Fractal dimension in health and heart failure.

BACKGROUND: Non-linear analysis of heart rate variability (HRV) can give additional information about autonomic control of the heart rate. This study applied the fractal dimension (FD) in a congestive heart failure (CHF) population. METHODS: FD and HRV were evaluated in a healthy population (n=21) and an end-stage heart failure population (n=21) using 1-h segments during the day and night from Holter recordings. RESULTS: CHF patients presented a loss of circadian variation in both FD and conventional time- and frequency-domain HRV indices. FD was higher in the CHF population both during the day and night. In the CHF population the correlation between FD and high-frequency power of HRV was lost. CONCLUSION: Day-night variations of heart rate fluctuations are lost in heart failure. Changes in FD reflecting physiological and pathophysiological changes were observed.     

Renal blood flow in heart failure patients during exercise

During exercise, reflex renal vasoconstriction maintains blood pressure and helps in redistributing blood flow to the contracting muscle. Exercise intolerance in heart failure (HF) is thought to involve diminished perfusion in active muscle. We studied the temporal relationship between static handgrip (HG) and renal blood flow velocity (RBV; duplex ultrasound) in 10 HF and in 9 matched controls during 3 muscle contraction paradigms. Fatiguing HG (protocol 1) at 40% of maximum voluntary contraction led to a greater reduction in RBV in HF compared with controls (group main effect: P <0.05). The reduction in RBV early in HG tended to be more prominent during the early phases of protocol 1. Similar RBV was observed in the two groups during post-HG circulatory arrest (isolating muscle metaboreflex). Short bouts (15 s) of HG at graded intensities (protocol 2; engages muscle mechanoreflex and/or central command) led to greater reductions in RBV in HF than controls (P <0.03). Protocol 3, voluntary and involuntary biceps contraction (eliminates central command), led to similar increases in renal vasoconstriction in HF (n=4). Greater reductions in RBV were found in HF than in controls during the early phases of exercise. This effect was not likely due to a metaboreflex or central command. Thus our data suggest that muscle mechanoreflex activity is enhanced in HF and serves to vigorously vasoconstrict the kidney. We believe this compensatory mechanism helps preserve blood flow to exercising muscle in HF.     

Blunted muscle vasodilatation during chemoreceptor stimulation in patients with heart failure

Chemoreflex control of sympathetic nerve activity is exaggerated in heart failure (HF) patients. However, the vascular implications of the augmented sympathetic activity during chemoreceptor activation in patients with HF are unknown. We tested the hypothesis that the muscle blood flow responses during peripheral and central chemoreflex stimulation would be blunted in patients with HF. Sixteen patients with HF (49 +/- 3 years old, Functional Class II-III, New York Heart Association) and 11 age-paired normal controls were studied. The peripheral chemoreflex control was evaluated by inhalation of 10% O(2) and 90% N(2) for 3 min. The central chemoreflex control was evaluated by inhalation of 7% CO(2) and 93% O(2) for 3 min. Muscle sympathetic nerve activity (MSNA) was directly evaluated by microneurography. Forearm blood flow was evaluated by venous occlusion plethysmography. Baseline MSNA were significantly greater in HF patients (33 +/- 3 vs. 20 +/- 2 bursts/min, P = 0.001). Forearm vascular conductance (FVC) was not different between the groups. During hypoxia, the increase in MSNA was significantly greater in HF patients than in normal controls (9.0 +/- 1.6 vs. 0.8 +/- 2.0 bursts/min, P = 0.001). The increase in FVC was significantly lower in HF patients (0.00 +/- 0.10 vs. 0.76 +/- 0.25 units, P = 0.001). During hypercapnia, MSNA responses were significantly greater in HF patients than in normal controls (13.9 +/- 3.2 vs. 2.1 +/- 1.9 bursts/min, P = 0.001). FVC responses were significantly lower in HF patients (-0.29 +/- 0.10 vs. 0.37 +/- 0.18 units, P = 0.001). In conclusion, muscle vasodilatation during peripheral and central chemoreceptor stimulation is blunted in HF patients. This vascular response seems to be explained, at least in part, by the exaggerated MSNA responses during hypoxia and hypercapnia.     

