Two Operational Modes of Cardio-Respiratory Coupling Revealed by Pulse-Respiration Quotient.

Due to the fact that respiratory breath-to-breath and cardiac intervals between two successive R peaks (BBI and RRI, respectively) are not temporally concurrent, in a previous paper, we proposed a method to calculate both the integer and non-integer parts of the pulse respiration quotient (PRQ = BBI/RRI = PRQint + b1 + b2), b1 and b2 being parts of the border RRIs for each BBI. In this work, we study the correlations between BBI and PRQ, as well as those between BBI and mean RRI within each BBI (mRRI), on a group of twenty subjects in four conditions: in supine and standing positions, in combination with spontaneous and slow breathing. Results show that the BBI vs. PRQ correlations are positive; whereas the breathing regime had little or no effect on the linear regression slopes, body posture did. Two types of scatter plots were obtained with the BBI vs. mRRI correlations: one showed points aggregated around the concurrent PRQint lines, while the other showed randomly distributed points. Five out of six of the proposed aggregation measures confirmed the existence of these two cardio-respiratory coupling regimes. We also used b1 to study the positions of R pulses relative to the respiration onsets and showed that they were more synchronous with sympathetic activation. Overall, this method should be used in different pathological states.

In Silico Screening of Natural Compounds for Candidates 5HT6 Receptor Antagonists against Alzheimer's Disease.

Alzheimer's disease (AD), a devastating neurodegenerative disease, is the focus of pharmacological research. One of the targets that attract the most attention for the potential therapy of AD is the serotonin 5HT6 receptor, which is the receptor situated exclusively in CNS on glutamatergic and GABAergic neurons. The neurochemical impact of this receptor supports the hypothesis about its role in cognitive, learning, and memory systems, which are of critical importance for AD. Natural products are a promising source of novel bioactive compounds with potential therapeutic potential as a 5HT6 receptor antagonist in the treatment of AD dementia. The ZINC-natural product database was in silico screened in order to find the candidate antagonists of 5-HT6 receptor against AD. A virtual screening protocol that includes both short-and long-range interactions between interacting molecules was employed. First, the EIIP/AQVN filter was applied for in silico screening of the ZINC database followed by 3D QSAR and molecular docking. Ten best candidate compounds were selected from the ZINC Natural Product database as potential 5HT6 Receptor antagonists and were proposed for further evaluation. The best candidate was evaluated by molecular dynamics simulations and free energy calculations.

Pulse respiration quotient as a measure sensitive to changes in dynamic behavior of cardiorespiratory coupling such as body posture and breathing regime.

Objective: In this research we explored the (homeo)dynamic character of cardiorespiratory coupling (CRC) under the influence of different body posture and breathing regimes. Our tool for it was the pulse respiration quotient (PRQ), representing the number of heartbeat intervals per breathing cycle. We obtained non-integer PRQ values using our advanced Matlab® algorithm and applied it on the signals of 20 healthy subjects in four conditions: supine position with spontaneous breathing (Supin), standing with spontaneous breathing (Stand), supine position with slow (0.1 Hz) breathing (Supin01) and standing with slow (0.1 Hz) breathing (Stand01). Main results: Linear features of CRC (in PRQ signals) were dynamically very sensitive to posture and breathing rhythm perturbations. There are obvious increases in PRQ mean level and variability under the separated and joined influence of orthostasis and slow (0.1 Hz) breathing. This increase was most pronounced in Stand01 as the state of joint influences. Importantly, PRQ dynamic modification showed greater sensitivity to body posture and breathing regime changes than mean value and standard deviation of heart rhythm and breathing rhythm. In addition, as a consequence of prolonged supine position, we noticed the tendency to integer quantization of PRQ (especially after 14 min), in which the most common quantization number was 4:1 (demonstrated in other research reports as well). In orthostasis and slow breathing, quantization can also be observed, but shifted to other values. We postulate that these results manifest resonance effects induced by coupling patterns from sympathetic and parasympathetic adjustments (with the second as dominant factor). Significance: Our research confirms that cardiorespiratory coupling adaptability could be profoundly explored by precisely calculated PRQ parameter since cardiorespiratory regulation in healthy subjects is characterized by a high level of autonomic adaptability (responsiveness) to posture and breathing regime, although comparisons with pathological states has yet to be performed. We found Stand01 to be the most provoking state for the dynamic modification of PRQ (cardiorespiratory inducement). As such, Stand01 has the potential of using for PRQ tuning by conditioning the cardiorespiratory autonomic neural networks, e.g., in the cases where PRQ is disturbed by environmental (i.e., microgravity) or pathologic conditions.

