Effect of compliance on haptic perception of curvature

The haptic sense of geometric properties such as the curvature of a contour is derived from somatosensory cues about the motions and forces experienced during exploratory actions. This study addressed the question of whether compliance, the relationship between force and displacement, influences haptic perception of curvature. Subjects traced a curved 30 cm long compliant contour by grasping the handle of a manipulandum and reported whether the contour curved towards or away from them. The contour at which there was equal probability of responding either way was taken to represent one that was sensed as being straight. The compliance of the contour was varied, being constant, greatest in the middle or greatest at the ends. Subjects exhibited a bias in what they sensed to be a straight edge. However, the actual handpath that was judged to be straight did not vary across the three compliance profiles. Our results rule out a hypothetical strategy in which an intended motion is planned and the actual trajectory is then inferred by sensing force feedback. Another strategy in which the force against the contour is controlled and the handpath is inferred from proprioceptive feedback is more consistent with the observations.     

Haptic perception of object curvature in Parkinson's disease

Background

The haptic perception of the curvature of an object is essential for adequate object manipulation and critical for our guidance of actions. This study investigated how the ability to perceive the curvature of an object is altered by Parkinson''s disease (PD).

Methodology/Principal Findings

Eight healthy subjects and 11 patients with mild to moderate PD had to judge, without vision, the curvature of a virtual “box” created by a robotic manipulandum. Their hands were either moved passively along a defined curved path or they actively explored the curved curvature of a virtual wall. The curvature was either concave or convex (bulging to the left or right) and was judged in two locations of the hand workspace–a left workspace location, where the curved hand path was associated with curved shoulder and elbow joint paths, and a right workspace location in which these joint paths were nearly linear. After exploring the curvature of the virtual object, subjects had to judge whether the curvature was concave or convex. Based on these data, thresholds for curvature sensitivity were established. The main findings of the study are: First, 9 out 11 PD patients (82%) showed elevated thresholds for detecting convex curvatures in at least one test condition. The respective median threshold for the PD group was increased by 343% when compared to the control group. Second, when distal hand paths became less associated with proximal joint paths (right workspace), haptic acuity was reduced substantially in both groups. Third, sensitivity to hand trajectory curvature was not improved during active exploration in either group.

Conclusion/Significance

Our data demonstrate that PD is associated with a decreased acuity of the haptic sense, which may occur already at an early stage of the disease.     

Differences in Context and Feedback Result in Different Trajectories and Adaptation Strategies in Reaching

Computational models of motor control have often explained the straightness of horizontal planar reaching movements as a consequence of optimal control. Departure from rectilinearity is thus regarded as sub-optimal. Here we examine if subjects may instead select to make curved trajectories following adaptation to force fields and visuomotor rotations. Separate subjects adapted to force fields with or without visual feedback of their hand trajectory and were retested after 24 hours. Following adaptation, comparable accuracies were achieved in two ways: with visual feedback, adapted trajectories in force fields were straight whereas without it, they remained curved. The results suggest that trajectory shape is not always straight, but is also influenced by the calibration of available feedback signals for the state estimation required by the task. In a follow-up experiment, where additional subjects learned a visuomotor rotation immediately after force field, the trajectories learned in force fields (straight or curved) were transferred when directions of the perturbations were similar but not when directions were opposing. This demonstrates a strong bias by prior experience to keep using a recently acquired control policy that continues to produce successful performance inspite of differences in tasks and feedback conditions. On relearning of force fields on the second day, facilitation by intervening visuomotor rotations occurred only when required motor adjustments and calibration of feedback signals were similar in both tasks. These results suggest that both the available feedback signals and prior history of learning influence the choice and maintenance of control policy during adaptations.     

Movement curvature planning through force field internal models

Human motion studies have focused primarily on modeling straight point-to-point reaching movements. However, many goal-directed reaching movements, such as movements directed towards oneself, are not straight but rather follow highly curved trajectories. These movements are particularly interesting to study since they are essential in our everyday life, appear early in development and are routinely used to assess movement deficits following brain lesions. We argue that curved and straight-line reaching movements are generated by a unique neural controller and that the observed curvature of the movement is the result of an active control strategy that follows the geometry of one’s body, for instance to avoid trajectories that would hit the body or yield postures close to the joint limits. We present a mathematical model that accounts for such an active control strategy and show that the model reproduces with high accuracy the kinematic features of human data during unconstrained reaching movements directed toward the head. The model consists of a nonlinear dynamical system with a single stable attractor at the target. Embodiment-related task constraints are expressed as a force field that acts on the dynamical system. Finally, we discuss the biological plausibility and neural correlates of the model’s parameters and suggest that embodiment should be considered as a main cause for movement trajectory curvature.     

