Applying a modified version of Lyapunov exponent for cancer diagnosis in biomedical images: the case of breast mammograms

Khodadadi, Hamed; Khaki‐Sedigh, Ali; Ataei, Mohammad; Jahed‐Motlagh, Mohammad Reza

doi:10.1007/s11045-016-0446-8

Cited by 14 publications

(11 citation statements)

References 36 publications

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“…Chaos theory is one of the powerful tools for discovering the mathematical biomarkers for various pathologies fields [32]. In this section, the selected chaotic indices are described and the methods of their calculations are presented.…”

Section: Methodsmentioning

confidence: 99%

“…If at least one positive LE has appeared in the LE spectrum of a time series, the chaos has emerged. For a one‐dimensional dynamical system

()(, X_{n + 1} = F false(X_{n} false))

, LE can be estimated as [32]

λ = \lim_{n false\to normal∞} \frac{1}{n} {false\sum}_{i = 0}^{n - 1} {\ln |\frac{d F (x)}{d x}|}_{x = x_{i}} .

For a multidimensional system, the number of LEs is as the same as the system dimension. Several methods such as Wolf algorithm have been employed for LEs calculation in time series in the literature.…”

Section: Methodsmentioning

confidence: 99%

“…However, these approaches calculate the largest LEs [34]. The method of this study for LEs calculation is similar to [32]. In this method, through the Time Delay Estimation (TDE) approach, the system phase space is reconstructed and named as the Reconstructed Phase Space (RPS).…”

Section: Methodsmentioning

confidence: 99%

“…In this method, via the available time series, the system state space is reconstructed. If all of the system dynamics is not accessible, the precise phase space is not available by using a time series [32]. Hence, an RPS is built which is a pseudo phase space of the system.…”

Section: Methodsmentioning

confidence: 99%

“…When the classifying is performed, four indices consist of true positive (TP), true negative (TN), false negative (FN), and false positive (FP) are computed. These features indicate the sample numbers identified as positives or negatives; properly or incorrectly [28, 32, 34]. The obtained indices are used for calculation of some classification functions such as sensitivity, specificity, and accuracy.…”

Section: Methodsmentioning

confidence: 99%

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Diagnosis of attention deficit hyperactivity disorder using non‐linear analysis of the EEG signal

Boroujeni

Khodadadi

2019

IET syst. biol.

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Attention deficit hyperactivity disorder (ADHD) is a common behavioural disorder that may be found in 5%–8% of the children. Early diagnosis of ADHD is crucial for treating the disease and reducing its harmful effects on education, employment, relationships, and life quality. On the other hand, non‐linear analysis methods are widely applied in processing the electroencephalogram (EEG) signals. It has been proved that the brain neuronal activity and its related EEG signals have chaotic behaviour. Hence, chaotic indices can be employed to classify the EEG signals. In this study, a new approach is proposed based on the combination of some non‐linear features to distinguish ADHD from normal children. Lyapunov exponent, fractal dimension, correlation dimension and sample, fuzzy and approximate entropies are the non‐linear extracted features. For computing, the chaotic time series of obtained EEG in the brain frontal lobe (FP1, FP2, F3, F4, and Fz) need to be analysed. Experiments on a set of EEG signal obtained from 50 ADHD and 26 normal cases yielded a sensitivity, specificity, and accuracy of 98, 92.31, and 96.05%, respectively. The obtained accuracy provides a significant improvement in comparison to the other similar studies in identifying and classifying children with ADHD.

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Section: Methodsmentioning

confidence: 99%

“…If at least one positive LE has appeared in the LE spectrum of a time series, the chaos has emerged. For a one‐dimensional dynamical system