Quantifying Human Gait Symmetry During Blindfolded Treadmill Walking.

Bilateral gait symmetry is an essential requirement for normal walking since asymmetric gait patterns increase the risk of falls and injuries. While human gait control heavily relies on the contribution of sensory inputs, the role of sensory systems in producing symmetric gait has remained unclear. This study evaluated the influence of vision as a dominant sensory system on symmetric gait production. Ten healthy adults performed treadmill walking with and without vision. Twenty-two gait parameters including ground reaction forces, joint range of motion, and other spatial-temporal gait variables were evaluated to quantify gait symmetry and compared between both visual conditions. Visual block caused increased asymmetry in most parameters of ground reaction force, however mainly in the vertical direction. When vision was blocked, symmetry of the ankle and knee joint range of motion decreased, but this change did not occur in the hip joint. Stance and swing time symmetry decreased during no-vision walking while no significant difference was found for step length symmetry between the two conditions. This study provides a comprehensive analysis to reveal how the visual system influences bilateral gait symmetry and highlights the important role of vision in gait control. This approach could be applied to investigate how vision alters gait symmetry in patients with disorders to help better understand the role of vision in pathological gaits.

Modeling of cerebellar transcranial electrical stimulation effects on hand tremor in Parkinson's disease.

Introduction: Parkinson's disease (PD) is a neurodegenerative disorder with different motor and neurocognitive symptoms. Tremor is a well-known symptom of this disease. Increasing evidence suggested that the cerebellum may substantially contribute to tremors as a clinical symptom of PD. However, the theoretical foundations behind these observations are not yet fully understood. Methods: In this study, a computational model is proposed to consider the role of the cerebellum and to show the effectiveness of cerebellar transcranial alternating current stimulation (tACS) on the rest tremor in participants with PD. The proposed model consists of the cortex, cerebellum, spinal circuit-muscular system (SC-MS), and basal ganglia blocks as the most critical parts of the brain, which are involved in generating rest tremors. The cortex, cerebellum, and SC-MS blocks were modeled using Van der Pol oscillators that interacted through synchronization procedures. Basal ganglia are considered as a regulator of the coupling weights defined between oscillators. In order to evaluate the global behavior of the model, we applied tACS on the cerebellum of fifteen PD patients for 15 min at each patient's peak frequency of their rest tremors. A tri-axial accelerometer recorded rest tremors before, during, and after the tACS. Results and Discussion: The simulation of the model provides a suggestion for the possible role of the cerebellum on rest tremors and how cerebellar tACS can affect these tremors. Results of human experiments also showed that the online and offline effects of cerebellar tACS could lead to the reduction of rest tremors significantly by about %76 and %68, respectively. Our findings suggest that the cerebellar tACS could serve as a reliable, therapeutic technique to suppress the PD tremor.

Closing the loop between brain and electrical stimulation: towards precision neuromodulation treatments.

One of the most critical challenges in using noninvasive brain stimulation (NIBS) techniques for the treatment of psychiatric and neurologic disorders is inter- and intra-individual variability in response to NIBS. Response variations in previous findings suggest that the one-size-fits-all approach does not seem the most appropriate option for enhancing stimulation outcomes. While there is a growing body of evidence for the feasibility and effectiveness of individualized NIBS approaches, the optimal way to achieve this is yet to be determined. Transcranial electrical stimulation (tES) is one of the NIBS techniques showing promising results in modulating treatment outcomes in several psychiatric and neurologic disorders, but it faces the same challenge for individual optimization. With new computational and methodological advances, tES can be integrated with real-time functional magnetic resonance imaging (rtfMRI) to establish closed-loop tES-fMRI for individually optimized neuromodulation. Closed-loop tES-fMRI systems aim to optimize stimulation parameters based on minimizing differences between the model of the current brain state and the desired value to maximize the expected clinical outcome. The methodological space to optimize closed-loop tES fMRI for clinical applications includes (1) stimulation vs. data acquisition timing, (2) fMRI context (task-based or resting-state), (3) inherent brain oscillations, (4) dose-response function, (5) brain target trait and state and (6) optimization algorithm. Closed-loop tES-fMRI technology has several advantages over non-individualized or open-loop systems to reshape the future of neuromodulation with objective optimization in a clinically relevant context such as drug cue reactivity for substance use disorder considering both inter and intra-individual variations. Using multi-level brain and behavior measures as input and desired outcomes to individualize stimulation parameters provides a framework for designing personalized tES protocols in precision psychiatry.

