Correlation-based model of artificially induced plasticity in motor cortex by a bidirectional brain-computer interface
The cerebral cortex contains interacting neurons whose functional connections are modified through repeated patterns of activation ., For example , motor and somatosensory cortices are typically organized into somatotopic regions in which localized neural populations are associated with muscles or receptive fields and show varied levels of correlated activity ( e . g . 1–5 ) ., Functional relationships between such neural populations are known to change over time , reinforcing relevant pathways 6–9 ., These changes are the result of plasticity mechanisms acting on myriad synaptic connections between cortical neurons ., Most of them are relatively weak but can potentiate under the right conditions ., However , it is not always clear what such conditions might be , or how one can interact with them for experimental or clinical purposes ., Unanswered questions include the way local synaptic plasticity rules lead to stable , emergent functional connections , and the role of neural activity—and its statistics—in shaping such connections ., While recent and ongoing work elucidates various plasticity mechanisms at the level of individual synapses , it is still unknown how these combine to shape the recurrently connected circuits that support population-level neural computations ., Bidirectional brain-computer interfaces ( BBCI ) capable of closed-loop recording and stimulation have enabled targeted conditioning experiments that probe these issues ., In a seminal experiment 10 , a BBCI called the Neurochip recorded action potentials of a neuron at one site in motor cortex ( MC ) and delivered spike-triggered stimuli at another for prolonged times in freely behaving macaque monkeys ., This conditioning was able to increase functional connectivity from neurons in the recorded site to the ones in the stimulated site ( c . f . 11 ) , as measured by electromyogram ( EMG ) of muscle activation evoked by intracortical microstimulation ( ICMS ) in MC ., Importantly , the relative strength of induced changes showed a strong dependence on the spike-stimulus delay , consistent with experimentally derived excitatory spike-timing-dependent plasticity ( STDP ) time windows 12–14 ., The effects of this protocol were apparent after about a day of ongoing conditioning , and lasted for several days afterwards ., Similar spike-triggered stimulation showed that corticospinal connections could increase or decrease , depending on whether the postsynaptic cells were stimulated after or before arrival of the presynaptic impulses 15 ., This BBCI protocol has potential clinical uses for recovery after injuries and scientific utility for probing information processing and learning in neural circuits ., The observations outlined above suggest that STDP is involved in shaping neural connections by normal activity during free behavior , and is the central mechanism behind the success of spike-triggered conditioning ., However , this could not be verified directly as current experiments only measure functional relationships between cortical sites ., Furthermore , interactions between BBCI signals and neural activity in recurrent networks are still poorly understood , and it remains unclear how BBCI protocols can be scaled up , made more efficient , and optimized for different experimental paradigms ., For example , during spike-triggered stimulation , the spikes from a single unit are used to trigger stimulation of a neural population ., While STDP can explain how the directly targeted synapses may be affected ( i . e . from the origin of the recorded spikes to the stimulated population ) , the observed functional changes must rely on a broader scope of plastic changes involving other neurons that are functionally related to the recorded ones ., What are the relevant network mechanisms that govern these population-level changes ?, How can a BBCI make use of population activity to trigger optimal stimulation ?, Here we advance a modeling platform capable of capturing the effects of BBCI on recurrent , plastic neuronal networks ., Our goal is to use the simplest dynamical assumptions in a “bottom-up” approach , motivated by neuronal and synaptic physiology , that enable the reproduction of key experimental findings from 10 at the functional level in MC and related muscles ., In turn , we seek to use this model to provide insights into plasticity mechanisms in recurrent MC circuits ( and other cortical regions ) that are not readily accessible experimentally , as well as establish a theoretical framework upon which future BBCI protocols can be developed ., We build on a well-established body of work that enables analytical estimates of synaptic changes based on network statistics 16–22 and compare theoretical results with experiments and numerical simulations of a probabilistic spiking network ., In our model , every neuron is excitatory—the modulatory role of