TY  - JOUR
AU  - Kalauzi, Aleksandar
AU  - Vučković, Aleksandra
AU  - Bojić, Tijana
PY  - 2018
UR  - http://link.springer.com/10.1007/s11517-017-1746-3
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7746
AB  - A number of measures, stemming from nonlinear dynamics, exist to estimate complexity of biomedical objects. In most cases they are appropriate, but sometimes unconventional measures, more suited for specific objects, are needed to perform the task. In our present work, we propose three new complexity measures to quantify complexity of topographic closed loops of alpha carrier frequency phase potentials (CFPP) of healthy humans in wake and drowsy states. EEG of ten adult individuals was recorded in both states, using a 14-channel montage. For each subject and each state, a topographic loop (circular directed graph) was constructed according to CFPP values. Circular complexity measure was obtained by summing angles which directed graph edges (arrows) form with the topographic center. Longitudinal complexity was defined as the sum of all arrow lengths, while intersecting complexity was introduced by counting the number of intersections of graph edges. Wilcoxon's signed-ranks test was used on the sets of these three measures, as well as on fractal dimension values of some loop properties, to test differences between loops obtained in wake vs. drowsy. While fractal dimension values were not significantly different, longitudinal and intersecting complexities, as well as anticlockwise circularity, were significantly increased in drowsy.
T2  - Medical & Biological Engineering & Computing
T1  - New complexity measures reveal that topographic loops of human alpha phase potentials are more complex in drowsy than in wake
VL  - 56
IS  - 6
SP  - 967
EP  - 978
DO  - 10.1007/s11517-017-1746-3
ER  - 

@article{
author = "Kalauzi, Aleksandar and Vučković, Aleksandra and Bojić, Tijana",
year = "2018",
abstract = "A number of measures, stemming from nonlinear dynamics, exist to estimate complexity of biomedical objects. In most cases they are appropriate, but sometimes unconventional measures, more suited for specific objects, are needed to perform the task. In our present work, we propose three new complexity measures to quantify complexity of topographic closed loops of alpha carrier frequency phase potentials (CFPP) of healthy humans in wake and drowsy states. EEG of ten adult individuals was recorded in both states, using a 14-channel montage. For each subject and each state, a topographic loop (circular directed graph) was constructed according to CFPP values. Circular complexity measure was obtained by summing angles which directed graph edges (arrows) form with the topographic center. Longitudinal complexity was defined as the sum of all arrow lengths, while intersecting complexity was introduced by counting the number of intersections of graph edges. Wilcoxon's signed-ranks test was used on the sets of these three measures, as well as on fractal dimension values of some loop properties, to test differences between loops obtained in wake vs. drowsy. While fractal dimension values were not significantly different, longitudinal and intersecting complexities, as well as anticlockwise circularity, were significantly increased in drowsy.",
journal = "Medical & Biological Engineering & Computing",
title = "New complexity measures reveal that topographic loops of human alpha phase potentials are more complex in drowsy than in wake",
volume = "56",
number = "6",
pages = "967-978",
doi = "10.1007/s11517-017-1746-3"
}

Kalauzi, A., Vučković, A.,& Bojić, T.. (2018). New complexity measures reveal that topographic loops of human alpha phase potentials are more complex in drowsy than in wake. in Medical & Biological Engineering & Computing, 56(6), 967-978.
https://doi.org/10.1007/s11517-017-1746-3

Kalauzi A, Vučković A, Bojić T. New complexity measures reveal that topographic loops of human alpha phase potentials are more complex in drowsy than in wake. in Medical & Biological Engineering & Computing. 2018;56(6):967-978.
doi:10.1007/s11517-017-1746-3 .

Kalauzi, Aleksandar, Vučković, Aleksandra, Bojić, Tijana, "New complexity measures reveal that topographic loops of human alpha phase potentials are more complex in drowsy than in wake" in Medical & Biological Engineering & Computing, 56, no. 6 (2018):967-978,
https://doi.org/10.1007/s11517-017-1746-3 . .

