Significance of trends in gait dynamics.

Trends in time series generated by physiological control systems are ubiquitous. Determining whether trends arise from intrinsic system dynamics or originate outside of the system is a fundamental problem of fractal series analysis. In the latter case, it is necessary to filter out the trends before attempting to quantify correlations in the noise (residuals). For over two decades, detrended fluctuation analysis (DFA) has been used to calculate scaling exponents of stride time (ST), stride length (SL), and stride speed (SS) of human gait. Herein, rather than relying on the very specific form of detrending characteristic of DFA, we adopt Multivariate Adaptive Regression Splines (MARS) to explicitly determine trends in spatio-temporal gait parameters during treadmill walking. Then, we use the madogram estimator to calculate the scaling exponent of the corresponding MARS residuals. The durations of ST and SL trends are determined to be independent of treadmill speed and have distributions with exponential tails. At all speeds considered, the trends of ST and SL are strongly correlated and are statistically independent of their corresponding residuals. The averages of scaling exponents of ST and SL MARS residuals are slightly smaller than 0.5. Thus, contrary to the interpretation prevalent in the literature, the statistical properties of ST and SL time series originate from the superposition of large scale trends and small scale fluctuations. We show that trends serve as the control manifolds about which ST and SL fluctuate. Moreover, the trend speed, defined as the ratio of instantaneous values of SL and ST trends, is tightly controlled about the treadmill speed. The strong coupling between the ST and SL trends ensures that the concomitant changes of their values correspond to movement along the constant speed goal equivalent manifold as postulated by Dingwell et al. 10.1371/journal.pcbi.1000856.

Alpha Wavelet Power as a Biomarker of Antidepressant Treatment Response in Bipolar Depression.

There is mounting evidence of a link between the properties of electroencephalograms (EEGs) of depressive patients and the outcome of pharmacotherapy. The goal of this study was to develop an EEG biomarker of antidepressant treatment response which would require only a single EEG measurement. We recorded resting 21-channel EEG in 17 in-patients suffering from bipolar depression in eyes-closed and eyes-open conditions. The EEG measurement was performed at the end of a short washout period which followed previous unsuccessful pharmacotherapy. We calculated the normalized wavelet power of alpha rhythm using two referential montages and an average reference montage. The difference in the normalized alpha wavelet power between 10 responders and 7 non-responders was most strongly pronounced in link mastoid montage in the eyes-closed condition. In particular, in the occipital (O1, O2, Oz) channels the wavelet power of responders was up to 84 % higher than that of non-responders. Using a novel classification algorithm we were able to correctly predict the outcome of treatment with 90 % sensitivity and 100 % specificity. The proposed biomarker requires only a single EEG measurement and consequently is intrinsically different from biomarkers which exploit the changes in prefrontal EEG induced by pharmacotherapy over a given time.

Dynamic cerebral autoregulation is compromised in ischaemic stroke of undetermined aetiology only in the non-affected hemisphere.

BACKGROUND AND PURPOSE: To assess dynamic cerebral autoregulation (CA) in patients with acute ischaemic stroke of undetermined aetiology, within 72h of stroke onset. MATERIALS AND METHODS: In 6 patients with ischaemic stroke of undetermined aetiology (aged 66±9 years, National Institutes of Health Stroke Scale [NIHSS] score on admission: 4.0, range: 4-11), selected based on screening of 118 consecutive ischaemic stroke patients and in 14 volunteers (aged 62±10 years), we continuously monitored RR intervals (RRI), mean arterial pressure (MAP) by means of photoplethysmography, mean cerebral blood flow velocity (CBFV) using transcranial Doppler ultrasonography, end-tidal CO2 (ETCO2) and respiration during 2-min deep breathing paced at 6min(-1) (0.1Hz). To assess CA, we evaluated the impact of breathing-induced MAP oscillations on fluctuations of CBFV in the hemispheres with stroke, the non-involved hemispheres and randomly selected hemispheres of controls by applying cross-spectral analysis and calculating coherence, transfer function gain (CBFV-MAP gain) and phase shift angle between the two oscillating signals. RESULTS: Phase shift angle between MAP and CBFV oscillations showed values >0 and was significantly reduced in the hemispheres without stroke as compared to controls (0.39±0.95 vs. -1.59±0.33rad, p=0.015), whereas in the hemispheres with stroke, phase shift angle did not differ significantly from that observed in the control hemispheres. Clinical status of stroke patients significantly improved at discharge from the hospital (NIHSS: 2.0, range: 1-8, p=0.028). CONCLUSIONS: During the first days of ischaemic stroke of undetermined aetiology, dynamic cerebral autoregulation is compromised in the non-affected hemisphere, but not in the hemisphere with ischaemic lesion.