inhibition in MC is instead represented implicitly by non-homogeneous probabilistic activation rates ., While inhibition likely plays an important role in cortical dynamics , we consider results from our exclusive use of excitation to be a significant finding , suggesting that a few key mechanisms can account for a wide range of experimental results ., Using data from previous work as well as from novel experiments , we calibrate STDP synaptic dynamics and activity correlation timescales to those typically found in MC neural populations ., The result is a spiking model with multiplicative excitatory STDP and stable connectivity dynamics which can reproduce three key experimental findings: Furthermore , we make the following novel findings: Together , these results provide quantifiable experimental predictions ., They arise from a theoretical framework that is easily scalable and serves as a potential testbed for next-generation applications of BBCIs ., We discuss ways to use this framework in state-dependent conditioning protocols ., When neurons in the network’s three groups a , b , c are subject to external commands ν, ( t ) = ( νa, ( t ) , νb, ( t ) , νc, ( t ) ) with stationary statistics , their averaged connectivity J ¯ ( t ) evolves toward an equilibrium J ¯ * that reflects these inputs’ correlations ( c . f . 24 , 25 ) , although individual synapses may continue to fluctuate ., This has been observed in a number of theoretical studies ( see e . g . 18 , 23 ) and is consistent with the formation and dissociation of muscle assemblies in MC due to complex movements that are regularly performed 8 ., The mean synaptic equilibrium J ¯ * strongly depends on the external inputs ν, ( t ) ’s correlation structure C ^ ( u ) ( see Fig 2A ) ., Indeed , a narrow peak near the origin for correlations within groups , as is the case for the periodic external rates shown in Fig 1B , along with the absence of such peaks for cross-group correlations , contribute to strengthening synapses within groups and weakening those across groups ., Under such conditions , what will be the impact of spike-triggered stimulation ?, Fig 2B shows the evolution of synaptic averages J ¯ α β ( t ) , analytically computed ( see Methods ) for a system initiated at the synaptic equilibrium associated with external rates ν, ( t ) from Fig 1B ., The inset of Fig 2B shows the evolution of individual synapses from group a to group b from full network simulations ., At 15 hours , the spike-triggered stimulation protocol is turned “on” , with a set delay d† = 20 milliseconds , and synapses start changing ., In ∼10 hours they reach a new equilibrium which differs from the initial one in a few striking ways , as seen in Fig 2C and 2D , where normalized differences ( J ¯ † - J ¯ ) / J m a x are plotted for all pre- and post-group combinations ., First , as expected and in accordance with experiments 10 , the mean strength of synapses from group a ( recorded site ) to group b ( stimulated site ) are considerably strengthened ( by about 80% ) ., As described in more detail below , this massive potentiation relies on two ingredients: correlated activity within group a and an appropriate choice of stimulation delay d† ., Perhaps more surprising are collateral changes in other synapses , although they are of lesser magnitude ., While this was previously unreported , it is consistent with unpublished data from the original spike-triggered stimulation experiment 10 ., It is unclear how many of these changes are due to the particular external rate statistics and other model parameters; we return to this question below when realistic activity statistics are considered ., We also show that spike-triggered stimulation induces novel correlation structures due to synaptic changes as illustrated in Fig 2A , which plots the correlation functions C ^ ( u ) , C, ( u ) , C†, ( u ) and C J † ( u ) ., Here , C J † ( u ) denotes the correlations one observes under baseline activity ( i . e . without ongoing stimulation ) but with the equilibrium connectivity J ¯ † * obtained after prolonged spike-triggered stimulation , i . e . , at the end of spike-triggered stimulation ., It is clear that every interaction involving group b is considerably changed , most strongly that with group a , which includes the neuron used to trigger stimulation ., More surprising is the increased cross-correlation of group b with itself , even though connectivity within group b is not explicitly potentiated by conditioning ., In fact , it is slightly depressed ( Fig 2D ) ., This happens because connections from group a to group b are considerably enhanced , which causes the mean firing rate of group b to grow and its correlations to increase ., Later , we explore similar collateral changes that occur because of multi-synaptic interactions ., We see in the next section how these correlations translate into functional changes in the network ., Finally , Fig 2B shows a crucial feature of our model: the timescale for the