Biomechanics of phalangeal curvature

Phalangeal curvature has been widely cited in primate functional morphology and is one of the key traits in the ongoing debate about whether the locomotion of early hominins included a significant degree of arboreality. This study examines the biomechanics of phalangeal curvature using data on hand posture, muscle recruitment, and anatomical moment arms to develop a finite element (FE) model of a siamang manual proximal phalanx during suspensory grasping. Strain patterns from experiments on intact cadaver forelimbs validated the model. The strain distribution in the curved siamang phalanx FE model was compared to that in a mathematically straight rendition in order to test the hypotheses that curvature: 1) reduces strain and 2) results in lower bending strains but relatively higher compression. In the suspensory posture, joint reaction forces load the articular ends of the phalanx in compression and dorsally, while muscle forces acting through the flexor sheath pull the mid-shaft palmarly. These forces compress the phalanx dorsally and tense it palmarly, effectively bending it 'open.' Strains in the curved model were roughly half that of the straight model despite equivalent lengths, areas, mechanical properties, and loading conditions in the two models. The curved model also experienced a higher ratio of compressive to tensile strains. Curvature reduces strains during grasping hand postures because the curved bone is more closely aligned with the joint reaction forces. Therefore, phalangeal curvature reduces the strains associated with arboreal, and especially suspensory, activity involving flexed digits. These results offer a biomechanical explanation for the observed association between phalangeal curvature and arboreality.     

Vibration influences haptic perception of surface compliance during walking

Background

The haptic perception of ground compliance is used for stable regulation of dynamic posture and the control of locomotion in diverse natural environments. Although rarely investigated in relation to walking, vibrotactile sensory channels are known to be active in the discrimination of material properties of objects and surfaces through touch. This study investigated how the perception of ground surface compliance is altered by plantar vibration feedback.

Methodology/Principal Findings

Subjects walked in shoes over a rigid floor plate that provided plantar vibration feedback, and responded indicating how compliant it felt, either in subjective magnitude or via pairwise comparisons. In one experiment, the compliance of the floor plate was also varied. Results showed that perceived compliance of the plate increased monotonically with vibration feedback intensity, and depended to a lesser extent on the temporal or frequency distribution of the feedback. When both plate stiffness (inverse compliance) and vibration amplitude were manipulated, the effect persisted, with both factors contributing to compliance perception. A significant influence of vibration was observed even for amplitudes close to psychophysical detection thresholds.

Conclusions/Significance

These findings reveal that vibrotactile sensory channels are highly salient to the perception of surface compliance, and suggest that correlations between vibrotactile sensory information and motor activity may be of broader significance for the control of human locomotion than has been previously acknowledged.     

The pattern of secondary root formation in curving roots of Arabidopsis thaliana (L.) Heynh.

Abstract. A gravitational stimulus was used to induce the curvature of the main root of Arabidopsis thaliana. The number of secondary roots increased on the convex side and decreased on the concave side of any curved main root axes in comparison with straight roots used as the control. The same phenomenon was observed with the curved main roots of plants grown on a clinostat and of mutant plants exhibiting random root orientation. The data suggest that the pattern of lateral root formation is associated with curvature but is independent of the environmental stimuli used to induce curvature.     

Curvature facilitates prey fixation in predatory insect claws

Insects show a large variety in prey capture strategies, with a correspondingly large diversity in predatory adaptations. We studied a specific type of predatory claws, these can for example be found in praying mantis species. The claw is closeable over its entire length and the prey is fixed between the femur (upper arm) and the tibia (lower arm) of the insect leg. The morphology of these predatory claws is diverse. Some species have straight claws covered with spines, while other species have smooth, curved claws. We have studied the mechanics of this femur-tibia type of predatory insect claws, by making a physical model, eventually trying to explain why in some insect species the claws are curved instead of straight. The main results are (1) when comparing curved claws to straight claws, curvature leads to a strong reduction of forces driving the prey away from the pivoting point, thereby reducing the need for friction generating structures. (2) In the curved claw model a position exists where the resulting force on the prey is exactly zero. This is because the normal forces on the femur and tibia are opposed, and in line. At this position the prey is perfectly clamped and not driven out of the claw. This feature does not exist in straight claws. (3) In the curved claw, the prey cannot be placed at a position further than a certain maximum distance from the pivoting point. Near this maximum position, the resulting force on the prey reaches high values because moment arms are near zero. (4) Between the zero position and the maximum position the resulting force is directed toward the pivoting point, which stabilizes prey fixation.     

