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4 DISCUSSION
In this study, we analyzed EGG time-series data
using complex dynamical methods. E
trans
and λ were
calculated from the EGG data.
SDEs were proposed as a mathematical model of
an EGG by Matsuura et al. (2008). SR occurs for an
appropriate coefficient, μ. Some biosystems are
based on the nonlinear phenomenon of SR, in which
the detection of small afferent signals can be
enhanced by the addition of an appropriate amount
of noise (Benzi et al., 1981). We examined whether
or not the SR generated using Equations (1) could
describe an EGG time series. Stationary EGGs are
well described by the SDEs in the case of μ = 11.6,
which might represent the SR (11 < μ
≤ 12). We
herein claim that SR can be regarded as a
mathematical model of an EGG. Moreover,
distribution of the numerical solutions in the SR fits
the distribution of the EGGs, which can be
correlated as shown in Figure 2 (R
2
= 0.972).
0
12500
25000
-3.01
-0.84
1.33
3.5
x(t)
arb. unit.
Times
0
1250
2500
EGG
Numerical solutions
Figure 2: Distributions of EGGs and numerical solutions
(μ = 11).
The diseases resulting from constipation and
erosive gastritis (an illness in which the inside of the
stomach becomes swollen and painful) are
accompanied by anomalous autonomic nervous
activity. A decline in the electrical activity of the
stomach should change the degree of determinism
(E
trans
) and the complexity (λ) in the attractor
reconstructed from the EGG data. By using the
mathematical model of an EGG, electrogastrography
will be of assistance in the diagnosis of diseases of
the alimentary canal and autonomic nervous system.
5 CONCLUSIONS
As a mathematical model of an EGG, we added the
van der Pol equation to a periodic function and
random white noises that represented the intestinal
motility and other biosignals, respectively. By
projecting the data from a stationary EGG obtained
for a subject in the supine position, along with the
numerical solutions, onto the E
trans
-λ plane, we
qualitatively evaluated the affinity between them.
The SR was statistically the most appropriate with
regard to the mathematical model of the stationary
EGG. It is necessary to further investigate the
reliability of a simplified measurement method by
increasing the number of EGGs studied. The next
step will also involve the suggestion of a
mathematical model for an EGG, derived from data
from elderly subjects and meal tolerance tests.
ACKNOWLEDGEMENTS
This work was supported in part by a Grant-in-Aid
for JSPS Fellows and the Hori Information Science
Promotion Foundation.
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A STUDY OF STOCHASTIC RESONANCE AS A MATHEMATICAL MODEL OF ELECTROGASTROGRAM
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