Integrated central-autonomic multifractal complexity in the heart rate variability of healthy humans

The Fractal Tapestry of Life: III Multifractals Entail the Fractional Calculus

This is the third essay advocating the use the (non-integer) fractional calculus (FC) to capture the dynamics of complex networks in the twilight of the Newtonian era. Herein, the focus is on drawing a distinction between networks described by monfractal time series extensively discussed in the prequels and how they differ in function from multifractal time series, using physiological phenomena as exemplars. In prequel II, the network effect was introduced to explain how the collective dynamics of a complex network can transform a many-body non-linear dynamical system modeled using the integer calculus (IC) into a single-body fractional stochastic rate equation. Note that these essays are about biomedical phenomena that have historically been improperly modeled using the IC and how fractional calculus (FC) models better explain experimental results. This essay presents the biomedical entailment of the FC, but it is not a mathematical discussion in the sense that we are not concerned with the formal infrastucture, which is cited, but we are concerned with what that infrastructure entails. For example, the health of a physiologic network is characterized by the width of the multifractal spectrum associated with its time series, and which becomes narrower with the onset of certain pathologies. Physiologic time series that have explicitly related pathology to a narrowing of multifractal time series include but are not limited to heart rate variability (HRV), stride rate variability (SRV) and breath rate variability (BRV). The efficiency of the transfer of information due to the interaction between two such complex networks is determined by their relative spectral width, with information being transferred from the network with the broader to that with the narrower width. A fractional-order differential equation, whose order is random, is shown to generate a multifractal time series, thereby providing a FC model of the information exchange between complex networks. This equivalence between random fractional derivatives and multifractality has not received the recognition in the bioapplications literature we believe it warrants.

Decomposing the complexity of heart-rate variability by the multifractal-multiscale approach to detrended fluctuation analysis: an application to low-level spinal cord injury

OBJECTIVE

While several studies have assessed autonomic cardiovascular control after a spinal cord lesion using heart-rate variability (HRV) indices in the frequency and time domains, complexity measures have rarely been used, even if detrended fluctuation analysis (DFA) appeared promising. Recent developments in DFA decompose the multifractal contributions using temporal scales. Our aim is to evaluate the potential of these new DFA tools, considering as an example application the decomposition of HRV complexity in individuals with spinal cord injury (SCI) at a low lesion level, for whom alterations in traditional indices are not expected.

APPROACH

We enrolled 14 subjects with SCI with a lesion below the eleventh thoracic vertebra and 34 able-bodied (AB) controls. We recorded the R-R intervals (RRI) for 10 min in supine and sitting postures. We applied the multifractal-multiscale (MFMS) DFA to derive scale coefficients, α(q,τ), with function of the multifractal order q and scale τ, and evaluated a scale-coefficient dispersion index, α _SD(τ), as the standard deviation of α(q,τ) over q. We calculated the RRI increments, their magnitude and sign, estimating the MFMS DFA coefficients for the series of magnitude α _m(q,τ) and sign α _s(q,τ).

MAIN RESULTS

While sitting, differences between SCI and AB groups depended on q for coefficients 16  <  τ  <  32 s, so that α _SD(τ) was lower in individuals with SCI at τ  =  25 s. In the supine condition, short-term scales were greater in individuals with SCI for all q, and α _SD(τ) did not differ between groups. Group differences were found in α _s(q,τ) and not in α _m(q,τ) or in traditional HRV indices. The surrogate analysis showed AB-SCI differences in linear HRV components at scales τ  <  16 s and nonlinear components at larger scales.

SIGNIFICANCE

Complexity decomposition by DFA describes autonomic alterations in HRV in low-level paraplegia better than traditional indices, probably pointing out a loss of system complexity in the sitting posture and an impaired sympatho/vagal modulation in the supine position.

Classification of prolapsed mitral valve versus healthy heart from phonocardiograms by multifractal analysis

Phonocardiography has shown a great potential for developing low-cost computer-aided diagnosis systems for cardiovascular monitoring. So far, most of the work reported regarding cardiosignal analysis using multifractals is oriented towards heartbeat dynamics. This paper represents a step towards automatic detection of one of the most common pathological syndromes, so-called mitral valve prolapse (MVP), using phonocardiograms and multifractal analysis. Subtle features characteristic for MVP in phonocardiograms may be difficult to detect. The approach for revealing such features should be locally based rather than globally based. Nevertheless, if their appearances are specific and frequent, they can affect a multifractal spectrum. This has been the case in our experiment with the click syndrome. Totally, 117 pediatric phonocardiographic recordings (PCGs), 8 seconds long each, obtained from 117 patients were used for PMV automatic detection. We propose a two-step algorithm to distinguish PCGs that belong to children with healthy hearts and children with prolapsed mitral valves (PMVs). Obtained results show high accuracy of the method. We achieved 96.91% accuracy on the dataset (97 recordings). Additionally, 90% accuracy is achieved for the evaluation dataset (20 recordings). Content of the datasets is confirmed by the echocardiographic screening.