Scale dependency and fractal dimension of rarity

The rarity of species in a country is usually determined by counting the number of grid cells occupied by those species on a geographical observation grid. In this paper, we present a measure of rarity that is less sensitive to the shape and size of a country. We demonstrate that the distribution of species on a national grid is not monofractal. Consequently, rarity figures cannot be scaled down to a finer grid merely using scale-area plots. We propose a downscaling method that takes into account the non-monofractal distribution of species. Rarity figures have often been published on a scale comprising a limited number of rarity classes. This article finally provides an insight into the degree of accuracy of such classes.     

Real-world heart failure management in 10,910 patients with chronic heart failure in the Netherlands

Aims

Data from patient registries give insight into the management of patients with heart failure (HF), but actual data from unselected real-world HF patients are scarce. Therefore, we performed a cross sectional study of current HF care in the period 2013–2016 among more than 10,000 unselected HF patients at HF outpatient clinics in the Netherlands.

Methods

In 34 participating centres, all 10,910 patients with chronic HF treated at cardiology centres were included in the CHECK-HF registry. Of these, most (96%) were managed at a specific HF outpatient clinic. Heart failure was typically diagnosed according to the ESC guidelines 2012, based on signs, symptoms and structural and/or functional cardiac abnormalities. Information on diagnostics, treatment and co-morbidities were recorded, with specific focus on drug therapy and devices. In our cohort, the mean age was 73 years (SD 12) and 60% were male. Frequent co-morbidities reported in the patient records were diabetes mellitus 30%, hypertension 43%, COPD 19%, and renal insufficiency 58%. In 47% of the patients, ischaemia was the origin of HF. In our registry, the prevalence of HF with preserved ejection fraction was 21%.

Conclusion

The CHECK-HF registry will provide insight into the current, real world management of patient with chronic HF, including HF with reduced ejection fraction, preserved ejection fraction and mid-range ejection fraction, that will help define ways to improve quality of care. Drug and device therapy and guideline adherence as well as interactions with age, gender and co-morbidities will receive specific attention.

     

Characterization of melanophore morphology by fractal dimension analysis

Fractal or focal dimension (FD) analysis is a valuable tool to identify physiologic stimuli at the cellular and tissue levels that allows for quantification of cell perimeter complexity. The FD analysis was determined on fluorescence images of caffeine- or epinephrine-treated (or untreated control) killifish Fundulus heteroclitus (Linneaus) melanophores in culture. Cell perimeters were indicated by rhodamine-phalloidin labeling of cortical microfilaments using box-counting FD analysis. Caffeine-treated melanophores displayed dispersed melanosomes in cells with less serrated edges and reduced FD and complexity. Complexity in epinephrine-treated cells was significantly higher than the caffeine-treated cells or in the control. Cytoarchitectural variability of the cell perimeter is expected because cells change shape when cued with agents. Epinephrine-treated melanophores demonstrated aggregated melanosomes in cells with more serrated edges, significantly higher FD and thus complexity. Melanophores not treated with caffeine or epinephrine produced variable distributions of melanosomes and resulted in cells with variably serrated edges and intermediate FD with a larger SE of the regression and greater range of complexity. Dispersion of melanosomes occurs with rearrangements of the cytoskeleton to accommodate centrifugal distribution of melanosomes throughout the cell and to the periphery. The loading of melanosomes onto cortical microfilaments may provide a less complex cell contour, with the even distribution of the cytoskeleton and melanosomes. Aggregation of melanosomes occurs with rearrangements of the cytoskeleton to accommodate centripetal distribution of melanosomes. The aggregation of melanosomes may contribute to centripetal retraction of the cytoskeleton and plasma membrane. The FD analysis is, therefore, a convenient method to measure contrasting morphologic changes within stimulated cells.     