Lack of visual information alters lower limb motor coordination to control center of mass trajectory during walking.

Vision, as queen of the senses, plays a critical role in guiding locomotion. Little is known about the effects of vision on gait coordination in terms of variability. The uncontrolled manifold (UCM) approach offers a window to the structure of motor variability that has been difficult to obtain from the traditional correlation analysis. In this study, we used the UCM analysis to quantify how the lower limb motion is coordinated to control the center of mass (COM) while walking under different visual conditions. We also probed how synergy strength evolved along the stance phase. Ten healthy participants walked on the treadmill with and without visual information. Leg joint angle variance with respect to the whole-body COM was partitioned into good (i.e., the one that kept the COM) and bad (i.e., the one that changed the COM) variances. We observed that after vision was eliminated, both variances increased throughout the stance phase while the strength of the synergy (the normalized difference between the two variances) decreased significantly and even reduced to zero at heel contact. Thus, walking with restricted vision alters the strength of the kinematic synergy to control COM in the plane of progression. We also found that the strength of this synergy varied across different walking phases and gait events in both visual conditions. We concluded that the UCM analysis can quantify altered coordination of COM when vision is blocked and sheds insights on the role of vision in the synergistic control of locomotion.

Reaction of human walking to transient block of vision: analysis in the context of indirect, referent control of motor actions.

Human locomotion may result from monotonic shifts in the referent position, R, of the body in the environment. R is also the spatial threshold at which muscles can be quiescent but are activated depending on the deflection of the current body configuration Q from R. Shifts in R are presumably accomplished with the participation of proprioceptive and visual feedback and responsible for transferring stable body balance (equilibrium) from one place in the environment to another, resulting in rhythmic activity of multiple muscles by a central pattern generator (CPG). We tested predictions of this two-level control scheme. In particular, in response to a transient block of vision during locomotion, the system can temporarily slow shifts in R. As a result, the phase of rhythmical movements of all four limbs will be changed for some time, even though the rhythm and other characteristics of locomotion will be fully restored after perturbation, a phenomenon called long-lasting phase resetting. Another prediction of the control scheme is that the activity of multiple muscles of each leg can be minimized reciprocally at specific phases of the gait cycle both in the presence and absence of vision. Speed of locomotion is related to the rate of shifts in the referent body position in the environment. Results confirmed that human locomotion is likely guided by feedforward shifts in the referent body location, with subsequent changes in the activity of multiple muscles by the CPG. Neural structures responsible for shifts in the referent body configuration causing locomotion are suggested.

Cortical Morphology in Cannabis Use Disorder: Implications for Transcranial Direct Current Stimulation Treatment.

Introduction: Transcranial direct current stimulation (tDCS) has been studied as an adjunctive treatment option for substance use disorders (SUDs). Alterations in brain structure following SUD may change tDCS-induced electric field (EF) and subsequent responses; however, group-level differences between healthy controls (HC) and participants with SUDs in terms of EF and its association with cortical architecture have not yet been modeled quantitatively. This study provides a methodology for group-level analysis of computational head models to investigate the influence of cortical morphology metrics on EFs. Methods: Whole-brain surface-based morphology was conducted, and cortical thickness, volume, and surface area were compared between participants with cannabis use disorders (CUD) (n=20) and age-matched HC (n=22). Meanwhile, EFs were simulated for bilateral tDCS over the dorsolateral prefrontal cortex. The effects of structural alterations on EF distribution were investigated based on individualized computational head models. Results: Regarding EF, no significant difference was found within the prefrontal cortex; however, EFs were significantly different in left-postcentral and right-superior temporal gyrus (P<0.05) with higher levels of variance in CUD compared to HC [F(39, 43)=5.31, P<0.0001, C=0.95]. Significant differences were observed in cortical area (caudal anterior cingulate and rostral middle frontal), thickness (lateral orbitofrontal), and volume (paracentral and fusiform) between the two groups. Conclusion: Brain morphology and tDCS-induced EFs may be changed following CUD; however, differences between CUD and HCs in EFs do not always overlap with brain areas that show structural alterations. To sufficiently modulate stimulation targets, whether individuals with CUD need different stimulation doses based on tDCS target location should be checked.

