Fractal dimension in health and heart failure

Understanding clinical complexity in organ and organizational systems: Challenges local and global

INTRODUCTION

Complexity in healthcare systems has been arbitrarily defined as tasks or systems ranging from complicated to intractable, with a general view of these not being 'simple'. Complexity in healthcare systems in first-world countries has been well elucidated, however, data from third-world countries is still scant. MATERIALS AND METHODS: We present four cases each from three different organ systems-chronic kidney disease, alcohol use disorder, and heart failure-in the backdrop of our healthcare organization. We present our analysis of the complexities faced clinically and, in our local healthcare system which led to these events.

RESULTS

Analysis of these cases showed that patients with chronic kidney disease had vertebral-spinal pathologies due to poor infection control measures during haemodialysis. All these patients were young with a long history of secondary hypertension. In patients with alcohol use disorder, a common theme of how government regulations and peer pressure promote alcohol use is analysed. In the four patients with unexplained heart failure, vascular health is viewed as a fractal dimension and the various factors affecting vascular health are elaborated.

CONCLUSION

Complexities exist clinically in making a diagnosis, and organizationally, in the variables and nodes dictating patient outcomes. Clinical complexities cannot be simplified but have to be navigated in an optimized way to improve clinical outcomes.

Fractal dimension of the aortic annulus: a novel predictor of paravalvular leak after transcatheter aortic valve implantation

To evaluate the prognostic relevance of aortic annulus (AA) and left ventricular outflow tract (LVOT) Fractal dimension (FD). FD is a mathematical concept that describes geometric complexity of a structure and has been shown to predict adverse outcomes in several contexts. Computed tomography (CT) scans from the SOLVE-TAVI trial, which, in a 2 × 2 factorial design, randomized 447 patients to TAVI with the balloon-expandable Edwards Sapien 3 or the self-expanding Medtronic Evolut R, and conscious sedation or general anesthesia, were analyzed semi-automatically with a custom-built software to determine border of AA and LVOT. FD was measured by box counting using grid calibers between 0.8 and 6.75 mm and was compared between patients with none/trivial and mild/moderate paravalvular regurgitation (PVR). Overall, 122 patients had CT scans sufficient for semi-automatic PVR in 30-day echocardiography. PVR was none in 65(53.3%) patients, trace in 9(7.4%), mild in 46(37.7%), moderate in 2(1.6%) and severe in 0 patients. FD determined in diastolic images was significantly higher in patients with mild/moderate PVR (1.0558 ± 0.0289 vs. 1.0401 ± 0.0284, p = 0.017). Annulus eccentricity was the only conventional measure of AA and LVOT geometry significantly correlated to FD (R = 0.337, p < 0.01). Area under the curve (AUC) of diastolic annular FD for prediction of mild/moderate PVR in ROC analysis was 0.661 (0.542-0.779, p = 0.014). FD shows promise in prediction of PVR after TAVI. Further evaluation using larger patient numbers and refined algorithms to better understand its predictive performance is warranted.Trial Registration: www.clinicaltrials.gov , identifier: NCT02737150, date of registration: 13.04.2016.

Similarity Changes Analysis for Heart Rate Fluctuation Regularity as a New Screening Method for Congestive Heart Failure

Congestive heart failure (CHF) is a chronic cardiovascular condition associated with dysfunction of the autonomic nervous system (ANS). Heart rate variability (HRV) has been widely used to assess ANS. This paper proposes a new HRV analysis method, which uses information-based similarity (IBS) transformation and fuzzy approximate entropy (fApEn) algorithm to obtain the fApEn_IBS index, which is used to observe the complexity of autonomic fluctuations in CHF within 24 h. We used 98 ECG records (54 health records and 44 CHF records) from the PhysioNet database. The fApEn_IBS index was statistically significant between the control and CHF groups (p < 0.001). Compared with the classical indices low-to-high frequency power ratio (LF/HF) and IBS, the fApEn_IBS index further utilizes the changes in the rhythm of heart rate (HR) fluctuations between RR intervals to fully extract relevant information between adjacent time intervals and significantly improves the performance of CHF screening. The CHF classification accuracy of fApEn_IBS was 84.69%, higher than LF/HF (77.55%) and IBS (83.67%). Moreover, the combination of IBS, fApEn_IBS, and LF/HF reached the highest CHF screening accuracy (98.98%) with the random forest (RF) classifier, indicating that the IBS and LF/HF had good complementarity. Therefore, fApEn_IBS effusively reflects the complexity of autonomic nerves in CHF and is a valuable CHF assessment tool.

