My poster for BMES 2010 held at Austin, TX

1. Validation of Granger Causality using Unidirectional Neuronal Networks
Sankaraleengam Alagapan, Liangbin Pan, Bruce Wheeler and Thomas DeMarse
J Crayton Pruitt Family Department of Biomedical Engineering
University of Florida
Introduction Methods Results Results
Materials
• Neurons cultured on microelectrode arrays (MEAs) form an • MEAs (Commercial (MCS, Germany)) 8 x 8 array, 200µm 60 Analysis of Data From Microwells and Microtunnels (Fig • Average causal values from Input well to Output well is higher
interesting system to study living (in vitro) neuronal network TiN electrodes on Glass substrate with SiN2 insulation 5) than Output well to Input well
properties • Dissociated neuronal culture from E18 rats, Medium: • Causal Measures are Sensitive to Time Constant:
• Microfluidic devices consisting of wells connected by tunnels Neurobasal/ B27/Glutamax – 1 ms bins, tau=4 ms: low causality within and between Bin size=10 ms Tau = 40ms
enable control over the direction of connections in in vitro group activity in the wells, but high values for propagation
networks Microtunnel Devices (Fig 2) by axons
• Sequential plating of neurons in wells ideally leads to tunnels • PDMS Devices Tunnels - (3µm x 10µm x 400µm), Wells 1 mm – 10 ms bins, tau=40 ms: high causality within and
filled with axons extending from the older to the younger high
population and hence unidirectional propagation between wells, but little for axonal propagation
• Well B cultured 10 days after culture in Well A
• Spontaneous Activity recorded 10 days after culture in Well B
Spike Train Bin size=1 ms Tau = 4ms
Microwell B
(Output Well)
Row 4 Output well (B) Tunnels to Well B Well A to Well B
Microtunnels
Row 5 Smoothed Waveform Tunnels
MEA Dissociated Neuronal Culture Multi Electrode Recordings
Microwell A
(Input Well)
Well B to Tunnels
Well A to Tunnels
Arrow indicates direction
100 µm of growth of axons
(a) (b)
(a) (b) (c) Fig 6 Average Region wise Causal Values (Average values from Fig 5(a) bottom
Fig 3. (a)Schematic of the device coupled MEA (b) Micrograph of device and
Well B to Well A Tunnels to Well A Input well
Microtunnel Device Microtunnel Device MEA (c) Preprocessing for Granger Analysis (A)
Fig 1. Overview of technology used in this work Results
Conclusion
• Granger Causality(GC) is a statistical measure finding
Analysis of Data From Microtunnels (Fig 4) Bin size=10 ms Tau = 40ms
widespread use in Neuroscience especially in LFPs and EEGs
• By design, action potentials should propagate from row 5 to • Granger analysis on the data from microtunnels shows that
for assessing functional connectivity between brain structures
row 4. This is supported by two measures. Granger Causality is effective in determining directionality
• Here we use data from unidirectional microtunnel networks
– Values of causal connection from row 5 to row 4 are higher from neuronal data.
to validate Granger Causality’s ability to infer direction of Output well (B) Tunnels to Well B Well A to Well B
than for row 4 to row 5 • Analysis of data from the entire system shows the
functional connectivity Tunnels
– Cross-correlograms show a significant peak at a delay at necessity to consider the time scale of interactions to
Well B to Tunnels
Methods
Well A to Tunnels
positive delay from row 4 to row 5 obtain the exact connectivity structure
• However, in 15% of the cases, propagation was in the other
Granger Causality direction as indicated by cross-correlogram and Granger
• Suppose X and Y are 2 time
0.5 Illustration
analysis. (Channels 84-85 in Fig 4) Acknowledgement
1 2 Well B to Well A Tunnels to Well A Input well
series modeled as autoregressive 0.25
Conditional Granger Values Between Electrodes Under Microtunnels (A)
processes, Y G-causes X if the
24
25 0.14 Funded by National Institute of Health (NIH) NS052233
including past of Y in modeling X
34
0.12
35
0.25
decreases the variability of 44
45
0.1
(a) References
residuals in the model and vice
Target
54 0.08
Bin size=1 ms Tau = 4ms Bin size=10 ms Tau = 40ms
versa. 0. 5
55
64 0.06
1. Cadotte AJ, Demarse TB, He P, Ding M. Causal
• The amount by which the 65
variability is reduced gives a
74 0.04 Measures of Structure and Plasticity in Simulated and
Living Neural Networks. PLOS One. 2008;3(10).
75
measure of strength and direction Fig2 Illustration of Granger Causality
Tunnels
0.02
Tunnels
84
is revealed in the relative strengths and representation
85
24 25 34 35 44 45 54 55 64 65 74 75 84 85
2. Dworak BJ, Wheeler BC. Novel MEA platform with
• Conditional Granger Causality: Same idea as Granger, with both
Source
PDMS microtunnels enables the detection of action
(a)
X and Y conditioned on another variable Z which might influence Channel_55 to Channel_54 Channel_85 to Channel_84 potential propagation from isolated axons in culture. Lab
the two time series (b) on a Chip. 2009:404-410.
3. Ding, M., Chen, Y., & Bressler, S.L. Granger causality:
400
200
Fig 5 (a) Granger Causal Values between different electrodes under the
Counts/bin
Counts/bin
Pre-processing for Granger Analysis (Fig 3c) 100 200
microtunnels and microwells for different values of bin size and tau.
Basic theory and application to neuroscience
• Spikes detected – Threshold crossing – Threshold = 5σ (b) Connectivity Diagrams for different bin size and tau. Connectivity Diagram Winterhalder, N., & Timmer, J. Schelter. S. Handbook of
• Spiketimes  Spiketrains (Bin size = 1ms or 10ms) 0
-2 -1 0 1 2
0
-2 -1 0 1 2
shows only stronger connections (GC values >0.025) Time Series Analysis. Wienheim : Wiley, 2006.
• Spiketrains smoothed with exponential curve (τ = 4ms or 40ms) 4. Seth AK. A MATLAB toolbox for Granger causal
Time (ms) Time (ms)
to get a continuous waveform (b)
Fig 4(a) Granger Causal Values from source(columns) to targets(rows) (b) connectivity analysis. Journal of neuroscience methods.
• Conditional Granger analysis using GCCA Toolbox4 Cross Correlograms for 2 examples showing unidirectional (left) and 2010;186(2):262-73
bidirectional (right) propagation
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