Movements in our body are controlled by a sensorimotor loop (SML), which is comprised by somatotopically organised² excitatory projections from cortical motor areas and primary somatosensory cortex to the BG input nuclei (Striatum and STN). Those in turn project to the motor regions of other BG nuclei. The BG output nuclei (GPi and SNr) then project to the Ventroanterior (VA) and Ventrolateral (VL) thalamic nuclei, which then project back to the motor regions of the cortex (Obeso et al., 2008). These connections within the sensorimotor loop are mediated by neurons that establish either excitatory or inhibitory synapses, which are mediated, respectively, by the neurotransmitters glutamate and Gamma-AminoButyric Acid (GABA) (Figure 2).

About 90% of Striatum cells are Medium Spiny Neurons (MSNs), which are GABAergic inhibitory cells that receive excitatory glutamatergic projections from the cortex and thalamus. The MSN projections form 2 distinct circuits, called direct and indirect pathways (Obeso et al., 2008; Lanciego et al., 2012; Figure 2A).

The MSNs from the direct pathway project directly to the BG output nuclei (GPi/SNr), while the MSNs from the indirect pathway project to the GPe. GPe is a BG nucleus containing GABAergic inhibitory neurons that project to the GPi/SNr directly and indirectly via the STN. In addition to GABAergic projections arriving from GPe, the STN receives excitatory glutamatergic projections directly from the cerebral cortex. This circuit is often called the hyperdirect pathway (Nambu et al., 2002; Figure 2A).

The STN is mainly composed of glutamatergic neurons that send excitatory projections to BG output nuclei (GPi/SNr). Both BG output nuclei (GPi and SNr) contain inhibitory GABAergic neurons that fire tonically (i.e., with a sustained firing frequency), inhibiting the VA/VL thalamic nuclei. The direct pathway facilitates movement by inhibiting the tonic activity of GPi/SNr, inducing a pause on their neuronal firing. The indirect and hyperdirect pathways, on the other hand, inhibit movement by increasing the tonic inhibitory activity of the BG inhibitory outputs.

Dopamine (DA) is another neurotransmitter involved in the sensorimotor loop. DA Projections from SNc to striatum modulate the activity of the direct and indirect pathways by regulating MSN excitability (Figure 2B). Specifically, dopamine excites MSN neurons in the direct pathway and inhibits MSN neurons in the indirect pathway. The combined effect of DA on direct and indirect pathways, therefore, leads to a decrease in GPi/SNr activity, decreasing the inhibition of the thalamocortical projection neurons. Therefore, the main effect of DA release in Striatum is movement facilitation.

In PD, there is a progressive degeneration of SNc DA neurons. The depletion of striatal DA leads to a functional imbalance of BG circuitry, with enhanced activation of the indirect pathway and decreased activation of the direct pathway, resulting in an increase in GPi/SNr activity that hampers movement execution (Surmeier et al., 2014). In addition to these changes in firing rates, the parkinsonian conditions is also characterised by changes in firing patterns within each nucleus and amongst the structures of the BG-T-C system, such as increased synchrony between neighboring neurons, increased bursting activity and enhanced beta oscillatory activity (Galvan et al., 2015).

The origin and mechanisms of motor symptoms of Parkinson's Disease (PD) are still under great dispute (McGregor and Nelson, 2019). In particular, there are several hypotheses for the origin of symptoms that are related to motor impairments but there is no consensus so far (Dovzhenok and Rubchinsky, 2012; Helmich et al., 2013). Most likely, a myriad of network interactions lead to motor disruptions that are observed in PD, including structures beyond the basal ganglia networks like the cerebellum. Traditionally, it is assumed that the basal ganglia and cerebellum are anatomically separated but interfaced via cortical networks. Please refer to Mori et al. (2016) for a more comprehensive discussion on the role of other structures.

Parkinson's tremor symptom is an involuntary motion, in particular on the upper limbs, with frequency of 4–6 Hz and high amplitude along a voluntary movement or at rest (Guyton and Hall, 2001; Haeri et al., 2005). A few previous works hypothesize that the dopamine depletion in the BG-T-C system may lead to the occurrence of the tremor symptom (Dovzhenok and Rubchinsky, 2012; Helmich et al., 2012; Cagnan et al., 2014). However, recent evidences from clinical, neuroimaging and postmortem studies link essential tremor to cerebellar dysfunction (Louis et al., 2006; Mirdamadi, 2016; Louis, 2018; Louis and Faust, 2020). The authors hypothesize that the cerebellum influenced by dopamine depletion may also contribute to the enhancement of the tremor. Nonetheless, the origin of the symptom is yet a mystery.