Association of Serum Proteases and Acute Phase Factors Levels with Survival Outcomes in Patients with Colorectal Cancer.

Colorectal cancer (CRC) represents a substantial burden on global healthcare, contributing to significant morbidity and mortality worldwide. Despite advances in screening methodologies, its incidence remains high, necessitating continued efforts in early detection and treatment. Neoplastic invasion and metastasis are primary determinants of CRC lethality, emphasizing the urgency of understanding underlying mechanisms to develop effective therapeutic strategies. This study aimed to explore the potential of serum biomarkers in predicting survival outcomes in CRC patients, with a focus on cathepsin B (CB), leukocytic elastase (LE), total sialic acid (TSA), lipid-associated sialic acid (LASA), antitrypsin activity (ATA), C-reactive protein (CRP), and cystatin C (CC). We recruited 185 CRC patients and 35 healthy controls, assessing demographic variables, tumor characteristics, and 7 serum biomarker levels, including (1) CB, (2) LE, (3) TSA, (4) LASA, (5) ATA, (6) CRP, and (7) CC. Statistical analyses included ANOVA with Tukey's post hoc tests and MANOVA for continuous variables. Student's t-test was used for dependent samples, while non-parametric tests like Mann-Whitney U and Wilcoxon signed-rank tests were applied for variables deviating from the normal distribution. Categorical variables were assessed using chi-square and Kruskal-Wallis tests. Spearman's rank correlation coefficient was utilized to examine variable correlations. Survival analysis employed the Kaplan-Meier method with a log-rank test for comparing survival times between groups. Significant associations were observed between CB (p = 0.04), LE (p = 0.01), and TSA (p = 0.008) levels and survival outcomes in CRC patients. Dukes' classification stages also showed a significant correlation with survival (p = 0.001). However, no significant associations were found for LASA, ATA, CRP, and CC. Multivariate analysis of LE, TSA, and ATA demonstrated a notable correlation with survival (p = 0.041), notwithstanding ATA's lack of significance in univariate analysis (p = 0.13). CB, LE, and TSA emerged as promising diagnostic markers with prognostic value in CRC, potentially aiding in early diagnosis and treatment planning. Further research is needed to validate these findings and explore additional prognostic indicators.

EEG phase synchronization during absence seizures.

