Fractal analysis of the EEG and clinical applications

2010/2011Most of the knowledge about physiological systems has been learned using linear system theory. The randomness of many biomedical signals has been traditionally ascribed to a noise-like behavior. An alternative explanation for the irregular behavior observed in systems which do not seem to be inherently stochastic is provided by one of the most striking mathematical developments of the past few decades, i.e., chaos theory. Chaos theory suggests that random-like behavior can arise in some deterministic nonlinear systems with just a few degrees of freedom. One of the most evocative aspects of deterministic chaos is the concept of fractal geometry. Fractal structure, characterized by self-similarity and noninteger dimension, is displayed in chaotic systems by a subset of the phase space known as strange attractor. However, fractal properties are observed also in the unpredictable time evolution and in the 1/f^β power-law of many biomedical signals. The research activities carried out by the Author during the PhD program are concerned with the analysis of the fractal-like behavior of the EEG. The focus was set on those methods which evaluate the fractal geometry of the EEG in the time domain, in the hope of providing physicians and researchers with new valuable tools of low computational cost for the EEG analysis. The performances of three widely used techniques for the direct estimation of the fractal dimension of the EEG were compared and the accuracy of the fBm scaling relationship, often used to obtain indirect estimates from the slope of the spectral density, was assessed. Direct estimation with Higuchi's algorithm turned out to be the most suitable methodology, producing correct estimates of the fractal dimension of the electroencephalogram also on short traces, provided that minimum sampling rate required to avoid aliasing is used. Based on this result, Higuchi's fractal dimension was used to address three clinical issues which could involve abnormal complexity of neuronal brain activity: 1) the monitoring of carotid endarterectomy for the prevention of intraoperative stroke, 2) the assessment of the depth of anesthesia to monitor unconsciousness during surgery and 3) the analysis of the macro-structural organization of the EEG in autism with respect to mental retardation. The results of the clinical studies suggest that, although linear spectral analysis still represents a valuable tool for the investigation of the EEG, time domain fractal analysis provides additional information on brain functioning which traditional analysis cannot achieve, making use of techniques of low computational cost.La maggior parte delle conoscenze acquisite sui sistemi fisiologici si deve alla teoria dei sistemi lineari. Il comportamento pseudo stocastico di molti segnali biomedici è stato tradizionalmente attribuito al concetto di rumore. Un'interpretazione alternativa del comportamento irregolare rilevato in sistemi che non sembrano essere intrinsecamente stocastici è fornita da uno dei più sorprendenti sviluppi matematici degli ultimi decenni: la teoria del caos. Tale teoria suggerisce che una certa componente casuale può sorgere in alcuni sistemi deterministici non lineari con pochi gradi di libertà. Uno degli aspetti più suggestivi del caos deterministico è il concetto di geometria frattale. Strutture frattali, caratterizzate da auto-somiglianza e dimensione non intera, sono rilevate nei sistemi caotici in un sottoinsieme dello spazio delle fasi noto con il nome di attrattore strano. Tuttavia, caratteristiche frattali possono manifestarsi anche nella non prevedibile evoluzione temporale e nella legge di potenza 1/f^β tipiche di molti segnali biomedici. Le attività di ricerca svolte dall'Autore nel corso del dottorato hanno riguardato l'analisi del comportamento frattale dell'EEG. L'attenzione è stata rivolta a quei metodi che affrontano lo studio della geometria frattale dell'EEG nel dominio del tempo, nella speranza di fornire a medici e ricercatori nuovi strumenti utili all'analisi del segnale EEG e caratterizzati da bassa complessità computazionale. Sono state messe a confronto le prestazioni di tre tecniche largamente utilizzate per la stima diretta della dimensione frattale dell'EEG e si è valutata l'accuratezza della relazione di scaling del modello fBm, spesso utilizzata per ottenere stime indirette a partire dalla pendenza della densità spettrale di potenza. Il metodo più adatto alla stima della dimensione frattale dell'elettroencefalogramma è risultato essere l'algoritmo di Higuchi, che produce stime accurate anche su segmenti di breve durata a patto che il segnale sia campionato alla minima frequenza di campionamento necessaria ad evitare il fenomeno dell'aliasing. Sulla base di questo risultato, la dimensione frattale di Higuchi è stata utilizzata per esaminare tre questioni cliniche che potrebbero coinvolgere una variazione della complessità dell'attività neuronale: 1) il monitoraggio dell'endoarterectomia carotidea per la prevenzione dell'ictus intraoperatorio, 2) la valutazione della profondità dell'anestesia per monitorare il livello di incoscienza durante l'intervento chirurgico e 3) l'analisi dell'organizzazione macro-strutturale del EEG nell'autismo rispetto alla condizione di ritardo mentale. I risultati degli studi clinici suggeriscono che, sebbene l'analisi spettrale rappresenti ancora uno strumento prezioso per l'indagine dell'EEG, l'analisi frattale nel dominio del tempo fornisce informazioni aggiuntive sul funzionamento del cervello che l'analisi tradizionale non è in grado di rilevare, con il vantaggio di impiegare tecniche a basso costo computazionale.XXIV Ciclo198

