Fractal Dimension Analysis of Transient Visual Evoked Potentials: Optimisation and Applications.
OBJECTIVE
The visual evoked potential (VEP) provides a time series signal response to an external visual stimulus at the location of the visual cortex. The major VEP signal components, peak latency and amplitude, may be affected by disease processes. Additionally, the VEP contains fine detailed and non-periodic structure, of presently unclear relevance to normal function, which may be quantified using the fractal dimension. The purpose of this study is to provide a systematic investigation of the key parameters in the measurement of the fractal dimension of VEPs, to develop an optimal analysis protocol for application.


METHODS
VEP time series were mathematically transformed using delay time, τ, and embedding dimension, m, parameters. The fractal dimension of the transformed data was obtained from a scaling analysis based on straight line fits to the numbers of pairs of points with separation less than r versus log(r) in the transformed space. Optimal τ, m, and scaling analysis were obtained by comparing the consistency of results using different sampling frequencies. The optimised method was then piloted on samples of normal and abnormal VEPs.


RESULTS
Consistent fractal dimension estimates were obtained using τ = 4 ms, designating the fractal dimension = D2 of the time series based on embedding dimension m = 7 (for 3606 Hz and 5000 Hz), m = 6 (for 1803 Hz) and m = 5 (for 1000Hz), and estimating D2 for each embedding dimension as the steepest slope of the linear scaling region in the plot of log(C(r)) vs log(r) provided the scaling region occurred within the middle third of the plot. Piloting revealed that fractal dimensions were higher from the sampled abnormal than normal achromatic VEPs in adults (p = 0.02). Variances of fractal dimension were higher from the abnormal than normal chromatic VEPs in children (p = 0.01).


CONCLUSIONS
A useful analysis protocol to assess the fractal dimension of transformed VEPs has been developed.
School of Optometry and Vision Science, UNSW Australia, Sydney, New South Wales, Australia.
Mei Ying
MY
Boon
School of Mathematics and Statistics, UNSW Australia, Sydney, New South Wales, Australia.
Bruce Ian
BI
Henry
School of Optometry and Vision Science, UNSW Australia, Sydney, New South Wales, Australia.
Byoung Sun
BS
Chu
School of Optometry and Vision Science, UNSW Australia, Sydney, New South Wales, Australia.
Nour
N
Basahi
School of Optometry and Vision Science, UNSW Australia, Sydney, New South Wales, Australia.
Catherine May
CM
Suttle
Centre for Eye Research Australia, Royal Victorian Eye and Ear Hospital, East Melbourne, Victoria, Australia.|Department of Surgery (Ophthalmology), Melbourne Medical School, The University of Melbourne, Parkville, Victoria, Australia.
Chi
C
Luu
Park Road Eye, Hurstville, New South Wales, Australia.
Harry
H
Leung
Park Road Eye, Hurstville, New South Wales, Australia.
Stephen
S
Hing
D000328:Adult; D001931:Brain Mapping; D004569:Electroencephalography / Q000379:methods; D004594:Electrophysiology / Q000379:methods; D005074:Evoked Potentials, Visual / Q000502:physiology*; D005260:Female; D017709:Fractals; D006801:Humans; D008297:Male; D009460:Neurologic Examination; D010364:Pattern Recognition, Visual / Q000502:physiology*; D010775:Photic Stimulation; D011930:Reaction Time / Q000502:physiology; D014793:Visual Cortex / Q000502:physiology*