The Study of Usefulness of a Set of Fractal Parameters to Build Classes of Disease Units Based on Images of Pigmented Skin Lesions

Dermatoscopic images are also increasingly used to train artificial neural networks for the future to provide fully automatic diagnostic systems capable of determining the type of pigmented skin lesion. Therefore, fractal analysis was used in this study to measure the irregularity of pigmented skin lesion surfaces. This paper presents selected results from individual stages of preliminary processing of the dermatoscopic image on pigmented skin lesion, in which fractal analysis was used and referred to the effectiveness of classification by fuzzy or statistical methods. Classification of the first unsupervised stage was performed using the method of analysis of scatter graphs and the fuzzy method using the Kohonen network. The results of the Kohonen network learning process with an input vector consisting of eight elements prove that neuronal activation requires a larger learning set with greater differentiation. For the same training conditions, the final results are at a higher level and can be classified as weaker. Statistics of factor analysis were proposed, allowing for the reduction in variables, and the directions of further studies were indicated.

Improving Diuretic Response in Heart Failure by Implementing a Patient-Tailored Variability and Chronotherapy-Guided Algorithm

Heart failure is a major public health problem, which is associated with significant mortality, morbidity, and healthcare expenditures. A substantial amount of the morbidity is attributed to volume overload, for which loop diuretics are a mandatory treatment. However, the variability in response to diuretics and development of diuretic resistance adversely affect the clinical outcomes. Morevoer, there exists a marked intra- and inter-patient variability in response to diuretics that affects the clinical course and related adverse outcomes. In the present article, we review the mechanisms underlying the development of diuretic resistance. The role of the autonomic nervous system and chronobiology in the pathogenesis of congestive heart failure and response to therapy are also discussed. Establishing a novel model for overcoming diuretic resistance is presented based on a patient-tailored variability and chronotherapy-guided machine learning algorithm that comprises clinical, laboratory, and sensor-derived inputs, including inputs from pulmonary artery measurements. Inter- and intra-patient signatures of variabilities, alterations of biological clock, and autonomic nervous system responses are embedded into the algorithm; thus, it may enable a tailored dose regimen in a continuous manner that accommodates the highly dynamic complex system.

Variability Predictors of Vasospasm in Subarachnoid Hemorrhage: A Feasibility Study

BACKGROUND

Mean cerebral blood flow velocity (mean-CBFV) obtained from Transcranial Doppler (TCD) poorly predicts cerebral vasospasm in patients with aneurysmal subarachnoid hemorrhage (aSAH). Variability descriptors of mean-CBFV obtained during extended TCD recordings may improve this prediction. We assessed the feasibility of generating reliable linear and non-linear descriptors of mean-CBFV variability using extended recordings in aSAH patients and in healthy controls. We also explored which of those metrics might have the ability to discriminate between aSAH patients and healthy controls, and among patients who would go on to develop vasospasm and those who would not.

METHODS

Bilateral mean-CBFV, blood pressure, and heart rate were continuously recorded for 40 minutes in aSAH patients (n = 8) within the first 5 days after ictus, in age-matched healthy controls (n = 8) and in additional young controls (n = 8). We obtained linear [standard deviation, coefficient of variations, and the very-low (0.003-0.040 Hz), low (0.040-0.150 Hz), and high-frequency (0.15-0.4 Hz) power spectra] and non-linear (Fractality, deterministic Chaos analyses) variability metrics.

RESULTS

We successfully obtained TCD recordings from patients and healthy controls and calculated the desired metrics of mean-CBFV variability. Differences were appreciable between aSAH patients and healthy controls, as well as between aSAH patients who later developed vasospasm and those who did not.

CONCLUSIONS

A 40-minute TCD recording provides reliable variability metrics in aSAH patients and healthy controls. Future studies are required to determine if mean-CBFV variability metrics remain stable over time, and whether they may serve to identify patients who are at greatest risk of developing cerebral vasospasm after aSAH.