According to Burkhard et al. (2002), there are central oscillators that are composed of oscillatory components involving neuronal networks capable of generating a naturally occurring neural oscillation. These central oscillators synchronise cerebral function in brains under both conditions (healthy and parkinsonian). However, it is not very clear which structures of the brain are involved in the generation of these oscillatory patterns. Although the physiological function of those structures are yet unknown, the authors consider them to be directly related to motor control and tremor iythn PD. Based on experiments with healthy subjects executing voluntarily simulated tremor and data from pathological tremors recorded from patients with PD and essential tremor, the authors noticed the influence of the central oscillators on motor tasks.

Based on PD patients with electrode implantation, Du et al. (2018) observed evidences of oscillatory patterns in different regions of the brain, like STN, GPi, and ventral intermediate thalamus (Vim). They named the cells oscillatory neurons and associated them to the tremor symptom. In a different study, using a helmet-shaped 122-channel whole-head neuromagnetometer (Neuromag^TM), Pollok et al. (2004) concluded that the same brain areas are involved in voluntary tremor as in parkinsonian resting tremor. Based on the acquired data, the authors considered that pathological tremors might be based on a physiological pre-existing cerebral oscillatory network. Unfortunately, more details on those oscillatory neurons are yet unknown.

The chosen computational model of PD (Romano et al., 2020) is capable of artificially reproducing the biophysical features of the BG-T-C system, thus replicating the biological SML mechanisms discussed in section 3. The model was adapted from Kumaravelu et al. (2016) to an open-source Python package to facilitate the development, simulation, and analysis of our biological neuronal network using the NEURON simulator. The equations (summarised in Supplementary Table 1) describing the dynamics of each type of neuron were replicated without any change. Romano et al. (2020) modelled the same three conditions representing control (normal), 6-OHDA lesioned (PD), and 6-OHDA lesioned plus STN DBS in rats. In this work, we focused only on the healthy and parkinsonian conditions. Kumaravelu et al. (2016) explained how the changes in the synaptic conductance of specific neurons allowed them to replicate the loss of striatal dopamine neurons. In short words, the shift from healthy to PD conditions can be described as follow: decreasing the maximal M-type potassium conductance in direct and indirect MSN neurons (MSN firing dysfunction) from 2.6 to 1.5 mS/cm²; decreasing the maximal corticostriatal synaptic conductance (reduced sensitivity of direct MSN to cortical inputs) from 0.07 to 0.026 mS/cm²; and increasing the maximal GPe axonal collaterals synaptic conductance from 0.125 to 0.5 mS/cm² (increase of GPe neuronal firing). More details of the implementation of each condition can be found in Kumaravelu et al. (2016).

To embed the computational model of PD in our humanoid robot, we first had to create the desired robot sensorimotor loop. Following the SML described in section 3, the robot should be able to get inputs from its sensory signals, incorporate them into the embedded computational model, and generate motor commands, which in turn will lead to new sensory inputs, thus closing the loop.

It is clear from section 2.1, that the BG-T-C system and its communication pathways allow mammalians to produce motor responses based on sensory information thus giving rise to a sensorimotor loop. Hence, the interplay between those parts allows animals to make decisions based on internal and external stimuli.

One can also observe that the thalamus and the cortex form a closely coupled system (Saalmann and Kastner, 2011), where the thalamus transmits information from the environment to the cortex, and the cortex sends the output from multiple processing stages back to the thalamus. Based on this assumption, we decided to stimulate the thalamus based on visual cues and to read the output neuronal signals from the cortex to create our sensorimotor loop.

