The fractal heart - embracing mathematics in the cardiology clinic

Feasibility of fractal dimension analysis for left ventricular trabecular complexity using cardiac computed tomography

AIMS

To evaluate the consistency between fractal dimensions (FD) derived from cardiac computed tomography (CT-FD) and cardiac magnetic resonance (MR-FD) in assessing left ventricular trabecular complexity.

METHODS

This retrospective study included 170 patients who underwent CCT and CMR scans within two weeks. Five short-axis cine images were selected at end-diastole: one basal, three mid, and one apical slice. Short-axis CCT views were reconstructed and aligned with the cine images. CT-FD and MR-FD values were calculated for each slice, with mean values determined for each patient. Severe left ventricular hypertrophy (LVH) was defined as a maximum wall thickness > 15 mm in end-diastolic cine images.

RESULTS

The diastolic CT-FD and MR-FD values exhibited high consistency, with values of 1.253 ± 0.091 and 1.250 ± 0.102, respectively (n = 535, ICC = 0.882, 95 % CI: 0.861-0.899, P < 0.001). Similarly, the systolic CT-FD and MR-FD values demonstrated good consistency, with values of 1.268 ± 0.072 and 1.286 ± 0.093, respectively (n = 390, ICC = 0.720, 95 % CI: 0.669-0.765, P < 0.001). For subgroups of systolic NLVH and LVH, the ICCs were 0.773 (n = 305, CI: 0.723-0.814, P < 0.001) and 0.565 (n = 85, 95 % CI: 0.402-0.694, P < 0.001), respectively. The diagnostic efficacy of mean CT-FD aligned with that of mean MR-FD in distinguishing abnormal cardiac conditions from the CMR-negative group.

CONCLUSIONS

CCT is a feasible method for assessing left ventricular trabecular complexity, with good agreement with CMR, except in cases of severe left ventricular hypertrophy during systole.

Trabeculations of the porcine and human cardiac ventricles are different in number but similar in total volume

An intricate meshwork of trabeculations lines the luminal side of cardiac ventricles. Compaction, a developmental process, is thought to reduce trabeculations by adding them to the neighboring compact wall which is then enlarged. When pig, a plausible cardiac donor for xenotransplantation, is compared to human, the ventricular walls appear to have fewer trabeculations. We hypothesized the trabecular volume is proportionally smaller in pig than in human. Macroscopically, we observed in 16 pig hearts that the ventricular walls harbor few but large trabeculations. Close inspection revealed a high number of tiny trabeculations, a few hundred, within the recesses of the large trabeculations. While tiny, these were still larger than embryonic trabeculations and even when considering their number, the total tally of trabeculations in pig was much fewer than in human. Volumetrics based on high-resolution MRI of additional six pig hearts compared to six human hearts, revealed the left ventricles were not significantly differently trabeculated (21.5 versus 22.8%, respectively), and the porcine right ventricles were only slightly less trabeculated (42.1 vs 49.3%, respectively). We then analyzed volumetrically 10 pig embryonic hearts from gestational day 14-35. The trabecular and compact layer always grew, as did the intertrabecular recesses, in contrast to what compaction predicts. The proportions of the trabecular and compact layers changed substantially, nonetheless, due to differences in their growth rate rather than compaction. In conclusion, processes that affect the trabecular morphology do not necessarily affect the proportion of trabecular-to-compact myocardium and they are then distinct from compaction.

Fractal analysis of left ventricular trabeculae in post-STEMI: from acute to chronic phase

PURPOSE

The temporal evolution of ventricular trabecular complexity and its correlation with major adverse cardiovascular events (MACE) remain indeterminate in patients presenting with acute ST elevation myocardial infarction (STEMI).

METHODS

This retrospective analysis enrolled patients undergoing primary percutaneous coronary intervention (pPCI) for acute STEMI, possessing cardiac magnetic resonance (CMR) data in the acute (within 7 days), subacute (1 month after pPCI), and chronic phases (6 months after pPCI) from January 2015 to January 2020 at the three participating sites. Fractal dimensions (FD) were measured for the global, infarct, and remote regions of left ventricular trabeculae during each phase. The potential association of FD with MACE was analyzed using multivariate Cox regression.

