Concepts of Neuronal Network Function December 2, 2011

Lawrence N Eisenman MD PhD

Adult Epilepsy Center

Washington University in St. Louis

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Disclosure

Name of Commercial

Interest

Johnson & Johnson, Medtronic, Merck, Pfizer

Type of Financial Relationship

Stock Ownership

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Symposium Learning Objectives

• Apply knowledge of motor-based signs and symptoms in

epilepsy with localization of partial seizures.

• Correlate common ictal semiology findings with

pathways of seizure propagation.

• Understand and, as appropriate, apply MRI-based

functional connectivity techniques in the diagnosis of

epileptic seizures.

• Utilize concepts of neuronal network function and

associated applications in MRI-based functional

connectivity techniques in evaluating patients with

epilepsy

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Neuronal network activity is

determined by:

• Intrinsic neuronal properties

– Neuronal morphology/passive properties

– Types and distributions of ion channels

• Synaptic properties

– Types and distributions of synaptic channels

• Pattern of network connectivity

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Network properties and activity

Netoff et al, J Neurosci 24:8075 2004

“Normal” “Pathologic”

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How do we think about

connectivity data?

Is there a way categorize and/or

quantify connectivity data?

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Learning Objectives

• Understand the basic concepts of graph theory.

• Recognize the potential utility of graph theory for advancing our understanding of the functioning of neuronal networks in epilepsy and other neuropsychiatric diseases.

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Graph Theory

• Graph theory is a branch of mathematics

devoted to the study of graphs.

• A graph is defined as a collection of nodes

and a collection of the edges

(connections) between nodes.

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Graph theory is used in a wide

variety of disciplines

• Social networks

• Computer networks

• Gene networks

• Neuroscience

Figure courtesy of Luigi Maccotta MD PhD

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Basic Graph Metrics • Degree = number of edges connected to a particular

node

– Hub = node with high degree

• Degree distribution = probability of a node having a

particular degree (often shown as a histogram)

• Average shortest path length = number of edges in the

shortest past between two nodes averaged over all pairs

of nodes

– Betweenness centrality = The ratio of number of shortest paths

between nodes that include the node to the total number of

shortest paths.

• Clustering coefficient = fraction of neighbors of a node

that are connected to each other Bullmore and Sporns, Nat Rev Neurosci 10:186 2009

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Random graph

• Graph with randomly

connected nodes

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Small World Graph

• High average

clustering coefficient

• Low average path

length

• Good compromise

between computational

efficiency and wiring

economy

Watts and Strogatz, Nature 393:440 1998

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0.1

1

pro

ba

bil

ity

12 3 4 5 6 7 8 9

10

number of edges

Scale Free Graph

• Degree distribution

follows a power law

– P(k) ~ k-

• Small number of

highly connected

nodes called hubs

• Especially resistant to

random loss of

individual nodes Barabasi and Albert, Science 286:509 1999

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Neuronal networks in the brain

are organized as:

• Small world networks?

– Functional neuroimaging suggests

connectivity between brain regions is

consistent with a small world network.

– There are also highly connected hub regions.

Bullmore and Sporns, Nat Rev Neurosci 10:186 2009

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Neuronal networks in the brain

are organized as:

• Scale free networks?

– Optical imaging in hippocampal slices

suggests neuronal networks in CA3 are

consistent with scale free networks (Bonifazi et al,

Science 326:1419 2009).

– Multi-electrode array recording in cultured

neurons suggests that neurons spontaneously

form scale free networks (Eisenman et al, in preparation).

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Functional connectivity in temporal

lobe epilepsy

• 7 of 8 L mTLE patients showed decreased

connectivity in the left temporal lobe (Bettus et

al, Hum Brain Mapp 30:1580 2009)

• R mTLE patients showed decreased

connectivity in both mesial temporal lobes (Zhang et al, Brain Res 1323:152 2010)

• mTLE patients showed increased

connectivity within the mesial temporal

lobes (Liao et al, PLoS One 5:e8525 2010)

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Graph theory may be useful for

identifying MTLE patients • Functional connectivity measured using

resting state fMRI in 52 controls and 16

MTLE patients.

• Graph theory measures calculated for each

subject.

• Data was used to construct a classifier with

77% sensitivity and 84% specificity calculated

with „leave one out‟ cross validation.

Zhang et al, J Neurosci Methods 199:129 2011

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Graph theory may be useful for

identifying the ictal onset zone

• 25 patients underwent intracranial

electrocorticography for refractory

neocortical onset epilepsy. 15 underwent

resection and 5 became seizure free.

• Graphs were constructed by considering

recording contacts as nodes and using the

directed transfer function calculated during

seizures to identify edges. Wilke et al, Epilepsia 52:1528 2011

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Graph theory may be useful for

identifying the ictal onset zone

• Betweenness centrality was calculated for

each node in the network and regions with

high betweenness centrality during

seizures were identified.

• Seizure free patients had more overlap

between regions of high betweenness

centrality and clinically identified ictal

onset zones. Wilke et al, Epilepsia 52:1528 2011

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Functional connectivity in other

neuropsychiatric diseases

• Alzheimer‟s disease is associated with

disruption of hubs which are highly

correlated with areas of high amyloid

deposition.

• Schizophrenia is associated with an

overall decrease in connectivity with less

highly connected hubs.

Sporns, Front Comput Neurosci 5:5 2011

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Hypothesis:

Some neuropsychiatric diseases

are associated with an increased

“randomization” of brain networks

Sporns, Front Comput Neurosci 5:5 2011

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Summary and impact on clinical

care and practice

• Neuronal network activity is dependent on

neuronal properties, synaptic properties and the

pattern of network connectivity.

• Graph theory can be used to classify and

quantify connectivity data to advance our

understanding of epilepsy and other

neuropsychiatric diseases.

• Graph theory may eventually be useful for the

diagnosis and treatment of epilepsy.