Bidirectional Control of Absence Seizures by the Basal Ganglia: A Computational Evidence
Absence epilepsy is a generalized non-convulsive seizure disorder of the brain , mainly occurring in the childhood years 1 ., A typical attack of absence seizures is characterized by a brief loss of consciousness that starts and terminates abruptly , and meanwhile an electrophysiological hallmark , i . e . the bilaterally synchronous spike and wave discharges ( SWDs ) with a slow frequency at approximately 2–4 Hz , can be observed on the electroencephalogram ( EEG ) of patients 1 , 2 ., There is a broad consensus that the generation of SWDs during absence seizures is due to the abnormal interactions between cerebral cortex and thalamus , which together form the so-called corticothalamic system ., The direct evidence in support of this view is based on simultaneous recordings of cortex and thalamus from both rodent animal models and clinical patients 3–5 ., Recent computational modelling studies on this prominent brain disorder also approved the above viewpoint and provided more deep insights into the possible generation mechanism of SWDs in the corticothalamic system 6–13 ., The basal ganglia comprise a group of interconnected subcortical nucleus and , as a whole , represent one fundamental processing unit of the brain ., It has been reported that the basal ganglia are highly associated with a variety of brain functions and diseases , such as cognitive 14 , emotional functions 15 , motor control 16 , Parkinsons disease 17 , 18 , and epilepsy 19 , 20 ., Anatomically , the basal ganglia receive multiple projections from both the cerebral cortex and thalamus , and in turn send both direct and indirect output projections to the thalamus ., These connections enable the activities of the basal ganglia to influence the dynamics of the corticothalamic system ., Therefore , it is naturally expected that the basal ganglia may provide an active role in mediating between seizure and non-seizure states for absence epileptic patients ., Such hypothesis has been confirmed by both previous animal experiments 19 , 21–23 and recent human neuroimage data 20 , 24 , 25 ., Nevertheless , due to the complicated interactions between basal ganglia and thalamus , the underlying neural mechanisms on how the basal ganglia control the absence seizure activities are still remain unclear ., From the anatomical perspective , the substantia nigra pars reticulata ( SNr ) is one of the major output nucleus of the basal ganglia to thalamus ., Previous experimental studies using various rodent animal models have demonstrated that suitable changes in the firing of SNr neurons can modulate the occurrence of absence seizures 21–23 , 26 ., Specifically , it has been found that pharmacological inactivation of the SNr by injecting -aminobutyric acids ( GABA ) agonists or glutamate antagonists suppresses absence seizures 21 , 22 ., Such antiepileptic effect was supposed to be attributed to the overall inhibitory effect of the indirect pathway from the SNr to thalamic reticular nucleus ( TRN ) relaying at superior colliculus 21 , 22 ., In addition to this indirect inhibitory pathway , it is known that the SNr also contains GABAergic neurons directly projecting to the TRN and specific relay nuclei ( SRN ) of thalamus 27 , 28 ., Theoretically , changing the activation level of SNr may also significantly impact the firing activities of SRN and TRN neurons 28 , 29 ., This contribution might further interrupt the occurrence of SWDs in the corticothalamic system , thus providing an alternative mechanism to regulate typical absence seizure activities ., To our knowledge , however , so far the precise roles of these direct basal ganglia-thalamic pathways in controlling absence seizures are not completely established ., To address this question , we develop a realistic mean-field model for the basal ganglia-corticothalamic ( BGCT ) network in the present study ., Using various dynamic analysis techniques , we show that the absence seizures are controlled and modulated either by the isolated SNr-TRN pathway or the isolated SNr-SRN pathway ., Under suitable conditions , these two types of modulations are observed to coexist in the same network ., Importantly , in this coexist region , both low and high activation levels of SNr neurons can suppress the occurrence of SWDs due to the competition between these two direct inhibitory basal ganglia-thalamic pathways ., These findings clearly outline a bidirectional control of absence seizures by the basal ganglia , which is a novel phenomenon that has never been identified both in previous experimental and modelling studies ., Our results , on the one hand , further improve the understanding of the significant role of basal ganglia in controlling absence seizure activities , and on the other hand , provide testable hypotheses for future experimental studies ., We build a biophysically based model that describes the population dynamics of the BGCT network to investigate the possible roles of basal ganglia in the control of absence seizures ., The network framework of this model is inspired by recent modelling studies on Parkinsons disease 30 , 31 , which is shown schematically in Fig . 