RESULTS

Among the 200 analyzed patients (182 men; median age, 61 years; age range, 50-66 years), 37 (18.5%) encountered MACE during a median follow-up of 31.2 months. FD exhibited a gradual decrement (global FD at acute, subacute, and chronic phases: 1.253 ± 0.049, 1.239 ± 0.046, 1.230 ± 0.045, p < 0.0001), with a more pronounced decrease observed in patients subsequently experiencing MACE (p < 0.001). The global FD at the subacute phase correlated with MACE (hazard ratio 0.89 (0.82, 0.97), p = 0.01), and a global FD value below 1.26 was associated with a heightened risk.

CONCLUSION

In patients post-STEMI, the global FD, serving as an indicator of left ventricular trabeculae complexity, independently demonstrated an association with subsequent major adverse cardiovascular events, beyond factors encompassing left ventricular ejection fraction, indexed left ventricular end-diastolic volume, infarct size, heart rate, NYHA class, and post-pPCI TIMI flow.

CRITICAL RELEVANCE STATEMENT

In patients who have had an ST-segment elevation myocardial infarction, global fractal dimension, as a measure of left ventricular trabeculae complexity, provided independent association with subsequent major adverse cardiovascular event.

KEY POINTS

• Global and regional FD decreased after STEMI, and more so in patients with subsequent MACE. • Lower global FD at the subacute phase and Δglobal FD from acute to subacute phase were associated with subsequent MACE besides clinical and CMR factors. • Global FD at the subacute phase independently correlated with MACE and global FD value below 1.26 was associated with higher risk.

Prognostic value of left ventricular trabeculae fractal analysis in patients with dilated cardiomyopathy

BACKGROUND

The prognostic value of left ventricular (LV) myocardial trabecular complexity on cardiovascular magnetic resonance (CMR) in dilated cardiomyopathy (DCM) remains unknown. This study aimed to evaluate the prognostic value of LV myocardial trabecular complexity using fractal analysis in patients with DCM.

METHODS

Consecutive patients with DCM who underwent CMR between March 2017 and November 2021 at two hospitals were prospectively enrolled. The primary endpoints were defined as the combination of all-cause death and heart failure hospitalization. The events of cardiac death alone were defined as the secondary endpoints.LV trabeculae complexity was quantified by measuring the fractal dimension (FD) of the endocardial border based on fractal geometry on CMR. Cox proportional hazards regression and Kaplan-Meier survival analysis were used to examine the association between variables and outcomes. The incremental prognostic value of FD was assessed in nested models.

RESULTS

A total of 403 patients with DCM (49.31 ± 14.68 years, 69% male) were recruited. After a median follow-up of 43 months (interquartile range, 28-55 months), 87 and 24 patients reached the primary and secondary endpoints, respectively. Age, heart rate, New York Heart Association functional class >II, N-terminal pro-B-type natriuretic peptide, LV ejection fraction, LV end-diastolic volume index, LV end-systolic volume index, LV mass index, presence of late gadolinium enhancement, global FD, LV mean apical FD, and LV maximal apical FD were univariably associated with the outcomes (all P < 0.05). After multivariate adjustment, LV maximal apical FD remained a significant independent predictor of outcome [hazard ratio = 1.179 (1.116, 1.246), P < 0.001]. The addition of LV maximal apical FD in the nested models added incremental prognostic value to other common clinical and imaging risk factors (all <0.001; C-statistic: 0.84-0.88, P < 0.001).

CONCLUSION

LV maximal apical FD was an independent predictor of the adverse clinical outcomes in patients with DCM and provided incremental prognostic value over conventional clinical and imaging risk factors.

Box-Counting Fractal Analysis: A Primer for the Clinician

This chapter lays out the elementary principles of fractal geometry underpinning much of the rest of this book. It assumes a minimal mathematical background, defines the key principles and terms in context, and outlines the basics of a fractal analysis method known as box counting and how it is used to perform fractal, lacunarity, and multifractal analyses. As a standalone reference, this chapter grounds the reader to be able to understand, evaluate, and apply essential methods to appreciate and heal the exquisitely detailed fractal geometry of the brain.