On the relationship between fractal dimension and encounters in three-dimensional trajectories

The encounter of individuals-prey, predators and mates-living in the surrounding environment is a fundamental process in the life of an organism. Along with the sensory abilities, this process will be regulated by the movement rules adopted by the individual. In this work we discuss the encounter-enhancement effect due to different natatorial modes by calculating the number of encounters realised by differently convoluted trajectories in two homogeneous distributions of particles. Using numerically generated trajectories representative of specific swimming behaviour, we demonstrate that high values of three-dimensional fractal dimension D(3D)(>1.9) are beneficial only at high concentration, whereas at low concentration less tortuous tracks (D(3D) approximately 1.5) are almost equally efficient. In the light of our results it is possible to better understand the behavioural adaptations evolved by individuals to thrive in their environment.     

Changes in adrenergic receptors during the development of heart failure

Moderate and severe stages of congestive heart failure due to the loss of myocardium upon coronary occlusion in rats was associated with an increase in alpha-adrenergic receptors and a decrease in beta-adrenergic receptors in the viable left ventricle. However, at early stages of heart failure the number of beta-adrenergic receptors was decreased without any changes in the number of alpha-adrenergic receptors. The affinities of these receptors to alpha receptor antagonist (³H-prazosin) and beta receptor antagonist (³H-dihydroalprenolol) were not altered in the failing hearts. On the other hand, the pattern of changes in both alpha- and beta-adrenergic receptors in heart membranes treated with oxygen free radical generating system was different from that seen in the failing hearts. In particular, the affinities for these receptors were decreased whereas the number of beta-receptors was increased and the number of alpha-receptors was decreased or unchanged. These results indicate that alterations in the adrenergic receptors in heart failure are not due to the formation of oxygen free radicals.     

Decreased fractal component of human heart rate variability during non-REM sleep

The physiological significance of the fractal component of short-term, spontaneous heart rate variability (HRV) in humans remains unclear. The aim of the present study was to gain further information about the respective fractal components by extracting them from HRV, blood pressure variability (BPV), and instantaneous lung volume (ILV) time series via coarse graining spectral analysis in nine healthy subjects during waking and sleep states. The results show that the contribution made by the fractal component to the total variance in the beat-to-beat R-R interval declined significantly as the depth of non-rapid eye movement (non-REM) sleep increased, that the ILV time series was largely periodic (i.e., nonfractal), and that BPV was unaffected by sleep stage. Finally, the fractal component of HRV during REM sleep was found to be quite similar to that seen during waking. These results suggest that mechanisms involving electroencephalographic desynchronization and/or conscious states of the brain are reflected in the fractal component of HRV.     

The arterial pattern and fractal dimension of the dog kidney.

A method has been developed by which it is possible to measure the fractal dimension of the arterial tree of the kidney. The objective of this work is to determine a method which permits us to discriminate between the architectures of specific organs by reference to a unique number, namely the fractal dimension of the arterial tree of that organ. This method opens the possibility of a new taxonomy for normal organs and for the pathological injiries related to the vascular morphology of those organs. The method that we have devised uses as its input the volume which is taken up by the arterial tree of the kidney. In order to calculate this volume we first obtained a plastic cast (the arteries were filled with Araldite CY233 plastic resin after which the organic tissues were corroded); thereafter we constructed a theoretical arterial tree having the same volume as the renal one. From this simplified tree, we were able to calculate its fractal dimension. The complete process of constructing the theoretical arterial tree and the subsequent calculation of its fractal dimension was carried out automatically by way of a computer programme to which we have given the name fractal program.     