Inspired by the existence of central oscillators (section 2.3), the motor commands from cortical neurons are then combined and modulated by this inherent oscillatory phenomena (Burkhard et al., 2002). Similar modulation techniques have been observed in neuronal activity in animals and humans. For instance, Tomassini et al. (2017) investigated how the rhythm of different neuronal signals may modulate the perceptions of animals; and Ferguson and Cardin (2020) discussed how multiple input streams of cognitive, sensory or motor origin may modulate cortical gain. In our work, we investigated how the dynamics of the cortical neurons from our BG-T-C system under both healthy and parkinsonian condition may modulate the oscillatory signals from the central oscillators that might be the cause of the tremor symptom in PD patients. Hence, the final motor command is a result of an emulated signal which is able to simulate motor perturbation in the robot's upper limbs movements in parkisonian condition, as further explained on section 6.4.

Our robot sensorimotor loop has four complementary modules (Figure 4): (i) the first module, Encoding Module (EM), is responsible for encoding environmental input into the BG-T-C system; (ii) the second module, Brain Module (BM), processes the input information respecting the dynamics of the embedded computational model of the brain; (iii) the third module, Decoding Module (DM), decodes the brain dynamics into motor stimulation; and (iv) the last module, Behavioural Module (BeM), translates the sensory inputs, the motor stimulation, and the oscillatory signals from the central oscillators into robot commands. Implementation details of each module will be discussed in section 6. The following subsections describe the modules as a generic framework which can be implemented in different ways without compromising the effectiveness of the entire sensorimotor loop.

The robot architecture chosen for the experiments was the NAO^T14 “torso only” robot (Gelin, 2018) (Figure 6A). NAO torso has a set of sensor and actuators like cameras, tactile sensors, and motors that allows the robot to move its upper limbs and interact with the environment. It is fully open and programmable and runs on NAOqi OS. Besides that, each arm of the robot has five degrees-of-freedom allowing it to reproduce several movements mimicking those of a human being.

We have implemented the four modules from our Neurorobotics Model (section 5) using Python programming language (Rossum, 1995) plus OpenCV (Bradski, 2000), NetPyNE/NEURON (Hines and Carnevale, 2001; Dura-Bernal et al., 2019), and ROS (Robot Operating System) (Cousins, 2010). The diagram in Figure 6B shows the connections between those modules [Encoding Module (EM), Brain Module (BM), Decoding Module (DM), Behavioural Module (BeM)]⁴ within NAO robot. It is important to mention that any other humanoid robot can be easily adjusted to this work if capable to communicate to our modules through ROS.

The behavioural task chosen to assess the sensorimotor loop (section 2.1) consists of a simple visual/motor activity. Basically, the robot performs two different behaviours in response to distinct visual cues as illustrated in Figure 7A. If the robot senses an object as a positive stimulus, it extends its right arm and opens its hand to grasp the object. Otherwise, if the robot senses an object as a negative stimulus, it moves its right arm closer to its torso similar to a rejection behaviour.

The task was designed using simple movements that simplify further analyses of the robot's performances in both conditions, healthy and parkinsonian. Movements are possible by a continuous update of the robot's motor trajectories control with the desired motion. The motion was defined as destination poses, which were pre-defined with specific joints' angles. Here, we opted for a discrete set of motor trajectories that result from transitions of a state machine.

The experimental scenarios are composed of one humanoid robot (NAO^T14), three balls with different colours (yellow, purple and green), and a computer to run ROS and NetPyNE/NEURON applications. We used the colour of the objects to trigger two different behaviours: curiosity and rejection to interact with an object (Nieuwboer et al., 2007) as presented in Figure 7B.

In short words, the behaviour task designed to support this work can be described as a sequence of interactions with the coloured balls by the robot. The main idea was to exploit our sensorimotor loop, which produces behavioural responses based on visual stimuli. In this work, when the task is initialised, the robot checks if there is any object ready to be sensed, as presented on Figure 7C. A small mark in front of the robot indicates the position where the objects are allocated so they can be easily detected. After the recognition of each object, the robot communicates the colour of the ball and, only then, initiates the related behaviour, rejection, or curiosity. A negative stimulus, indicated by the yellow or purple balls, produces the rejection behaviour while a positive one, represented by the green ball, produces the curiosity behaviour. After completing the last iteration, the robot communicates the end of the task and moves to its final pose.