Slow 0.1 Hz Breathing and Body Posture Induced Perturbations of RRI and Respiratory Signal Complexity and Cardiorespiratory Coupling.

Objective: We explored the physiological background of the non-linear operating mode of cardiorespiratory oscillators as the fundamental question of cardiorespiratory homeodynamics and as a prerequisite for the understanding of neurocardiovascular diseases. We investigated 20 healthy human subjects for changes using electrocardiac RR interval (RRI) and respiratory signal (Resp) Detrended Fluctuation Analysis (DFA, α1RRI, α2RRI, α1Resp, α2Resp), Multiple Scaling Entropy (MSERRI1-4, MSERRI5-10, MSEResp1-4, MSEResp5-10), spectral coherence (CohRRI-Resp), cross DFA (ρ1 and ρ2) and cross MSE (XMSE1-4 and XMSE5-10) indices in four physiological conditions: supine with spontaneous breathing, standing with spontaneous breathing, supine with 0.1 Hz breathing and standing with 0.1 Hz breathing. Main results: Standing is primarily characterized by the change of RRI parameters, insensitivity to change with respiratory parameters, decrease of CohRRI-Resp and insensitivity to change of in ρ1, ρ2, XMSE1-4, and XMSE5-10. Slow breathing in supine position was characterized by the change of the linear and non-linear parameters of both signals, reflecting the dominant vagal RRI modulation and the impact of slow 0.1 Hz breathing on Resp parameters. CohRRI-Resp did not change with respect to supine position, while ρ1 increased. Slow breathing in standing reflected the qualitatively specific state of autonomic regulation with striking impact on both cardiac and respiratory parameters, with specific patterns of cardiorespiratory coupling. Significance: Our results show that cardiac and respiratory short term and long term complexity parameters have different, state dependent patterns. Sympathovagal non-linear interactions are dependent on the pattern of their activation, having different scaling properties when individually activated with respect to the state of their joint activation. All investigated states induced a change of α1 vs. α2 relationship, which can be accurately expressed by the proposed measure-inter-fractal angle θ. Short scale (α1 vs. MSE1-4) and long scale (α2 vs. MSE5-10) complexity measures had reciprocal interrelation in standing with 0.1 Hz breathing, with specific cardiorespiratory coupling pattern (ρ1 vs. XMSE1-4). These results support the hypothesis of hierarchical organization of cardiorespiratory complexity mechanisms and their recruitment in ascendant manner with respect to the increase of behavioral challenge complexity. Specific and comprehensive cardiorespiratory regulation in standing with 0.1 Hz breathing suggests this state as the potentially most beneficial maneuver for cardiorespiratory conditioning.

Generalized Poincaré plots analysis of heart period dynamics in different physiological conditions: Trained vs. untrained men.

BACKGROUND: Recently we proposed a new method called generalized Poincaré plot (gPp) analysis which gave a new insight into the pattern of neurocaridac control. In this study we examined potential of gPp method to reveal changes in cardiac neural control in young athletes during three conditions: supine rest, running and relaxation, with respect to untrained subjects. METHODS: This method is based on the quantification of Pearson's correlation coefficients r(j, k), between symmetrical (j = k) and asymmetrical summed j previous and k following RR intervals up to the 100th order (j,k≤100). RESULTS: Differences between groups were obtained at all levels of this analysis. The main result is the significant difference of NAI, normalized index of asymmetry, between groups in running, which was originated in different positions of local maxima of r(j, k). Compared with untrained subjects, these findings indicate modified neural control and altered intrinsic heart rate behavior in athletes which are related to some kind of memory mechanism between RR intervals. CONCLUSION: Obtained results provide great potential of gPp method analysis in the recognition of changes in neurocardiac control in healthy subjects. Further studies are needed for identification of altered cardiac regulatory mechanisms whose background may be useful in the evaluation of genesis of athletes neurocardiovascular pathology.