TY  - JOUR
AU  - Kalauzi, Aleksandar
AU  - Vučković, Aleksandra
AU  - Bojić, Tijana
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/475
AB  - Organization of resting state cortical networks is of fundamental importance for the phenomenon of awareness, which is altered in the first part of hypnagogic period (Hori stages 1-4). Our aim was to investigate the change in brain topography pattern of EEG alpha attractor correlation dimension (CD) in the period of transition from Hori stage 1 to 4. EEG of ten healthy adult individuals was recorded in the wake and drowsy states, using a 14 channel average reference montage, from which 91 bipolar channels were derived and filtered in the wider alpha (6-14 Hz) range. Sixty 1 s long epochs of each state and individual were subjected to CD calculation according to the Grassberger-Procaccia method. For such a collection of signals, two embedding dimensions, d = {5,10}, and 22 time delays 7 = 2-23 samples were explored. Optimal values were d = 10 and 7 = 18, where both saturation and second zero crossing of the autocorrelation function occurred. Bipolar channel CD underwent a significant decrease during the transition and showed a positive linear correlation with electrode distance, stronger in the wake individuals. Topographic distribution of bipolar channels with above median CD changed from longitudinal anterior-posterior pattern (awake) to a more diagonal pattern, with localization in posterior regions (drowsiness). Our data are in line with the literature reporting functional segregation of neuronal assemblies in anterior and posterior regions during this transition. Our results should contribute to understanding of complex reorganization of the cortical part of alpha generators during the wake/drowsy transition. (C) 2014 Elsevier B.V. All rights reserved.
T2  - International Journal of Psychophysiology
T1  - Topographic distribution of EEG alpha attractor correlation dimension values in wake and drowsy states in humans
VL  - 95
IS  - 3
SP  - 278
EP  - 291
DO  - 10.1016/j.ijpsycho.2014.11.008
ER  - 

@article{
author = "Kalauzi, Aleksandar and Vučković, Aleksandra and Bojić, Tijana",
year = "2015",
abstract = "Organization of resting state cortical networks is of fundamental importance for the phenomenon of awareness, which is altered in the first part of hypnagogic period (Hori stages 1-4). Our aim was to investigate the change in brain topography pattern of EEG alpha attractor correlation dimension (CD) in the period of transition from Hori stage 1 to 4. EEG of ten healthy adult individuals was recorded in the wake and drowsy states, using a 14 channel average reference montage, from which 91 bipolar channels were derived and filtered in the wider alpha (6-14 Hz) range. Sixty 1 s long epochs of each state and individual were subjected to CD calculation according to the Grassberger-Procaccia method. For such a collection of signals, two embedding dimensions, d = {5,10}, and 22 time delays 7 = 2-23 samples were explored. Optimal values were d = 10 and 7 = 18, where both saturation and second zero crossing of the autocorrelation function occurred. Bipolar channel CD underwent a significant decrease during the transition and showed a positive linear correlation with electrode distance, stronger in the wake individuals. Topographic distribution of bipolar channels with above median CD changed from longitudinal anterior-posterior pattern (awake) to a more diagonal pattern, with localization in posterior regions (drowsiness). Our data are in line with the literature reporting functional segregation of neuronal assemblies in anterior and posterior regions during this transition. Our results should contribute to understanding of complex reorganization of the cortical part of alpha generators during the wake/drowsy transition. (C) 2014 Elsevier B.V. All rights reserved.",
journal = "International Journal of Psychophysiology",
title = "Topographic distribution of EEG alpha attractor correlation dimension values in wake and drowsy states in humans",
volume = "95",
number = "3",
pages = "278-291",
doi = "10.1016/j.ijpsycho.2014.11.008"
}

Kalauzi, A., Vučković, A.,& Bojić, T.. (2015). Topographic distribution of EEG alpha attractor correlation dimension values in wake and drowsy states in humans. in International Journal of Psychophysiology, 95(3), 278-291.
https://doi.org/10.1016/j.ijpsycho.2014.11.008

Kalauzi A, Vučković A, Bojić T. Topographic distribution of EEG alpha attractor correlation dimension values in wake and drowsy states in humans. in International Journal of Psychophysiology. 2015;95(3):278-291.
doi:10.1016/j.ijpsycho.2014.11.008 .

Kalauzi, Aleksandar, Vučković, Aleksandra, Bojić, Tijana, "Topographic distribution of EEG alpha attractor correlation dimension values in wake and drowsy states in humans" in International Journal of Psychophysiology, 95, no. 3 (2015):278-291,
https://doi.org/10.1016/j.ijpsycho.2014.11.008 . .