Curvature of the forelimb bones of anthropoid primates: Overall allometric patterns and specializations in suspensory species

It has previously been reported that brachiating primates, particularly gibbons, are characterized by distinctively straight forelimb long bones, yet no hypotheses have been proposed to explain why straight limb bones may be adaptive to suspensory locomotion. This study explores quantitatively the curvature of the long bones in 13 species of anthropoid primates and analyzes the functional consequences of curvature in biomechanical terms. These analyses demonstrate that, whereas the humeri of gibbons and spider monkeys are functionally less curved than those of other taxa, the ulnae of brachiators are neither more nor less curved than those of other anthropoids, and the gibbon radius is far more curved than would be predicted from body size alone. The humerus is likely significantly less curved in brachiators because of its torsion-dominated loading regime and the greatly increased stress magnitude developed in torsionally loaded curved beams. The large curvature of the radius is localized in the region of attachment of the supinator muscle. Analysis presented here of muscle mass allometry in catarrhines demonstrates that gibbons are characterized by an extremely massive supinator, and the large radial curvature is therefore most likely due to forearm muscle mechanics. This study also demonstrates that the overall pattern of limb bone curvature for anthropoids is distinct from the pattern reported for mammals as a whole. This distinctive scaling relationship may be related to the increased length of the limb bones of primates in comparison to other mammals.     

Role of gravitation in solving a haptic comparison problem

The effect of haptic perception-reproduction task performed by means of a force feedback handle was studied under ground-based conditions and on board an orbital station. In contrast to visual perception, which exhibits a pronounced domination of vertically and horizontally oriented stimuli in such experiments, haptic perception did not display a dependence of responses on the tilt of the reference stimulus in the presence or absence of gravity. Thus, when solving a purely haptic problem, the CNS uses only proprioception, even in the presence of gravitation.     

Stathmin and Interfacial Microtubule Inhibitors Recognize a Naturally Curved Conformation of Tubulin Dimers

Tubulin is able to switch between a straight microtubule-like structure and a curved structure in complex with the stathmin-like domain of the RB3 protein (T₂RB3). GTP hydrolysis following microtubule assembly induces protofilament curvature and disassembly. The conformation of the labile tubulin heterodimers is unknown. One important question is whether free GDP-tubulin dimers are straightened by GTP binding or if GTP-tubulin is also curved and switches into a straight conformation upon assembly. We have obtained insight into the bending flexibility of tubulin by analyzing the interplay of tubulin-stathmin association with the binding of several small molecule inhibitors to the colchicine domain at the tubulin intradimer interface, combining structural and biochemical approaches. The crystal structures of T₂RB3 complexes with the chiral R and S isomers of ethyl-5-amino-2-methyl-1,2-dihydro-3-phenylpyrido[3,4-b]pyrazin-7-yl-carbamate, show that their binding site overlaps with colchicine ring A and that both complexes have the same curvature as unliganded T₂RB3. The binding of these ligands is incompatible with a straight tubulin structure in microtubules. Analytical ultracentrifugation and binding measurements show that tubulin-stathmin associations (T₂RB3, T₂Stath) and binding of ligands (R, S, TN-16, or the colchicine analogue MTC) are thermodynamically independent from one another, irrespective of tubulin being bound to GTP or GDP. The fact that the interfacial ligands bind equally well to tubulin dimers or stathmin complexes supports a bent conformation of the free tubulin dimers. It is tempting to speculate that stathmin evolved to recognize curved structures in unassembled and disassembling tubulin, thus regulating microtubule assembly.     

Cycling around a Curve: The Effect of Cycling Speed on Steering and Gaze Behavior

Although it is generally accepted that visual information guides steering, it is still unclear whether a curvature matching strategy or a ‘look where you are going’ strategy is used while steering through a curved road. The current experiment investigated to what extent the existing models for curve driving also apply to cycling around a curve, and tested the influence of cycling speed on steering and gaze behavior. Twenty-five participants were asked to cycle through a semicircular lane three consecutive times at three different speeds while staying in the center of the lane. The observed steering behavior suggests that an anticipatory steering strategy was used at curve entrance and a compensatory strategy was used to steer through the actual bend of the curve. A shift of gaze from the center to the inside edge of the lane indicates that at low cycling speed, the ‘look where you are going’ strategy was preferred, while at higher cycling speeds participants seemed to prefer the curvature matching strategy. Authors suggest that visual information from both steering strategies contributes to the steering system and can be used in a flexible way. Based on a familiarization effect, it can be assumed that steering is not only guided by vision but that a short-term learning component should also be taken into account.     

