Causal Measures of Structure and Plasticity in Simulated and Living Neural Networks
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{"title"=>"Causal measures of structure and plasticity in simulated and living neural networks", "type"=>"journal", "authors"=>[{"first_name"=>"Alex J.", "last_name"=>"Cadotte", "scopus_author_id"=>"9735726900"}, {"first_name"=>"Thomas B.", "last_name"=>"DeMarse", "scopus_author_id"=>"6603227089"}, {"first_name"=>"Ping", "last_name"=>"He", "scopus_author_id"=>"36076655800"}, {"first_name"=>"Minzhou", "last_name"=>"Ding", "scopus_author_id"=>"55421086400"}], "year"=>2008, "source"=>"PLoS ONE", "identifiers"=>{"issn"=>"19326203", "pmid"=>"18839039", "doi"=>"10.1371/journal.pone.0003355", "pui"=>"352543816", "sgr"=>"54349100736", "scopus"=>"2-s2.0-54349100736", "isbn"=>"1932-6203 (Electronic)"}, "id"=>"4edefbeb-fdc5-359d-8426-b70d1e7b381e", "abstract"=>"A major goal of neuroscience is to understand the relationship between neural structures and their function. Recording of neural activity with arrays of electrodes is a primary tool employed toward this goal. However, the relationships among the neural activity recorded by these arrays are often highly complex making it problematic to accurately quantify a network's structural information and then relate that structure to its function. Current statistical methods including cross correlation and coherence have achieved only modest success in characterizing the structural connectivity. Over the last decade an alternative technique known as Granger causality is emerging within neuroscience. This technique, borrowed from the field of economics, provides a strong mathematical foundation based on linear auto-regression to detect and quantify \"causal\" relationships among different time series. This paper presents a combination of three Granger based analytical methods that can quickly provide a relatively complete representation of the causal structure within a neural network. These are a simple pairwise Granger causality metric, a conditional metric, and a little known computationally inexpensive subtractive conditional method. Each causal metric is first described and evaluated in a series of biologically plausible neural simulations. We then demonstrate how Granger causality can detect and quantify changes in the strength of those relationships during plasticity using 60 channel spike train data from an in vitro cortical network measured on a microelectrode array. We show that these metrics can not only detect the presence of causal relationships, they also provide crucial information about the strength and direction of that relationship, particularly when that relationship maybe changing during plasticity. Although we focus on the analysis of multichannel spike train data the metrics we describe are applicable to any stationary time series in which causal relationships among multiple measures is desired. These techniques can be especially useful when the interactions among those measures are highly complex, difficult to untangle, and maybe changing over time.", "link"=>"http://www.mendeley.com/research/causal-measures-structure-plasticity-simulated-living-neural-networks", "reader_count"=>125, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>15, "Researcher"=>34, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>43, "Student > Postgraduate"=>6, "Student > Master"=>11, "Other"=>3, "Student > Bachelor"=>2, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>1, "Professor"=>6, "Unspecified"=>1}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>15, "Researcher"=>34, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>43, "Student > Postgraduate"=>6, "Student > Master"=>11, "Other"=>3, "Student > Bachelor"=>2, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>1, "Professor"=>6, "Unspecified"=>1}, "reader_count_by_subject_area"=>{"Engineering"=>20, "Mathematics"=>5, "Agricultural and Biological Sciences"=>49, "Medicine and Dentistry"=>9, "Neuroscience"=>8, "Physics and Astronomy"=>13, "Psychology"=>6, "Computer Science"=>11, "Linguistics"=>1, "Energy"=>1, "Unspecified"=>2}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>20}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>9}, "Neuroscience"=>{"Neuroscience"=>8}, "Energy"=>{"Energy"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>13}, "Psychology"=>{"Psychology"=>6}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>49}, "Computer Science"=>{"Computer Science"=>11}, "Linguistics"=>{"Linguistics"=>1}, "Mathematics"=>{"Mathematics"=>5}, "Unspecified"=>{"Unspecified"=>2}}, "reader_count_by_country"=>{"Canada"=>3, "South Korea"=>1, "Korea (South)"=>1, "United States"=>8, "Japan"=>3, "Brazil"=>1, "United Kingdom"=>4, "Switzerland"=>1, "Portugal"=>1, "Germany"=>2, "Russia"=>1, "Spain"=>2}, "group_count"=>2}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/919915"], "description"=>"<p>Random synaptic weights of 15 mV and 45 mV were generated between each neuron in a five-neuron serial chain and 100 realizations of this chain were created for analysis. These plots demonstrate that DGC values recovered from entangled pathways (top right, bottom right, and bottom left) along the serial chain mirror those calculated using PGC on the first pathway (top left). This suggests that DGC values represent the direct influence between two neurons similar to the PGC relationship that can be calculated between neurons that are not entangled by mediated influences.</p>", "links"=>[], "tags"=>["recovered", "synapses", "serial"], "article_id"=>590368, "categories"=>["Neuroscience", "Infectious Diseases", "Medicine"], "users"=>["Alex J. Cadotte", "Thomas B. DeMarse", "Ping He", "Mingzhou Ding"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003355.g007", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_DGC_values_can_be_recovered_at_each_of_the_synapses_in_the_serial_chain_/590368", "title"=>"DGC values can be recovered at each of the synapses in the serial chain.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:59:40"}