TY  - JOUR
AU  - Kalauzi, Aleksandar
AU  - Bojić, Tijana
AU  - Vučković, Aleksandra
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4908
AB  - The exact mathematical relationship between FFT spectrum and fractal dimension (FD) of an experimentally recorded signal is not known. In this work, we tried to calculate signal FD directly from its Fourier amplitudes. First, dependence of Higuchis FD of mathematical sinusoids on their individual frequencies was modeled with a two-parameter exponential function. Next, FD of a finite sum of sinusoids was found to be a weighted average of their FDs, weighting factors being their Fourier amplitudes raised to a fractal degree. Exponent dependence on frequency was modeled with exponential, power and logarithmic functions. A set of 280 EEG signals and Weierstrass functions were analyzed. Cross-validation was done within EEG signals and between them and Weierstrass functions. Exponential dependence of fractal exponents on frequency was found to be the most accurate. In this work, signal FD was for the first time expressed as a fractal weighted average of FD values of its Fourier components, also allowing researchers to perform direct estimation of signal fractal dimension from its FFT spectrum.
T2  - Medical and Biological Engineering and Computing
T1  - Modeling the relationship between Higuchis fractal dimension and Fourier spectra of physiological signals
VL  - 50
IS  - 7
SP  - 689
EP  - 699
DO  - 10.1007/s11517-012-0913-9
ER  - 

@article{
author = "Kalauzi, Aleksandar and Bojić, Tijana and Vučković, Aleksandra",
year = "2012",
abstract = "The exact mathematical relationship between FFT spectrum and fractal dimension (FD) of an experimentally recorded signal is not known. In this work, we tried to calculate signal FD directly from its Fourier amplitudes. First, dependence of Higuchis FD of mathematical sinusoids on their individual frequencies was modeled with a two-parameter exponential function. Next, FD of a finite sum of sinusoids was found to be a weighted average of their FDs, weighting factors being their Fourier amplitudes raised to a fractal degree. Exponent dependence on frequency was modeled with exponential, power and logarithmic functions. A set of 280 EEG signals and Weierstrass functions were analyzed. Cross-validation was done within EEG signals and between them and Weierstrass functions. Exponential dependence of fractal exponents on frequency was found to be the most accurate. In this work, signal FD was for the first time expressed as a fractal weighted average of FD values of its Fourier components, also allowing researchers to perform direct estimation of signal fractal dimension from its FFT spectrum.",
journal = "Medical and Biological Engineering and Computing",
title = "Modeling the relationship between Higuchis fractal dimension and Fourier spectra of physiological signals",
volume = "50",
number = "7",
pages = "689-699",
doi = "10.1007/s11517-012-0913-9"
}

Kalauzi, A., Bojić, T.,& Vučković, A.. (2012). Modeling the relationship between Higuchis fractal dimension and Fourier spectra of physiological signals. in Medical and Biological Engineering and Computing, 50(7), 689-699.
https://doi.org/10.1007/s11517-012-0913-9

Kalauzi A, Bojić T, Vučković A. Modeling the relationship between Higuchis fractal dimension and Fourier spectra of physiological signals. in Medical and Biological Engineering and Computing. 2012;50(7):689-699.
doi:10.1007/s11517-012-0913-9 .

Kalauzi, Aleksandar, Bojić, Tijana, Vučković, Aleksandra, "Modeling the relationship between Higuchis fractal dimension and Fourier spectra of physiological signals" in Medical and Biological Engineering and Computing, 50, no. 7 (2012):689-699,
https://doi.org/10.1007/s11517-012-0913-9 . .