A fuzzy-oscillatory model of medial prefrontal cortex control function in spatial memory retrieval in human navigation function.

Navigation can be broadly defined as the process of moving from an origin to a destination through path-planning. Previous research has shown that navigation is mainly related to the function of the medial temporal lobe (MTL), including the hippocampus (HPC), and medial prefrontal cortex (mPFC), which controls retrieval of the spatial memories from this region. In this study, we suggested a cognitive and computational model of human navigation with a focus on mutual interactions between the hippocampus (HPC) and the mPFC using the concept of synchrony. The Van-der-pol oscillator was used to model the synchronous process of receiving and processing "what stream" information. A fuzzy lookup table system was applied for modeling the controlling function of the mPFC in retrieving spatial information from the HPC. The effect of attention level was also included and simulated. The performance of the model was evaluated using information reported in previous experimental research. Due to the inherent stability of the proposed fuzzy-oscillatory model, it is less sensitive to the exact values of the initial conditions, and therefore, it is shown that it is consistent with the actual human performance in real environments. Analyzing the proposed cognitive and fuzzy-oscillatory computational model demonstrates that the model is able to reproduce certain cognitive and functional disturbances in navigation in related diseases such as Alzheimer's disease (AD). We have shown that an increase in the bifurcation parameter of the Van-der-pol equation represents an increase in the low-frequency spectral power density and a decrease in the high-frequency spectral power as occurs in AD due to an increase in the amyloid plaques in the brain. These changes in the frequency characteristics of neuronal activity, in turn, lead to impaired recall and retrieval of landmarks information and learned routes upon encountering them. As a result, and because of the wrong frequency code being transmitted, the relevant set of rules in the mPFC is not activated, or another unrelated set will be activated, which leads to forgetfulness and erroneous decisions in routing and eventually losing the route in Alzheimer's patients.

DLPFC stimulation alters large-scale brain networks connectivity during a drug cue reactivity task: A tDCS-fMRI study.

Transcranial direct current stimulation (tDCS) is a promising intervention for reducing craving/consumption in individuals with substance use disorders. However, its exact mechanism of action has not yet been well explored. We aimed to examine the network-based effects of tDCS while people with methamphetamine use disorders (MUDs) were exposed to drug cues. In a randomized, double-blind sham-controlled trial with a crossover design, 15 participants with MUDs were recruited to receive 20 min of active/sham tDCS with an anode/cathode over F4/F3. MRI data, including structural and task-based functional MRI during a standard drug cue-reactivity task, were collected immediately before and after stimulation sessions. Craving scores were also recorded before and after MRI scans. Individualized head models were generated to determine brain regions with strong electric fields (EFs). Using atlas-based parcellation of head models, averaged EFs were extracted from the main nodes of three large-scale networks that showed abnormalities in MUDs; executive control (ECN), default mode (DMN), and ventral attention (VAN) networks. Main nodes with high EF intensity were used as seed regions for task-based functional connectivity (FC) [using generalized psychophysiological interaction (gPPI)] and activity [using a general linear model (GLM)] calculations. Subjective craving showed a significant reduction in immediate craving after active (-15.42 ± 5.42) compared to sham (-1 ± 2.63). In seed-to-whole brain results, the PFC node in ECN showed an enhanced PPI connectivity with precuneus and visual cortex; the cluster center in MNI (6, -84, -12); the PFC node in DMN showed a decreased PPI connectivity with contralateral parietal cortex;(-48, -60, 46). ROI-to-ROI results showed increased PPI connectivity within/between ECN-VAN while connectivity between ECN-DMN decreased. In line with connectivity, functional activity in the right PFC node in DMN decreased after tDCS while activity in PFC nodes of ECN/VAN increased. EF calculations in PFC nodes revealed that EF in DMN was outward, while the direction of EFs was inward in ECN/VAN. This study provides new insight into neural circuitry underlying MUDs that can be modulated by tDCS at the network level and specifically suggests that bilateral tDCS increases cortical excitability in ECN and VAN, while it has opposite effects on DMN that may be related to the direction of EFs.

A Neuro-Computational Model for Discrete-Continuous Dual-Task Process.