Absence seizures-generalized rhythmic spike-and-wave discharges (SWDs) are the defining property of childhood (CAE) and juvenile (JAE) absence epilepsies. Such seizures are the most compelling examples of pathological neuronal hypersynchrony. All the absence detection algorithms proposed so far have been derived from the properties of individual SWDs. In this work, we investigate EEG phase synchronization in patients with CAE/JAE and healthy subjects to explore the possibility of using the wavelet phase synchronization index to detect seizures and quantify their disorganization (fragmentation). The overlap of the ictal and interictal probability density functions was high enough to preclude effective seizure detection based solely on changes in EEG synchronization. We used a machine learning classifier with the phase synchronization index (calculated for 1 s data segments with 0.5 s overlap) and the normalized amplitude as features to detect generalized SWDs. Using 19 channels (10-20 setup), we identified 99.2% of absences. However, the overlap of the segments classified as ictal with seizures was only 83%. The analysis showed that seizures were disorganized in approximately half of the 65 subjects. On average, generalized SWDs lasted about 80% of the duration of abnormal EEG activity. The disruption of the ictal rhythm can manifest itself as the disappearance of epileptic spikes (with high-amplitude delta waves persisting), transient cessation of epileptic discharges, or loss of global synchronization. The detector can analyze a real-time data stream. Its performance is good for a six-channel setup (Fp1, Fp2, F7, F8, O1, O2), which can be implemented as an unobtrusive EEG headband. False detections are rare for controls and young adults (0.03% and 0.02%, respectively). In patients, they are more frequent (0.5%), but in approximately 82% cases, classification errors are caused by short epileptiform discharges. Most importantly, the proposed detector can be applied to parts of EEG with abnormal EEG activity to quantitatively determine seizure fragmentation. This property is important because a previous study reported that the probability of disorganized discharges is eight times higher in JAE than in CAE. Future research must establish whether seizure properties (frequency, length, fragmentation, etc.) and clinical characteristics can help distinguish CAE and JAE.

Persistence and anti-persistence in treadmill walking.

BACKGROUND: Strong, long-range persistent correlations in stride time (ST) and length (SL) are the fundamental traits of treadmill gait. Our recent work showed that the ST and SL time series' statistical properties originated from the superposition of large-scale trends and small-scale fluctuations (residuals). Trends served as the control manifolds about which ST and SL fluctuated. RESEARCH QUESTION: Do random changes in treadmill belt speed affect the trend properties and ST/SL scaling exponents? METHODS: We used Multivariate Adaptive Regression Splines (MARS) to determine gait trends during a walk on a treadmill whose belt speed was perturbed by a strong random noise (coefficient of variation was equal to 0.075, 0.1, and 0.13 for treadmill speed 0.8 m/s, 1.2 m/s, and 1.6 m/s, respectively). Then, we calculated the ST/SL scaling exponents of the experimental time series and the corresponding MARS residuals with the madogram estimator. RESULTS: Except for the ST at the lowest treadmill speed, the normalized trend duration was at least two times greater than that for the unperturbed walk. The Cauchy distribution scale parameter, which served as a measure of the width of SL and ST trend slope distributions, was at v=1.2m/s, almost 50% and 25% smaller than the unperturbed values. The differences were even greater at v=1.6 m/s: 73% and 83%. Apart from ST at v=0.8m/s, the ST/SL scaling indices were close to 0.5. For all speeds, the ST and SL MARS residuals were strongly anti-persistent. At v=1.2m/s, the corresponding scaling exponents were equal to 0.37±0.10 and 0.25±0.09. SIGNIFICANCE: At normal and moderate treadmill speeds, in the presence of random belt speed perturbations, strongly anti-persistent fluctuations about gentle, persistent trends can lead to weak persistence/antipersistence of ST/SL time series.

Diagnostic usefulness of selected proteases and acute phase factors in patients with colorectal adenocarcinoma.