In this work, we ran our experiments using only three iterations by the following order: yellow, green and purple. However, the number of iterations and the sequence of colours of the balls can be adjusted a priori any experiment. During the first 30 s of our experiment, the robot was initiated and none of the objects presented. This period allowed the robot to bring up all the sensors and actuators of the robot, and also to move the arms to their initial position. Then, each ball was allocated in front of the robot respecting the pre-defined sequence, which was the yellow ball at 30 s, followed by a green ball at 55 s, and a purple ball at 75 s after the beginning of the task. The duration of the entire task was 90 s. The time between those events allowed the robot to react to the objects by producing the expected behaviours.

The computational model of PD embedded in the humanoid robot was adapted from Kumaravelu et al. (2016) by Romano et al. (2020) to make use of NetPyNE (Networks in Python and NEURON), a tool which provides a simplified interface to implement multiscale network models in the NEURON simulation environment (Hines and Carnevale, 2001). The simulator is a well-known tool that has been extensively used by neuroscientists due to its high reliability in terms of computational neuroscience.

The dynamics of the computational model brings a realism that is fundamental for the purpose of this work. The Hodgkin and Huxley, and Izhikevich neuron models allow the neurorobot to reproduce most of the neurocomputational dynamical features of specific neurons. For instance, the excitatory pattern from cortical neurons also known as regular spiking (RS). In this way, it is possible to generate equivalent patterns observed on real data, collected from animal experimentation, in response to injected pulses of DC current.

We decided to use the Robot Operating System (ROS) to create a bridge between NetPyNE and the robot. ROS is a free and open-source system that has grown out of a novel collaboration between industry and academia (Cousins, 2010). It provides mechanisms to communicate between different applications via topics and services. Thus, the model implemented on NetPyNE could be simulated in NEURON and, in parallel, communicate to other running packages besides the robot. In other to test the entire environment integration, we used Webots simulator (Michel, 2004) to run our experiments. Then, we moved to a real robot.

The neurorobotics model embedded in the robot was designed in subroutines that can be easily replaced without causing a chain of changes. In this way, it is more suitable for updates in the code and even new applications. For example, any module of the SML can be substituted to adapt to a new application. They have separate functionalities as described in section 5.2.

Each robot behaviour corresponds to a combination of four different joint angles of the right arm. The joints used in our behavioural task are “RShoulderRoll,” “RElbowRoll,” “RElbowYaw,” and “RHand.” Figure 10 shows the dynamics of each joint during the performance of the entire task for both conditions of the computational model. As described in section 6.2, there are two different experimental scenarios, the rejection and curiosity behaviours. Those two scenarios produce different movements and are represented by different activities in those joints. As mentioned previously, the robot acts a few seconds after the recognition of the object. Because of that, there is a delay on the change of the angles in all cases. Additionally, the interaction with the robot was manually executed which caused reactions of the robot to the same objects not exactly at the same instance of time but yet close to the experimental scenario presented in section 6.3.

In both conditions, one can notice the increase in the intensity of the motor perturbation when the parkinsonian condition is activated. The motor perturbation, which could be in a sense analogous to the PD tremor symptom, is reproduced based on subtle oscillations of the joint angles throughout the task. In Figure 10, the dotted line for each joint indicates the tremor pattern that is characteristic in patients diagnosed with PD. However, the frequency and even the amplitude of the movement had to be limited to avoid damaging the joints of the robot. The frequency was adjusted to be the same as the control loop, which is 1 Hz. In this way, every second, the robot could update the joints' angles based on the dynamics of the BeM without compromising the motors. Also, the amplitude of the tremor was constrained based on each joint operational range (SoftBank, 2006).

The trajectory of the arm goes through positive and negative adjustments as already illustrated in Figure 10. During the first 30 s of the experiment, the robot did not interact with any objects which allowed the arm to keep the same position or set of angles. In Table 1, the values present the fluctuation of the arm during this period of time. Since the same values produced by the modulation process are incorporated to all the joints of the arm, we can see that the standard deviation only differs between the condition of the BM. Those two values highlight the disturbance in the robot's arm under parkinsonian conditions. By checking those angles in radians, you could think they may not represent a significant change in the trajectory of the robot's arm. But, as you can see in our experiment (https://youtu.be/KEa_2lG8V5s), those extra angles in a joint were enough to create the abnormal movements. Due an increase in the oscillation, the motors needed to move from more distinct positions in the same period of time which caused an increase of velocity and acceleration of the motors.