Studies on dual-task (DT) procedures in human behavior are important, as they can offer great insight into the cognitive control system. Accordingly, a discrete-continuous auditory-tracking DT experiment was conducted in this study with different difficulty conditions, including a continuous mouse-tracking task concurrent with a discrete auditory task (AT). Behavioral results of 25 participants were investigated via different factors, such as response time (RT), errors, and hesitations (pauses in tracking tasks). In DT, synchronization of different target neuron units was observed in corresponding brain regions; consequently, a computational model of the stimulus process was proposed to investigate the DT interference procedure during the stimulus process. This generally relates to the bottom-up attention system that a neural resource allocates for various ongoing stimuli. We proposed a black-box model based on interactions and mesoscopic behaviors of neural units. Model structure was implemented based on neurological studies and oscillator units to represent neural activities. Each unit represents one stimulus feature of task concept. Comparing the model's output behavior with the experiment results (RT) validates the model. Evaluation of the proposed model and data on RT implies that the stimulus of the AT affects the DT procedure in the model output (84% correlation). However, the continuous task is not significantly changed (26% correlation). The continuous task simulation results were inconsistent with the experiment, suggesting that continuous interference occurs in higher cognitive processing regions and is controlled by the top-down attentional system. However, this is consistent with the psychological research finding of DT interference occurring in response preparation rather than the stimulus process stage. Furthermore, we developed the proposed model by adding qualitative interpretation and saving the model's generality to address various types of discrete continuous DT procedures. The model predicts a justification method for brain rhythm interactions by synchronization, and manipulating parameters would produce different behaviors. The decrement of coupling parameter and strength factor would predict a similar pattern as in Parkinson's disease and ADHD disorder, respectively. Also, by increasing the similarity factor among the features, the model's result shows automatic task performance in each task.

Group and individual level variations between symmetric and asymmetric DLPFC montages for tDCS over large scale brain network nodes.

Two challenges to optimizing transcranial direct current stimulation (tDCS) are selecting between, often similar, electrode montages and accounting for inter-individual differences in response. These two factors are related by how tDCS montage determines current flow through the brain considered across or within individuals. MRI-based computational head models (CHMs) predict how brain anatomy determines electric field (EF) patterns for a given tDCS montage. Because conventional tDCS produces diffuse brain current flow, stimulation outcomes may be understood as modulation of global networks. Therefore, we developed a network-led, rather than region-led, approach. We specifically considered two common "frontal" tDCS montages that nominally target the dorsolateral prefrontal cortex; asymmetric "unilateral" (anode/cathode: F4/Fp1) and symmetric "bilateral" (F4/F3) electrode montages. CHMs of 66 participants were constructed. We showed that cathode location significantly affects EFs in the limbic network. Furthermore, using a finer parcellation of large-scale networks, we found significant differences in some of the main nodes within a network, even if there is no difference at the network level. This study generally demonstrates a methodology for considering the components of large-scale networks in CHMs instead of targeting a single region and specifically provides insight into how symmetric vs asymmetric frontal tDCS may differentially modulate networks across a population.

Brain activity during time to contact estimation: an EEG study.

Understanding the neural mechanisms associated with time to contact (TTC) estimation is an intriguing but challenging task. Despite the importance of TTC estimation in our everyday life, few studies have been conducted on it, and there are still a lot of unanswered questions and unknown aspects of this issue. In this study, we intended to address one of these unknown aspects. We used independent component analysis to systematically assess EEG substrates associated with TTC estimation using two experiments: (1) transversal motion experiment (when a moving object passes transversally in the frontoparallel plane from side to side in front of the observer), and (2) head-on motion experiment (when the observer is on the motion path of the moving object). We also studied the energy of all EEG sources in these two experiments. The results showed that brain regions involved in the transversal and head-on motion experiments were the same. However, the energy used by some brain regions in the head-on motion experiment, including some regions in left parietotemporal and left frontal lobes, was significantly higher than the energy used by those regions in the transversal motion experiment. These brain regions are dominantly associated with different kinds of visual attention, integration of visual information, and responding to visual motion.

Visual deprivation is met with active changes in ground reaction forces to minimize worsening balance and stability during walking.