convergence from the normal to the artificial equilibrium is different from that of the decay back to normal equilibrium after the end of spike-triggered stimulation ., In the conditioning experiments from 10 , 15 , the effect of spike-triggered stimulation was seen after about 5–24 hours of conditioning , while the changes decayed after 1 to 7 days ., With the simplified external drives producing a reasonable mean firing rate of about 10Hz for individual cells , an STDP learning rate of η = 10−8 was adequate to capture the two timescales of synaptic changes ., Thus , the simple excitatory STDP mechanisms in our model give rise to distinct timescales for increases and decay of synaptic connectivity strength produced by spike-triggered conditioning , in agreement with experimental observations ., The emergence of distinct timescales was previously reported and studied in related modelling contexts 30 , 31 ., It should be noted that a number of parameters are shown to affect the magnitude of timescale separation , such as types of synaptic delays , weight dependence of the STDP rule , the firing rate of ongoing baseline activity , etc ., We reiterate that many of these parameters are not well resolved experimentally for macaque MC , and that we have made simplifying choices ( see Methods ) that can be adapted to new experimental data ., Nevertheless , we expect our model to robustly produce distinct synaptic timescales that can be fitted by a single time-scaling parameter ., This does not contradict the findings from human psychophysical studies that feedback error-driven motor adaptation may involve two or more different and independent parallel processes with different temporal dynamics for learning and decay of the motor skill 35 ., Nevertheless , the cellular mechanisms in our model may have some relation to the different timescales proposed to underlie motor adaptation at the system level 35 ., Such relationships could be further investigated by direct experimentation and appropriate simulations ., In summary , our model satisfies the first experimental observation from 10 we set out to reproduce ( point a . in Introduction ) ., Indeed , we find that two distinct timescales of synaptic changes ( during and after conditioning ) are an emergent property of our model , and tuning a single parameter is sufficient to fit the rates observed in experiments ., Changes in correlations due to spike-triggered conditioning indicate that there is an activity-relevant effect of induced synaptic changes , which is measurable from spiking statistics ( see Fig 2A ) ., We now show how this is directly observable in evoked activity patterns that are consistent with intra-cortical microstimulation ( ICMS ) protocols employed in experiments ., In 10 , connectivity changes were inferred using ICMS and electromyogram ( EMG ) recordings of the monkey’s wrist muscles , as well as evoked isometric torques ., To summarize , a train of ICMS stimuli lasting 50 ms was delivered to each MC site; simultaneously , EMG activity in three target muscles were recorded ., The average EMG responses for repeated trials were documented for each of three MC sites ( i . e . group a , b and c ) before and after spike-triggered conditioning ., The experiment showed that prior to conditioning , ICMS stimulation of any MC site elicited well-resolved average EMG responses , largest in one muscle but not the two others ., After conditioning , ICMS stimulation of the recording site ( group, a ) not only elicited an EMG response in its associated muscle , but also in that of stimulated site ( group, b ) ., While it was conjectured that synaptic changes in MC were responsible for the changes , this could not be verified directly ., Our model suggests that synaptic changes can indeed occur in MC-like networks , but it remains unclear if such changes can lead to the experimentally observed motor output changes ., We address this by simulating EMG responses of our model , before and after spike-triggered conditioning ( † ) ., Fig 3 shows a simulated ICMS protocol before ( panel A ) and after ( panel B ) spike-triggered stimulation conditioning ., For each case , synaptic matrices are chosen from full network simulations and fixed ( STDP is turned off ) , as shown in the top row of Fig 3 ( reproduced from Fig 2C ) ., To mimic the ICMS stimulus , we add a square-pulse input rate of 100 Hz lasting 50 ms to the external rate να, ( t ) of a target group ., An example of the spiking output of our network for α = a is shown in the top row of Fig 3 where the solid black bar below the graph shows the stimulus duration ., Next , we filter the spike output of all neurons within a group using the synaptic filter ε, ( t ) described in Methods , and add them to obtain population activity time-courses ., Finally , we take these summed profiles and pass them through a sigmoidal non-linearity— ( 1 + exp−a ( x −, b ) ) −1 where x is the filtered activity—meant to represent the transformation of neural activity to EMG signals ., Here , we assume that the hypothetical motoneurons whose target muscle EMG is recorded receive inputs only from a single neural group and that network interactions are responsible for cross-group muscle activation ., We label our modelled motor output EMG measurements by Mα , α ∈ {a , b , c} ., We choose the nonlinearity parameters a = 2 . 