Correlations in state space can cause sub-optimal adaptation of optimal feedback control models

Control of our movements is apparently facilitated by an adaptive internal model in the cerebellum. It was long thought that this internal model implemented an adaptive inverse model and generated motor commands, but recently many reject that idea in favor of a forward model hypothesis. In theory, the forward model predicts upcoming state during reaching movements so the motor cortex can generate appropriate motor commands. Recent computational models of this process rely on the optimal feedback control (OFC) framework of control theory. OFC is a powerful tool for describing motor control, it does not describe adaptation. Some assume that adaptation of the forward model alone could explain motor adaptation, but this is widely understood to be overly simplistic. However, an adaptive optimal controller is difficult to implement. A reasonable alternative is to allow forward model adaptation to ‘re-tune’ the controller. Our simulations show that, as expected, forward model adaptation alone does not produce optimal trajectories during reaching movements perturbed by force fields. However, they also show that re-optimizing the controller from the forward model can be sub-optimal. This is because, in a system with state correlations or redundancies, accurate prediction requires different information than optimal control. We find that adding noise to the movements that matches noise found in human data is enough to overcome this problem. However, since the state space for control of real movements is far more complex than in our simple simulations, the effects of correlations on re-adaptation of the controller from the forward model cannot be overlooked.     

Ganzfeld Stimulation or Sleep Enhance Long Term Motor Memory Consolidation Compared to Normal Viewing in Saccadic Adaptation Paradigm

Adaptation of saccade amplitude in response to intra-saccadic target displacement is a type of implicit motor learning which is required to compensate for physiological changes in saccade performance. Once established trials without intra-saccadic target displacement lead to de-adaptation or extinction, which has been attributed either to extra-retinal mechanisms of spatial constancy or to the influence of the stable visual surroundings. Therefore we investigated whether visual deprivation (“Ganzfeld”-stimulation or sleep) can partially maintain this motor learning compared to free viewing of the natural surroundings. Thirty-five healthy volunteers performed two adaptation blocks of 100 inward adaptation trials – interspersed by an extinction block – which were followed by a two-hour break with or without visual deprivation (VD). Using additional adaptation and extinction blocks short and long (4 weeks) term memory of this implicit motor learning were tested. In the short term, motor memory tested immediately after free viewing was superior to adaptation performance after VD. In the long run, however, effects were opposite: motor memory and relearning of adaptation was superior in the VD conditions. This could imply independent mechanisms that underlie the short-term ability of retrieving learned saccadic gain and its long term consolidation. We suggest that subjects mainly rely on visual cues (i.e., retinal error) in the free viewing condition which makes them prone to changes of the visual stimulus in the extinction block. This indicates the role of a stable visual array for resetting adapted saccade amplitudes. In contrast, visual deprivation (GS and sleep), might train subjects to rely on extra-retinal cues, e.g., efference copy or prediction to remap their internal representations of saccade targets, thus leading to better consolidation of saccadic adaptation.     

Spatial Interactions between Successive Eye and Arm Movements: Signal Type Matters

Spatial interactions between consecutive movements are often attributed to inhibition of return (IOR), a phenomenon in which responses to previously signalled locations are slower than responses to unsignalled locations. In two experiments using peripheral target signals offset by 0°, 90°, or 180°, we show that consecutive saccadic (Experiment 1) and reaching (Experiment 3) responses exhibit a monotonic pattern of reaction times consistent with the currently established spatial distribution of IOR. In contrast, in two experiments with central target signals (i.e., arrowheads pointing at target locations), we find a non-monotonic pattern of reaction times for saccades (Experiment 2) and reaching movements (Experiment 4). The difference in the patterns of results observed demonstrates different behavioral effects that depend on signal type. The pattern of results observed for central stimuli are consistent with a model in which neural adaptation is occurring within motor networks encoding movement direction in a distributed manner.     

Effect of muscle fatigue on internal model formation and retention during reaching with the arm.