Previous studies suggest that visual information is essential for balance and stability of locomotion. We investigated whether visual deprivation is met with active reactions tending to minimize worsening balance and stability during walking in humans. We evaluated effects of vision on kinetic characteristics of walking on a treadmill-ground reaction forces (GRFs) and shifts in the center of mass (COM). Young adults (n = 10) walked on a treadmill at a comfortable speed. We measured three orthogonal components of GRFs and COM shifts during no-vision (NV) and full-vision (FV) conditions. We also computed the dynamic balance index (DN)-the perpendicular distance from the projection of center of mass (pCOM) to the inter-foot line (IFL) normalized to half of the foot length. Locally weighted regression smoothing with alpha-adjusted serial T tests was used to compare GRFs and DN between two conditions during the entire stance phase. Results showed significant differences in GRFs between FV and NV conditions in vertical and ML directions. Variability of peak forces of all three components of GRF increased in NV condition. We also observed significant increase in DN for NV condition in eight out of ten subjects. The pCOM was kept within BOS during walking, in both conditions, suggesting that body stability was actively controlled by adjusting three components of GRFs during NV walking to minimize stability loss and preserve balance.

Drift-diffusion explains response variability and capacity for tracking objects.

Being able to track objects that surround us is key for planning actions in dynamic environments. However, rigorous cognitive models for tracking of one or more objects are currently lacking. In this study, we asked human subjects to judge the time to contact (TTC) a finish line for one or two objects that became invisible shortly after moving. We showed that the pattern of subject responses had an error variance best explained by an inverse Gaussian distribution and consistent with the output of a biased drift-diffusion model. Furthermore, we demonstrated that the pattern of errors made when tracking two objects showed a level of dependence that was consistent with subjects using a single decision variable for reporting the TTC for two objects. This finding reveals a serious limitation in the capacity for tracking multiple objects resulting in error propagation between objects. Apart from explaining our own data, our approach helps interpret previous findings such as asymmetric interference when tracking multiple objects.

A modified Hodgkin-Huxley model to show the effect of motor cortex stimulation on the trigeminal neuralgia network.

BACKGROUND: Trigeminal neuralgia (TN) is a severe neuropathic pain, which has an electric shock-like characteristic. There are some common treatments for this pain such as medicine, microvascular decompression or radio frequency. In this regard, transcranial direct current stimulation (tDCS) is another therapeutic method to reduce pain, which has been recently attracting the therapists' attention. The positive effect of tDCS on TN was shown in many previous studies. However, the mechanism of the tDCS effect has remained unclear. OBJECTIVE: This study aims to model the neuronal behavior of the main known regions of the brain participating in TN pathways to study the effect of transcranial direct current stimulation. METHOD: The proposed model consists of several blocks: (1) trigeminal nerve, (2) trigeminal ganglion, (3) PAG (periaqueductal gray in the brainstem), (4) thalamus, (5) motor cortex (M1) and (6) somatosensory cortex (S1). Each of these components is represented by a modified Hodgkin-Huxley (HH) model. The modification of the HH model was done based on some neurological facts of pain sodium channels. The input of the model involves any stimuli to the 'trigeminal nerve,' which cause the pain, and the output is the activity of the somatosensory cortex. An external current, which is considered as an electrical current, was applied to the motor cortex block of the model. RESULT: The results showed that by decreasing the conductivity of the slow sodium channels (pain channels) and applying tDCS over the M1, the activity of the somatosensory cortex would be reduced. This reduction can cause pain relief. CONCLUSION: The proposed model provided some possible suggestions about the relationship between the effects of tDCS and associated components in TN, and also the relationship between the pain measurement index, somatosensory cortex activity, and the strength of tDCS.

A mathematical model to mimic the shape of event related desynchronization/synchronization.

Rhythmic oscillatory activities of the sensory cortex have been observed after a presentation of a stimulus. This activity first drops dramatically and then increases considerably that are respectively named event-related desynchronization (ERD) and event-related synchronization (ERS). There are several effective factors that can alter the ERD and ERS pattern. In this study, a mathematical model was presented that produced ERD and ERS pattern in response to a stimulus. This model works based on the synchronization concepts. The proposed model provided different suggestions about the reason behind the relationship between the encoding of incoming sensory information and the oscillatory activities, effective factors on the characteristics of neuronal units, and how may these factors affect the amplitude and latency of the ERD and ERS.

Computational human head models of tDCS: Influence of brain atrophy on current density distribution.