TY  - JOUR
AU  - Kalauzi, Aleksandar
AU  - Vučković, Aleksandra
AU  - Bojić, Tijana
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5215
AB  - Phases of alpha oscillations recorded by EEG were typically studied in the context of event or task related experiments, rarely during spontaneous alpha activity and in different brain states. During wake-to-drowsy transition they change unevenly, depending on the brain region. To explore their dynamics, we recorded ten adult healthy individuals in these two states. Alpha waves were treated as stable frequency and variable amplitude signals with one carrier frequency (CF). A method for calculating their CF phase shifts (CFPS) and CF phase potentials (CFPP) was developed and verified on surrogate signals as more accurate than phase shifts of Fourier components. Probability density estimate (PDE) of CFPS, CFPP and CF phase locking showed that frontal and fronto-temporal areas of the cortex underwent more extensive changes than posterior regions. The greatest differences were found between pairs of channels involving F7, F8, F3 and F4 (PDE of CFPS); F7, F8. T3 and 14 (CFPP); F7, F8, F3, F4, C3, C4 and T3 (decrease in CF phase locking). A topographic distribution of channels with above the average phase locking in the wake state revealed two separate regions occupying anterior and posterior brain areas (with intra regional and inter hemispheric connections). These regions merged and became mutually phase locked longitudinally in the drowsy state. Changes occurring primarily in the frontal and fronto-temporal regions correlated with an early decrease of alertness. Areas of increased phase locking might be correlated with topography of synchronous neuronal assemblies conceptualized within neural correlates of consciousness. (C) 2012 Elsevier B.V. All rights reserved.
T2  - International Journal of Psychophysiology
T1  - EEG alpha phase shifts during transition from wakefulness to drowsiness
VL  - 86
IS  - 3
SP  - 195
EP  - 205
DO  - 10.1016/j.ijpsycho.2012.04.012
ER  - 

@article{
author = "Kalauzi, Aleksandar and Vučković, Aleksandra and Bojić, Tijana",
year = "2012",
abstract = "Phases of alpha oscillations recorded by EEG were typically studied in the context of event or task related experiments, rarely during spontaneous alpha activity and in different brain states. During wake-to-drowsy transition they change unevenly, depending on the brain region. To explore their dynamics, we recorded ten adult healthy individuals in these two states. Alpha waves were treated as stable frequency and variable amplitude signals with one carrier frequency (CF). A method for calculating their CF phase shifts (CFPS) and CF phase potentials (CFPP) was developed and verified on surrogate signals as more accurate than phase shifts of Fourier components. Probability density estimate (PDE) of CFPS, CFPP and CF phase locking showed that frontal and fronto-temporal areas of the cortex underwent more extensive changes than posterior regions. The greatest differences were found between pairs of channels involving F7, F8, F3 and F4 (PDE of CFPS); F7, F8. T3 and 14 (CFPP); F7, F8, F3, F4, C3, C4 and T3 (decrease in CF phase locking). A topographic distribution of channels with above the average phase locking in the wake state revealed two separate regions occupying anterior and posterior brain areas (with intra regional and inter hemispheric connections). These regions merged and became mutually phase locked longitudinally in the drowsy state. Changes occurring primarily in the frontal and fronto-temporal regions correlated with an early decrease of alertness. Areas of increased phase locking might be correlated with topography of synchronous neuronal assemblies conceptualized within neural correlates of consciousness. (C) 2012 Elsevier B.V. All rights reserved.",
journal = "International Journal of Psychophysiology",
title = "EEG alpha phase shifts during transition from wakefulness to drowsiness",
volume = "86",
number = "3",
pages = "195-205",
doi = "10.1016/j.ijpsycho.2012.04.012"
}

Kalauzi, A., Vučković, A.,& Bojić, T.. (2012). EEG alpha phase shifts during transition from wakefulness to drowsiness. in International Journal of Psychophysiology, 86(3), 195-205.
https://doi.org/10.1016/j.ijpsycho.2012.04.012

Kalauzi A, Vučković A, Bojić T. EEG alpha phase shifts during transition from wakefulness to drowsiness. in International Journal of Psychophysiology. 2012;86(3):195-205.
doi:10.1016/j.ijpsycho.2012.04.012 .

Kalauzi, Aleksandar, Vučković, Aleksandra, Bojić, Tijana, "EEG alpha phase shifts during transition from wakefulness to drowsiness" in International Journal of Psychophysiology, 86, no. 3 (2012):195-205,
https://doi.org/10.1016/j.ijpsycho.2012.04.012 . .