  • {"files"=>["https://ndownloader.figshare.com/files/919976"], "description"=>"<p>A chain of 5 neurons (shown in red) is embedded within a larger network of 100 neurons connected in an all-to-all fashion (grey lines where only a fraction of the total connections are shown for clarity). The goal of this simulation is to extract the causal core shown in panel A using Granger Methods. Each synaptic weight in the chain is is set at 40 mV. Panel (B) shows the activity of these five neurons within the full network. Panel (C) shows the results from only PGC analysis in which the causal serial relationship can be seen along the diagonal. Panel (D) shows the remaining significant connectivity after CGC analysis and their corresponding synaptic weights. Note that the weights down the chain are significantly underestimated, this is likely due to the influence of the rest of the network on recovered weights.</p>", "links"=>[], "tags"=>["gc", "cgc", "biologically", "plausible", "100-neuron"], "article_id"=>590430, "categories"=>["Neuroscience", "Infectious Diseases", "Medicine"], "users"=>["Alex J. Cadotte", "Thomas B. DeMarse", "Ping He", "Mingzhou Ding"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003355.g008", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Recovery_of_Structural_Information_Using_GC_and_CGC_in_a_Biologically_Plausible_Complex_100_Neuron_Network_/590430", "title"=>"Recovery of Structural Information Using GC and CGC in a Biologically Plausible Complex 100-Neuron Network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 08:00:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/920020"], "description"=>"<p>The neural activity of rat cortical neurons were stimulated to induce plasticity and recorded using an 8×8 grid of MEA electrodes (shown earlier in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003355#pone-0003355-g001\" target=\"_blank\">Figure 1</a>). The left, middle, and right panel represent plasticity suggested by changes (enhancement or depression) in firing rate, pairwise Granger causality for outgoing “source” and incoming “sink” relationships, respectively. Each panel presents in clockwise order the distribution of values, average total changes by spatial location, distribution of the direction of change, and changes by probe location for each of the three measures. The vertical axis represents the stimulation probe site among the 60 electrodes on the MEA. The horizontal axis represents the network's response at each electrode to each probe. Each pixel is color coded to indicate the magnitude and direction of any changes that occurred following the tetanus. Application of the tetanus resulted in substantial changes in the strength of connections among neurons in this network. Comparison of those changes using a firing rate based verses a Granger causality based measure indicates a great deal of similarity between each measure. Rows where spike rate was enhanced in left panel also tended show a stronger causal relationship in the right panel. Similarly, rows indicating depression were associated with depressed causal strength in the right panel. A black arrow along the vertical and horizontal axis denote the electrode that received the tetanizing stimulus to induce plasticity. The color scale has been set to +/−3 standard deviations for each plot.</p>", "links"=>[], "tags"=>["firing", "pairwise", "granger", "causality", "plasticity"], "article_id"=>590473, "categories"=>["Neuroscience", "Infectious Diseases", "Medicine"], "users"=>["Alex J. Cadotte", "Thomas B. DeMarse", "Ping He", "Mingzhou Ding"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003355.g009", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_Firing_Rate_and_Pairwise_Granger_Causality_Plasticity_Measures_/590473", "title"=>"Comparison of Firing Rate and Pairwise Granger Causality Plasticity Measures.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 08:00:46"}
  • {"files"=>["https://ndownloader.figshare.com/files/919888"], "description"=>"<p>Direct influences between N2 and N3 were recovered by both methods to allow a comparison of Geweke's subtraction method to CGC. Each point was generated from a Monte Carlo simulation of the serial simulation using randomly generated synaptic weights between 15 mV and 45 mV. This plot suggests that both methods provide results consistent with the linear region expected from the sigmoid plot shown in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003355#pone-0003355-g004\" target=\"_blank\">Figure 4</a>. However, Geweke's subtraction method is computationally simple providing the researcher with a clear advantage in large networks especially under conditions where the structural connectivity is known to be serially arranged.</p>", "links"=>[], "tags"=>["causality", "conditional", "granger", "computational"], "article_id"=>590339, "categories"=>["Neuroscience", "Infectious Diseases", "Medicine"], "users"=>["Alex J. Cadotte", "Thomas B. DeMarse", "Ping He", "Mingzhou Ding"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003355.g006", "stats"=>{"downloads"=>1, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_Causality_Values_from_a_Traditional_Conditional_Granger_Causality_Analysis_and_the_Computational_Alternative_Described_in_the_Text_/590339", "title"=>"Comparison of Causality Values from a Traditional Conditional Granger Causality Analysis and the Computational Alternative Described in the Text.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:59:21"}