1 ., The network totally includes nine neural populations , which are indicated as follows: excitatory pyramidal neurons ( EPN ) ; inhibitory interneurons ( IIN ) ; TRN; SRN; striatal D1 neurons; striatal D2 neurons; SNr; globus pallidus external ( GPe ) segment; subthalamic nucleus ( STN ) ., Similar to other modelling studies 30–32 , we do not model the globus pallidus internal ( GPi ) segment independently but consider SNr and GPi as a single structure in the present study , because they are reported to have closely related inputs and outputs , as well as similarities in cytology and function ., Three types of neural projections are contained in the BGCT network ., For sake of clarity , we employ different line types and heads to distinguish them ( see Fig . 1 ) ., The red lines with arrow heads denote the excitatory projections mediated by glutamate , whereas the blue solid and dashed lines with round heads represent the inhibitory projections mediated by and , respectively ., It should be noted that in the present study the connections among different neural populations are mainly inspired by previous modelling studies 30 , 31 ., Additionally , we also add the connection sending from SNr to TRN in our model , because recent anatomical findings have provided evidence that the SNr also contains GABAergic neurons directly projecting to the TRN 27–29 ., The dynamics of neural populations are characterized by the mean-field model 9 , 11 , 33–35 , which was proposed to study the macroscopic dynamics of neural populations in a simple yet efficient way ., The first component of the mean-field model describes the average response of populations of neurons to changes in cell body potential ., For each neural population , the relationship between the mean firing rate and its corresponding mean membrane potential satisfies an increasing sigmoid function , given by ( 1 ) where indicate different neural populations , denotes the maximum firing rate , r represents the spatial position , is the mean firing threshold , and is the threshold variability of firing rate ., If exceeds the threshold , the neural population fires action potentials with an average firing rate ., It should be noted that the sigmoid shape of is physiologically crucial for this model , ensuring that the average firing rate cannot exceed the maximum firing rate ., The changes of the average membrane potential at the position r , under incoming postsynaptic potentials from other neurons , are modeled as 9 , 33–36 ( 2 ) ( 3 ) where is a differential operator representing the dendritic filtering of incoming signals ., and are the decay and rise times of cell-body response to incoming signals , respectively ., is the coupling strength between neural populations of type and type ., is the incoming pulse rate from the neural population of type to type ., For simplicity , we do not consider the transmission delay among most neural populations in the present work ., However , since the functions via second messenger processes , a delay parameter is introduced to its incoming pulse rate ( i . e . , ) to mimic its slow synaptic kinetics ., This results in a delay differential equation in the final mathematical description of the BGCT model ., Note that the similar modelling method has also been used in several previous studies 13 , 37 ., In our system , each neural population gives rise to a field of pulses , which travels to other neural population at a mean conduction velocity ., In the continuum limit , this type of propagation can be well-approximated by a damped wave equation 9 , 33–35 , 38: ( 4 ) Here is the Laplacian operator ( the second spatial derivative ) , is the characteristic range of axons of type , and governs the temporal damping rate of pulses ., In our model , only the axons of cortical excitatory pyramidal neurons are assumed to be sufficiently long to yield significant propagation effect ., For other neural populations , their axons are too short to support wave propagation on the relevant scales ., This gives ( ) ., Moreover , as one of typical generalized seizures , the dynamical activities of absence seizures are believed to occur simultaneously throughout the brain ., A reasonable simplification is therefore to assume that the spatial activities are uniform in our model , which has been shown as the least stable mode in models of this class 33 , 34 , 36 ., To this end , we ignore the spatial derivative and set in Eq ., ( 4 ) ., Accordingly , the propagation effect of cortical excitatory axonal field is finally given by 33 , 34 , 36: ( 5 ) where ., For the population of cortical inhibitory interneurons , the BGCT model can be further reduced by using and , which is based on the assumption that intracortical connectivities are proportional to