The computational model in parkinsonian condition is characterised by the depletion of striatal DA. As explained in section 3, it leads to a functional imbalance of BG circuitry which hampers movement execution. In our experiments, after embedding the model under those conditions in a humanoid robot engaged in a behavioural task, the intensity of the tremor symptom was enhanced.

In our SML, the DM module produces motor stimulation responsible to modulate the oscillatory signal based only on three different input data (average firing rate, average of ISIs, and standard deviation of ISIs) extracted from cortical neurons. For more details about the DM, please consider reading section 6.4.3. Figure 11A shows those inputs plotted after two experiments, one for each condition of the model. The model under parkinsonian conditions produced a higher average firing rate which means more spikes were generated per second (1 Hz). Because of that, there was a reduction in the average of ISIs. In other words, the timing between spikes became shorter. Besides that, the third graphic in Figure 11A shows a slight reduction in synchronicity which means the spikes were generated in a more aleatory manner. During the task, different objects were presented to the robot which produced different levels of excitation in the cortical neurons. For both conditions, the firing rates increased after a positive stimulus which directly produced a certain reduction on the interval between spikes. However, the synchronicity of the neurons seemed to not be affected much.

The distinguishable cortical dynamics allows our trained network to produce different outputs based on the condition of the model. Figure 11B shows the response of the MLP network under both conditions. As it can be seen, abnormal values emerged during the performance of the task under parkinsonian condition. We performed a simple filtering process on both output signals since neural activities are known by their intense oscillation. In this way, the second graphic shows clearly the different patterns that was generated. Under healthy conditions, the signal oscillates around the value zero which represents low motor stimulation. Meanwhile, the parkinsonian condition brings slightly higher values. Then, we applied a linear transformation as explained in section 6.4.3 to make the motor stimulation suitable for the robot. The generated output represents the motor stimulation in radians produced by the DM during the performance of the task.

As the final step, the motor stimulation modulate the oscillatory signal, generating the emulated signal (Figure 11C), which then tune the angles of the joints defined by our state machine. Basically, for every iteration of the motor loop, a motor stimulus establish the intensity of the motor noise and the central oscillators its signal before adjusting the trajectory of the robot's arm as observed in Figure 10. The tremor symptom is a response from this modulation process between the motor stimulation and the central oscillators.

In our experiments, the colour of the object used to interact with the robot triggers different thalamic stimulus which directly affect the dynamics of cortical neurons (Figure 12). When the green ball is sensed by the robot after a negative or non stimulus the cortical neurons intensify the spiking generation, and the opposite happens when a negative stimuli is presented after a positive one.

By simulating the entire network, we could analyse the dynamics of the robot sensorimotor loop. In Figure 13, the link between the average firing rates of neurons from TH and CTX during the execution of our behavioural task is clear. Every time neurons from TH become more excited, more glutamate is released stimulating even more the motor cortex. And, when TH is inhibited, a reduction of excitation on motor CTX can be also observed. Some other features of the model could be also recognised. For instance, after injecting extra DC current directly to the membrane of the thalamic neurons, there was a significant increase in the number of spikes per second in that region of the brain. In this sense, an external current applied on TH, regardless of the network being on healthy or parkinsonian condition, contributes to an increase in thalamic firing rate (please refer to section 2.5 from Kumaravelu et al., 2016 for the equations). However, we emphasise that the firing rate in each region results from nonlinear effects. Additionally, due to a cortical network composite of inhibitory (Fast-Spiking Interneurons) and excitatory (Regular-Spiking) neurons, the firing rates of the cortical neurons were considerably lower than the ones from TH. Finally, Kumaravelu et al. (2016) adjusted their model based on data from rats, which shows a higher thalamic firing rate compared to that from CTX. In fact, this is true for primates as well (Van Albada and Robinson, 2009).

Since the initial state of the network does not incorporate external stimulus to TH, a low firing rate is characteristic on both conditions of the computational model. After the first stimuli (experimental scenario 1), the CTX under both conditions kept the average firing rate low since the object (yellow ball) was not excitatory to the robot. It is important to mention that the external stimulus are kept until a new object is placed in front of the robot. Consequently, when the first positive stimulus (experimental scenario 2) was presented, an abrupt increase of the firing rate was detected. For a few seconds, the robot interacted with the green ball, maintaining the high rate. Then, the last object reduced the average firing rate to its initial low level since the object (purple ball) was not excitatory to the robot.