  • {"files"=>["https://ndownloader.figshare.com/files/920041"], "description"=>"<p>Conditional Granger causality was applied to the center block of electrodes (excluding border electrodes) to illustrate the effect of removing mediated influences. For the analysis of each probe the causal effect of each electrode upon each target was conditioned by conditioning out the effects of all other electrodes. The left and right panel shows the results of the conditional analysis for the source and sink measure, respectively. Removing erroneous mediation influences from PGC's causal estimates substantially refined the pattern of causal connections. This is most apparent in the total causality (upper right plots of each panel) where only a few primary electrodes remain, electrodes which may represent the major pathways that were modified by the tetanus.</p>", "links"=>[], "tags"=>["connectivity", "patterns", "conditional", "granger"], "article_id"=>590494, "categories"=>["Neuroscience", "Infectious Diseases", "Medicine"], "users"=>["Alex J. Cadotte", "Thomas B. DeMarse", "Ping He", "Mingzhou Ding"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003355.g010", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Refinement_of_Connectivity_Patterns_With_Conditional_Granger_Causality_/590494", "title"=>"Refinement of Connectivity Patterns With Conditional Granger Causality.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 08:01:11"}
  • {"files"=>["https://ndownloader.figshare.com/files/919799"], "description"=>"<p>The PGC results from a mono-directional simulation with the weight from neuron 4 to 5 varied from 0–75 mV in increments of 5 mV. Synaptic weight is plotted on the x-axis while the resulting PGC values calculated from the spike timing is plotted on the y-axis. The error bars represent the standard deviation of the results of 100 simulations for each point in the plot. The relationship between synaptic weight and PGC is sigmoid described by Equation 12. Notice that only the region in which the synaptic weights are between 15 mV and 45 mV is linearly related with the magnitude of the causality estimate. Areas in which the synaptic weights are very small or very large will result in a distorted causality value that changes very little.</p>", "links"=>[], "tags"=>["causal", "pairwise", "granger", "causality", "synaptic"], "article_id"=>590255, "categories"=>["Neuroscience", "Infectious Diseases", "Medicine"], "users"=>["Alex J. Cadotte", "Thomas B. DeMarse", "Ping He", "Mingzhou Ding"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003355.g004", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_Relationship_Between_the_Causal_Strength_From_Pairwise_Granger_causality_and_Actual_Synaptic_Weights_/590255", "title"=>"The Relationship Between the Causal Strength From Pairwise Granger causality and Actual Synaptic Weights.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:58:39"}
  • {"files"=>["https://ndownloader.figshare.com/files/920076"], "description"=>"<p>Pairwise causal influences using Granger causality following application of significance thresholds, conditional Granger causality analysis, and removal of mediated influences.</p>", "links"=>[], "tags"=>["causal", "influences", "granger", "causality", "conditional", "mediated"], "article_id"=>590526, "categories"=>["Neuroscience", "Infectious Diseases", "Medicine"], "users"=>["Alex J. Cadotte", "Thomas B. DeMarse", "Ping He", "Mingzhou Ding"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003355.t002", "stats"=>{"downloads"=>3, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Pairwise_causal_influences_using_Granger_causality_following_application_of_significance_thresholds_conditional_Granger_causality_analysis_and_removal_of_mediated_influences_/590526", "title"=>"Pairwise causal influences using Granger causality following application of significance thresholds, conditional Granger causality analysis, and removal of mediated influences.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 08:01:46"}
  • {"files"=>["https://ndownloader.figshare.com/files/919713"], "description"=>"<p>If pairwise Granger causality were applied to determine the connectivity of both of these network configurations the results for both would resemble panel a). Using pairwise Granger causality alone, it is not possible to differentiate between these network configurations. Conditional Granger causality is needed to determine if the connection from X to Z is real or mediated through Y by determining how well Z can be predicted by X with versus without the inclusion of Y.</p>", "links"=>[], "tags"=>["pairwise", "granger", "causality", "neuron"], "article_id"=>590169, "categories"=>["Neuroscience", "Infectious Diseases", "Medicine"], "users"=>["Alex J. Cadotte", "Thomas B. DeMarse", "Ping He", "Mingzhou Ding"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003355.g002", "stats"=>{"downloads"=>1, "page_views"=>15, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Conditional_Pairwise_Granger_Causality_In_a_Three_Neuron_Network_/590169", "title"=>"Conditional Pairwise Granger Causality In a Three Neuron Network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:58:03"}