BACKGROUND: Uncontrolled growth and loss of control over basic metabolic functions, leading to invasive proliferation and metastases, are the salient traits of malignant tumors in general and colorectal cancer in particular. Invasion and metastases hinder effective tumor treatment. While surgical techniques and radiotherapy can be used to remove tumor focus, only chemotherapy can eliminate dispersed neoplastic cells. However, the efficacy of the latter method is limited in the advanced stages of the disease. Therefore, recognition of the mechanisms involved in neoplastic cell spreading is indispensable for developing effective therapies. AIM: To use a number of biomarkers involved in cancer progression and identify a panel that could be used for effective early diagnosis. METHODS: We recruited 185 patients with colorectal adenocarcinoma (98 men, 87 women with median age 63). Thirty-five healthy controls were sex and age-matched. Dukes' staging was as follows: A = 22, B = 52, C = 72, D = 39. We analyzed patients' blood serum before surgery. We determined: (1) Cathepsin B (CB) with Barrett's method (fluorogenic substrate); (2) Leukocytic elastase (LE) in a complex with alpha 1 trypsin inhibitor (AAT) using the immunoenzymatic MERCK test; (3) Total sialic acid (TSA) with the colorimetric periodate-resorcinol method; (4) Lipid-bound sialic acid (LASA) with the colorimetric Taut's method; and (5) The antitrypsin activity (ATA) employing the colorimetric test. RESULTS: In patients, the values of the five biochemical parameters were as follows: CB = 16.1 ± 8.8 mU/L, LE = 875 ± 598 µg/L, TSA = 99 ± 31 mg%, LASA = 0.68 ± 0.33 mg%, and ATA = 3211 ± 1504 U/mL. Except for LASA, they were significantly greater than those of controls: CB = 11.4 ± 6.5 mU/L, LE = 379 ± 187 µg/L, TSA = 71.4 ± 15.1 mg%, LASA = 0.69 ± 0.28 mg%, and ATA = 2016 ± 690 U/mL. For CB and LASA, the differences between the four Dukes' stages and controls were not statistically significant. The inter-stage differences for CB and LASA were also absent. The receiver operating characteristic (ROC) analysis revealed the potential diagnostic value of CB, TSA, and ATA. The area under ROC, sensitivity, and specificity for these three parameters were: 0.85, 72%, 90%; 0.75, 66%, 77%; and 0.77, 63%, 84%, respectively. The sensitivity and specificity for the three-parameter panel CB-TSA-ATA were equal to 88.2% and 100%, respectively. CONCLUSION: The increased value of CB, TSA, and ATA parameters are associated with tumor biology, invasion, and metastasis of colorectal cancer. The presented evidence suggests the potential value of the CB-TSA-ATA biochemical marker panel in early diagnostics.

Efficacy of DiscoGel in Treatment of Degenerative Disc Disease: A Prospective 1-Year Observation of 67 Patients.

Patients with degenerative disc disease may suffer from chronic lumbar discogenic (DP) or radicular leg (RLP) pain. Minimally invasive DiscoGel therapy involves the percutaneous injection of an ethanol gel into the degenerated disk's nucleus pulposus. This paper compares the 1-year outcome of such treatment in DP and RLP patients. We operated on 67 patients (49 men and 18 women) aged 20-68 years (mean age 46 ± 11 years) with DP (n = 45) and RLP (n = 22), of at least 6-8 weeks duration, with no adverse effects. We evaluated the treatment outcome with Core Outcome Measures Index (COMI) and Visual Analog Scale (VAS). A year after the ethanol gel injection, in the DP cohort, COMI and VAS dropped by 66% (6.40 vs. 2.20) and 53% (6.33 vs. 2.97), respectively. For the RLP patients, the corresponding values dropped 48% (7.05 vs. 3.68) and 54% (6.77 vs. 3.13). There were no differences between the cohorts in COMI and VAS at the follow-up end. Six months into the study, 74% of DP and 81% of RLP patients did not use any analgesics. Ethanol gel therapy can be effective for many patients. Moreover, its potential failure does not exclude surgical treatment options.

Absence Seizure Detection Algorithm for Portable EEG Devices.

