Overview of Body Sway Data Overview of Body Sway Data AnalysisAnalysis

Robert Harrington

Winter 2003

GoalsGoals

Ultimate goal: to determine likelihood of a person’s falling by analyzing small motion while standing

Prof. David Garelick

Northeastern University

617.373.2936

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Body Position versus Time Body Position versus Time

Fourier Transform:Fourier Transform:

Fourier Transform of Data (cont.):Fourier Transform of Data (cont.):

Fourier Transform of Data (cont.):Fourier Transform of Data (cont.):

Fourier Transform of Data (cont.):Fourier Transform of Data (cont.):

Fourier Transform of Data (cont.):Fourier Transform of Data (cont.):

Fourier Transform of Data (cont.):Fourier Transform of Data (cont.):

Difficulties with Fourier Difficulties with Fourier transform:transform:

• No statistically meaningful differences between fallers and non-fallers

• Fixed range of frequencies:

–1/(2t) to +1/(2t)

• Does not directly include exponential damping

Proposed ModelProposed Model

Body can be modeled as a simple spring with the restoring force proportional to the displacement at an earlier time:

F = - k • x ( t - ) This model gives solutions which have the

form: a e-t sin(o t)

Laplace TransformLaplace Transform

Allows determination of exponential damping term

Problem: Discrete Laplace Transform very difficult

Laplace Transform graphLaplace Transform graph

Laplace Transform (cont.):Laplace Transform (cont.):

Laplace Transform problem:Laplace Transform problem:

Analytical solution with non-infinite integration limits gives extra term

Extra term depends on limits AND position in frequency space

Creates peaks at spurious frequencies As limit goes to infinity, peaks converge to

one at the correct frequency

Laplace Transform problem:Laplace Transform problem:

Laplace Transform problem:Laplace Transform problem:

Current StatusCurrent Status

Analysis of Fourier peak-widths to determine exponential damping term

Fitting curves to function, using model to predict corresponding to know Fourier peaks (parameter )