  • {"files"=>["https://ndownloader.figshare.com/files/919651"], "description"=>"<p>A 60 electrode MEA (upper left) used to measure neural activity from a small network of cultured neurons. The upper right corner shows a magnified view of the array consisting of an 8×8 grid of 60 electrodes with living rat cortical neurons at 6 days in vitro. Each electrode is spaced 200 um apart and measures the extracellular potential of neurons nearby the electrode. Example of an extracellular action potential measured with a single electrode (window scale 100 ms×50 uV). Neurons on these arrays are spontaneously active producing synchronized bursts of activity throught their lifetime (up to two years).</p>", "links"=>[], "tags"=>["cortical", "neurons", "60", "electrode", "microelectrode", "multichannel"], "article_id"=>590103, "categories"=>["Neuroscience", "Infectious Diseases", "Medicine"], "users"=>["Alex J. Cadotte", "Thomas B. DeMarse", "Ping He", "Mingzhou Ding"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003355.g001", "stats"=>{"downloads"=>8, "page_views"=>404, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Living_Rat_Cortical_Neurons_on_a_60_Electrode_Microelectrode_Array_MEA_from_MultiChannel_Systems_/590103", "title"=>"Living Rat Cortical Neurons on a 60 Electrode Microelectrode Array (MEA) from MultiChannel Systems.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:57:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/919854"], "description"=>"<p>This was carried out where a) shows the synaptic weights before simulation. Calculation of PGC for all possible connections for the 5 neurons yields the plot shown in b). Notice that using PGC alone many new false connections are shown. When CGC is used to eliminate the false connection the plot is reduced to what is shown in c). After CGC plot c) begins to resemble the connectivity pattern as shown in a), however, the values associated with c) do not scale with the synaptic weights shown in a). A further step using CGC a second time or using Geweke's subtraction method is required to detangle direct and mediated influences. The results after the use of Geweke's subtraction method to calculate DGC are shown in d) along with corresponding approximations of synaptic weight.</p>", "links"=>[], "tags"=>["pairwise", "conditional", "granger", "causality", "five-neuron", "serial"], "article_id"=>590309, "categories"=>["Neuroscience", "Infectious Diseases", "Medicine"], "users"=>["Alex J. Cadotte", "Thomas B. DeMarse", "Ping He", "Mingzhou Ding"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003355.g005", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Application_of_Pairwise_and_Conditional_Granger_Causality_Analysis_to_a_Five_Neuron_Serial_Chain_/590309", "title"=>"Application of Pairwise and Conditional Granger Causality Analysis to a Five-Neuron Serial Chain.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:59:01"}
  • {"files"=>["https://ndownloader.figshare.com/files/920062"], "description"=>"<p>The left column indicates what the source neuron and the top row indicates the target neuron. For example, to locate the influence of neuron 2 on neuron 3 a value of 1.38 is reported in entry From N4, To N1.</p>", "links"=>[], "tags"=>["causal", "influences", "calculated", "granger", "causality", "neurons", "simulation", "displayed"], "article_id"=>590515, "categories"=>["Neuroscience", "Infectious Diseases", "Medicine"], "users"=>["Alex J. Cadotte", "Thomas B. DeMarse", "Ping He", "Mingzhou Ding"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003355.t001", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Pairwise_causal_influences_calculated_using_Granger_causality_between_the_5_neurons_in_the_simulation_displayed_in_Figure_8_/590515", "title"=>"Pairwise causal influences calculated using Granger causality between the 5 neurons in the simulation displayed in Figure 8.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 08:01:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/919752"], "description"=>"<p>In panel a) the synaptic weights from N1 to N2 and N4 to N5 have been synaptically coupled. N3 is left uncoupled to demonstrate that a pairwise GC will indicate null connectivity. Equivalent but independent random processes drive each of the five neurons. 100 realizations of this network using Izhikevich's simple neuron model with these weights yields the results shown in panel b) using pairwise Granger causality. These results demonstrate that pairwise Granger causality can not only resolve the difference between null and actual connectivity, but also determine the directionality of those influences.</p>", "links"=>[], "tags"=>["five-neuron", "pairwise", "granger"], "article_id"=>590209, "categories"=>["Neuroscience", "Infectious Diseases", "Medicine"], "users"=>["Alex J. Cadotte", "Thomas B. DeMarse", "Ping He", "Mingzhou Ding"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003355.g003", "stats"=>{"downloads"=>1, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Topology_of_a_Simple_Five_Neuron_Network_Using_Pairwise_Granger_causality_/590209", "title"=>"Topology of a Simple Five-Neuron Network Using Pairwise Granger causality.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:58:18"}

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Relative Metric

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