modeling the evolution of neurophysiological signals

Modeling the Evolution of Neurophysiological Signals

Mark FiecasHernando Ombao

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Data Characteristics

Small signal-to-noise ratios

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Data Characteristics

Nonstationary time series data

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Data Characteristics

Evolving over time within a replicate

Nonidentical replicates across the experiment

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Example

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A Learning Association Experiment

Time

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A Learning Association Experiment

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Evolving Evolutionary Coherence

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Evolving Evolutionary Coherence

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Evolving Evolutionary Spectrum

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Evolving Evolutionary Spectrum

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The Time Series Models

Weakly stationary time series (Brillinger, 1981):

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The Time Series Models

Locally stationary time series (Dahlhaus, 2000):

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The Time Series Models

Locally stationary time series with slowly evolving replicates:

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The Time Series Models

1. Replicates are uncorrelated. For each replicate, use existing methods to address nonstationarity over time.

2. Smooth the estimates over time and replicate-time.

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Performance

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Hippocampus Log Periodogram

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Nucleus Accumbens Log Periodogram

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A Relevant Scientific Question

Is the power in a frequency band of interest the same between “familiar” and “novel” trials?

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Log Periodogram Models

Weakly stationary data (Krafty et al, 2011):

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Log Periodogram Models

Weakly stationary data (Krafty et al, 2011):

where

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The Log Periodogram Models

Locally stationary data (Krafty, 2007; Qin and Guo, 2009):

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The Log Periodogram Models

Locally stationary data (Krafty et al, 2007):

where

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The Proposed Log Periodogram Model

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The Proposed Log Periodogram Model

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The Proposed Log Periodogram Model

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Calling All Statisticians

“Understanding how the brain works is arguably one of the greatest scientific challenges of our time.”

- Alivisatos et al, 2013

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Calling All Statisticians

• The BRAIN Initiative (USA)• The Human Brain Project (European

Union)– 86 Institutions in Europe involved– €1 billion in funding / year

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Calling All Statisticians

Very rich data sets– High temporal resolution (EEG, MEG, LFP)– High spatial resolution (PET, fMRI)– 300k spatial locations in fMRI– Imaging genetics

Many open problems

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Calling All Statisticians

Handbook of Modern Statistical Methods: Neuroimaging Data Analysis (eds: H. Ombao, M. Lindquist, W. Thompson, and J. Aston)

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Acknowledgments

• Shaun Patel, Boston University• Emad Eskandar, MGH