5 and b = 5 to qualitatively reproduce the EMG responses seen in the experiment before spike-triggered conditioning: namely , well-resolved EMG responses Mα are observed only when the relevant MC group α is stimulated ., The bottom row of Fig 3 shows Mα responses of each group , averaged over 15 trials each , when ICMS stimulation is delivered to a single group at a time ., Panel A shows little cross-group response to ICMS stimulation before spike-triggered stimulation conditioning ., However , after conditioning , stimulation of group a evokes an emergent response in the muscle activated from group b ( see circles in Fig 3 ) , as well as a small increase for group c ., These features were both present in the original experiments ( see Figure 2 in 10 ) and are consistent with the synaptic strengths across groups before and after conditioning ., In addition to EMG , the authors of 10 also measured the effects of ICMS using a manipulandum that recorded isometric torques produced by evoked wrist motion ., In our model , the newly evoked EMG responses , after conditioning , agree with the observation that torques evoked from the recorded site ( group, a ) typically changed toward those previously evoked from the stimulated site ( group, b ) ., As such , from now on we equate an increase in mean synaptic strength J ¯ α β between groups to an increase in functional connectivity ., We conclude that our model satisfies the second experimental observation from 10 we set out to reproduce ( point, b . in Introduction ) ., That is , a simple interpretation of evoked network activity—a filtered output of distinct neural group spiking activity—is consistent with the functional changes in muscle activation in ICMS protocols observed before and after conditioning ., Up to now , we used toy activation profiles ν, ( t ) in the form of truncated sinusoidal bumps to drive neural activity ( Fig 1B ) ., In this section , we modify our simple model to incorporate experimentally observed cross correlation functions , whenever possible , in an effort to eliminate artificial activation commands and capture more realistic regimes ., As a result , we no longer rely on numerical simulations of spiking activity , but rather on analytically derived averaged quantities to explore a wide range of conditioning regimes ., There is no longer a need to specifically define the activation functions ν, ( t ) , we instead rely solely on cross-correlation functions C ^ ( u ) and C, ( u ) ., Below , we aim to construct versions of these functions that are as close to experimental data as possible ., Before discussing spiking statistics , we note an important advantage of only considering mean synaptic strengths J ¯ ( t ) ., For spiking simulations shown above , we used networks of N = 60 neurons with probability of connection p = 0 . 3 , which are considerably far from realistic numbers ., Nevertheless , the important quantity for mean synaptic dynamics is the averaged summed strengths of synaptic inputs that a neuron receives from any given group: p N 3 J ¯ α β ., Notice that many choices of p and N can lead to the same quantity , therefore creating a scaling equivalence ., Moreover , additional scaling of Jmax can further accommodate different network sizes ., So far , we assumed that every neuron receives an average of 6 synapses from each group ., If each of these synapse were at maximal value Jmax = 0 . 1 , then simultaneous spiking from a pre-synaptic group would increase the post-synaptic neuron’s spiking probability by 60% , a number we consider reasonable ., It remains unclear if the mechanisms described above are consistent with the experimentally observed relationship between stimulation delay ( d† ) and efficacy of spike-triggered conditioning in macaque MC ., We investigated this by comparing efficacy , as measured by the percentage of torque direction change evoked by ICMS before and after conditioning 10 , to relative synaptic strength changes in our model ., This is motivated by the above demonstration that synaptic strengths are well correlated with amplitude of evoked muscle activations in a ICMS experiment ( see Fig 3 and point, b . in Introduction ) ., Nevertheless , the following comparison between model and experiment is qualitative , and meant to establish a correspondence of ( delay ) timescales only ., We use the data originally presented in Figure 4 of 10 , describing the shift in mean change in evoked wrist torque direction by ICMS of the recorded site ( group, a ) , as a function of stimulation delay d† ., We plot the same data in Fig 4E , with the maximal change ( in degrees ) normalized to