in the speed of locomotion and with reduction in energy expenditure as speed increases. An analytical model explaining the conditions underlying the emergence of this plane and predicting its orientation reveals that it suffices to examine the amplitudes of the elevation angles of the different segments along with the phase shifts between them (Barliya et al. in Exp Brain Res 193:371-385, 2009). We thus investigated the influence of different emotions on the parameters directly determining the orientation of the intersegmental plane and on the angular rotation profiles of the leg segments, examining both the effect of changes in walking speed and effects independent of speed. Subjects were professional actors and naïve subjects with no training in acting. As expected, emotions were found to strongly affect the kinematics of locomotion, particularly walking speed. The intersegmental coordination patterns revealed that emotional expression caused additional modifications to the locomotion patterns that could not be explained solely by a change in speed. For all emotions except sadness, the amplitude of thigh elevation angles changed from those in neutral locomotion. The intersegmental plane was also differently oriented, especially during anger. We suggest that, while speed is the dominant variable allowing discrimination between different emotional gaits, emotion can be reliably recognized in locomotion only when speed is considered together with these kinematic changes.

Neurobiology: motor control of flexible octopus arms.

Animals with rigid skeletons can rely on several mechanisms to simplify motor control--for example, they have skeletal joints that reduce the number of variables and degrees of freedom that need to be controlled. Here we show that when the octopus uses one of its long and highly flexible arms to transfer an object from one place to another, it employs a vertebrate-like strategy, temporarily reconfiguring its arm into a stiffened, articulated, quasi-jointed structure. This indicates that an articulated limb may provide an optimal solution for achieving precise, point-to-point movements.

Neuronal encoding of human kinematic invariants during action observation.

Human movements, besides entailing the presence of a body shape, comply with characteristic kinematic laws of motion. Psychophysical studies show that low-level motion perception is biased toward stimuli complying with these laws. However, the neuronal structures that are sensitive to the kinematic laws of observed bodily movements are still largely unknown. We investigated this issue by dissociating, by means of computer-generated characters, form and motion information during the observation of human movements. In a functional imaging experiment, we compared the levels of blood oxygen level-dependent activity elicited by human actions complying with or violating the kinematic laws of human movements. Actions complying with normal kinematic laws of motion differentially activated the left dorsal premotor and dorsolateral prefrontal cortex as well as the medial frontal cortex. These findings suggest that the kinematic laws of human movements specifically modulate the responses of neuronal circuits also involved in action recognition and that are predominantly located in the left frontal lobe.

Movement timing and invariance arise from several geometries.

Human movements show several prominent features; movement duration is nearly independent of movement size (the isochrony principle), instantaneous speed depends on movement curvature (captured by the 2/3 power law), and complex movements are composed of simpler elements (movement compositionality). No existing theory can successfully account for all of these features, and the nature of the underlying motion primitives is still unknown. Also unknown is how the brain selects movement duration. Here we present a new theory of movement timing based on geometrical invariance. We propose that movement duration and compositionality arise from cooperation among Euclidian, equi-affine and full affine geometries. Each geometry posses a canonical measure of distance along curves, an invariant arc-length parameter. We suggest that for continuous movements, the actual movement duration reflects a particular tensorial mixture of these canonical parameters. Near geometrical singularities, specific combinations are selected to compensate for time expansion or compression in individual parameters. The theory was mathematically formulated using Cartan's moving frame method. Its predictions were tested on three data sets: drawings of elliptical curves, locomotion and drawing trajectories of complex figural forms (cloverleaves, lemniscates and limaçons, with varying ratios between the sizes of the large versus the small loops). Our theory accounted well for the kinematic and temporal features of these movements, in most cases better than the constrained Minimum Jerk model, even when taking into account the number of estimated free parameters. During both drawing and locomotion equi-affine geometry was the most dominant geometry, with affine geometry second most important during drawing; Euclidian geometry was second most important during locomotion. We further discuss the implications of this theory: the origin of the dominance of equi-affine geometry, the possibility that the brain uses different mixtures of these geometries to encode movement duration and speed, and the ontogeny of such representations.