the numbers of synapses involved 9 , 13 , 33–36 ., It has been demonstrated that by making these above reductions , the developed BGCT model becomes computationally more tractable without significant deteriorating the precision of numerical results ., We then rewrite above equations in the first-order form for all neural populations ., Following above assumptions , we use Eqs ., ( 1 ) – ( 3 ) and ( 5 ) for modelling the dynamics of excitatory pyramidal neurons , and Eqs ., ( 1 ) – ( 3 ) for modelling the dynamics of other neural populations ., This yields the final mathematical description of the BGCT model given as follows: ( 6 ) ( 7 ) ( 8 ) ( 9 ) where ( 10 ) ( 11 ) ( 12 ) In Eq ., ( 10 ) , the superscript T denotes transposition ., The detailed expression of for different neural populations is represented by , and , given by ( 13 ) with ( 14 ) ( 15 ) ( 16 ) Here the variable in Eq ., ( 15 ) denotes the delay and the parameter in Eq ., ( 16 ) represents the constant nonspecific subthalamic input onto SRN ., The parameters used in our BGCT model are compatible with physiological experiments and their values are adapted from previous studies 9 , 11 , 13 , 30 , 31 , 36 ., Unless otherwise noted , we use the default parameter values listed in Table 1 for numerical simulations ., Most of the default values of these parameters given in Table 1 are based on either their nominal values or parameter ranges reported in above literature ., A small number of parameters associated with the basal ganglia ( i . e . , , and ) are adjusted slightly , but still within their normal physiological ranges , to ensure our developed model can generate the stable 2–4 Hz SWDs under certain conditions ., Note that due to lack of quantitative data , the coupling strength of the SNr-TRN pathway needs to be estimated ., Considering that the SNr sends GABAergic projections both to SRN and TRN and also both of these two nuclei are involved in thalamus , it is reasonable to infer that the coupling strengths of these two pathways are comparable ., For simplicity , here we chose by default ., In the following studies , we also change ( decrease or increase ) the value of several folds by employing a scale factor ( see below ) to examine how the inhibition from the SNr-TRN pathway regulates absence seizures ., Additionally , during this study , several other critical parameters ( i . e . , , and ) are also varied within certain ranges to obtain different dynamical states and investigate their possible effects on the modulation of absence seizures ., In the present study , several data analysis methods are employed to quantitatively evaluate the dynamical states as well as the properties of SWDs generated by the model ., To reveal critical transitions between different dynamical states , we perform the bifurcation analysis for several key parameters of the model ., For one specific parameter , the bifurcation diagram is simply obtained by plotting the “stable” local minimum and maximum values of cortical excitatory axonal fields ( i . e . , ) over changes in this parameter 11 , 39 ., To this end , all simulations are executed for sufficiently long time ( 10 seconds of simulation time , after the system reaches its stable time series ) , and only the local minimum and maximum values obtained from the latter stable time series are used ., Using the above bifurcation analysis , we can also easily distinguish different dynamical states for combined parameters ., Such analysis technique allows us to further identify different dynamical state regions in the two-parameter space ( for example , see Fig . 2D ) ., On the other hand , the power spectral analysis is used to estimate the dominant frequency of neural oscillations ., To do this , the power spectral density is obtained from the time series ( over a period of 10 seconds ) by using the fast Fourier transform ., Then , the maximum peak frequency is defined as the dominant frequency of neural oscillations ., It should be noted that , by combining the results of both the state and frequency analysis , we can outline the SWD oscillation region that falls into the 2–4 Hz frequency range in the two-parameter space ( for example , see the asterisk region in Fig . 2E ) ., Moreover , we calculate the mean firing rates ( MFRs ) for several key neural populations in some figures ., To compute the MFRs , all corresponding simulations are performed up to 25 seconds and the data from 5 to 25 seconds are used for statistical analysis ., To obtain convincing results , we carry out 20 independent simulations with different random seeds for each experimental setting , and report the averaged result as the final result ., Finally , in some cases , we also compute the low and high triggering mean firing rates ( TMFRs ) for SNr neurons ., In the following simulations , we find that the mean firing rate of SNr neurons is increased with the growth of the excitatory coupling strength , which serves as a control parameter to modulate the activation level of SNr in our work ( see the Results section ) ., Based on this property , the low and high TMFRs can be determined by the mean firing rates of SNr neurons occurring at the boundaries of the typical region of 2–4 Hz SWDs ( for example , see the black dashed lines in Fig . 