Multifractal foundations of biomarker discovery for heart disease and stroke

Any reliable biomarker has to be specific, generalizable, and reproducible across individuals and contexts. The exact values of such a biomarker must represent similar health states in different individuals and at different times within the same individual to result in the minimum possible false-positive and false-negative rates. The application of standard cut-off points and risk scores across populations hinges upon the assumption of such generalizability. Such generalizability, in turn, hinges upon this condition that the phenomenon investigated by current statistical methods is ergodic, i.e., its statistical measures converge over individuals and time within the finite limit of observations. However, emerging evidence indicates that biological processes abound with nonergodicity, threatening this generalizability. Here, we present a solution for how to make generalizable inferences by deriving ergodic descriptions of nonergodic phenomena. For this aim, we proposed capturing the origin of ergodicity-breaking in many biological processes: cascade dynamics. To assess our hypotheses, we embraced the challenge of identifying reliable biomarkers for heart disease and stroke, which, despite being the leading cause of death worldwide and decades of research, lacks reliable biomarkers and risk stratification tools. We showed that raw R-R interval data and its common descriptors based on mean and variance are nonergodic and non-specific. On the other hand, the cascade-dynamical descriptors, the Hurst exponent encoding linear temporal correlations, and multifractal nonlinearity encoding nonlinear interactions across scales described the nonergodic heart rate variability more ergodically and were specific. This study inaugurates applying the critical concept of ergodicity in discovering and applying digital biomarkers of health and disease.

Application of Cardiovascular Computed Tomography to the Assessment of Patients With Hypertrophic Cardiomyopathy

Hypertrophic cardiomyopathy is a common inherited cardiac condition in which regional myocardial thickening and scarring can lead to a range of symptoms including breathlessness, dizziness, chest pain, and collapse with loss of consciousness. It is vital to be able to understand the mechanisms behind these epiphenomena and to be able to distinguish, for example, between syncope because of arrhythmia versus syncope because of mechanical outflow tract obstruction. Therefore, we require a technique that can characterize anatomy, physiology, and myocardial substrate. Traditionally, this role has been the preserve of cardiac magnetic resonance (CMR) imaging. This review makes the case for cardiac computed tomography (CT) as an alternative imaging method. We review the use of functional CT to identify the components of outflow tract obstruction (and obstruction at other levels, which may be simultaneous), and as an aid to interventional and surgical planning. We demonstrate the added value of multiplanar isotropic reformats in this condition, particularly in cases where the diagnosis may be more challenging or where complications (such as early apical aneurysm) may be difficult to recognize with 2-dimensional techniques. In conclusion, our aim is to convince readers that cardiac CT is a highly valuable and versatile tool, which deserves wider usage and greater recognition in those caring for patients with hypertrophic cardiomyopathy.

Quantitative Image Processing for Three-Dimensional Episcopic Images of Biological Structures: Current State and Future Directions

Episcopic imaging using techniques such as High Resolution Episcopic Microscopy (HREM) and its variants, allows biological samples to be visualized in three dimensions over a large field of view. Quantitative analysis of episcopic image data is undertaken using a range of methods. In this systematic review, we look at trends in quantitative analysis of episcopic images and discuss avenues for further research. Papers published between 2011 and 2022 were analyzed for details about quantitative analysis approaches, methods of image annotation and choice of image processing software. It is shown that quantitative processing is becoming more common in episcopic microscopy and that manual annotation is the predominant method of image analysis. Our meta-analysis highlights where tools and methods require further development in this field, and we discuss what this means for the future of quantitative episcopic imaging, as well as how annotation and quantification may be automated and standardized across the field.

Characterization of autonomic states by complex sympathetic and parasympathetic dynamics

Assessment of heartbeat dynamics provides a promising framework for non-invasive monitoring of cardiovascular and autonomic states. Nevertheless, the non-specificity of such measurements among clinical populations and healthy conditions associated with different autonomic states severely limits their applicability and exploitation in naturalistic conditions. This limitation arises especially when pathological or postural change-related sympathetic hyperactivity is compared to autonomic changes across age and experimental conditions. In this frame, we investigate the intrinsic irregularity and complexity of cardiac sympathetic and vagal activity series in different populations, which are associated with different cardiac autonomic dynamics. Sample entropy, fuzzy entropy, and distribution entropy are calculated on the recently proposed sympathetic and parasympathetic activity indices (SAI and PAI) series, which are derived from publicly available heartbeat series of congestive heart failure patients, elderly and young subjects watching a movie in the supine position, and healthy subjects undergoing slow postural changes. Results show statistically significant differences between pathological/old subjects and young subjects in the resting state and during slow tilt, with interesting trends in SAI- and PAI-related entropy values. Moreover, while CHF patients and healthy subjects in upright position show the higher cardiac sympathetic activity, elderly and young subjects in resting state showed higher vagal activity. We conclude that quantification of intrinsic cardiac complexity from sympathetic and vagal dynamics may provide new physiology insights and improve on the non-specificity of heartbeat-derived biomarkers.