Use of the fractal dimension for the analysis of electroencephalographic time series

 Electroencephalogram (EEG) traces corresponding to different physiopathological conditions can be characterized by their fractal dimension, which is a measure of the signal complexity. Generally this dimension is evaluated in the phase space by means of the attractor dimension or other correlated parameters. Nevertheless, to obtain reliable values, long duration intervals are needed and consequently only long-term events can be analysed; also much calculation time is required. To analyse events of brief duration in real-time mode and to apply the results obtained directly in the time domain, thus providing an easier interpretation of fractal dimension behaviour, in this work we optimize and propose a new method for evaluating the fractal dimension. Moreover, we study the robustness of this evaluation in the presence of white or line noises and compare the results with those obtained with conventional spectral methods. The non-linear analysis carried out allows us to investigate relevant EEG events shorter than those detectable by means of other linear and non-linear techniques, thus achieving a better temporal resolution. An interesting link between the spectral distribution and the fractal dimension value is also pointed out. Received: 21 November 1996 / Accepted in revised form: 1 July 1997     

Load compensation in obese patients during quiet tidal breathing

Seventeen eucapnic massively obese patients and eight normal subjects had their respiratory cycle parameters studied while breathing room air at rest. Despite large variations in the degree of obesity, our patients demonstrated normal mean inspiratory and expiratory flow rates, duty cycles, and minute ventilation. The maintenance of normal mean inspiratory flow rates was found to be dependent on an augmentation of neuromuscular drive (P0.1); furthermore, a strong positive correlation between percentage ideal body weight (i.e., the degree of obesity) and P0.1 was present. The obese were found to partition their tidal volume preferentially to their rib cage compartment, choosing to leave the abdominal compartment relatively immobile. Analysis of the diaphragmatic electromyogram revealed a persistence of activity into early expiration, the length of which also depended on the degree of obesity. These findings suggest that the diaphragm's volume-generating function in the obese is reduced, and furthermore the persistence of its activity in expiration serves to attenuate the rate of expiratory flow. No significant difference in any respiratory cycle parameter was found between simple obesity patients and formerly hypercapnic obese patients.     

A single-cell model to study changes in neuronal fractal dimension

Many methods have been developed to quantify neuronal morphology: measurement of neurite length, neurite number, etc. However, none of these approaches provides a comprehensive view of the complexity of neuronal morphology. In this work we have analyzed the evaluation of fractal dimension (D) as a tool to represent and quantify changes in complexity of the dendritic arbor, in in vitro cultures grown under low-density conditions. Neurons grown in isolation developed a bipolar morphology corresponding to a fractal dimension close to the unit. The analysis showed that neuronal complexity increased when cells were incubated with a depolarizing potassium concentration and there was a correlation with an increase in fractal dimension (D5 mM KCl = 1.08 +/- 0.01, D25 mM KCl =1.25 +/- 0.01). We conclude that fractal dimension is a suitable parameter to quantify changes in neuronal morphological complexity.     

An approximate solution to the periodic bidomain equations in one dimension

An approximate, computationally tractable solution is proposed for the potentials in the bidomain model with periodic intracellular junctions (the periodic bidomain model). This new approach is based on the one-dimensional rigorous spectral method described previously by Trayanova and Pilkington (IEEE Trans. Biomed. Eng., May 1993). The total solution to the one-dimensional periodic bidomain problem is decomposed in the spectral domain into solutions to (1) the single-fiber classical bidomain problem in which the intracellular conductivity value incorporates the average contribution from cytoplasm and junction and (2) the “junctional” potential problem due to the presence of junctions at discrete locations alone. Solving for the junctional term rigorously requires most of the numerical effort in the solution for the periodic bidomain potentials. Here the junctional potential is found approximately with little numerical effort. A comparison between the rigorous and the approximate solutions serves as a justification for the proposed approximate solution procedure. The procedure outlined in this paper is applicable to higher spatial dimensions where both tissue anisotropy and junctional inhomogeneities play a role in establishing the transmembrane potential distribution.