3B ) ., All network simulations are written and performed under the MATLAB environment ., The aforementioned dynamical equations are integrated by using the standard fourth-order Runge-Kutta method , with a fixed temporal resolution of 40 ., In additional simulations , it turns out that the chosen integration step is sufficiently small to ensure the numerical accuracy of our developed BGCT model ., The computer codes used in the present study are available on ModelDB ( https://senselab . med . yale . edu/ModelDB/showmodel . asp ? model=152113 ) ., The fundamental implementation of the BGCT model is provided as supplementary information to this paper ( we also provide a XPPAUT code for comparison 41; see Text S1 and S2 ) ., Previous studies have suggested that the slow kinetics of receptors in TRN are a candidate pathological factor contributing to the generation of absence seizures both in animal experiments and biophysical models of corticothalamic network 7 , 13 , 42 , 43 ., To explore whether this mechanism also applies to the developed BGCT model , we perform one-dimensional bifurcation analysis for the inhibitory coupling strength and the delay parameter , respectively ., The corresponding bifurcation diagrams and typical time series of are depicted in Figs ., 2A–2C , which reveal that different dynamical sates emerge in our system for different values of and ., When the coupling strength is too weak , the inhibition from TRN cannot effectively suppress the firing of SRN ., In this case , due to the strong excitation from pyramidal neurons , the firing of SRN rapidly reaches a high level after the beginning of the simulation ., Such high activation level of SRN in turn drives the firing of cortical neurons to their saturation states within one or two oscillation periods ( region I ) ., As the coupling strength grows , the inhibition from TRN starts to affect the firing of SRN ., For sufficiently long , this causes our model to successively undergo two different oscillation patterns ., The first one is the SWD oscillation pattern , in which multiple pairs of maximum and minimum values are found within each periodic complex ( region II ) ., Note that this oscillation pattern has been extensively observed on the EEG recordings of real patients during absence seizures 1 ., The other one is the simple oscillation pattern , in which only one pair of maximum and minimum values appears within each periodic complex ( region III ) ., However , if the coupling strength is too strong , the firing of SRN is almost completely inhibited by TRN ., In this situation , the model is kicked into the low firing region and no oscillation behavior can be observed anymore ( region IV ) ., Additionally , we also find that the model dynamics are significantly influenced by the delay , and only sufficiently long can ensure the generation of SWDs in the developed model ( see Fig . 2B ) ., To check whether our results can be generalized within a certain range of parameters , we further carry out the two-dimensional state analysis in the ( ) panel ., As shown in Fig . 2D , the whole ( ) panel is divided into four state regions , corresponding to those regions identified above ., Unsurprisingly , we find that the BGCT model can generate the SWD oscillation pattern only for appropriately intermediate and sufficiently long ., This observation is in consistent with our above finding , demonstrating the generalizability of our above results ., To estimate the frequency characteristics of different oscillation patterns , we compute the dominant frequency based on the spectral analysis in the ( ) panel ., For both the simple and SWD oscillation patterns , the dominant frequency is influenced by and , and increasing their values can both reduce the dominant frequency of neural oscillations ( Fig . 2E ) ., However , compared to , our results indicate that the delay may have a more significant effect on the dominant oscillation frequency ( Fig . 2E ) ., By combining the results in Figs ., 2D and 2E , we roughly outline the SWD oscillation region that falls into the 2–4 Hz frequency range ( asterisk region ) ., It is found that most of , but not all , the SWD oscillation region is contained in this specific region ., Here we emphasize the importance of this specific region , because the SWDs within this typical frequency range is commonly observed during the paroxysm of absence epilepsy in human patients 1 , 2 ., Why can the slow kinetics of receptors in TRN induce absence seizure activities ?, Anatomically , the SRN neurons receive the TRN signals from the inhibitory pathway mediated by both and receptors ., Under suitable condition , the double suppression caused by these two types of GABA receptors