Since the neurorobot depends on different thalamic stimulation to perform the task, we decided to evaluate the injection of a set of different DC currents on thalamic neurons in order to avoid selecting one that could compromise the biological plausibility of the entire computational model. Hence, we believe it is important to elucidate the effect of different thalamic stimulation over cortical neurons before discussing the results about the emerged parkinsonian symptom in the robot.

Steriade et al. (1998) once investigated the interplay between those neurons in in vivo after repetitive stimuli at around 10 Hz. Based on that, it is known that different thalamic stimuli provoke different responses on cortical neurons. A recent work made a similar experiment but in a PD scope. Tucker et al. (2021) analysed how motor thalamic DBS alters cortical activity by testing different stimulation frequencies, current amplitudes and pulse widths in order to reduce motor symptoms in rats. The authors observed an increase of spike frequencies of cortical neurons after using DBS.

In this work, we tested different thalamic stimuli in our BG-T-C circuitry. Figure 14 shows the cortical response to the increase of thalamic stimulation. Since the computational model was designed with excitatory projections from TH to CTX, we expected a proportional increase of the average firing rate in both conditions of the model. However, the model demonstrated a non-linear proportionality within two ranges of thalamic stimulation. For instance, a noticeable peak indicates that the model changes the cortical dynamics after reaching 3.2 mA. Then, it rapidly reduces the average firing rate, reaching zero at 4.6 mA approximately. Besides that, a slight increase of spikes can be observed when the parkinsonian condition is activated for several ranges of thalamic stimuli.

Based on that, we choose different pairs of DC currents and ran some analyses. We selected values that could respect PD features and generate distinguishable dynamics on cortical neurons. We assessed the model following some PD features like spike train variability of neighbouring neurons and anomalous beta oscillation. Then, we decided to inject 1.2 mA of DC current on thalamic neurons every time the robot sense a negative stimulus and 3.5 mA for the positive stimulus.

In order to evaluate the variability, we built histograms of ISIs of cortical neurons under different thalamic stimulation using both conditions of the model. Figure 15A shows the resulting non-symmetric distributions. The ISI values produced right-skewed distributions that are characterised as having a higher concentration on its left side of the curve and a longer tail on the other side. The intervals with a higher concentration can be visualised around 200 ms for the 1.2 mA scenario and 125 ms for the 3.5 mA scenario. In both cases, under the parkinsonian condition, the peaks indicate a clear reduction in variability. On other words, the neurons produce more often spikes with same intervals.

Another characteristic that can be observed from both distributions is the increase of the number of ISIs. As exhibited in Figure 14, 3.5 mA of thalamic current generates more spikes on cortical neurons. As a consequence, it reveals more intervals between spikes which obviously increases the number of ISIs. Because of this feature, it can be observed that one peak reach values close to 4,000 ISIs while the other goes over 18,000. Despite this noticeable variation, the graphics maintains the shape of the distributions in both scenarios and conditions.

In order to quantify the variability, the normalised version of the standard deviation of ISIs known as CV was used. Figure 15B makes evident the reduction of variability of cortical neurons after activating the parkinsonian condition in both scenarios. This feature relates to an increase of synchronicity between neighbouring neurons.

The other PD feature investigated in this work was the enhance of beta activity in the corticothalamic-basal ganglia network. As it can be seen in Figure 15C, the beta band was enhanced after activating the parkinsonian condition of the model in both scenarios (under 1.2 and 3.5 mA of thalamic stimulation). The peaks in both graphics show a significant increase of activity.

The embodiment of autonomous neural systems that are based on the structure of animal brains is yet a young field. However, it has already brought important discussions on neural models and their applications. It permits the conduction of experiments in a repeatable manner without bringing any ethical constraint. As discussed in section 4, only a few works have embedded computational models of neural disorders in robots. We could observe that the majority of the researches in neurorobotics focus on common robotics problems, like navigation and decision-making, instead of building tools to support neuroscientists with their findings on neural disorders.