Absence seizures are generalized nonmotor epileptic seizures with abrupt onset and termination. Transient impairment of consciousness and spike-slow wave discharges (SWDs) in EEG are their characteristic manifestations. This type of seizure is severe in two common pediatric syndromes: childhood (CAE) and juvenile (JAE) absence epilepsy. The appearance of low-cost, portable EEG devices has paved the way for long-term, remote monitoring of CAE and JAE patients. The potential benefits of this kind of monitoring include facilitating diagnosis, personalized drug titration, and determining the duration of pharmacotherapy. Herein, we present a novel absence detection algorithm based on the properties of the complex Morlet continuous wavelet transform of SWDs. We used a dataset containing EEGs from 64 patients (37 h of recordings with almost 400 seizures) and 30 age and sex-matched controls (9 h of recordings) for development and testing. For seizures lasting longer than 2 s, the detector, which analyzed two bipolar EEG channels (Fp1-T3 and Fp2-T4), achieved a sensitivity of 97.6% with 0.7/h detection rate. In the patients, all false detections were associated with epileptiform discharges, which did not yield clinical manifestations. When the duration threshold was raised to 3 s, the false detection rate fell to 0.5/h. The overlap of automatically detected seizures with the actual seizures was equal to ~96%. For EEG recordings sampled at 250 Hz, the one-channel processing speed for midrange smartphones running Android 10 (about 0.2 s per 1 min of EEG) was high enough for real-time seizure detection.

[The empirical mode decomposition and Lempel-Ziv complexity. The new possibility in diagnosis of EEG in schizophrenic patients?]. / Empiryczna dekompozycja modalna i metoda zlozonosci Lempel-Ziv'a. Nowa mozliwosc w diagnostyce EEG chorych na schizofrenie?

BACKGROUND: Over the last few decades, numerous attempts have been made to identify electroencephalographic (EEG) manifestations of schizophrenia. However, clinical applicability of these studies has not been demonstrated. MATERIAL AND METHODS: A novel approach to EEG analysis which is based on combination of two methods of time series analysis was presented. Empirical mode decomposition is used to decompose a signal into several independent mode functions (IMF). Then, Lempel-Ziv complexity is used to quantify variability of such modes. We dub this approach EMD-LZC analysis. We carry out EMD-LZC analysis of EEG (performed according to 10-20 standard) of 21 healthy volunteers and 19 schizophrenic patients who were not medicated for at least a week. RESULTS: We find that variability of the third IMF mode is lower in the patients. The statistically significant differences were observed in 14 channels. Interestingly enough, the Fourier power spectra of both cohorts were not statistically different in any of 19 EEG channels. CONCLUSIONS: Unlike traditional spectral analysis, the combination of empirical mode decomposition and Lempel-Ziv complexity enabled us to identify the properties of EEG that are affected by schizophrenia. The future, more extensive, studies should verify the applicability of the proposed algorithm to diagnostics of schizophrenia. Moreover, we would like to link the observed differences in EEG variability to the pathogenesis of this disease.

Changes in Interictal Pretreatment and Posttreatment EEG in Childhood Absence Epilepsy.

Spike and wave discharges (SWDs) are a characteristic manifestation of childhood absence epilepsy (CAE). It has long been believed that they unpredictably emerge from otherwise almost normal interictal EEG. Herein, we demonstrate that pretreatment closed-eyes theta and beta EEG wavelet powers of CAE patients (20 girls and 10 boys, mean age 7.4 ± 1.9 years) are much higher than those of age-matched healthy controls at multiple sites of the 10-20 system. For example, at the C4 site, we observed a 100 and 63% increase in power of theta and beta rhythms, respectively. We were able to compare the baseline and posttreatment wavelet power in 16 patients. Pharmacotherapy brought about a statistically significant decrease in delta and theta wavelet power in all the channels, e.g., for C4 the reduction was equal to 45% (delta) and 63% (theta). The less pronounced attenuation of posttreatment beta waves was observed in 13 channels (36% at C4 site). The beta and theta wavelet power were positively correlated with the percentage of time in seizure (defined as the ratio of the duration of all absences which patients experienced to the duration of recording) for majority of channels. We hypothesize that the increased theta and beta powers result from cortical hyperexcitability and propensity for epileptic spike generation, respectively. We argue that the distinct features of CAE wavelet power spectrum may be used to define an EEG biomarker which could be used for diagnosis and monitoring of patients.