Pathophysiology of Subjective Tinnitus: Triggers and Maintenance.

Tinnitus is the conscious perception of a sound without a corresponding external acoustic stimulus, usually described as a phantom perception. One of the major challenges for tinnitus research is to understand the pathophysiological mechanisms triggering and maintaining the symptoms, especially for subjective chronic tinnitus. Our objective was to synthesize the published literature in order to provide a comprehensive update on theoretical and experimental advances and to identify further research and clinical directions. We performed literature searches in three electronic databases, complemented by scanning reference lists from relevant reviews in our included records, citation searching of the included articles using Web of Science, and manual searching of the last 6 months of principal otology journals. One-hundred and thirty-two records were included in the review and the information related to peripheral and central mechanisms of tinnitus pathophysiology was collected in order to update on theories and models. A narrative synthesis examined the main themes arising from this information. Tinnitus pathophysiology is complex and multifactorial, involving the auditory and non-auditory systems. Recent theories assume the necessary involvement of extra-auditory brain regions for tinnitus to reach consciousness. Tinnitus engages multiple active dynamic and overlapping networks. We conclude that advancing knowledge concerning the origin and maintenance of specific tinnitus subtypes origin and maintenance mechanisms is of paramount importance for identifying adequate treatment.

New complexity measures reveal that topographic loops of human alpha phase potentials are more complex in drowsy than in wake.

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. Graphical abstract An example of closed topographic carrier frequency phase potential (CFPP) loops, recorded in one of the subjects in the wake (A) and drowsy (C) states. Lengths of loop graph edges, r(c j, c j + 1), plotted against the series of EEG channels with decreasing CFPP values, c j , in the wake (B) and drowsy (D) states. Conventional fractal analysis did not reveal any difference between them; therefore, three new complexity measures were introduced.

Identification of Candidate Allosteric Modulators of the M1 Muscarinic Acetylcholine Receptor Which May Improve Vagus Nerve Stimulation in Chronic Tinnitus.

Chronic tinnitus is characterized by neuroplastic changes of the auditory cortex. A promising method for therapy of chronic tinnitus is vagus nerve stimulation (VNS) combined with auditory stimulation. The principle of VNS is reversal of pathological neuroplastic changes of the auditory cortex toward physiological neural activity and synchronicity. The VNS mechanism of action in chronic tinnitus patients is prevailingly through the muscarinic neuromodulation of the auditory cortex by the activation of nc. basalis Meynerti. The aim of this study is to propose potential pharmaceutics which may improve the neuromodulatory effects of VNS. The working hypothesis is that M1 receptors have a dominant role in the neural plasticity of the auditory cortex. We propose that allosteric agonists of the muscarinic receptor type 1 (M1) receptor could improve specificity and selectivity of the neuromodulatory effect of VNS on the auditory cortex of chronic tinnitus patients even in the circumstances of lower acetylcholine brain concentration. This intervention would also reinforce the re-learning process of tinnitus (sub)networks by acting on cholinergic memory and learning mechanisms. We performed in silico screening of drug space using the EIIP/AQVN filter and selected 50 drugs as candidates for allosteric modulators of muscarinic receptors. Further filtering of these compounds by means of 3D QSAR and docking revealed 3 approved drugs-bromazepam, estazolam and flumazenil as the most promising candidates for combined chronic tinnitus therapy. These drugs should be further evaluated by biological tests and clinical trials.

Uncoupling of cardiac and respiratory rhythm in atrial fibrillation.

Rearranged origin of heart rhythm in patients with atrial fibrillation (AF) influences the regulation of the heart and consequently the respiratory rhythm, and the bidirectional interaction of these rhythms not documented. Hence, we examined coupling of the RR interval and the respiration (Resp) signal by coherence, Granger causality and the cross-sample entropy method of time series analysis in patients with AF and a healthy control group. In healthy subjects, the influence of respiration on cardiac rhythm was found as increased coherence at the breathing frequency (BF) range, significantly stronger interaction and synchrony from Resp to RR than from RR to Resp. On the contrary, in patients with AF, coherence at BF diminished, there were no causal interactions between signals in both directions, which resulted in equally great asynchrony between them. In AF, the absence of full functionality of the sinoatrial node, as an integrator of neural cardiac control, resulted in diminished vagal modulation of heart periods and consequently impaired bidirectional cardio-respiratory interaction.