Excessive Trabeculation of the Left Ventricle: JACC: Cardiovascular Imaging Expert Panel Paper

Excessive trabeculation, often referred to as "noncompacted" myocardium, has been described at all ages, from the fetus to the adult. Current evidence for myocardial development, however, does not support the formation of compact myocardium from noncompacted myocardium, nor the arrest of this process to result in so-called noncompaction. Excessive trabeculation is frequently observed by imaging studies in healthy individuals, as well as in association with pregnancy, athletic activity, and with cardiac diseases of inherited, acquired, developmental, or congenital origins. Adults with incidentally noted excessive trabeculation frequently require no further follow-up based on trabecular pattern alone. Patients with cardiomyopathy and excessive trabeculation are managed by cardiovascular symptoms rather than the trabecular pattern. To date, the prognostic role of excessive trabeculation in adults has not been shown to be independent of other myocardial disease. In neonates and children with excessive trabeculation and normal or abnormal function, clinical caution seems warranted because of the reported association with genetic and neuromuscular disorders. This report summarizes the evidence concerning the etiology, pathophysiology, and clinical relevance of excessive trabeculation. Gaps in current knowledge of the clinical relevance of excessive trabeculation are indicated, with priorities suggested for future research and improved diagnosis in adults and children.

Wrist accelerometer temporal analysis as a prognostic tool for aged care residents: A sub‐study of the ReMInDAR trial

BACKGROUND

Objective measures for screening, prioritizing, and planning care for frail individuals are essential for appropriate aged care provision. This study evaluates metrics derived from actigraphy measures (captured by wrist accelerometer) as a digital biomarker to identify frail individuals at risk of adverse outcomes, including death, hospitalization, and cognitive decline.

METHODS

This was a secondary study using data from a randomized controlled trial assessing the effectiveness of an ongoing pharmacist service in residential aged care facilities. Three metrics are studied and compared: the Frailty Index, the daily time spent in light time activity, and the temporal correlation of the actigraphy signal, measured by detrended fluctuation analysis. The association between actigraphy-derived metrics at baseline and adverse events within 12 months (death, cognitive decline, and hospitalizations) was assessed using logistic regression.

RESULTS

Actigraphy records were available for 213 participants living in aged-care, median age of 85 years. Individuals with higher temporal correlation (activity is less random) were at lower risk of death (Standardized OR: 0.49; 95% CI 0.34, 0.7, p < 0.001) and hospitalization (Standardized OR: 0.57; 95% CI 0.42, 0.77, p < 0.001) in 12 months, but there was no difference in cognitive decline (Standardized OR: 1; 95% CI 0.74, 1.35, p = 0.98). The predictive model that included temporal correlation had an area under the curve of 0.70 (CI 0.60-0.80) for death and 0.64 (CI 0.54-0.72) for hospitalization.

CONCLUSION

Temporal correlation of the actigraphy signal from aged care residents was strongly associated with death and hospitalization, but not cognitive decline. Digital biomarkers may have a place as an objective, accurate, and low-cost patient metric to support risk stratification and clinical planning.

Detection of Atrial Fibrillation Episodes based on 3D Algebraic Relationships between Cardiac Intervals

In this study, the notion of perfect matrices of Lagrange differences is employed to detect atrial fibrillation episodes based on three ECG parameters (JT interval, QRS interval, RR interval). The case study comprised 8 healthy individuals and 7 unhealthy individuals, and the mean and standard deviation of age was 65.84 ± 1.4 years, height was 1.75 ± 0.12 m, and weight was 79.4 ± 0.9 kg. Initially, it was demonstrated that the sensitivity of algebraic relationships between cardiac intervals increases when the dimension of the perfect matrices of Lagrange differences is extended from two to three. The baseline dataset was established using statistical algorithms for classification by means of the developed decision support system. The classification helps to determine whether the new incoming candidate has indications of atrial fibrillation or not. The application of probability distribution graphs and semi-gauge indicator techniques aided in visualizing the categorization of the new candidates. Though the study's data are limited, this work provides a strong foundation for (1) validating the sensitivity of the perfect matrices of Lagrange differences, (2) establishing a robust baseline dataset for supervised classification, and (3) classifying new incoming candidates within the classification framework. From a clinical standpoint, the developed approach assists in the early detection of atrial fibrillation in an individual.