occurring at different time instants may provide an effective mechanism to create multiple firing peaks for the SRN neurons ( see below ) ., Such firing pattern of SRN in turn impacts the dynamics of cortical neurons , thus leading to the generation of SWDs ., It should be noted that , during the above processes , both and play critical roles ., In each oscillation period , after the -induced inhibition starts to suppress the firing of SRN neurons , these neurons need a certain recovery time to restore their mean firing rate to the rising state ., Theoretically , if this recovery time is shorter than the delay , another firing peak can be introduced to SRN neurons due to the latter -induced inhibition ., The above analysis implies that our model requires a sufficient long delay to ensure the occurrence of SWDs ., However , as described above , too long is also a potential factor which may push the dominant frequency of SWDs beyond the typical frequency range ., For a stronger , the inhibition caused by is also strong ., In this situation , it is obvious that the SRN neurons need a longer time to restore their firing rate ., As a consequent , a relatively longer is required for the BGCT model to ensure the occurrence of SWDs for stronger ( see Fig . 2D ) ., These findings provide consistent evidence that our developed BGCT model can replicate the typical absence seizure activities utilizing previously verified pathological mechanism ., Because we do not change the normal parameter values for basal ganglia during above studies , our results may also indicate that , even though the basal ganglia operate in the normal state , the abnormal alteration within the corticothalamic system may also trigger the onset of absence epilepsy ., Throughout the following studies , we set for all simulations ., For this choice , the delay parameter is within the physiological range and modest , allowing the generation of SWD oscillation pattern while preserving its dominant frequency around 3 Hz in most considered parameter regions ., It should be noted that , in additional simulations , we have shown that by slightly tuning the values of several parameters our developed BGCT model is also powerful to reproduce many other typical patterns of time series , such as the alpha and beta rhythms ( see Fig . S1 ) , which to a certain extent can be comparable with real physiological EEG signals 9 , 36 ., Using the developed BGCT model , we now investigate the possible roles of basal ganglia in controlling absence seizure activities ., Here we mainly concentrate on how the activation level of SNr influence the dynamics generated by the model ., This is because , on the one hand , the SNr is one of chief output nucleus of the basal ganglia to thalamus , and on the other hand , its firing activity has been found to be highly associated with the regulation of absence seizures 21 , 22 ., To this end , the excitatory coupling strength is employed to control the activation level of SNr and a three-step strategy is pursued in the present work ., In this and next subsections , we assess the individual roles of two different pathways emitted from SNr to thalamus ( i . e . , the SNr-TRN and SNr-SRN pathways ) in the control of absence seizures and discuss their corresponding biophysical mechanisms , respectively ., In the final two subsections , we further analyze the combination effects of these two pathways on absence seizure control and extend our results to more general cases ., To explore the individual role of the SNr-TRN pathway , we estimate both the state regions and frequency characteristics in the ( ) panel ., Note that during these investigations the SNr-SRN pathway is artificially blocked ( i . e . , ) ., With this “naive” method , the modulation of absence seizure activities by the SNr-SRN pathway is removed and the effect caused by the SNr-TRN pathway is theoretically amplified to the extreme ., Similar to previous results , we find that the whole ( ) panel can be also divided into four different regions ( Fig . 3A ) ., These regions are the same as those defined above ., For weak inhibitory coupling strength , increasing the excitatory coupling strength moves the model dynamics from the SWD oscillation state to the saturation state ., Here we have to notice that the saturation state is a non-physiological brain state even though it does not belong to typical seizure activities ., In strong region , the suppression of SWDs is observed by decreasing the excitatory coupling strength , suggesting that inactivation of SNr neurons may result in seizure termination through the SNr-TRN pathway ( Fig . 3A , right side ) ., For strong enough inhibitory coupling strength , such suppression effect is rather remarkable that sufficiently low activation of SNr can even kick the network dynamics into the low firing region ( compare the results in Figs . 