Common molecular mechanism of the hepatic lesion and the cardiac parasympathetic regulation in chronic hepatitis C infection: a critical role for the muscarinic receptor type 3.

BACKGROUND: The pathophysiological overlapping between Sjorgen's Syndrome (SS) and HCV, presence of anti- muscarinic receptor type 3 (M3R) antibodies in SS, the role that M3R plays in the regulation of the heart rate, has led to the assumption that cardiovagal dysfunction in HCV patients is caused by anti-M3R antibodies elicited by HCV proteins or by their direct interaction with M3R. RESULTS: To identify HCV protein which possibly is crossreactive with M3R or which binds to this receptor, we performed the Informational Spectrum Method (ISM) analysis of the HCV proteome. This analysis revealed that NS5A protein represents the most probable interactor of M3R or that this viral protein could elicit antibodies which modulate function of this receptor. Further detailed structure/function analysis of NS5A and M3R performed by the ISM method extended with other Digital Signal processing (DSP) approaches revealed domains of these proteins which participate in their crossreactivity or in their direct interaction, representing promising diagnostic and therapeutic targets. CONCLUSIONS: Application of the ISM with other compatible bioinformatics methods offers new perspectives for identifying diagnostic and therapeutic targets for complicated forms of HCV and other viral infections. We show how the electron-ion interaction potential (EIIP) amino-acid scale used in the ISM combined with a robust, high performance hydrophobicity scale can provide new insights for understanding protein structure/function and protein-protein interactions.

Generalized Poincaré Plots-A New Method for Evaluation of Regimes in Cardiac Neural Control in Atrial Fibrillation and Healthy Subjects.

Classical Poincaré plot is a standard way to measure nonlinear regulation of cardiovascular control. In our work we propose a generalized form of Poincaré plot where we track correlation between the duration of j preceding and k next RR intervals. The investigation was done in healthy subjects and patients with atrial fibrillation, by varying j,k ≤ 100. In cases where j = k, in healthy subjects the typical pattern was observed by "paths" that were substituting scatterplots and that were initiated and ended by loops of Poincaré plot points. This was not the case for atrial fibrillation patients where Poincaré plot had a simple scattered form. More, a typical matrix of Pearson's correlation coefficients, r(j,k), showed different positions of local maxima, depending on the subject's health condition. In both groups, local maxima were grouped into four clusters which probably determined specific regulatory mechanisms according to correlations between the duration of symmetric and asymmetric observed RR intervals. We quantified matrices' degrees of asymmetry and found that they were significantly different: distributed around zero in healthy, while being negative in atrial fibrillation. Also, Pearson's coefficients were higher in healthy than in atrial fibrillation or in signals with reshuffled intervals. Our hypothesis is that by this novel method we can observe heart rate regimes typical for baseline conditions and "defense reaction" in healthy subjects. These data indicate that neural control mechanisms of heart rate are operating in healthy subjects in contrast with atrial fibrillation, identifying it as the state of risk for stress-dependent pathologies. Regulatory regimes of heart rate can be further quantified and explored by the proposed novel method.

Topographic distribution of EEG alpha attractor correlation dimension values in wake and drowsy states in humans.

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 1s 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 τ=2-23 samples were explored. Optimal values were d=10 and τ=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.

In silico Therapeutics for Neurogenic Hypertension and Vasovagal Syncope.

Neurocardiovascular diseases (NCVD) are the leading cause of death in the developed world and will remain so till 2020. In these diseases the pathologically changed nervous control of cardiovascular system has the central role. The actual NCV syndromes are neurogenic hypertension, representing the sympathetically mediated disorder, and vasovagal syncope, which is the vagally mediated disorders. Vasovagal syncope, the disease far from its etiological treatment, could benefit from recruiting and application of antimuscarinic drugs used in other parasympathetic disorders. The informational spectrum method (ISM), a method widely applied for the characterization of protein-protein interactions in the field of immunology, endocrinology and anti HIV drug discovery, was applied for the first time in the analysis of neurogenic hypertension and vasovagal syncope therapeutic targets. In silico analysis revealed the potential involvement of apelin in neurogenic hypertension. Applying the EIIP/ISM bioinformatics concept in investigation of drugs for treatment of vasovagal syncope suggests that 78% of tested antimuscarinic drugs could have anti vasovagal syncope effect. The presented results confirm that ISM is a promissing method for investigation of molecular mechanisms underlying pathophysiological proceses of NCV syndromes and discovery of therapeutics targets for their treatment.