Morning surge of ventricular arrhythmias in a new arrhythmogenic canine model of chronic heart failure is associated with attenuation of time-of-day dependence of heart rate and autonomic adaptation, and reduced cardiac chaos

Patients with chronic heart failure (CHF) exhibit a morning surge in ventricular arrhythmias, but the underlying cause remains unknown. The aim of this study was to determine if heart rate dynamics, autonomic input (assessed by heart rate variability (HRV)) and nonlinear dynamics as well as their abnormal time-of-day-dependent oscillations in a newly developed arrhythmogenic canine heart failure model are associated with a morning surge in ventricular arrhythmias. CHF was induced in dogs by aortic insufficiency & aortic constriction, and assessed by echocardiography. Holter monitoring was performed to study time-of-day-dependent variation in ventricular arrhythmias (PVCs, VT), traditional HRV measures, and nonlinear dynamics (including detrended fluctuations analysis α1 and α2 (DFAα1 & DFAα2), correlation dimension (CD), and Shannon entropy (SE)) at baseline, as well as 240 days (240 d) and 720 days (720 d) following CHF induction. LV fractional shortening was decreased at both 240 d and 720 d. Both PVCs and VT increased with CHF duration and showed a morning rise (2.5-fold & 1.8-fold increase at 6 AM-noon vs midnight-6 AM) during CHF. The morning rise in HR at baseline was significantly attenuated by 52% with development of CHF (at both 240 d & 720 d). Morning rise in the ratio of low frequency to high frequency (LF/HF) HRV at baseline was markedly attenuated with CHF. DFAα1, DFAα2, CD and SE all decreased with CHF by 31, 17, 34 and 7%, respectively. Time-of-day-dependent variations in LF/HF, CD, DFA α1 and SE, observed at baseline, were lost during CHF. Thus in this new arrhythmogenic canine CHF model, attenuated morning HR rise, blunted autonomic oscillation, decreased cardiac chaos and complexity of heart rate, as well as aberrant time-of-day-dependent variations in many of these parameters were associated with a morning surge of ventricular arrhythmias.

A shift to randomness of brain oscillations in people with autism

BACKGROUND

Resting-state functional magnetic resonance imaging (fMRI) enables investigation of the intrinsic functional organization of the brain. Fractal parameters such as the Hurst exponent, H, describe the complexity of endogenous low-frequency fMRI time series on a continuum from random (H = .5) to ordered (H = 1). Shifts in fractal scaling of physiological time series have been associated with neurological and cardiac conditions.

METHODS

Resting-state fMRI time series were recorded in 30 male adults with an autism spectrum condition (ASC) and 33 age- and IQ-matched male volunteers. The Hurst exponent was estimated in the wavelet domain and between-group differences were investigated at global and voxel level and in regions known to be involved in autism.

RESULTS

Complex fractal scaling of fMRI time series was found in both groups but globally there was a significant shift to randomness in the ASC (mean H = .758, SD = .045) compared with neurotypical volunteers (mean H = .788, SD = .047). Between-group differences in H, which was always reduced in the ASC group, were seen in most regions previously reported to be involved in autism, including cortical midline structures, medial temporal structures, lateral temporal and parietal structures, insula, amygdala, basal ganglia, thalamus, and inferior frontal gyrus. Severity of autistic symptoms was negatively correlated with H in retrosplenial and right anterior insular cortex.

CONCLUSIONS

Autism is associated with a small but significant shift to randomness of endogenous brain oscillations. Complexity measures may provide physiological indicators for autism as they have done for other medical conditions.

Fractal feature of sEMG from Flexor digitorum superficialis muscle correlated with levels of contraction during low-level finger flexions

This research paper reports an experimental study on identification of the changes in fractal properties of surface Electromyogram (sEMG) with the changes in the force levels during low-level finger flexions. In the previous study, the authors have identified a novel fractal feature, Maximum fractal length (MFL) as a measure of strength of low-level contractions and has used this feature to identify various wrist and finger movements. This study has tested the relationship between the MFL and force of contraction. The results suggest that changes in MFL is correlated with the changes in contraction levels (20%, 50% and 80% maximum voluntary contraction (MVC)) during low-level muscle activation such as finger flexions. From the statistical analysis and by visualisation using box-plot, it is observed that MFL (p ≈ 0.001) is a more correlated to force of contraction compared to RMS (p≈0.05), even when the muscle contraction is less than 50% MVC during low-level finger flexions. This work has established that this fractal feature will be useful in providing information about changes in levels of force during low-level finger movements for prosthetic control or human computer interface.

