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Analysis of the brain activity to external stimulation is an important area of research in biomedical engineering. In this paper, for the first time, we analyzed the brain reaction to visual stimuli with different frequencies using three complexity methods. For this purpose, we utilized fractal theory, sample entropy, and approximate entropy to study the variations of the complexity EEG signals while subjects received visual stimuli at 7, 9, 11, and 13 Hz. The results showed that, in general, by moving from 9 Hz to 13 Hz stimuli, the complexity of EEG signals increases, except in the case of 11 Hz stimulus. The statistical analysis also supported the results of the analysis. The conducted analysis in this research can be performed in the case of other types of external stimuli to study how the brain reacts in different conditions.

In this research, we investigated the effect of changes in walking speed on variations of the complexity of electromyogram (EMG) signals recorded from the right and left legs of subjects. We specifically employed fractal theory and approximate entropy to analyze the changes in the complexity of EMG signals recorded from 13 subjects walked at 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 km/h on a flat surface. The results showed that by increasing of walking speed, the complexity of EMG signals decreases. The statistical analysis also indicated the significant effect of variations in walking speed on the variations of the complexity of EMG signals. This method analysis can be applied to other physiological signals of humans (e.g. electroencephalogram (EEG) signals) to investigate the effect of walking speed on other organs’ activations (e.g. brain).

In this research, we apply complexity-based techniques to study the activations of the brain while the subjects perform different types of locomotion, including walking, jogging, and running. Therefore, we can study the effect of locomotion speed (or toughness level) on brain’s reactions. For this purpose, we analyzed the fractal dimension and approximate entropy of electroencephalogram (EEG) signals recorded from subjects while they walked, jogged, and ran for 20 s in the case of each activity. The analysis of 21 recorded samples showed that the complexity of EEG signals increases by increasing the locomotion speed. This result indicates a higher level of processing in the brain while the subjects perform a harder task. This analysis can be extended to the case of other physiological signals to study the effect of the level of exercise on different organs’ activations.

One of the important areas of research in neuroscience is to investigate how brain activity changes during aging. In this research, we employ complexity techniques to analyze how brain activity changes based on the age of subjects during sleep. For this purpose, we analyze the Electroencephalogram (EEG) signals of 22 subjects induced by sleep medication using fractal theory and sample entropy. The analysis showed that the fractal dimension and sample entropy of EEG signals decrease due to aging. Therefore, we concluded that aging causes lower complexity in EEG signals during sleep. The employed method of analysis could be applied to analyze the effect of aging on the variations of the activity of other organs (e.g. heart, muscle) during aging by studying their related physiological signals (e.g. ECG, EMG).

Since the brain controls heart activations, there should be a correlation between their activities in different conditions. This study investigates the correlation between heart and brain responses to olfactory stimulation. We employed fractal theory and sample entropy to evaluate the complexity of EEG signals and Heart Rate Variability (HRV) in the form of R–R time series. We applied four different pleasant odors with different molecular complexities to 13 participants and analyzed their EEG and ECG signals. The results demonstrated that the complexities of HRV and EEG signals are strongly correlated; a bigger alteration in the complexity of olfactory stimuli is mapped to a bigger alteration in the complexity of HRV and EEG signals. This investigation can be similarly done to examine the correlation between various organs and the brain by quantifying the complexity of their signals versus brain signals.

Our facial muscles react due to exposure to various stimuli. For example, when we sniff an odor, our facial muscles react. Since the brain controls the activities of muscles, therefore, a coupling should exist between their activities. This paper studies the coupling between the activations of the brain and facial muscles in auditory stimulation by the complexity-based analysis of Electroencephalogram (EEG) and Electromyogram (EMG) signals. Three pieces of music were chosen according to the differences in their complexities. We calculated the fractal dimension and sample entropy of EEG and EMG signals for 13 subjects in rest and response to different music. The results showed strong couplings among the alterations of the complexities of these signals and music, which indicate the correlation between brain and facial muscle activities. This complexity-based analysis could be further extended to the case of other physiological signals to decode the correlation between the responses of different organs and the brain.

This work was supported in part by Long-Term Conceptual Development of Research Organization at Institute of Technology and Business in Ceske Budejovice (2021), Project (2021/2204), Grant Agency of Excellence, University of Hradec Kralove, Faculty of Informatics and Management, Czech Republic; and by the Spanish Ministry of Science with the FEDER financing of Project PID2019103880RB-I00., The evaluation of the correlation between the activations of various organs has great importance. This work investigated the synchronization of the brain and heart responses to different auditory stimuli using complexity-based analysis. We selected three pieces of music based on the difference in the complexity of embedded noise (including white noise, brown noise, and pink noise) in them. We played these pieces of music for 11 subjects (7 M and 4 F) and computed the fractal dimension and sample entropy of EEG signals and R–R time series [as heart rate variability (HRV)]. We found strong correlations (r = 0.9999 in the case of fractal dimension and r = 0.7862 in the case of sample entropy) among the complexities of EEG signals and HRV. This finding demonstrates the synchronization of the brain and heart responses and auditory stimuli from the complexity perspective., Grant Agency of Excellence, University of Hradec Kralove, Faculty of Informatics and Management, Czech Republic, Spanish Government, European Commission PID2019103880RB-I00

Attention deficit hyperactivity disorder (ADHD) is a mental health disorder that is very common among children and may last into their adulthood. It is known that ADHD affects the attention of patients due to problems with short-term memory. Therefore, analysis of attention and memory of these patients should come into consideration. In this study, the complexity and memory of Electroencephalogram (EEG) signals are analyzed to investigate the reduction in attention and memory of patients with ADHD compared to normal subjects while playing a serious game. To achieve this, the fractal dimension and sample entropy of EEG signals are analyzed to evaluate the alterations in the complexity of EEG signals. Moreover, the Hurst exponent of EEG signals for ADHD and non-ADHD subjects is calculated to discuss the memory of EEG signals. The results showed a smaller fractal dimension and sample entropy of EEG signals for patients with ADHD that reflects their lower attention. Besides, the Hurst exponent of EEG signals for these patients reflects their lower memory than normal subjects. Therefore, it can be concluded that the reductions of attention and memory in ADHD subjects are mapped on the reduction of complexity and memory of their EEG signals.