Measurement of the force and torque produced in the calcium response of reactivated rat sperm flagella

Rat sperm that are demembranated with Triton X-100 and reactivated with Mg-ATP show a strong mechanical response to the presence of free calcium ion. At pCa < 4, the midpiece region of the flagellum develops a strong and sustained curvature that gives the cell the overall appearance of a fishhook [Lindemann and Goltz, 1988: Cell Motil. Cytoskeleton 10:420-431]. In the present study, the force and torque that maintain the calcium-induced hook have been examined quantitatively. In addition, full-length and shortened flagella were manipulated to evaluate the plasticity of the hooks and determined the critical length necessary for maintaining the curvature. The hooks were found to be highly resilient, returning to their original configuration (>95%) after being straightened and released. The results from manipulating the shortened flagella suggest that the force holding the hook in the curved configuration is generated in the basal 60 microm of the flagellum. The force required to straighten the calcium-induced hooks was measured with force-calibrated glass microprobes, and the bending torque was calculated from the measured force. The force and torque required to straighten the flagellum were found to be proportional to the change in curvature of the hooked region of the flagellum, suggesting an elastic-like behavior. The average torque to open the hooks to a straight position was 2.6 (+/-1.4) x 10(-7) dyne x cm (2.6 x 10(-14) N x m) and the apparent stiffness was 4.3 (+/-1.3) x 10(-10) dyne x cm(2) (4.3 x 10(-19) N x m(2)). The stiffness of the hook was determined to be approximately one quarter the rigor stiffness of a rat sperm flagellum measured under comparable conditions.     

Can Force Feedback and Science Learning Enhance the Effectiveness of Neuro-Rehabilitation? An Experimental Study on Using a Low-Cost 3D Joystick and a Virtual Visit to a Zoo

In this paper, we demonstrate that healthy adults respond differentially to the administration of force feedback and the presentation of scientific content in a virtual environment, where they interact with a low-cost haptic device. Subjects are tasked with controlling the movement of a cursor on a predefined trajectory that is superimposed on a map of New York City’s Bronx Zoo. The system is characterized in terms of a suite of objective indices quantifying the subjects’ dexterity in planning and generating the multijoint visuomotor tasks. We find that force feedback regulates the smoothness, accuracy, and duration of the subject’s movement, whereby converging or diverging force fields influence the range of variations of the hand speed. Finally, our findings provide preliminary evidence that using educational content increases subjects’ satisfaction. Improving the level of interest through the inclusion of learning elements can increase the time spent performing rehabilitation tasks and promote learning in a new context.     

Impact of Coronary Artery Curvature on the Longitudinal Stent Foreshortening: Real-World Observations

Longitudinal stent foreshortening is a known phenomenon, however, the impact of coronary artery curvature on longitudinal stent foreshortening remains unclear. The aim of this study is to determine the impact of coronary artery curvature on the longitudinal stent foreshortening in the real-world scenarios. A total of 86 consecutive patients underwent coronary stent implantation were included in the present study. The degree of coronary artery curvature was defined as the length of the coronary artery curvature divided by the straight length. Longitudinal stent foreshortening was defined as the stent length after implantation divided by the stent length before implantation. The mean longitudinal foreshortening rate of coronary stents was about 94% in curved coronary arteries. Longitudinal stent foreshortening rate was positively correlated with the degree of coronary artery curvature (r = –0.86, P < 0.01). Coronary artery curvature is associated with significant longitudinal foreshortening of coronary stents, thus longitudinal foreshortening should be considered on deciding the stent length in curved coronary artery and a longer stent is usually needed in curved coronary artery.     

Grouping by Proximity in Haptic Contour Detection

We investigated the applicability of the Gestalt principle of perceptual grouping by proximity in the haptic modality. To do so, we investigated the influence of element proximity on haptic contour detection. In the course of four sessions ten participants performed a haptic contour detection task in which they freely explored a haptic random dot display that contained a contour in 50% of the trials. A contour was defined by a higher density of elements (raised dots), relative to the background surface. Proximity of the contour elements as well as the average proximity of background elements was systematically varied. We hypothesized that if proximity of contour elements influences haptic contour detection, detection will be more likely when contour elements are in closer proximity. This should be irrespective of the ratio with the proximity of the background elements. Results showed indeed that the closer the contour elements were, the higher the detection rates. Moreover, this was the case independent of the contour/background ratio. We conclude that the Gestalt law of proximity applies to haptic contour detection.     