3C and 3D ) ., The SNr-TRN pathway induced SWD suppression is complicated and its biophysical mechanism is presumably due to competition-induced collision ., On the one side , the decrease of excitatory coupling strength inactivates the SNr ( Fig . 3E , top panel ) , which should potentially enhance the firing of TRN neurons ., On the other side , however , increasing the activation level of TRN tends to suppress the firing of SRN , which significantly reduces the firing of cortical neurons and in turn inactivates the TRN neurons ., Furthermore , the inactivation of cortical neurons also tends to reduce the firing level of TRN neurons ., As the excitatory coupling strength is decreased , the collision caused by such complicated competition and information interactions finally leads to the inactivation for all the TRN , SRN , and cortical neurons ( Fig . 3E , bottom panel ) , which potentially provides an effective mechanism to destabilize the original pathological balance within the corticothalamic system , thus causing the suppression of SWDs ., Indeed , we find that not only the dynamical state but also the oscillation frequency is greatly impacted by the activation level of SNr , through the SNr-TRN pathway ., For both the simple and SWD oscillation patterns , increasing the excitatory strength can enhance their dominant frequencies ., The combined results of Figs ., 3A and 3B reveal that , for a fixed , whether the model can generate the SWDs within the typical 2–4 Hz is determined by at least one and often two critical values of ( Fig . 3B , asterisk region ) ., Because the activation level of SNr is increased with the growth of , this finding further indicates that , due to effect of the SNr-TRN pathway , the model might exist the corresponding low and high triggering mean firing rates ( TMFRs ) for SNr neurons ( Fig . 3E , dashed lines ) ., If the long-term mean firing rate of SNr neurons falls into the region between these two TMFRs , the model can highly generate typical 2–4 Hz SWDs as those observed on the EEG recordings of absence epileptic patients ., In Fig . 3F , we plot both the low and high TMFRs as a function of the inhibitory coupling strength ., With the increasing of , the high TMFR grows rapidly at first and then reaches a plateau region , whereas the low TMFR almost linearly increases during this process ., Consequently , it can be seen that these two critical TMFRs approach each other as the inhibitory coupling strength is increased until they almost reach an identical value ( Fig . 3F ) ., The above findings indicate that the SNr-TRN pathway may play a vital role in controlling the absence seizures and appropriately reducing the activation level of SNr neurons can suppress the typical 2–4 Hz SWDs ., The similar antiepileptic effect induced by inactivating the SNr has been widely reported in previous electrophysiological experiments based on both genetic absence epilepsy rats and tottering mice 21–23 , 26 ., Note that , however , in literature such antiepileptic effect by reducing the activation of SNr is presumed to be accomplished through the indirect SNr-TRN pathway relaying at superior colliculus 21 , 22 ., Our computational results firstly suggest that such antiepileptic process can be also triggered by the direct SNr-TRN GABAergic projections ., Combining these results , we postulate that for real absence epileptic patients both of these two pathways might work synergistically and together provide a stable mechanism to terminate the onset of absence epilepsy ., We next turn on the SNr-SRN pathway and investigate whether this pathway is also effective in the control of absence seizures ., Similar to the previous method , we artificially block the SNr-TRN pathway ( i . e . , ) to enlarge the effect of the SNr-SRN pathway to the extreme ., Fig . 4A shows the two-dimensional state analysis in the ( ) panel , and again the whole panel is divided into four different state regions ., Compared to the results in Fig . 3A , the suppression of SWDs appears in a relatively weaker region by increasing the excitatory coupling strength ., This finding suggests that the increase in the activation of SNr can also terminate the SWDs , but through the SNr-SRN pathway ., For relatively weak within the suppression region , the SNr-SRN pathway induced suppression is somewhat strong ., In this case , the high activation level of SNr directly kicks the network dynamics into the low firing region , without undergoing the simple oscillation state ( Fig . 4C2 and compare with Fig . 4C3 ) ., Note that this type of state transition is a novel one which has not been observed in the SWD suppression caused by the SNr-TRN pathway ., For relatively strong within the suppression region , the double peak characteristic of SWDs generated by our model is weak ., In this situation , as the inhibitory coupling strength is increased , we observe that the network dynamics firstly transit from the SWD oscillation state to the simple oscillation state , and then to the low firing state ( Fig . 