Cuffless blood pressure estimation using chaotic features of photoplethysmograms and parallel convolutional neural network

BACKGROUND AND OBJECTIVE

As a nonlinear framework in dynamical system analysis, chaotic approaches are mainly applied to evolve the complexity of biological systems. Due to the chaotic nature of the cardiovascular systems, the nonlinear features can intuitively provide a reliable framework in blood pressure (BP) estimation. Cuffless BP estimation is usually carried out by establishing deep neural network models estimating the BP values through machine-learned features of photoplethysmogram (PPG) signals.

METHODS

In this study, a novel parallel deep architecture is proposed to handle the machine-learned and chaotic features of PPG signals in estimating the actual BP values. The chaotic handcrafted features were the signal properties associated with the Poincare sections in the phase space and the recurrence plot-based measures called recurrence quantification analysis (RQA). Moreover, the measures quantifying the nonlinear properties of the temporal sequences such as correlation dimension, fractal dimension, Lyapunov exponent, and entropy-based quantities were also employed. The parallel architecture not only embedded the chaotic nature of PPG signals but also provided a facility to include the pseudo-periodic variations of PPGs by utilizing a concatenating layer.

RESULTS

Our framework was examined on the public dataset, namely, Multi-Parameter Intelligent in Intensive Care II contained the recording of PPG, ECG and arterial blood pressure. The performance of the employed handcrafted features in distinguishing between the levels of BP values was investigated based on Spearman's statistics. In addition, our proposed scheme is evaluated in terms of Pearson's correlation coefficient (R), root mean square error (RMSE), and mean absolute error (MAE). The best performance was achieved when the employed handcrafted features accompanied by PPG sequences were applied to the parallel deep network. In particular, the values of R, RMSE, and MAE were obtained 0.9529, 2.76 mmHg, and 1.73 mmHg for diastolic BP, and 0.9444, 6.18 mmHg, and 3.8 mmHg for systolic BP, respectively. Moreover, based on the requirements of the standards set by the British Hypertension Society (BHS), the proposed scheme achieved a grade of A.

CONCLUSIONS

Our proposed scheme outperformed the state-of-the-art BP estimation methods. In addition, the results confirmed that the concatenation of the PPG-related machine-learned and nonlinear handcrafted features can be properly applied in continuous BP monitoring.

Distinct fatty acid redistribution and textural changes in the brain tissue upon the static magnetic field exposure

We observed different outcomes upon the subacute exposure to the 128 mT highly homogeneous static magnetic field (SMF) when its orientation was (i) aligned with the vertical component of the geomagnetic field; (ii) in the opposite direction. We employed the fatty acids (FA) composition and digital image analyses (DIA) to provide insights into the underlying processes and examine the possible weak SMF effects. Swiss-Webster male mice were whole-body exposed for 1 h/day over five days. Brain tissue's thin liquid chromatography resulted in brain FA composition, indicating a possible sequence of changes due to the SMF exposure. Quantitative DIA accurately assessed different image parameters. Delicate textural changes were revealed in the group where pathohistological or biochemical alterations have not been detected. DIA-based biological markers seem to be very promising for studying delicate tissue changes, which results from the high sensitivity and wide availability of DIA.