Safety and efficacy of cervical disc arthroplasty in preventing the adjacent segment disease: a meta-analysis of mid- to long-term outcomes in prospective, randomized, controlled multicenter studies.

OBJECTIVES: Cervical disc arthroplasty (CDA) has become an alternative treatment for cervical radiculopathy and myelopathy. This technique preserves appropriate motion at both the index and adjacent disc levels and consequently may prevent adjacent segment degeneration (ASD). The authors performed a meta-analysis to compare the safety and efficacy of CDA to those of the gold standard, anterior cervical discectomy and fusion (ACDF). Both surgical and clinical parameters were employed to verify the hypothesis that CDA can reduce the risk of ASD. METHODS: The meta-analysis comprised high-quality randomized controlled trials that compared CDA and ACDF treatments of cervical degenerative disc disease. Included papers reported data for at least one of the following outcomes: 1) surgical parameters, 2) questionnaire clinical indices (pre- and postoperative values), and 3) complication rates at 24 months; in addition, for ASD we analyzed 60 month or longer follow-ups. We used mean differences (MDs) or ORs to compare treatment effects between CDA and ACDF. RESULTS: Twenty studies with 3,656 patients (2,140 with CDA and 1,516 with ACDF) met the inclusion criteria. CDA surgery, with mean duration longer than that of ACDF, was associated with higher blood loss. Visual analog scale neck pain score was significantly smaller for CDA (mean difference =-2.30, 95% CI [-3.72; -0.87], P=0.002). The frequency of dysphagia/dysphonia (OR =0.69, 95% CI [0.49; 0.98], P=0.04) as well as the long-term ASD rate for CDA was significantly smaller (OR =0.33, 95% CI [0.21; 0.50], P<0.0001). CONCLUSION: A significantly lower probability of ASD reoperations in the CDA cohort after a 60-month or longer follow-up was the most important finding of this study. Despite the moderate quality of this evidence, the pooled data corroborated for the very first time that CDA was efficacious in preventing ASD.

Generation of very low frequency cerebral blood flow fluctuations in humans.

BACKGROUND: Slow oscillations of cerebral blood flow induced by synchronous variations of arterial blood pressure (ABP) are often used for clinical assessment of cerebral autoregulation. In the alternative scenario, spontaneous cerebral vasocycling may produce waves in cerebral blood flow that are, to a large extent, independent of ABP fluctuations. We use wavelet analysis to test the latter hypothesis. METHODS: The wavelet variability V(f), defined as the time averaged moduli of frequency dependent wavelet coefficients, is employed to analyze the relation between dynamics of arterial blood pressure and that of cerebral blood flow velocity in middle cerebral artery (MCA). FINDINGS: In the very low frequency (VLF, 0.02-0.07 Hz) band the variability in traumatic brain injury (TBI) patients with low intracranial pressure (V(ABP) = 0.36 +/- 0.28) is significantly smaller than that of the volunteers (V(ABP) = 0.70 +/- 0.25) with p = 7 x 10(-5). Interestingly, the corresponding variabilities of MCA flow velocity for both cohorts are comparable. V(MCA) = 0.83 +/- 0.65 of the brain injury patients is not statistically different from that of the volunteers V(MCA) = 1.06 +/- 0.41 (p = 0.11). CONCLUSIONS: In TBI patients without cerebral hypertension, the VLF oscillations must have been spontaneously generated within intracranial volume to compensate for the reduced ABP variability. Vasomotion is identified as a plausible physiological mechanism underlying such oscillations. We argue that vasomotion may be beneficial for brain tissue oxygenation especially during periods of critically low perfusion.

Asymmetry of short-term control of spatio-temporal gait parameters during treadmill walking.