4C3 ) ., To understand how the SNr-SRN pathway induced SWD suppression arises , we present the mean firing rates of several key neural populations within the corticothalamic system , as shown in Fig . 4D ., It can be seen that increasing the strength significantly improves the activation level of SNr ( Fig . 4D , top panel ) , which in turn reduces the firing of SRN neurons ( Fig . 4D , bottom panel ) ., The inactivation of SRN neurons further suppresses the mean firing rates for both cortical and TRN neurons ( Fig . 4D , bottom panel ) ., These chain reactions lead to the overall inhibition of firing activities in the corticothalamic system , which weakens the double peak shaping effect due to the slow kinetics of receptors in TRN ., For strong , such weakening effect is considerable , thus causing the suppression of SWDs ., Our results provide the computational evidence that high activation of SNr can also effectively terminate absence seizure activities by the strong inhibition effect from the SNr-SRN pathway ., Compared to the SWD suppression induced by the SNr-TRN pathway , it is obvious that the corresponding biophysical mechanism caused by the SNr-SRN pathway is simpler and more direct ., Moreover , our two-dimensional frequency analysis indicates that the dominant frequency of neural oscillations depends on the excitatory coupling strength ( see Fig . 4B ) ., For a constant , progressive increase of reduces the dominant frequency , but not in a very significant fashion ., Thus , we find that almost all the SWD oscillation region identified in Fig . 4A falls into the typical 2–4 Hz frequency range ( Fig . 4B , asterisk region ) ., Unlike the corresponding results presented in previous subsection , the combination results of Figs ., 4A and 4B demonstrate that the BGCT model modulated by the isolated SNr-SRN pathway only exhibits one TMFR for SNr neurons ., For a suitably fixed strength , the generation of SWDs can be highly triggered when the mean firing rate of SNr neurons is lower than this critical firing rate ( Fig . 4D , dashed line ) ., With the increasing of , we observe that this TMFR rapidly reduces from a hi
Absence epilepsy is believed to be associated with the abnormal interactions between the cerebral cortex and thalamus ., Besides the direct coupling , anatomical evidence indicates that the cerebral cortex and thalamus also communicate indirectly through an important intermediate bridge–basal ganglia ., It has been thus postulated that the basal ganglia might play key roles in the modulation of absence seizures , but the relevant biophysical mechanisms are still not completely established ., Using a biophysically based model , we demonstrate here that the typical absence seizure activities can be controlled and modulated by the direct GABAergic projections from the substantia nigra pars reticulata ( SNr ) to either the thalamic reticular nucleus ( TRN ) or the specific relay nuclei ( SRN ) of thalamus , through different biophysical mechanisms ., Under certain conditions , these two types of seizure control are observed to coexist in the same network ., More importantly , due to the competition between the inhibitory SNr-TRN and SNr-SRN pathways , we find that both decreasing and increasing the activation of SNr neurons from the normal level may considerably suppress the generation of spike-and-slow wave discharges in the coexistence region ., Overall , these results highlight the bidirectional functional roles of basal ganglia in controlling and modulating absence seizures , and might provide novel insights into the therapeutic treatments of this brain disorder .
Epilepsy is a general term for conditions with recurring seizures ., Absence seizures are one of several kinds of seizures , which are characterized by typical 2–4 Hz spike-and-slow wave discharges ( SWDs ) ., There is accumulating evidence that absence seizures are due to abnormal interactions between cerebral cortex and thalamus , and the basal ganglia may take part in controlling such brain disease via the indirect basal ganglia-thalamic pathway relaying at superior colliculus ., Actually , the basal ganglia not only send indirect signals to thalamus , but also communicate with several key nuclei of thalamus through multiple direct GABAergic projections ., Nevertheless , whether and how these direct pathways regulate absence seizure activities are still remain unknown ., By computational modelling , we predicted that two direct inhibitory basal ganglia-thalamic pathways emitting from the substantia nigra pars reticulata may also participate in the control of absence seizures ., Furthermore , we showed that these two types of seizure control can coexist in the same network , and depending on the instant network state , both lowing and increasing the activation of SNr neurons may inhibit the SWDs due to the existence of competition ., Our findings emphasize the bidirectional modulation effects of basal ganglia on absence seizures , and might have physiological implications on the treatment of absence epilepsy .
theoretical biology, biology