Fractal properties of human heart period variability: physiological and methodological implications

Fractal frequency scaling of heart period variability is used as a concise index of overall cardiac control. However, no prior study has assessed within-individual reproducibility of fractal indices of heart period, or reported how the estimated indices respond to autonomic blockade. Therefore, we examined fractal properties of the heart period from ten young, healthy individuals during three separate experimental sessions under control (saline) conditions and twice under combined autonomic blockade (atenolol and atropine sulfate) conditions. Under each condition, R-R intervals were recorded with the subject in the supine and the 40 deg upright tilt positions during 20 min of controlled breathing in each position. We calculated the fractal scaling exponent using detrended fluctuation analysis and estimated confidence intervals of the scaling exponents for each R-R interval time series within each individual. In the control condition, upright tilt significantly increased the scaling exponents (from 0.73 +/- 0.11 (+/-S.D., session 1), 0.72 +/- 0.10 (session 2) and 0.75 +/- 0.13 (session 3) to 0.82 +/- 0.12, 0.82 +/- 0.11 and 0.84 +/- 0.10; Student's paired t-test, t = 2.79, P = 0.02; t = 2.80, P = 0.02; and t = 2.07, P = 0.07). However, neither the absolute scaling exponents nor their change in response to upright tilt were reproducible (Lin's concordance coefficient less than 0.9, P > 0.1 for all comparisons). Following autonomic blockade, the scaling exponents were significantly increased (supine: 1.08 +/- 0.13 and 1.08 +/- 0.14; tilt: 1.07 +/- 0.21 and 1.08 +/- 0.14) for both experimental sessions (two-way repeated-measures ANOVA; F(17,1) = 40.89, P < 0.001 and F(17,1) = 42.72, P < 0.001) regardless of position. However, within individuals, the scaling exponents failed to distinguish between control and blockade for half of the subjects in at least one experimental session. Thus, fractal scaling exponents are not reproducible within individuals and do not reliably reflect the autonomic mechanisms responsible for heart period variability. In fact, data from combined blockade suggest that physiological effects of autonomic outflow may mask intrinsic fractal behaviour of the sinoatrial node.

Complexity of cardiovascular regulation in small animals

Oscillations of heart rate and blood pressure are related to the activity of the underlying control mechanism. They have been investigated mostly with linear methods in the time and frequency domains. Also, in recent years, many different nonlinear analysis methods have been applied for the evaluation of cardiovascular variability. This review presents the most commonly used nonlinear methods. Physiological understanding is obtained from various results from small animals.

Non-linear complexity measures of heart rate variability in acute schizophrenia

OBJECTIVE

Cardiovascular mortality is significantly increased in patients suffering from schizophrenia. The mechanisms currently discussed contain unhealthy lifestyle with obesity and smoking, increased incidence of diabetes, adverse pro-arrhythmic effects of antipsychotic medication and altered autonomic function. It is therefore likely that the adaptation of the heart rate to different requirements is faulty in schizophrenia. One way to detect adaptive capabilities and thus stability of regulation is to measure complexity of heart rate fluctuations, with more complex heart rate fluctuations indicating better adaptability of the underlying system.

METHODS

We calculated novel non-linear measures for beat-to-beat interval complexity from short-term ECG recordings in 20 unmedicated patients suffering from acute schizophrenia and compared them to those obtained from matched controls.

RESULTS

Data from all mathematical models applied, i.e. joint symbolic dynamics, compression entropy, fractal dimension and approximate entropy, revealed significantly reduced complexity of heart rate time series in acute schizophrenia. When using heart rate as a covariate, only fractal dimension remained significantly altered, thus appearing to be a relatively more important heart rate independent parameter.

CONCLUSIONS

Complexity of heart rate modulation is significantly reduced in acute, untreated schizophrenia, thus indicating an increased risk for cardiovascular events in these patients.

SIGNIFICANCE

These data might eventually add to the currently discussed monitoring of physical health in patients with schizophrenia, possibly providing a promising tool for cardio-arrhythmic risk stratification.