The motor system adapts to novel dynamic environments by forming internal models that predict the muscle forces needed to move skillfully. The goal of this study was to determine how muscle fatigue affects internal model formation during arm movement and whether an internal model acquired while fatigued could be recalled accurately after rest. Twelve subjects adapted to a viscous force field applied by a lightweight robot as they reached to a target. They then reached while being resisted by elastic bands until they could no longer touch the target. This protocol reduced the strength of the muscles used to resist the force field by approximately 20%. The bands were removed, and subjects adapted again to the viscous force field. Their adaptive ability, quantified by the amount and time constant of adaptation, was not significantly impaired following fatigue. The subjects then rested, recovering approximately 70% of their lost force-generation ability. When they reached in the force field again, their prediction of the force field strength was different than in a nonfatigued state. This alteration was consistent with the use of a higher level of effort than normally used to counteract the force field. These results suggest that recovery from fatigue can affect recall of an internal model, even when the fatigue did not substantially affect the motor system's ability to form the model. Recovery from fatigue apparently affects recall because the motor system represents internal models as a mapping between effort and movement and relies on practice to recalibrate this mapping.     

Modelling the learning of biomechanics and visual planning for decision-making of motor actions

Recent experiments showed that the bio-mechanical ease and end-point stability associated to reaching movements are predicted prior to movement onset, and that these factors exert a significant influence on the choice of movement. As an extension of these results, here we investigate whether the knowledge about biomechanical costs and their influence on decision-making are the result of an adaptation process taking place during each experimental session or whether this knowledge was learned at an earlier stage of development. Specifically, we analysed both the pattern of decision-making and its fluctuations during each session, of several human subjects making free choices between two reaching movements that varied in path distance (target relative distance), biomechanical cost, aiming accuracy and stopping requirement. Our main result shows that the effect of biomechanics is well established at the start of the session, and that, consequently, the learning of biomechanical costs in decision-making occurred at an earlier stage of development. As a means to characterise the dynamics of this learning process, we also developed a model-based reinforcement learning model, which generates a possible account of how biomechanics may be incorporated into the motor plan to select between reaching movements. Results obtained in simulation showed that, after some pre-training corresponding to a motor babbling phase, the model can reproduce the subjects’ overall movement preferences. Although preliminary, this supports that the knowledge about biomechanical costs may have been learned in this manner, and supports the hypothesis that the fluctuations observed in the subjects’ behaviour may adapt in a similar fashion.     

The remapping of space in motor learning and human–machine interfaces

Studies of motor adaptation to patterns of deterministic forces have revealed the ability of the motor control system to form and use predictive representations of the environment. One of the most fundamental elements of our environment is space itself. This article focuses on the notion of Euclidean space as it applies to common sensory motor experiences. Starting from the assumption that we interact with the world through a system of neural signals, we observe that these signals are not inherently endowed with metric properties of the ordinary Euclidean space. The ability of the nervous system to represent these properties depends on adaptive mechanisms that reconstruct the Euclidean metric from signals that are not Euclidean. Gaining access to these mechanisms will reveal the process by which the nervous system handles novel sophisticated coordinate transformation tasks, thus highlighting possible avenues to create functional human–machine interfaces that can make that task much easier. A set of experiments is presented that demonstrate the ability of the sensory-motor system to reorganize coordination in novel geometrical environments. In these environments multiple degrees of freedom of body motions are used to control the coordinates of a point in a two-dimensional Euclidean space. We discuss how practice leads to the acquisition of the metric properties of the controlled space. Methods of machine learning based on the reduction of reaching errors are tested as a means to facilitate learning by adaptively changing he map from body motions to controlled device. We discuss the relevance of the results to the development of adaptive human–machine interfaces and optimal control.     

Do we have an internal model of the outside world?

Our phenomenal world remains stationary in spite of movements of the eyes, head and body. In addition, we can point or turn to objects in the surroundings whether or not they are in the field of view. In this review, I argue that these two features of experience and behaviour are related. The ability to interact with objects we cannot see implies an internal memory model of the surroundings, available to the motor system. And, because we maintain this ability when we move around, the model must be updated, so that the locations of object memories change continuously to provide accurate directional information. The model thus contains an internal representation of both the surroundings and the motions of the head and body: in other words, a stable representation of space. Recent functional MRI studies have provided strong evidence that this egocentric representation has a location in the precuneus, on the medial surface of the superior parietal cortex. This is a region previously identified with ‘self-centred mental imagery’, so it seems likely that the stable egocentric representation, required by the motor system, is also the source of our conscious percept of a stable world.     

