300
M. Thanaj et al.
the system’s ability to adapt to pathophysiological conditions and/or is an indicator
of disease severity.
19.5 Multiscale Frequency, Complexity and Scale
Conventional entropy and complexity methods have the disadvantage that they can
only study behaviour at one scale. However, the physiological processes that regulate
flow motion operate across multiple temporal scales ranging from 0.001 to 2 Hz and
appear to vary under a wide range of physiological and pathophysiological conditions
as discussed previously. To account for these multiple and potentially varying process
scales, LZ complexity and entropy has be evaluated in multiple time-scales using a
coarse-graining approach. Such multiscale analyses have been shown to be effective
in the general understanding of a wide range of physiological signals [15, 23, 40].
Costa et al. [22] applied multiscale entropy to the cardiac inter-beat interval to
determine the regularity of the cardiac properties in the young, elderly and individuals with heart failure during both waking and sleeping periods. They found good
discrimination between these periods for all groups and reported that the multiscale
entropy analysis was a valid method for quantifying the complexity of biological
signals across multiple spatial and temporal scales. Kalev et al. [43] using multiscale LZ complexity, were able to demonstrate an 86% classification accuracy by
accounting for the different frequencies of information content in the electroencephalogram. Similarly, Papaioannou et al. [63] showed that multiscale complexity
analysis of temperature signals from patients with systematic inflammation, sepsis
or septic shock could be used to determine the early presence of pathology.
In this approach, the sampling frequency is altered by a scale factor τ defining
the scale level used to resample the original signal reducing the scale of the time
series. For the time series {x 1 , . . . , x N }, where N is the number of samples, the
coarse-grained time series, y
τ , is:
y
τ
i =
1
τ
iτ
i=(i−1)τ +1
x j , 1 ≤ i ≤ N /τ
(19.5.1)
Thus, for an LDF signal originally sampled at 40 Hz, the LZC can be evaluated
at different LDF sample rates, where the sampling frequency is f τ = 40/τ where
τ is the scale factor. At scale τ = 1 the original signal is preserved at 40 Hz and
at scale τ = 24 resampled to 1.67 Hz. At scale factor one, the time series y
1 is the
original signal and the length of each coarse-grained time series {y
τ
} is equal to the
original signal divided by the scale factor, τ. It has been suggested that the length
of signal required to obtain viable complexity measures and reported that a signal
length > 1000 samples are required which equates to 10 min captured at 40 Hz at
scale τ = 24 [83].
An example of the application of the multiscale approach is shown in Fig. 19.2
M. Thanaj et al.
the system’s ability to adapt to pathophysiological conditions and/or is an indicator
of disease severity.
19.5 Multiscale Frequency, Complexity and Scale
Conventional entropy and complexity methods have the disadvantage that they can
only study behaviour at one scale. However, the physiological processes that regulate
flow motion operate across multiple temporal scales ranging from 0.001 to 2 Hz and
appear to vary under a wide range of physiological and pathophysiological conditions
as discussed previously. To account for these multiple and potentially varying process
scales, LZ complexity and entropy has be evaluated in multiple time-scales using a
coarse-graining approach. Such multiscale analyses have been shown to be effective
in the general understanding of a wide range of physiological signals [15, 23, 40].
Costa et al. [22] applied multiscale entropy to the cardiac inter-beat interval to
determine the regularity of the cardiac properties in the young, elderly and individuals with heart failure during both waking and sleeping periods. They found good
discrimination between these periods for all groups and reported that the multiscale
entropy analysis was a valid method for quantifying the complexity of biological
signals across multiple spatial and temporal scales. Kalev et al. [43] using multiscale LZ complexity, were able to demonstrate an 86% classification accuracy by
accounting for the different frequencies of information content in the electroencephalogram. Similarly, Papaioannou et al. [63] showed that multiscale complexity
analysis of temperature signals from patients with systematic inflammation, sepsis
or septic shock could be used to determine the early presence of pathology.
In this approach, the sampling frequency is altered by a scale factor τ defining
the scale level used to resample the original signal reducing the scale of the time
series. For the time series {x 1 , . . . , x N }, where N is the number of samples, the
coarse-grained time series, y
τ , is:
y
τ
i =
1
τ
iτ
i=(i−1)τ +1
x j , 1 ≤ i ≤ N /τ
(19.5.1)
Thus, for an LDF signal originally sampled at 40 Hz, the LZC can be evaluated
at different LDF sample rates, where the sampling frequency is f τ = 40/τ where
τ is the scale factor. At scale τ = 1 the original signal is preserved at 40 Hz and
at scale τ = 24 resampled to 1.67 Hz. At scale factor one, the time series y
1 is the
original signal and the length of each coarse-grained time series {y
τ
} is equal to the
original signal divided by the scale factor, τ. It has been suggested that the length
of signal required to obtain viable complexity measures and reported that a signal
length > 1000 samples are required which equates to 10 min captured at 40 Hz at
scale τ = 24 [83].
An example of the application of the multiscale approach is shown in Fig. 19.2