Relationship between fractal dimension and power-law exponent of heart rate variability in normal and heart failure subjects

Among the plethora of indices that can describe the fractal-like behaviour of heart rate variability (HRV), the fractal dimension (FD) and the power-law exponent (β) have gained wide acceptance. Since HRV is generally modelled with fractional Brownian motion (fBm), the linear scaling relationship between β and FD, valid for fBm, is often applied to HRV series to derive one index from the other. In this paper the relationship between β and FD is calculated in normal (NR) and heart failure (HF) HRV series. Results revealed that a linear dependence between β and FD can be found only when the slope of the spectral density is calculated over the whole spectrum instead of considering more widespread very low frequency ranges. Moreover, the relationship is slightly different from that characterizing fBm and is not unique for the two categories of subjects. The common practice of estimating β from FD for HRV applying the theoretical relationship should be reconsidered

Adjuvant anastrozole versus exemestane versus letrozole, upfront or after 2 years of tamoxifen, in endocrine-sensitive breast cancer (FATA-GIM3): a randomised, phase 3 trial

Background: Uncertainty exists about the optimal schedule of adjuvant treatment of breast cancer with aromatase inhibitors and, to our knowledge, no trial has directly compared the three aromatase inhibitors anastrozole, exemestane, and letrozole. We investigated the schedule and type of aromatase inhibitors to be used as adjuvant treatment for hormone receptor-positive early breast cancer. Methods: FATA-GIM3 is a multicentre, open-label, randomised, phase 3 trial of six different treatments in postmenopausal women with hormone receptor-positive early breast cancer. Eligible patients had histologically confirmed invasive hormone receptor-positive breast cancer that had been completely removed by surgery, any pathological tumour size, and axillary nodal status. Key exclusion criteria were hormone replacement therapy, recurrent or metastatic disease, previous treatment with tamoxifen, and another malignancy in the previous 10 years. Patients were randomly assigned in an equal ratio to one of six treatment groups: oral anastrozole (1 mg per day), exemestane (25 mg per day), or letrozole (2·5 mg per day) tablets upfront for 5 years (upfront strategy) or oral tamoxifen (20 mg per day) for 2 years followed by oral administration of one of the three aromatase inhibitors for 3 years (switch strategy). Randomisation was done by a computerised minimisation procedure stratified for oestrogen receptor, progesterone receptor, and HER2 status; previous chemotherapy; and pathological nodal status. Neither the patients nor the physicians were masked to treatment allocation. The primary endpoint was disease-free survival. The minimum cutoff to declare superiority of the upfront strategy over the switch strategy was assumed to be a 2% difference in disease-free survival at 5 years. Primary efficacy analyses were done by intention to treat; safety analyses included all patients for whom at least one safety case report form had been completed. Follow-up is ongoing. This trial is registered with the European Clinical Trials Database, number 2006-004018-42, and ClinicalTrials.gov, number NCT00541086. Findings: Between March 9, 2007, and July 31, 2012, 3697 patients were enrolled into the study. After a median follow-up of 60 months (IQR 46–72), 401 disease-free survival events were reported, including 211 (11%) of 1850 patients allocated to the switch strategy and 190 (10%) of 1847 patients allocated to upfront treatment. 5-year disease-free survival was 88·5% (95% CI 86·7–90·0) with the switch strategy and 89·8% (88·2–91·2) with upfront treatment (hazard ratio 0·89, 95% CI 0·73–1·08; p=0·23). 5-year disease-free survival was 90·0% (95% CI 87·9–91·7) with anastrozole (124 events), 88·0% (85·8–89·9) with exemestane (148 events), and 89·4% (87·3 to 91·1) with letrozole (129 events; p=0·24). No unexpected serious adverse reactions or treatment-related deaths occurred. Musculoskeletal side-effects were the most frequent grade 3–4 events, reported in 130 (7%) of 1761 patients who received the switch strategy and 128 (7%) of 1766 patients who received upfront treatment. Grade 1 musculoskeletal events were more frequent with the upfront schedule than with the switch schedule (924 [52%] of 1766 patients vs 745 [42%] of 1761 patients). All other grade 3–4 adverse events occurred in less than 2% of patients in either group. Interpretation: 5 years of treatment with aromatase inhibitors was not superior to 2 years of tamoxifen followed by 3 years of aromatase inhibitors. None of the three aromatase inhibitors was superior to the others in terms of efficacy. Therefore, patient preference, tolerability, and financial constraints should be considered when deciding the optimal treatment approach in this setting. Funding: Italian Drug Agency