The effect of intrinsic curvature on supercoiling: Predictions of elasticity theory

Elasticity theory of naturally curved rods is employed to study the effects of intrinsic curvature on the properties of the equilibrium conformations of supercoiled DNA. The results stand in sharp contrast to those obtained when the molecule is viewed as being straight in its relaxed form. Starting from very fundamental principles of the theory, we show that the torsion of an open segment with a curved duplex axis can vary when the temperature, and along with it, the intrinsic twist is changed. Conversely, an imposed helicity, such as might be associated with binding to a histone, can change the intrinsic twist. It is also shown that another consequence of the presence of naturally curved sequences is that the twist density will, in general, vary with position along the chain in all equilibrium states. Then portions of the molecule will be more or less susceptible to interaction with other agents sensitive to such a variation. Finally, some closed equilibrium global structures uniquely associated with intrinsic curvature are discussed. © 1993 John Wiley & Sons, Inc.     

Magnitude Estimation of Contact Force When Objects with Different Shapes Are Applied Passively to the Fingerpad

Stimuli with spherically curved surfaces were presented passively to the fingerpads of human subjects. There were 28 stimuli, consisting of all combinations of 4 different curvatures and 7 different contact forces; these were presented in random order. Subjects scaled their perceived magnitude of the contact force using magnitude estimation. Perceived force increased markedly with an increase in experimentally applied contact force. An increase in curvature resulted in a slight increase in perceived contact force. Thus, when humans are passively presented with objects changing in both shape and contact force, they are able to extract information about the force. Because of the passive nature of the task, all such information must be conveyed to the brain by the cutaneous mechanoreceptors.     

Time to task failure and motor cortical activity depend on the type of feedback in visuomotor tasks

The present study aimed to elucidate whether the type of feedback influences the performance and the motor cortical activity when executing identical visuomotor tasks. For this purpose, time to task failure was measured during position- and force-controlled muscular contractions. Subjects received either visual feedback about the force produced by pressing a force transducer or about the actual position between thumb and index finger. Participants were instructed to either match the force level of 30% MVC or the finger position corresponding to the thumb and index finger angle at this contraction intensity. Subjects demonstrated a shorter time to task failure when they were provided with feedback about their joint position (11.5 ± 6.2 min) instead of force feedback (19.2 ± 12.8 min; P = 0.01). To test differences in motor cortical activity between position- and force-controlled contractions, subthreshold transcranial magnetic stimulation (subTMS) was applied while executing submaximal (20% MVC) contractions. SubTMS resulted in a suppression of the first dorsal interosseus muscle (FDI) EMG in both tasks. However, the mean suppression for the position-controlled task was significantly greater (18.6 ± 9.4% vs. 13.3 ± 7.5%; P = 0.025) and lasted longer (13.9 ± 7.5 ms vs. 9.3 ± 4.3 ms; P = 0.024) compared to the force-controlled task. The FDI background EMG obtained without stimulation was comparable in all conditions. The present results demonstrate that the presentation of different feedback modalities influences the time to task failure as well as the cortical activity. As only the feedback was altered but not the mechanics of the task, the present results add to the body of evidence that suggests that the central nervous system processes force and position information in different ways.     

Deducing planning variables from experimental arm trajectories: Pitfalls and possibilities

This paper investigates whether endpoint Cartesian variables or joint variables better describe the planning of human arm movements. For each of the two sets of planning variables, a coordination strategy of linear interpolation is chosen to generate possible trajectories, which are to be compared against experimental trajectories for best match. Joint interpolation generates curved endpoint trajectories calledN-leaved roses. Endpoint Cartesian interpolation generates curved joint trajectories, which however can be qualitatively characterized by joint reversal points.Though these two sets of planning variables ordinarily lead to distinct predictions under linear interpolation, three situations are pointed out where the two strategies may be confused. One is a straight line through the shoulder, where the joint trajectories are also straight. Another is any trajectory approaching the outer boundary of reach, where the joint rate ratio always appears to be approaching a constant. A third is a generalization to staggered joint interpolation, where endpoint trajectories virtually identical to straight lines can sometimes be produced. In examining two different sets of experiments, it is proposed that staggered joint interpolation is the underlying planning strategy.