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Brain's Circuit Connectivity and Its Dynamics

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Brain's Circuit Connectivity and Its Dynamics Brain's Circuit Connectivity and its Dynamics Behnaam Aazhang J.S. Abercrombie Professor Electrical and Computer Engineering Rice University Can Electrical Engineers Impact Neuroscience? Behnaam Aazhang J.S. Abercrombie Professor Electrical and Computer Engineering Rice University acknowledgement • Nitin Tandon, MD at UTHSC • John Byrne, UTHSC • Valentin Dragoi, UTHSC acknowledgement acknowledgement NSF, UT System, and Texas Instruments a scientific curiosity • how does human brain work? a scientific curiosity • how does human brain work? • ancient Egypt and Greece • Roman empire • the seat of intelligence a scientific curiosity • how does human brain work? • ancient Egypt and Greece • Roman empire • the seat of intelligence • 19th century • 90s the “decade of the brain” • 2013 “the brain initiative” quantum leap in understanding • neuron doctrine quantum leap in understanding • neuron doctrine • brain is an electrical circuit quantum leap in understanding • neuron doctrine • brain is an electrical circuit quantum leap in understanding • neuron doctrine • brain is an electrical circuit • probe using electrodes • manipulate using electrical signals quantum leap in understanding • neuron doctrine • brain is an electrical circuit • probe using electrodes • manipulate using electrical signals • problem: millions of neurons! the sheer size • human • 86 billion neurons the sheer size • human • 86 billion neurons the sheer size • human • 86 billion neurons it is all about connections! the connections • 86 billion neurons • 10 micron diameter • 100 trillion synapses • 100 Hz clock speed • 1000s of chemical and genetic effectors the connections • 86 billion neurons • 10 micron diameter • 100 trillion synapses • 100 Hz clock speed • 1000s of chemical and genetic effectors grand challenges • … • how neuronal circuit connectivity relates to behavior • transition of neuronal circuits grand challenges • … • how neuronal circuit connectivity relates to behavior • transition of neuronal circuits • disease state to healthy state • learning • memory • … our research focus • understanding circuit’s connectivity and its dynamics • epilepsy, parkinson, alzheimers, aphasia • behavior, learning, memory • network analysis • large-scale recording • network modulation • closed-loop real-time signal processing • experimental • clinical this talk • one set of information theoretic tools • two applications • impact of learning on feeding circuits in Aplysia • seizure circuits in epileptic patients application 1 • micro level • learning in feeding circuits in Aplysia • study and manipulate individual neurons application 2 • micro level • learning in feeding circuits in Aplysia • study and manipulate individual neurons • macro level • seizure circuits in epileptic patients • study and manipulate of populations of neurons application 1 learning • Aplysia • 20,000 neurons • feeding neurons’ connectivity • micro level study • changes due to learning? • anatomical connectivity • functional connectivity! the experiment • Aplysia buccal ganglion • learning circuit • voltage sensitive dye the experiment • Aplysia • learning circuit • voltage sensitive dye (VSD) • spectral absorption of VSD changes with changes in voltage L. Cohen, B. Salzberg (1978). "Optical Measurement of Membrane Potential". Reviews of Physiology, Biochemistry and Pharmacology. the experiment • Aplysia buccal ganglion • learning circuit • voltage sensitive dye learning • Aplysia • learning circuit • buccal ganglion learning • neurons’ spike learning • does neuron 3 excite neuron 8? learning • does neuron 3 excite neuron 8? learning • did neuron 3 causally influence firing of neuron 8? Neuron 3 …00011110000001001100001100000001100001… Neuron 8 …00000111100000010111100001100000001111… learning • did neuron 3 causally influence firing of neuron 8? Neuron 3 …00011110000001001100001100000001100001… Neuron 8 …00000111100000010111100001100000001111… • causal relation • a probabilistic measure • data driven causality • one time series forecasting another • economics • transportation • … N. Wiener (1956), C. Granger (1969), H. Marko (1973), J. Massey (1990), G. Kramer (1998), C. Quinn, T. Coleman, N. Kiyavash (2011) a little background • directed information and causality N N N n n 1 I(X Y )= I(X ; Y Y − ) 1 ! 1 1 n| 1 n=1 X • directional with temporal information N N X (X1,X2,...,XN ) Y (Y ,Y ,...,Y ) 1 ⌘ 1 ⌘ 1 2 N …00011110000001001100001100000001100001… …00000111100000010111100001100000 N N N n n 1 I(X Y )= I(X ; Y Y − ) 1 ! 1 1 n| 1 a little background n=1 X • mutual information of time series N N N N n 1 I(X ; Y )= I(X ; Y Y − ) 1 1 1 n| 1 n=1 X • no temporal and no causal information N N X (X1,X2,...,XN ) Y (Y ,Y ,...,Y ) 1 ⌘ 1 ⌘ 1 2 N I(XN ; Y N )=H(Y N ) H(Y N XN ) 1 1 1 − 1 | 1 a little background • directed information of time series I(XN Y N )=H(Y N ) H(Y N XN ) 1 ! 