Despite increasing attention to the application of transcranial Direct Current Stimulation (tDCS) for enhancing cognitive functions in subjects exposing to varying degree of cerebral atrophy such as Alzheimer's disease (AD), aging, and mild cognitive impairment (MCI), there is no general information for customizing stimulation protocol. OBJECTIVE: The objective of this study is to examine how cerebral shrinkage associated with cognitive impairment and aging can perturb current density distribution through the brain. METHODS: We constructed three high-resolution human head models representing young, elder, and MCI subjects and modeled two electrode configurations using rectangular electrodes. RESULTS: Our results showed that decreasing gray matter volume in MCI, as well as aging, reduced the magnitude of the current density in the brain compared to the young model. Also, morphology alterations of the cerebral sulcus could shape the vectors of the current density to flow in the depth of cortical regions by cerebrospinal fluid. CONCLUSION: This study provides a framework for further advanced studies in establishing new methodologies or modifying stimulation parameters.

Left and right reaction time differences to the sound intensity in normal and AD/HD children.

OBJECTIVES: Right hemisphere, which is attributed to the sound intensity discrimination, has abnormality in people with attention deficit/hyperactivity disorder (AD/HD). However, it is not studied whether the defect in the right hemisphere has influenced on the intensity sensation of AD/HD subjects or not. In this study, the sensitivity of normal and AD/HD children to the sound intensity was investigated. METHODS: Nineteen normal and fourteen AD/HD children participated in the study and performed a simple auditory reaction time task. Using the regression analysis, the sensitivity of right and left ears to various sound intensity levels was examined. RESULTS: The statistical results showed that the sensitivity of AD/HD subjects to the intensity was lower than the normal group (p < 0.0001). Left and right pathways of the auditory system had the same pattern of response in AD/HD subjects (p > 0.05). However, in control group the left pathway was more sensitive to the sound intensity level than the right one (p = 0.0156). CONCLUSIONS: It can be probable that the deficit of the right hemisphere has influenced on the auditory sensitivity of AD/HD children. The possible existent deficits of other auditory system components such as middle ear, inner ear, or involved brain stem nucleuses may also lead to the observed results. The development of new biomarkers based on the sensitivity of the brain hemispheres to the sound intensity has been suggested to estimate the risk of AD/HD. Designing new technique to correct the auditory feedback has been also proposed in behavioral treatment sessions.

Response of the Pre-Oriented Goal-Directed Attention to Usual and Unusual Distractors: A Preliminary Study.

INTRODUCTION: In this study, we investigated the distraction power of the unusual and usual images on the attention of 20 healthy primary school children. METHODS: Our study was different from previous ones in that the participants were asked to fix the initial position of their attention on a predefined location after being presented with unusual images as distractors. The goals were presented in locations, which were far from the attraction basin of distractors. We expected that the pre-orienting of the attention to the position of targets would reduce the attractive effect of unusual images compared to the usual ones. The percentage of correct responses and the reaction time were measured as behavioral indicators of attention performance. RESULTS: Results showed that using the goal-directed attention, subjects ignored both kinds of distractors nearly the same way. CONCLUSION: With regard to previous reports about more attraction towards the unusual images, it is suggested that the dynamics of the visual attention system be sensitive to the initial condition. That is, changing the initial position of the attention can lead to the decrement of the unusual images effects. However, several other possibilities such as a probable delay in processing unusual features could explain this observation, too.

A mathematical and biological plausible model of decision-execution regulation in "Go/No-Go" tasks: Focusing on the fronto-striatal-thalamic pathway.

Discovering factors influencing the speed and accuracy of responses in tasks such as "Go/No-Go" is one of issues which have been raised in neurocognitive studies. Mathematical models are considered as tools to identify and to study decision making procedure from different aspects. In this paper, a mathematical model has been presented to show several factors can alter the output of decision making procedure before execution in a "Go/No-Go" task. The dynamic of this model has two stable fixed points, each of them corresponds to the "Press" and "Not-press" responses. This model that focuses on the fronto-striatal-thalamic direct and indirect pathways, receives planned decisions from frontal cortex and sends a regulated output to motor cortex for execution. The state-space analysis showed that several factors could affect the regulation procedure such as the input strength, noise value, initial condition, and the values of involved neurotransmitters. Some probable analytical reasons that may lead to changes in decision-execution regulation have been suggested as well. Bifurcation diagram analysis demonstrates that an optimal interaction between these factors can compensate the weaknesses of some others. It is predicted that abnormalities of response control in different brain disorders such as attention deficit hyperactivity disorder may be resolved by providing treatment techniques that target the regulation of the interaction. The model also suggests a possible justification to show why so many studies insist on the important role of dopamine in some brain disorders.