Reduction in Learning Rates Associated with Anterograde Interference Results from Interactions between Different Timescales in Motor Adaptation

Prior experiences can influence future actions. These experiences can not only drive adaptive changes in motor output, but they can also modulate the rate at which these adaptive changes occur. Here we studied anterograde interference in motor adaptation – the ability of a previously learned motor task (Task A) to reduce the rate of subsequently learning a different (and usually opposite) motor task (Task B). We examined the formation of the motor system''s capacity for anterograde interference in the adaptive control of human reaching-arm movements by determining the amount of interference after varying durations of exposure to Task A (13, 41, 112, 230, and 369 trials). We found that the amount of anterograde interference observed in the learning of Task B increased with the duration of Task A. However, this increase did not continue indefinitely; instead, the interference reached asymptote after 15–40 trials of Task A. Interestingly, we found that a recently proposed multi-rate model of motor adaptation, composed of two distinct but interacting adaptive processes, predicts several key features of the interference patterns we observed. Specifically, this computational model (without any free parameters) predicts the initial growth and leveling off of anterograde interference that we describe, as well as the asymptotic amount of interference that we observe experimentally (R² = 0.91). Understanding the mechanisms underlying anterograde interference in motor adaptation may enable the development of improved training and rehabilitation paradigms that mitigate unwanted interference.     

Social Suppressive Behavior Is Organized by the Spatiotemporal Integration of Multiple Cortical Regions in the Japanese Macaque

Under social conflict, monkeys develop hierarchical positions through social interactions. Once the hierarchy is established, the dominant monkey dominates the space around itself and the submissive monkey tries not to violate this space. Previous studies have shown the contributions of the frontal and parietal cortices in social suppression, but the contributions of other cortical areas to suppressive functions remain elusive. We recorded neural activity in large cortical areas using electrocorticographic (ECoG) arrays while monkeys performed a social food-grab task in which a target monkey was paired with either a dominant or a submissive monkey. If the paired monkey was dominant, the target monkey avoided taking food in the shared conflict space, but not in other areas. By contrast, when the paired monkey was submissive, the target monkey took the food freely without hesitation. We applied decoding analysis to the ECoG data to see when and which cortical areas contribute to social behavioral suppression. Neural information discriminating the social condition was more evident when the conflict space was set in the area contralateral to the recording hemisphere. We found that the information increased as the social pressure increased during the task. Before food presentation, when the pressure was relatively low, the parietal and somatosensory–motor cortices showed sustained discrimination of the social condition. After food presentation, when the monkey faced greater pressure to make a decision as to whether it should take the food, the prefrontal and visual cortices started to develop buildup responses. The social representation was found in a sustained form in the parietal and somatosensory–motor regions, followed by additional buildup form in the visual and prefrontal cortices. The representation was less influenced by reward expectation. These findings suggest that social adaptation is achieved by a higher-order self-regulation process (incorporating motor preparation/execution processes) in accordance with the embodied social contexts.     

Learning the dynamics of reaching movements results in the modification of arm impedance and long-latency perturbation responses

 Some characteristics of arm movements that humans exhibit during learning the dynamics of reaching are consistent with a theoretical framework where training results in motor commands that are gradually modified to predict and compensate for novel forces that may act on the hand. As a first approximation, the motor control system behaves as an adapting controller that learns an internal model of the dynamics of the task. It approximates inverse dynamics and predicts motor commands that are appropriate for a desired limb trajectory. However, we had previously noted that subtle motion characteristics observed during changes in task dynamics challenged this simple model and raised the possibility that adaptation also involved sensory–motor feedback pathways. These pathways reacted to sensory feedback during the course of the movement. Here we hypothesize that adaptation to dynamics might also involve a modification of how the CNS responds to sensory feedback. We tested this through experiments that quantified how the motor system's response to errors during voluntary movements changed as it adapted to dynamics of a force field. We describe a nonlinear approach that approximates the impedance of the arm, i.e., force response as a function of arm displacement trajectory. We observe that after adaptation, the impedance function changes in a way that closely matches and counters the effect of the force field. This is particularly prominent in the long-latency (>100 ms) component of response to perturbations. Therefore, it appears that practice not only modifies the internal model with which the brain generates motor commands that initiate a movement, but also the internal model with which sensory feedback is integrated with the ongoing descending commands in order to respond to error during the movement. Received: 10 January 2001 / Accepted in revised form: 30 May 2001     