1 1 − 1 || 1 • where N N N n 1 n H(Y X )= H(y Y − ,X ) 1 || 1 n| 1 1 n=1 X I(XN ; Y N )=H(Y N ) H(Y N XN ) 1 1 1 − 1 | 1 a little background • directed information of time series I(XN Y N )=H(Y N ) H(Y N XN ) 1 ! 1 1 − 1 || 1 causal conditional entropy • where N N N n 1 n H(Y X )= H(y Y − ,X ) 1 || 1 n| 1 1 n=1 X estimating directed information • estimating entropy and causally conditioned entropy N N N N N I(X1 Y1 )=H(Y1 ) H(Y1 X1 ) • model free ! − || N N N n 1 n H(Y X )= H(y Y − ,X ) 1 || 1 n| 1 1 n=1 • data driven—universal X • tree based density estimation for discrete variables • kernel density estimation for continuous variables back to learning • causal relation …00011110000001001100001100000001100001… • data driven …00000111100000010111100001100000001111… • tree based density estimation • directed information • causal relation …00011110000001001100001100000001100100? 1 0 • data driven 0 • tree based density estimation ? • directed information • causal relation …00011110000001001100001100000001100100? 1 0 • data driven 0 • tree based density estimation ? • directed information ...000111100000010 p H(X),H(X, Y ) I(X Y ) ! X,Y ! ! ! learning • causal relation • direction information learning I(X X ) • causal relation 3 ! 8 • direction information learning • causal relation • direction information • excitatory learning • causal relation • direction information • excitatory • inhibitory • excitatory versus inhibitory • slow versus fast causality Network Analysis • Out- and in-degree • Changes in distribution of degrees due to learning 24 A B 19 8 Indegree Outdegree 12 15 7 2 1 6 18 14 22 10 5 4 20 9 3 2 27 13 23 17 Numberconnections of 1 8 7 0 11 6 1 22 9 23 7 27 10 15 5 11 12 19 6 18 3 17 8 13 20 14 2 3 5 Neuron Fig. 9. Patterns of connectivity of the preparation in Fig. 8. A: The inferred connectivity diagram. B: Indegrees and outdegrees of neurons. Neurons without any connections are not shown. This graph shows neurons that primarily receive connections (left) and those that send out connections (right). 457 IV. DISCUSSION 458 Our method of exploiting the context tree maximizing entropy estimator together with directed infor- 459 mation can infer functional connectivity in small realistic simulated neural networks. The CTM based 460 estimator has the advantage of low computational complexity, fast convergence, being non-parametric, as 461 well as being able to mitigate overfitting. We have shown that our implementation of CTM can identify 462 direct connections, eliminate indirect connections, reliably distinguish excitatory from inhibitory synaptic 463 actions and quantify the amount of information flow from one neuron to another (Fig. 5). Furthermore, 464 this inference technique based on DI is robust against signal nonlinearities, which linear methods such 465 as Granger Causality or estimates based on the generalized linear model might not be able to capture. 466 For example, it is able to detect connections with facilitation or depression (Fig. 6), which are common 467 throughout invertebrate and vertebrate nervous systems. 468 A sound CTM-DI theoretical framework requires the observed sequences to be stationary. We believe 469 this assumption is valid because in the VSD recordings, the BMPs are similar from one to the next and so 470 the underlying system appears to be stationary during the limited frame of the analysis. The context tree 471 method analyzes different contexts, which are patterns, independently. Therefore, it is not only able to 472 analyze tonic activity but also phasic activity. The result of the CTM-DI algorithm is the average strength 473 taken into account all the different spiking patterns in the recording window. 474 The CTM-DI based method has its own limitations. A challenge for the DI-CTM approach is a dynamics of the network 0.3 0.3 0.25 0.25 5 5 0.2 0.2 0.15 0.15 10 10 0.1 0.1 15 0.05 15 0.05 0 0 20 −0.05 20 −0.05 −0.1 −0.1 25 25 −0.15 −0.15 −0.2 −0.2 5 10 15 20 25 5 10 15 20 25 neuron index Z. Cai, …, B. Aazhang, “Inferring Neuronal Network Functional Connectivity with Directed Information”, Journal of Neurophysiology, 2017. application 2 application 2 • micro level • learning in feeding circuits in Aplysia • study and manipulate individual neurons • macro level • seizure circuits in epileptic patients • study and manipulate of populations of neurons connectivity and epilepsy • a macro level study • million of neurons • individual neuronal activities are less relevant epilepsy • unprovoked and recurring seizures epilepsy • unprovoked and recurring seizures • seizure • no standard definition • abnormally hyper-excited neuronal activities epilepsy • unprovoked and recurring seizures • seizure •
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