one ., On the same graph , we plot the ( J ¯ b a † - J ¯ b a ) / J m a x v . s . d† curve for the value of σ that offers the best fit ( in L1-norm ) ., This amounts to finding the best “σ-slice” of the graph in Fig 4D to fit the experimental data ., We found that σ ≃ 17 ms gives the best correspondence ., We reiterate that this comparison is qualitative ., Nevertheless , the fit between the d†-dependence of experimentally observed functional changes and modelled synaptic ones is clear ., As our model’s spiking activity and STDP rule are calibrated with experimentally observed parameters ( see Methods ) , this evidence suggests that our simplified framework is consistent with experiments ., Importantly , σ = 17 ms is comparable to correlation timescales between functionally related MC neurons in macaque , as reported in 41 ( see also 5 , 40 ) and discussed earlier ., It was shown that such neurons have gaussian-like correlation functions with mean peak width at half height on the order of 22 ms , corresponding roughly to σ = 10 ms . While this is slightly lower than our estimate , we note that task-specific motion is known to introduce sharp correlations and that free behaving , rest and sleep states induce longer-range statistics 42 ., Cross-correlation functions reported above were recorded during a stereotyped center-out reach task experiment , in contrast to the spike-triggered conditioning experiment which was conducted over a wide range of states , including sleep , which may lead to longer mean cross-correlation timescales 10 ., A prediction of our model is that spike-triggered conditioning restricted to periods of long timescale correlations in MC , such as during sleep 42 , could lead to a more robust conditioning dependence on stimulation delays ( see Discussion ) ., This finding implies that our model successfully reproduces the third and last experimental observation from 10 ( point c . from Introduction ) : using simplified cross-correlation functions of MC neural populations calibrated from experimental measurements , our model reproduces the relationship between the magnitude of plastic changes and the stimulation delay in a spike-triggered conditioning protocol ., We now explore the effects of spike-triggered stimulation on collateral synaptic strengths , i . e . , other than the targeted a-to-b pathway ., For a wide range of parameters , there is little change other than for the a-to-b synapses ., Indeed , when cross-correlation width σ is moderate to large , spike-triggered stimulation has little effect on collateral connections , for any stimulation delay ., This is in conjunction with the robustness of a-to-b changes discussed in the previous section ( see Fig 4D ) ., Nevertheless , some localized features arise when cross-correlation width σ is small ., Fig 5A shows color plots of these changes as a function of d† and σ , for the nine combinations of pre- and post-synaptic groups ., We now review the mechanisms responsible for these indirect synaptic alterations ., First , b-to-b synapses become depressed , regardless of stimulation delay , for short correlation timescales ., This is due to the occurrence of synchronized population spiking produced by artificial stimulation which , because of our choice of dendritic and axonal delays ( see Methods ) , promote depression ., Such synchronized spikes induce sharp δ-peaks in the network’s cross-correlation ( see Methods ) and the combination of transmission delays shifts this peak toward the depression side of the STDP rule ., When cross-correlations are narrow ( i . e . small σ ) , their interaction with the STDP rule –which manifests in the integral in Eq ( 13 ) – is more sensitive to the addition of such δ-peaks , resulting in overall depression ., In contrast , when cross-correlations are wider , the addition of δ-peaks has a smaller effect since a wider range of correlations contribute to the integrated STDP changes ., Second , the b-to-a synapses become potentiated for short delays d† when σ is small enough ., This happens because of a combination of factors ., When the recorded neuron in group a spikes , the population-wide spike artificially elicited in b quickly follows and travels to the b-to-a synapses ., This means that the spike of a single neuron in a effectively reaches all neurons in a , with an effect amplified by the strength of many synapses , shortly after the neuron originally fired ., When cross-correlations among a-neurons are wide , the effect of this mechanism is diluted , similarly to the b-to-b synapses discussed above ., However , when neurons in a are highly synchronous , this short-latency feedback produces synaptic potentiation of the b-to-a synapses ., Third , the synapses from both groups a and b onto the control group c are also potentiated when σ and d† are small enough ., This can be explained in two parts and involves di- and tri-synaptic mechanisms ., When the recorded neuron in a fires a spike , a population-wide spike is artificially