Nonlinear properties of cardiac rhythm and respiratory signal under paced breathing in young and middle-aged healthy subjects.

We examined the effects of gender and age in young and middle-aged subjects on the level of cardio-respiratory interaction by analyzing properties of cardiac, respiratory and cardiac-respiratory regulatory mechanisms under paced breathing. In 56 healthy subjects, ECG (RR interval) and respiratory signal were simultaneously acquired in supine position at paced (0.1-0.45 Hz, steps of 0.05 Hz) and spontaneous breathing. The participants were divided into gender matched group of young adults (19-25 years old) and middle-aged adults (35-44 years old). Power spectral analysis was applied on RR interval time series and spectral components in very low frequency (VLF), low frequency (LF) and high frequency (HF) ranges were computed. We also calculated sample entropy of RR interval series (SampEnRR), respiratory series (SampEnResp), and their cross-sample entropy (cross-SampEn). Under paced breathing, reduction of all spectral powers with age (p<0.05) is not gender dependent but reduction of some entropy measures is; SampEnRR and SampEnResp were lower only in men (p<0.05). In the middle-aged subjects, effect of gender on spectral measures is significant; males had lower HF (p < 0.05). Pattern of dependencies of SampEn and cross-SampEn on paced breathing frequency were significantly different in men (young vs. middle-aged, p = 0.001 and p = 0.037) and in middle-aged subjects (females vs. males, p = 0.011 and p = 0.008). In middle-aged males, lower entropy measures indicated reduced and less complex partial cardiac and respiratory control, and central cardio-respiratory control. In conclusion, in healthy middle-aged subjects changes in cardio-respiratory coupling are detectable only in males.

RR interval-respiratory signal waveform modeling in human slow paced and spontaneous breathing.

Our aim was to model the dependence of respiratory sinus arrhythmia (RSA) on the respiratory waveform and to elucidate underlying mechanisms of cardiorespiratory coupling. In 30 subjects, RR interval and respiratory signal were recorded during spontaneous and paced (0.1Hz/0.15Hz) breathing and their relationship was modeled by a first order linear differential equation. This model has two parameters: a0 (related to the instantaneous degree of abdominal expansion) and a1 (referring to the speed of abdominal expansion). Assuming that a0 represents slowly adapting pulmonary stretch receptors (SARs) and a1 SARs in coordination with other stretch receptors and central integrative coupling; then pulmonary stretch receptors relaying the instantaneous lung volume are the major factor determining cardiovagal output during inspiration. The model's results depended on breathing frequency with the least error occurring during slow paced breathing. The role of vagal afferent neurons in cardiorespiratory coupling may relate to neurocardiovascular diseases in which weakened coupling among venous return, arterial pressure, heart rate and respiration produces cardiovagal instability.

Influenza vaccine as prevention for cardiovascular diseases: possible molecular mechanism.

Despite plausible evidence for beneficial effects of the vaccination against influenza in cardiovascular diseases (CVD) very limited studies have been carried out to explain the molecular mechanism of this phenomenon. Using the informational spectrum method (ISM), a virtual spectroscopy method for analysis of protein-protein interactions, the bradykinin 2 receptor (BKB2R) was identified as a principal host protein which could mediate molecular processes underlying the cardioprotective effect of influenza vaccines. Based on this finding we suggest that some antibodies elicited by influenza vaccines act as agonists, which activate a BKB2R-associated signaling pathway contributing to the protection against CVD. The ISM analysis of 14 influenza viruses, which were used as components of seasonal vaccines, revealed four vaccine viruses A/Beijing/262/95(H1N1), A/NewCaledonia/20/1999(H1N1), A/Christchurch/28/2003(H3N2) and A/Perth/16/2009(H3N2), which could be suited best for further studies on the cardioprotective effect of influenza vaccines.

EEG alpha phase shifts during transition from wakefulness to drowsiness.

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 T4 (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.

Modeling the relationship between Higuchi's fractal dimension and Fourier spectra of physiological signals.

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 Higuchi's 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.