Since skin activity, like other organs, is controlled by the brain, we decoded the correlation among the brain and skin responses in auditory stimulation by complexity-based analysis of EEG and GSR signals. Three pieces of music were selected according to the difference in the fractal exponent and sample entropy of embedded noises in them. We calculated the fractal dimension and sample entropy of EEG and GSR signals for 11 subjects in rest and response to these music pieces. The correlation coefficients of 0.9525 and 0.9822 in the case of fractal dimension and sample entropy demonstrated a strong correlation between the complexities of the GSR and EEG signals. Therefore, we can state that the skin and brain responses are coupled. This method can be applied to evaluate the relationship between the human brain and other organs.

In this paper, we investigated the learning ability of students in normal versus virtual reality (VR) watching of videos by mathematical analysis of electroencephalogram (EEG) signals. We played six videos in the 2D and 3D modes for nine subjects and calculated the Shannon entropy of recorded EEG signals to investigate how much their embedded information changes between these modes. We also calculated the Hurst exponent of EEG signals to compare the changes in the memory of signals. The analysis results showed that watching the videos in a VR condition causes greater information and memory in EEG signals. A strong correlation was obtained between the increment of information and memory of EEG signals. These increments also have been verified based on the answers that subjects gave to the questions about the content of videos. Therefore, we can say that when subjects watch a video in a VR condition, more information is transferred to their brains that cause increments in their memory.

It is known that heart activity changes during aging. In this paper, we evaluated alterations of heart activity from the complexity point of view. We analyzed the variations of heart rate of patients with congestive heart failure that are categorized into four different age groups, namely 30–39, 50–59, 60–69, and 70–79 years old. For this purpose, we employed three complexity measures that include fractal dimension, sample entropy, and approximate entropy. The results showed that the trend of increment of subjects’ age is reflected in the trend of increment of the complexity of heart rate variability (HRV) since the values of fractal dimension, approximate entropy, and sample entropy increase as subjects get older. The analysis of the complexity of other physiological signals can be further considered to investigate the variations of activity of other organs due to aging.

Evaluation of the correlation among the activities of various organs is an important research area in physiology. In this paper, we analyzed the correlation between the brain and skin reactions in response to various auditory stimuli. We played three different music (relaxing, pop, and rock music) to eleven subjects (4 M and 7 F, 18–22 years old) and accordingly analyzed the changes in the complexity of Electroencephalogram (EEG) and Galvanic Skin Response (GSR) signals by calculating their fractal exponent and sample entropy. A strong correlation was observed among the alterations of the complexity of GSR and EEG signals in the case of fractal dimension ([Formula: see text]) and also sample entropy ([Formula: see text]), which indicates the correlation between the activities of skin and brain. This analysis method could be further applied to investigate the correlation among the activities of the brain and other organs of the human body.

The coronavirus has influenced the lives of many people since its identification in 1960. In general, there are seven types of coronavirus. Although some types of this virus, including 229E, NL63, OC43, and HKU1, cause mild to moderate illness, SARS-CoV, MERS-CoV, and SARS-CoV-2 have shown to have severer effects on the human body. Specifically, the recent known type of coronavirus, SARS-CoV-2, has affected the lives of many people around the world since late 2019 with the disease named COVID-19. In this paper, for the first time, we investigated the variations among the complex structures of coronaviruses. We employed the fractal dimension, approximate entropy, and sample entropy as the measures of complexity. Based on the obtained results, SARS-CoV-2 has a significantly different complex structure than SARS-CoV and MERS-CoV. To study the high mutation rate of SARS-CoV-2, we also analyzed the long-term memory of genome walks for different coronaviruses using the Hurst exponent. The results demonstrated that the SARS-CoV-2 shows the lowest memory in its genome walk, explaining the errors in copying the sequences along the genome that results in the virus mutation.

SARS-CoV-2 is a deadly virus that has affected human life since late 2019. Between all the countries that have reported the cases of patients with SARS-CoV-2 disease (COVID-19), the United States of America has the highest number of infected people and mortality rate. Since different states in the USA reported different numbers of patients and also death cases, analyzing the difference of SARS-CoV-2 between these states has great importance. Since the generated RNA walk from the SARS-CoV-2 genome includes complex random fluctuations that also contain information, in this study, we employ the complexity and information theories to investigate the variations of SARS-CoV-2 genome between different states in the USA for the first time. The results of our analysis showed that the fractal dimension and Shannon entropy of genome walk significantly change between different states. Based on these results, we can conclude that the SARS-CoV-2 genomic structure significantly changes between different states, which is resulted from the virus evolution. Therefore, developing a vaccine for SARS-CoV-2 is very challenging since it should be able to fight various structures of the virus in different states.