Monofractal analysis of functional magnetic resonance imaging: An introductory review

The following review will aid readers in providing an overview of scale-free dynamics and monofractal analysis, as well as its applications and potential in functional magnetic resonance imaging (fMRI) neuroscience and clinical research. Like natural phenomena such as the growth of a tree or crashing ocean waves, the brain expresses scale-invariant, or fractal, patterns in neural signals that can be measured. While neural phenomena may represent both monofractal and multifractal processes and can be quantified with many different interrelated parameters, this review will focus on monofractal analysis using the Hurst exponent (H). Monofractal analysis of fMRI data is an advanced analysis technique that measures the complexity of brain signaling by quantifying its degree of scale-invariance. As such, the H value of the blood oxygenation level-dependent (BOLD) signal specifies how the degree of correlation in the signal may mediate brain functions. This review presents a brief overview of the theory of fMRI monofractal analysis followed by notable findings in the field. Through highlighting the advantages and challenges of the technique, the article provides insight into how to best conduct fMRI fractal analysis and properly interpret the findings with physiological relevance. Furthermore, we identify the future directions necessary for its progression towards impactful functional neuroscience discoveries and widespread clinical use. Ultimately, this presenting review aims to build a foundation of knowledge among readers to facilitate greater understanding, discussion, and use of this unique yet powerful imaging analysis technique.

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.

Heart rate variability and the dawn of complex physiological signal analysis: methodological and clinical perspectives

Spontaneous beat-to-beat variations of heart rate (HR) have intrigued scientists and casual observers for centuries; however, it was not until the 1970s that investigators began to apply engineering tools to the analysis of these variations, fostering the field we now know as heart rate variability or HRV. Since then, the field has exploded to not only include a wide variety of traditional linear time and frequency domain applications for the HR signal, but also more complex linear models that include additional physiological parameters such as respiration, arterial blood pressure, central venous pressure and autonomic nerve signals. Most recently, the field has branched out to address the nonlinear components of many physiological processes, the complexity of the systems being studied and the important issue of specificity for when these tools are applied to individuals. When the impact of all these developments are combined, it seems likely that the field of HRV will soon begin to realize its potential as an important component of the toolbox used for diagnosis and therapy of patients in the clinic. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Frequent attendance at the emergency department shows typical features of complex systems: analysis of multicentre linked data

OBJECTIVE

Frequent attendance at the ED is a worldwide problem. We hypothesised that frequent attendance could be understood as a feature of a complex system comprising patients, healthcare and society. Complex systems have characteristic statistical properties, with stable patterns at the level of the system emerging from unstable patterns at the level of individuals who make up the system.

METHODS

Analysis of a linked dataset of routinely collected health records from all 13 hospital trusts providing ED care in the Yorkshire and Humber region of the UK (population 5.5 million). We analysed the distribution of attendances per person in each of 3 years and measured the transition of individual patients between frequent, infrequent and non-attendance. We fitted data to power law distributions typically seen in complex systems using maximum likelihood estimation.

RESULTS

The data included 3.6 million attendances at EDs in 13 hospital trusts. 29/39 (74.3%) analyses showed a statistical fit to a power law; 2 (5.1%) fitted an alternative distribution. All trusts' data fitted a power law in at least 1 year. Differences over time and between hospital trusts were small and partly explained by demographics. In contrast, individual patients' frequent attendance was unstable between years.

CONCLUSIONS

ED attendance patterns are stable at the level of the system, but unstable at the level of individual frequent attenders. Attendances follow a power law distribution typical of complex systems. Interventions to address ED frequent attendance need to consider the whole system and not just the individual frequent attenders.

Decrements in Adolescent Cardiac Complexity During Mother-Adolescent Conflicts

The present study aimed to provide further evidence on the usefulness of non-linear cardiac measures when examining the output of the cardiac system. Scale-invariant self-similarity and entropy, in addition to heart rate variability (HRV) given by time- and frequency-domain measures were calculated in a sample of N = 55 healthy adolescents (M_age = 14.122, SD_age = 0.698) during 10-min positive (non-stressful) and negative (stressful) interactions with their mothers. We also explored sex influence in adolescents' cardiac output using both HRV measures and non-linear cardiac measures. Repeated measures MANOVA revealed a marginal within-group effect for HRV measures, F(3,51) = 2.438, p = 0.075, η²_p = 0.125), and a significant within-group effect for non-linear cardiac measures, F(6, 48) = 3.296, p = 0.009, η²_p = 0.292, showing a significant decrement in adolescents' cardiac complexity during the negative interaction. No significant effect for sex was found in either non-linear cardiac measures or HRV measures, but results suggest lower cardiac scaling in females than in males. These findings suggest a real-time scale predominance in heart rate output when adolescents face an aversive situation and support the importance of non-linear cardiac measures to gain insight into the cardiac system and its regulatory mechanisms. Further research is needed to examine sex-differences in cardiac complexity during aversive situations.