In this work, we embedded a composite model of the BG-T-C system in a real humanoid robot to perform movements based on sensory information. The realistic biophysical model allowed the robot to replicate the interplay between neurons from different regions of the brain during the performance of the task without demanding a high computational power. With our neurorobot, we could stimulate thalamic neurons and analyse its response over the entire model using different approaches, like mean firing rate, spike train variability, and even beta oscillation activity. Several experiments were executed without compromising our robot and the model. We choose thalamic neurons to be injected with external DC currents since they control the flow of information that are transmitted to cortical neurons. However, some other works have decided to explore other regions of the brain (Kim et al., 2017; Mulcahy et al., 2020). In our experiments, the robot was able to sense the environment, process the information and act respecting the same dynamics observed on data sets from animal's brains.

When activated the “parkinsonian” condition, one of the PD symptoms was reproduced during the performance of the task. The combination of different frameworks and libraries made possible to embed the PD model in a robot engaged in a behavioural task. In this way, the sensory information collected from the environment had an important role in our SML which allowed the robot to take its action with incorporated motor noise. Since this work represents the first step toward a realistic neurorobotics model of PD, the main idea was to develop those components in a modulated way, allowing future replacements. Five different modules were created. Simple updates can be made on each module and, even, a complete different implementation. However, the communication between modules must be respected in order to maintain the data flow through our SML. ROS made possible not only the communication between those applications but also the interaction with the robot's hardware.

It is important to highlight that for both conditions, healthy and parkinsonian, the entire SML used was the same except by the conditions applied to the BM, and the motor stimuli generated was constantly used to modulate the oscillatory signal to incorporate different intensities of motor tremor in the robot motion. However, the parkinsonian condition produces values that cause more perturbation to the robot's upper limbs movement, while the healthy condition produces minimum-variance trajectory or unnoticeable tremor similar to what happens in healthy animals (Harris and Wolpert, 1998). Hence, the major change between the conditions of our neurorobotics model is the amplitude of the tremor.

This research produced a novel tool that can be used in several contexts, not only PD. The computational model of PD represent the biophysical state of an entire SML. Each module designed within this loop can be modified and adapted to different scenarios and even completely different applications. Neuroscientists could generate new hypotheses relate to other neural disorder that is involved to the BG-T-C system. And, even use the model to understand the dynamics of those neurons respecting the different motor pathways.

Prescott et al. (2006) once questioned which would be the most suitable interpretation of the inputs and output of computational models of the brain. Authors explain that is common to associate “sensory” signals as input and “motor” signals as output of those models but it might be not the most appropriate representation. We are searching for a more biologically plausible mechanism to coordinate movements in a robot.

In neuroscience, some works investigate the mechanical properties of muscles (Harris and Wolpert, 1998). They bring interesting research questions like how trajectories of arm movements can be performed smoothly and how much control the central nervous system has in this scenario. By using the same theory of control systems, we assume there is an autonomous mechanism responsible for optimising the integration of those movements. For instance, a mechanism capable of generating the correct amount of stimulus for each muscle in small instances of time during the entire trajectory. In this context, we will adapt our SML to new behavioural tasks that will allow us to focus more on the motion of the arm. The BM will be evolved with new components, a novel DM will be designed and implemented allowing the reproduction of the motor pathways between brain and muscles, and a new BeM will allow the execution of more complex tasks.

Another point that is important to discuss is the level of realism of the humanoid robots used in our experiments. Since a more realistic DM will be built, it will be important to move the experiments to a more complex scenario where the robot can reproduce movements that resemble more humans. In this way, we will use the iCub robot instead of keeping using the NAO robot for the upcoming experiments. Movements that are commonly used in therapy sessions with PD patients will be replicated by the iCub robot. And this task will allow us to asses our model by comparing its movements to data collected from real patients under same activities.

Finally, the origin of the PD tremor symptom is yet elusive. Many hypotheses have been created by different research groups but no consensus is in sight. By finding how this neural disorder is triggered and developed, it improves the chances of 1 day finding the cure. Here, we investigated the BG-C-T system and observed the cortical neurons dynamics through different thalamic stimulation and different conditions of the model. The emerged symptom was a result of a combination of different properties extracted from cortical neurons and the oscillatory signal. It might be a naive approach initially. But this is only our first step toward the PD neurorobotics model. We understand the complexity of this problem and we hope that our research outcome might become a new tool for neuroscientists in their further works.