Optimization of energy cost determines average values of spatio-temporal gait parameters such as step duration, step length or step speed. However, during walking, humans need to adapt these parameters at every step to respond to exogenous and/or endogenic perturbations. While some neurological mechanisms that trigger these responses are known, our understanding of the fundamental principles governing step-by-step adaptation remains elusive. We determined the gait parameters of 20 healthy subjects with right-foot preference during treadmill walking at speeds of 1.1, 1.4 and 1.7 m/s. We found that when the value of the gait parameter was conspicuously greater (smaller) than the mean value, it was either followed immediately by a smaller (greater) value of the contralateral leg (interleg control), or the deviation from the mean value decreased during the next movement of ipsilateral leg (intraleg control). The selection of step duration and the selection of step length during such transient control events were performed in unique ways. We quantified the symmetry of short-term control of gait parameters and observed the significant dominance of the right leg in short-term control of all three parameters at higher speeds (1.4 and 1.7 m/s).

Wavelet analysis of scaling properties of gastric electrical activity.

We present a novel approach to the analysis of fluctuations in human myoelectrical gastric activity measured noninvasively from the surface of the abdomen. The time intervals between successive maxima of the wavelet transformed quasi-periodic electrogastrographic waveform define the gastric rate variability (GRV) time series. By using the method of average wavelet coefficients, the statistical fluctuations in the GRV signal in healthy individuals are determined to scale in time. Such scaling was previously found in a variety of physiological phenomena, all of which support the hypothesis that physiological dynamics utilize fractal time series. We determine the scaling index in a cohort of 17 healthy individuals to be 0.80 +/- 0.14, which compared with a set of surrogate data is found to be significant at the level P < 0.01. We also determined that the dynamical pattern, so evident in the spectrum of average wavelet coefficients of the GRV time series of healthy individuals, is significantly reduced in a cohort of systemic sclerosis patients having a scaling index 0.64 +/- 0.17. These results imply that the long-term memory in GRV time series is significantly reduced from healthy individuals to those with systemic sclerosis. Consequently, this disease degrades the complexity of the underlying gastrointestinal control system and this degradation is manifest in the loss of scaling in the GRV time series.

Fractional Langevin model of gait variability.

The stride interval in healthy human gait fluctuates from step to step in a random manner and scaling of the interstride interval time series motivated previous investigators to conclude that this time series is fractal. Early studies suggested that gait is a monofractal process, but more recent work indicates the time series is weakly multifractal. Herein we present additional evidence for the weakly multifractal nature of gait. We use the stride interval time series obtained from ten healthy adults walking at a normal relaxed pace for approximately fifteen minutes each as our data set. A fractional Langevin equation is constructed to model the underlying motor control system in which the order of the fractional derivative is itself a stochastic quantity. Using this model we find the fractal dimension for each of the ten data sets to be in agreement with earlier analyses. However, with the present model we are able to draw additional conclusions regarding the nature of the control system guiding walking. The analysis presented herein suggests that the observed scaling in interstride interval data may not be due to long-term memory alone, but may, in fact, be due partly to the statistics.

Wavelet analysis of epileptic spikes.

Interictal spikes and sharp waves in human EEG are characteristic signatures of epilepsy. These potentials originate as a result of synchronous pathological discharge of many neurons. The reliable detection of such potentials has been the long standing problem in EEG analysis, especially after long-term monitoring became common in investigation of epileptic patients. The traditional definition of a spike is based on its amplitude, duration, sharpness, and emergence from its background. However, spike detection systems built solely around this definition are not reliable due to the presence of numerous transients and artifacts. We use wavelet transform to analyze the properties of EEG manifestations of epilepsy. We demonstrate that the behavior of wavelet transform of epileptic spikes across scales can constitute the foundation of a relatively simple yet effective detection algorithm.

[Fractal analysis of MCA blood flow velocity fluctuations in migraine--preliminary report]. / Fraktalna analiza fluktuacji predkosci krwi w tetnicach srodkowych mózgu u pacjentów z migrena--doniesienie wstepne.