evoked in b shortly after , which travels down to b-to-c synapses and elicits a response from neurons in c ., Narrow cross-correlations imply that many spikes in a fall within a favorable potentiation window of spikes in c , thereby contributing to the potentiation of a-to-c synapses ., To test this mechanism , we compute the relative synaptic changes due to spike-triggered stimulation in an altered network , where b-to-c synapses are inactivated ( Jcb ≡ 0 ) ., Fig 5B shows the synaptic changes for the normal network ( top ) and this altered one ( middle ) for fixed parameters d† = 5 ms and σ = 17 ms ( same σ that best fitted experiments , see Fig 4E ) ., We can clearly see that without b-to-c synapses , a-to-c synapses do not potentiate under spike-triggered stimulation ., In turn , the strengthening of a-to-c synapses imply that spikes in a are more likely to directly elicit spikes in c , thereby repeating the same process in a different order for b-to-c synapses ., Note that without a-to-c synapses , the b-to-c synapses would not potentiate ., Indeed , as was the case for b-to-b synapses , the combination of transmission delays do not conspire to promote direct potentiation following a population-wide synchronous spike ., This is tested by inactivating the a-to-c synapses , which prevents the potentiation of b-to-c synapses , as shown in the bottom panel of Fig 5B ., Finally , there is a moderate increase of the c-to-b synapses for stimulation delays d† from about 5 to 20 ms . These are observed because of a-to-c synapses , promoting spikes in c that precede the stimulation of group, b . This mechanism only works if neurons in a are tightly correlated , i . e . , for small σ ., Using the same process described above , we tested this mechanism by inactivating a-to-c synapses which prevents the potentiation of c-to-b synapses ., We reiterate that our specific choice of synaptic transmission delays may influence the magnitude of the changes described above ., This is because many of the outlined mechanisms rely on well-timed series events ., See e . g . 18 , 19 , 30 , 31 for more details about the impact of delays ., We expect that tuning our model to experimentally measured delay distributions , as they become available , will help validate and/or improve our framework’s predictive power ., Together , these mechanisms form our second novel finding ( point 2 . from the Introduction ) : multi-synaptic mechanisms give rise to significant changes in collateral synapses during conditioning with short delays , and these cannot be attributed to STDP mechanisms directly targeted by the BBCI , instead emerging from network activity ., We note that the correlation time-scale that best fits experiments ( σ = 17ms , see Fig 4E ) falls within the parameter range where these effects occur ., We have assumed that spike-triggered stimulation elicits population-wide synchronous spiking of all neurons in group b ( Nstim in 10 ) ., This is valid if the neural group b represents all the neurons activated by the stimulating electrode of a BBCI , but is not necessarily representative of the larger population of neurons that share external activation statistics due to a common input νb, ( t ) ., Indeed , some neurons that activate in conjunction with those close to the electrode may be far enough from it so they do not necessarily spike in direct response to a stimulating pulse ., Alternatively , selective activation of neurons within a group can also be achieved via optogenetic stimulation in a much more targeted fashion 43 ., We now consider the situation in which only a certain proportion of neurons from group b is activated by the spike-triggered stimulus ., We denote the stimulated subgroup by b† and the unstimulated subgroup by b∘ ., All neurons in group b receive the same external rates νb, ( t ) as before , but only a few ( solid red dots in Fig 6A ) are stimulated by the BBCI ., Let Nb = N/3 be the number of neurons in group b and the parameter ρ , with 0 ≤ ρ ≤ 1 , represent the proportion of stimulated neurons in, b . The sizes of groups b† and b∘ are given by N b † = ρ N b and N b ∘ = ( 1 - ρ ) N b , respectively ., We now adapt our analytical averaged model ( 23 ) to explore the effect of stimulation on subdivided synaptic equilibria ., We verified that the analytical derivations used below match the full spiking network simulations as before ., Both subgroups of b receive the external rate νb, ( t ) but only one receives spike-triggered stimulation ., These changes are captured in the averaged analytical derivations by tracking the number of neurons in each sub-group in the averaging steps leading to Eqs ( 22 ) and ( 23 ) accordingly—replacing N/3 by N b † and N b ∘ where necessary ., This way , we obtain subgroup-specific synaptic averages ( e . g . J ¯ b †, a ) ., Fig 6B shows the group-averaged connectivity strength between group a ( the recording site ) and both subgroups of b , before and after spike-triggered stimulation ., External cross-correlations C ^ ( u ) are as in Fig 4B with σ = 20ms , and the stimulation delay is set at d† = 30ms ., The proportion of stimulated neurons in b is set to ρ = 0 . 