Reinforcement Learning of Targeted Movement in a Spiking Neuronal Model of Motor Cortex

Sensorimotor control has traditionally been considered from a control theory perspective, without relation to neurobiology. In contrast, here we utilized a spiking-neuron model of motor cortex and trained it to perform a simple movement task, which consisted of rotating a single-joint “forearm” to a target. Learning was based on a reinforcement mechanism analogous to that of the dopamine system. This provided a global reward or punishment signal in response to decreasing or increasing distance from hand to target, respectively. Output was partially driven by Poisson motor babbling, creating stochastic movements that could then be shaped by learning. The virtual forearm consisted of a single segment rotated around an elbow joint, controlled by flexor and extensor muscles. The model consisted of 144 excitatory and 64 inhibitory event-based neurons, each with AMPA, NMDA, and GABA synapses. Proprioceptive cell input to this model encoded the 2 muscle lengths. Plasticity was only enabled in feedforward connections between input and output excitatory units, using spike-timing-dependent eligibility traces for synaptic credit or blame assignment. Learning resulted from a global 3-valued signal: reward (+1), no learning (0), or punishment (−1), corresponding to phasic increases, lack of change, or phasic decreases of dopaminergic cell firing, respectively. Successful learning only occurred when both reward and punishment were enabled. In this case, 5 target angles were learned successfully within 180 s of simulation time, with a median error of 8 degrees. Motor babbling allowed exploratory learning, but decreased the stability of the learned behavior, since the hand continued moving after reaching the target. Our model demonstrated that a global reinforcement signal, coupled with eligibility traces for synaptic plasticity, can train a spiking sensorimotor network to perform goal-directed motor behavior.     

Flexible cognitive strategies during motor learning

Visuomotor rotation tasks have proven to be a powerful tool to study adaptation of the motor system. While adaptation in such tasks is seemingly automatic and incremental, participants may gain knowledge of the perturbation and invoke a compensatory strategy. When provided with an explicit strategy to counteract a rotation, participants are initially very accurate, even without on-line feedback. Surprisingly, with further testing, the angle of their reaching movements drifts in the direction of the strategy, producing an increase in endpoint errors. This drift is attributed to the gradual adaptation of an internal model that operates independently from the strategy, even at the cost of task accuracy. Here we identify constraints that influence this process, allowing us to explore models of the interaction between strategic and implicit changes during visuomotor adaptation. When the adaptation phase was extended, participants eventually modified their strategy to offset the rise in endpoint errors. Moreover, when we removed visual markers that provided external landmarks to support a strategy, the degree of drift was sharply attenuated. These effects are accounted for by a setpoint state-space model in which a strategy is flexibly adjusted to offset performance errors arising from the implicit adaptation of an internal model. More generally, these results suggest that strategic processes may operate in many studies of visuomotor adaptation, with participants arriving at a synergy between a strategic plan and the effects of sensorimotor adaptation.     

Rethinking motor learning and savings in adaptation paradigms: model-free memory for successful actions combines with internal models

Although motor learning is likely to involve multiple processes, phenomena observed in error-based motor learning paradigms tend to be conceptualized in terms of only a single process: adaptation, which occurs through updating an internal model. Here we argue that fundamental phenomena like movement direction biases, savings (faster relearning), and interference do not relate to adaptation but instead are attributable to two additional learning processes that can be characterized as model-free: use-dependent plasticity and operant reinforcement. Although usually "hidden" behind adaptation, we demonstrate, with modified visuomotor rotation paradigms, that these distinct model-based and model-free processes combine to learn an error-based motor task. (1) Adaptation of an internal model channels movements toward successful error reduction in visual space. (2) Repetition of the newly adapted movement induces directional biases toward the?repeated movement. (3) Operant reinforcement through association of the adapted movement with successful error reduction is responsible for savings.     

Interacting adaptive processes with different timescales underlie short-term motor learning

Multiple processes may contribute to motor skill acquisition, but it is thought that many of these processes require sleep or the passage of long periods of time ranging from several hours to many days or weeks. Here we demonstrate that within a timescale of minutes, two distinct fast-acting processes drive motor adaptation. One process responds weakly to error but retains information well, whereas the other responds strongly but has poor retention. This two-state learning system makes the surprising prediction of spontaneous recovery (or adaptation rebound) if error feedback is clamped at zero following an adaptation-extinction training episode. We used a novel paradigm to experimentally confirm this prediction in human motor learning of reaching, and we show that the interaction between the learning processes in this simple two-state system provides a unifying explanation for several different, apparently unrelated, phenomena in motor adaptation including savings, anterograde interference, spontaneous recovery, and rapid unlearning. Our results suggest that motor adaptation depends on at least two distinct neural systems that have different sensitivity to error and retain information at different rates.     