Many reports confirm the existence of long-range correlations between fluctuations of various physiological signals in healthy subjects and demonstrate disappearance of these correlations in pathological conditions. Blood flow velocity in intracranial vessels is changeable over time and depends on complex physiological regulatory mechanisms. The character of blood flow velocity fluctuations may indicate the presence of vascular disorders associated with various diseases. The aim of our study was to establish whether fluctuations in MCA blood flow velocity are fractal in physiological conditions and if so, whether this feature is lost in migraine, as the role of vasomotoric disturbances has been already evidenced in pathophysiology of this disease. The axial flow velocity changes averaged over a cardiac beat interval were monitored continuously via two channels through the temporal windows using a DWL Multi-DopT TCD device with 2-MHz probes. The examinations were performed in supine rest in two-hour periods in two groups: of 7 patients with clinically confirmed migraine with aura during headache-free intervals (15 recordings), and in the control group of 4 young, healthy volunteers (10 recordings). The results in the form of time series were analysed using the methods of fractal statistics. Multifractality in the recordings in physiological conditions was clearly confirmed, as well as its absence in the averaged recordings in the group of migraneurs. The findings justify a supposition that the breakdown of multifractal properties of MCA blood flow time series in migraine may result from the vasomotor disturbances present even during headache-free intervals. However, possible usefulness of this method in the diagnostics of migraine requires further investigation.

[Fractal analysis of intracranial blood flow velocity fluctuations in continuous TCD recordings]. / Fraktalna analiza szeregów czasowych uzyskiwanych z monitorowania predkosci przeplywu krwi w naczyniach mózgowych--propozycja nowego podejscia do oceny fluktuacji w zapisie TCD.

Many physiological signals fluctuate in an apparently irregular and complex manner. The fractal analysis of these changes often confirms the existence of long-range correlations in healthy subjects and demonstrate a lack of such correlations in pathological conditions. The authors discuss usefulness of the fractal statistics methods in the analysis of intracranial blood flow velocity changes averaged over a cardiac beat interval measured in humans, using transcranial Doppler ultrasonography (TCD). An assumption was made that fractal properties of blood velocity time series in healthy individuals result from a proper autoregulation of their cerebral blood flow and that in cases of vascular disturbances fractuality may disappear. A review of the literature is presented to provide a theoretical rationale for the proposed method.

Phase dynamics in cerebral autoregulation.

Complex continuous wavelet transforms are used to study the dynamics of instantaneous phase difference delta phi between the fluctuations of arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV) in a middle cerebral artery. For healthy individuals, this phase difference changes slowly over time and has an almost uniform distribution for the very low-frequency (0.02-0.07 Hz) part of the spectrum. We quantify phase dynamics with the help of the synchronization index gamma = (sin delta phi)2 + (cos delta phi)2 that may vary between 0 (uniform distribution of phase differences, so the time series are statistically independent of one another) and 1 (phase locking of ABP and CBFV, so the former drives the latter). For healthy individuals, the group-averaged index gamma has two distinct peaks, one at 0.11 Hz [gamma = 0.59 +/- 0.09] and another at 0.33 Hz (gamma = 0.55 +/- 0.17). In the very low-frequency range (0.02-0.07 Hz), phase difference variability is an inherent property of an intact autoregulation system. Consequently, the average value of the synchronization parameter in this part of the spectrum is equal to 0.13 +/- 0.03. The phase difference variability sheds new light on the nature of cerebral hemodynamics, which so far has been predominantly characterized with the help of the high-pass filter model. In this intrinsically stationary approach, based on the transfer function formalism, the efficient autoregulation is associated with the positive phase shift between oscillations of CBFV and ABP. However, the method is applicable only in the part of the spectrum (0.1-0.3 Hz) where the coherence of these signals is high. We point out that synchrony analysis through the use of wavelet transforms is more general and allows us to study nonstationary aspects of cerebral hemodynamics in the very low-frequency range where the physiological significance of autoregulation is most strongly pronounced.