5 ., The bottom of the same panel shows the normalized changes of mean synaptic strengths due to spike-triggered stimulation ., As established for the original network ( see Fig 2B ) , the biggest change occurs for synapses from a to the subgroup that is directly stimulated ( b† ) ., However for subgroup b∘ , we see a noticeable change in its incoming synapses from group a , in contrast to synapses of other unstimulated groups ( c ) that do not appreciably change ., This means that sharing activation statistics with stimulated neurons is enough to transfer the plasticity-inducing effect of conditioning to a secondary neural population ., Next , we investigate how this phenomenon is affected by the proportion of neurons in b that receive stimulation , ρ ., Fig 6C shows the subgroup-averaged normalized changes of synapses from group a to subgroups b† and b∘ , as ρ varies between 0 and 1 ., When more neurons get stimulated , the transferred effect on the unstimulated group is amplified ., This means that the combined outcome on the entirety of group b grows even faster—supralinearly—with ρ , as shown in Fig 6C , where the combined b-averaged changes in synaptic strength , J ¯ b a = ρ J ¯ b † a + ( 1 - ρ ) J ¯ b ∘ a , are plotted as a function of ρ ., In summary , this phenomenon represents our third and final finding ( point 3 . in Introduction ) ., Our model shows that neurons not directly stimulated during spike-triggered conditioning can be entrained into artificially induced plasticity changes by a subgroup of stimulated cells , and that the combined population-averaged effect grows supra-linearly with the size of the stimulated subgroup ., In this study , we used a probabilistic model of spiking neurons with plastic synapses obeying a simple STDP rule to investigate the effect of a BBCI on the connectivity of recurrent cortical-like networks ., Here the BBCI records from a single neuron within a population and delivers spike-triggered stimuli to a different population after a set delay ., We developed
Experiments show that spike-triggered stimulation performed with Bidirectional Brain-Computer-Interfaces ( BBCI ) can artificially strengthen connections between separate neural sites in motor cortex ( MC ) ., When spikes from a neuron recorded at one MC site trigger stimuli at a second target site after a fixed delay , the connections between sites eventually strengthen ., It was also found that effective spike-stimulus delays are consistent with experimentally derived spike-timing-dependent plasticity ( STDP ) rules , suggesting that STDP is key to drive these changes ., However , the impact of STDP at the level of circuits , and the mechanisms governing its modification with neural implants remain poorly understood ., The present work describes a recurrent neural network model with probabilistic spiking mechanisms and plastic synapses capable of capturing both neural and synaptic activity statistics relevant to BBCI conditioning protocols ., Our model successfully reproduces key experimental results , both established and new , and offers mechanistic insights into spike-triggered conditioning ., Using analytical calculations and numerical simulations , we derive optimal operational regimes for BBCIs , and formulate predictions concerning the efficacy of spike-triggered conditioning in different regimes of cortical activity .
Recent developments in Bidirectional Brain-Computer Interfaces ( BBCI ) not only allow the reading out of neural activity from cortical neurons , but also the delivery of electrical signals ., These drive neural dynamics and shape synaptic plasticity , thus opening the possibility of engineering novel neural circuits , with important applications for clinical treatments of spinal cord injuries and stroke ., However , synaptic changes in recurrent networks of neurons are hard to predict: they involve complex dynamic mechanisms on multiple temporal and spatial scales ., Based on experiments , we develop a computational network model with plastic synapses that serves as a predictive tool for BBCI protocols ., We show how the efficacy of BBCIs is influenced by cortical activity statistics and we propose state-based stimulation strategies for driving artificially-induced synaptic plasticity .
action potentials, medicine and health sciences, neural networks, nervous system, membrane potential, electrophysiology, neuroscience, synaptic plasticity, bioassays and physiological analysis, muscle electrophysiology, neuronal plasticity, research and analysis methods, developmental neuroscience, computer and information sciences, animal cells, behavior, electrophysiological techniques, behavioral conditioning, cellular neuroscience, cell biology, anatomy, synapses, electromyography, physiology, neurons, biology and life sciences, cellular types, neurophysiology