End-Point Variability Is Not Noise in Saccade Adaptation

When each of many saccades is made to overshoot its target, amplitude gradually decreases in a form of motor learning called saccade adaptation. Overshoot is induced experimentally by a secondary, backwards intrasaccadic target step (ISS) triggered by the primary saccade. Surprisingly, however, no study has compared the effectiveness of different sizes of ISS in driving adaptation by systematically varying ISS amplitude across different sessions. Additionally, very few studies have examined the feasibility of adaptation with relatively small ISSs. In order to best understand saccade adaptation at a fundamental level, we addressed these two points in an experiment using a range of small, fixed ISS values (from 0° to 1° after a 10° primary target step). We found that significant adaptation occurred across subjects with an ISS as small as 0.25°. Interestingly, though only adaptation in response to 0.25° ISSs appeared to be complete (the magnitude of change in saccade amplitude was comparable to size of the ISS), further analysis revealed that a comparable proportion of the ISS was compensated for across conditions. Finally, we found that ISS size alone was sufficient to explain the magnitude of adaptation we observed; additional factors did not significantly improve explanatory power. Overall, our findings suggest that current assumptions regarding the computation of saccadic error may need to be revisited.     

Robust Brain-Machine Interface Design Using Optimal Feedback Control Modeling and Adaptive Point Process Filtering

Much progress has been made in brain-machine interfaces (BMI) using decoders such as Kalman filters and finding their parameters with closed-loop decoder adaptation (CLDA). However, current decoders do not model the spikes directly, and hence may limit the processing time-scale of BMI control and adaptation. Moreover, while specialized CLDA techniques for intention estimation and assisted training exist, a unified and systematic CLDA framework that generalizes across different setups is lacking. Here we develop a novel closed-loop BMI training architecture that allows for processing, control, and adaptation using spike events, enables robust control and extends to various tasks. Moreover, we develop a unified control-theoretic CLDA framework within which intention estimation, assisted training, and adaptation are performed. The architecture incorporates an infinite-horizon optimal feedback-control (OFC) model of the brain’s behavior in closed-loop BMI control, and a point process model of spikes. The OFC model infers the user’s motor intention during CLDA—a process termed intention estimation. OFC is also used to design an autonomous and dynamic assisted training technique. The point process model allows for neural processing, control and decoder adaptation with every spike event and at a faster time-scale than current decoders; it also enables dynamic spike-event-based parameter adaptation unlike current CLDA methods that use batch-based adaptation on much slower adaptation time-scales. We conducted closed-loop experiments in a non-human primate over tens of days to dissociate the effects of these novel CLDA components. The OFC intention estimation improved BMI performance compared with current intention estimation techniques. OFC assisted training allowed the subject to consistently achieve proficient control. Spike-event-based adaptation resulted in faster and more consistent performance convergence compared with batch-based methods, and was robust to parameter initialization. Finally, the architecture extended control to tasks beyond those used for CLDA training. These results have significant implications towards the development of clinically-viable neuroprosthetics.     

Interference and Shaping in Sensorimotor Adaptations with Rewards

When a perturbation is applied in a sensorimotor transformation task, subjects can adapt and maintain performance by either relying on sensory feedback, or, in the absence of such feedback, on information provided by rewards. For example, in a classical rotation task where movement endpoints must be rotated to reach a fixed target, human subjects can successfully adapt their reaching movements solely on the basis of binary rewards, although this proves much more difficult than with visual feedback. Here, we investigate such a reward-driven sensorimotor adaptation process in a minimal computational model of the task. The key assumption of the model is that synaptic plasticity is gated by the reward. We study how the learning dynamics depend on the target size, the movement variability, the rotation angle and the number of targets. We show that when the movement is perturbed for multiple targets, the adaptation process for the different targets can interfere destructively or constructively depending on the similarities between the sensory stimuli (the targets) and the overlap in their neuronal representations. Destructive interferences can result in a drastic slowdown of the adaptation. As a result of interference, the time to adapt varies non-linearly with the number of targets. Our analysis shows that these interferences are weaker if the reward varies smoothly with the subject''s performance instead of being binary. We demonstrate how shaping the reward or shaping the task can accelerate the adaptation dramatically by reducing the destructive interferences. We argue that experimentally investigating the dynamics of reward-driven sensorimotor adaptation for more than one sensory stimulus can shed light on the underlying learning rules.     