TY  - JOUR
AU  - Bojić, Tijana
AU  - Vučković, Aleksandra
AU  - Kalauzi, Aleksandar
PY  - 2010
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8869
AB  - Aim of this preliminary study was to examine and compare topographic distribution of Higuchi's fractal dimension (FD, measure of signal complexity) of EEG signals between states of relaxed wakefulness and drowsiness, as well as their FD differences. The experiments were performed on 10 healthy individuals using a fourteen-channel montage. An explanation is offered on the causes of the detected FD changes. FD values of 60 s records belonging to wake (Hori's stage 1) and drowsy (Hori's stages 2-4) states were calculated for each channel and each subject. In 136 out of 140 epochs an increase in FD was obtained. Relationship between signal FD and its relative alpha amplitude was mathematically modeled and we quantitatively demonstrated that the increase in FD was predominantly due to a reduction in alpha activity. The model was generalized to include other EEG oscillations. By averaging FD values for each channel across 10 subjects, four clusters (O2O1; T6P4T5P3; C3F3F4C4F8F7; T4T3) for the wake and two clusters (O2O1P3T6P4T5; C3C4F4F3F8T4T3F7) for the drowsy state were statistically verified. Topographic distribution of FD values in wakefulness showed a lateral symmetry and a partial fronto-occipital gradient. In drowsiness, a reduction in the number of clusters was detected, due to regrouping of channels T3, T4, O1 and O2. Topographic distribution of absolute FD differences revealed largest values at F7, O1 and F3. Reorganization of channel clusters showed that regionalized brain activity, specific for wakefulness, became more global by entering into drowsiness. Since the global increase in FD during wake-to-drowsy transition correlated with the decrease of alpha power, we inferred that increase of EEG complexity may not necessarily be an index of brain activation. © 2009 Elsevier Ltd. All rights reserved.
T2  - Journal of Theoretical Biology
T1  - Modeling EEG fractal dimension changes in wake and drowsy states in humans—a preliminary study
VL  - 262
IS  - 2
SP  - 214
EP  - 222
DO  - 10.1016/j.jtbi.2009.10.001
ER  - 

@article{
author = "Bojić, Tijana and Vučković, Aleksandra and Kalauzi, Aleksandar",
year = "2010",
abstract = "Aim of this preliminary study was to examine and compare topographic distribution of Higuchi's fractal dimension (FD, measure of signal complexity) of EEG signals between states of relaxed wakefulness and drowsiness, as well as their FD differences. The experiments were performed on 10 healthy individuals using a fourteen-channel montage. An explanation is offered on the causes of the detected FD changes. FD values of 60 s records belonging to wake (Hori's stage 1) and drowsy (Hori's stages 2-4) states were calculated for each channel and each subject. In 136 out of 140 epochs an increase in FD was obtained. Relationship between signal FD and its relative alpha amplitude was mathematically modeled and we quantitatively demonstrated that the increase in FD was predominantly due to a reduction in alpha activity. The model was generalized to include other EEG oscillations. By averaging FD values for each channel across 10 subjects, four clusters (O2O1; T6P4T5P3; C3F3F4C4F8F7; T4T3) for the wake and two clusters (O2O1P3T6P4T5; C3C4F4F3F8T4T3F7) for the drowsy state were statistically verified. Topographic distribution of FD values in wakefulness showed a lateral symmetry and a partial fronto-occipital gradient. In drowsiness, a reduction in the number of clusters was detected, due to regrouping of channels T3, T4, O1 and O2. Topographic distribution of absolute FD differences revealed largest values at F7, O1 and F3. Reorganization of channel clusters showed that regionalized brain activity, specific for wakefulness, became more global by entering into drowsiness. Since the global increase in FD during wake-to-drowsy transition correlated with the decrease of alpha power, we inferred that increase of EEG complexity may not necessarily be an index of brain activation. © 2009 Elsevier Ltd. All rights reserved.",
journal = "Journal of Theoretical Biology",
title = "Modeling EEG fractal dimension changes in wake and drowsy states in humans—a preliminary study",
volume = "262",
number = "2",
pages = "214-222",
doi = "10.1016/j.jtbi.2009.10.001"
}

Bojić, T., Vučković, A.,& Kalauzi, A.. (2010). Modeling EEG fractal dimension changes in wake and drowsy states in humans—a preliminary study. in Journal of Theoretical Biology, 262(2), 214-222.
https://doi.org/10.1016/j.jtbi.2009.10.001

Bojić T, Vučković A, Kalauzi A. Modeling EEG fractal dimension changes in wake and drowsy states in humans—a preliminary study. in Journal of Theoretical Biology. 2010;262(2):214-222.
doi:10.1016/j.jtbi.2009.10.001 .

Bojić, Tijana, Vučković, Aleksandra, Kalauzi, Aleksandar, "Modeling EEG fractal dimension changes in wake and drowsy states in humans—a preliminary study" in Journal of Theoretical Biology, 262, no. 2 (2010):214-222,
https://doi.org/10.1016/j.jtbi.2009.10.001 . .