Smooth Pursuit and Visual Occlusion: Active Inference and Oculomotor Control in Schizophrenia

This paper introduces a model of oculomotor control during the smooth pursuit of occluded visual targets. This model is based upon active inference, in which subjects try to minimise their (proprioceptive) prediction error based upon posterior beliefs about the hidden causes of their (exteroceptive) sensory input. Our model appeals to a single principle – the minimisation of variational free energy – to provide Bayes optimal solutions to the smooth pursuit problem. However, it tries to accommodate the cardinal features of smooth pursuit of partially occluded targets that have been observed empirically in normal subjects and schizophrenia. Specifically, we account for the ability of normal subjects to anticipate periodic target trajectories and emit pre-emptive smooth pursuit eye movements – prior to the emergence of a target from behind an occluder. Furthermore, we show that a single deficit in the postsynaptic gain of prediction error units (encoding the precision of posterior beliefs) can account for several features of smooth pursuit in schizophrenia: namely, a reduction in motor gain and anticipatory eye movements during visual occlusion, a paradoxical improvement in tracking unpredicted deviations from target trajectories and a failure to recognise and exploit regularities in the periodic motion of visual targets. This model will form the basis of subsequent (dynamic causal) models of empirical eye tracking measurements, which we hope to validate, using psychopharmacology and studies of schizophrenia.     

Proprioceptive Body Illusions Modulate the Visual Perception of Reaching Distance

The neurobiology of reaching has been extensively studied in human and non-human primates. However, the mechanisms that allow a subject to decide—without engaging in explicit action—whether an object is reachable are not fully understood. Some studies conclude that decisions near the reach limit depend on motor simulations of the reaching movement. Others have shown that the body schema plays a role in explicit and implicit distance estimation, especially after motor practice with a tool. In this study we evaluate the causal role of multisensory body representations in the perception of reachable space. We reasoned that if body schema is used to estimate reach, an illusion of the finger size induced by proprioceptive stimulation should propagate to the perception of reaching distances. To test this hypothesis we induced a proprioceptive illusion of extension or shrinkage of the right index finger while participants judged a series of LEDs as reachable or non-reachable without actual movement. Our results show that reach distance estimation depends on the illusory perceived size of the finger: illusory elongation produced a shift of reaching distance away from the body whereas illusory shrinkage produced the opposite effect. Combining these results with previous findings, we suggest that deciding if a target is reachable requires an integration of body inputs in high order multisensory parietal areas that engage in movement simulations through connections with frontal premotor areas.     

Losing the beat: deficits in temporal coordination

Tapping or clapping to an auditory beat, an easy task for most individuals, reveals precise temporal synchronization with auditory patterns such as music, even in the presence of temporal fluctuations. Most models of beat-tracking rely on the theoretical concept of pulse: a perceived regular beat generated by an internal oscillation that forms the foundation of entrainment abilities. Although tapping to the beat is a natural sensorimotor activity for most individuals, not everyone can track an auditory beat. Recently, the case of Mathieu was documented (Phillips-Silver et al. 2011 Neuropsychologia 49, 961–969. (doi:10.1016/j.neuropsychologia.2011.02.002)). Mathieu presented himself as having difficulty following a beat and exhibited synchronization failures. We examined beat-tracking in normal control participants, Mathieu, and a second beat-deaf individual, who tapped with an auditory metronome in which unpredictable perturbations were introduced to disrupt entrainment. Both beat-deaf cases exhibited failures in error correction in response to the perturbation task while exhibiting normal spontaneous motor tempi (in the absence of an auditory stimulus), supporting a deficit specific to perception–action coupling. A damped harmonic oscillator model was applied to the temporal adaptation responses; the model''s parameters of relaxation time and endogenous frequency accounted for differences between the beat-deaf cases as well as the control group individuals.