Computationally efficient sandbox algorithm for multifractal analysis of large-scale complex networks with tens of millions of nodes

Among various algorithms of multifractal analysis (MFA) for complex networks, the sandbox MFA algorithm behaves with the best computational efficiency. However, the existing sandbox algorithm is still computationally expensive for MFA of large-scale networks with tens of millions of nodes. It is also not clear whether MFA results can be improved by a largely increased size of a theoretical network. To tackle these challenges, a computationally efficient sandbox algorithm (CESA) is presented in this paper for MFA of large-scale networks. Distinct from the existing sandbox algorithm that uses the shortest-path distance matrix to obtain the required information for MFA of networks, our CESA employs the compressed sparse row format of the adjacency matrix and the breadth-first search technique to directly search the neighbor nodes of each layer of center nodes, and then to retrieve the required information. A theoretical analysis reveals that the CESA reduces the time complexity of the existing sandbox algorithm from cubic to quadratic, and also improves the space complexity from quadratic to linear. Then the CESA is demonstrated to be effective, efficient, and feasible through the MFA results of (u,v)-flower model networks from the fifth to the 12th generations. It enables us to study the multifractality of networks of the size of about 11 million nodes with a normal desktop computer. Furthermore, we have also found that increasing the size of (u,v)-flower model network does improve the accuracy of MFA results. Finally, our CESA is applied to a few typical real-world networks of large scale.

Application of a Diagnostic Methodology of Cardiac Systems Based on the Proportions of Entropy in Normal Patients and with Different Pathologies

Introduction

Dynamical systems theory, probability, and entropy were the substrate for the development of the diagnostic and predictive methodology of adult heart dynamics.

Objective

To apply a previously developed methodology from dynamical systems, probability, and entropy in both normal and pathological subjects.

Methods

Electrocardiographic records were selected from 30 healthy subjects and 200 with different pathologies, with a length of least 18 h. Numerical attractors from dynamical attractors and the probability of occurrence of ordered pairs of consecutive heart rates were built. A calculation of entropy and its proportions was performed and statistical analysis was conducted.

Results

The normal patients' heart dynamics were evaluated according to the methodology of entropy proportions, highlighting that there are differences in normal patients with different pathologies. There was maximal level of sensitivity, specificity, and diagnostic agreement.

Conclusion

Proportional entropy constitutes a diagnostic and predictive method of heart systems, and may be useful as a tool to objectively diagnose and perform the follow-up of normal and pathological cases.

Lack of morphometric evidence for ventricular compaction in humans

The remodeling of the compact wall by incorporation of trabecular myocardium, referred to as compaction, receives much attention because it is thought that its failure causes left ventricular non-compaction cardiomyopathy (LVNC). Although the notion of compaction is broadly accepted, the nature and strength of the evidence supporting this process is underexposed. Here, we review the literature that quantitatively investigated the development of the ventricular wall to understand the extent of compaction in humans, mice, and chickens. We queried PubMed using several search terms, screened 1127 records, and selected 56 publications containing quantitative data on ventricular growth. For humans, only 34 studies quantified wall development. The key premise of compaction, namely a reduction of the trabecular layer, was never documented. Instead, the trabecular layer grows slower than the compact wall in later development and this changes wall architecture. There were no reports of a sudden enlargement of the compact layer (from incorporated trabeculae), be it in thickness, area, or volume. Therefore, no evidence for compaction was found. Only in chickens, a sudden increase in compact myocardial thickness layer was reported coinciding with a decrease in trabecular thickness. In mice, morphometric and lineage tracing investigations have yielded conflicting results that allow for limited compaction to occur. In conclusion, compaction in human development is not supported while rapid intrinsic growth of the compact wall is supported in all species. If compaction takes place, it likely plays a much smaller role in determining wall architecture than intrinsic growth of the compact wall.

Trabecular complexity as an early marker of cardiac involvement in Fabry disease

AIMS

Fabry cardiomyopathy is characterized by glycosphingolipid storage and increased myocardial trabeculation has also been demonstrated. This study aimed to explore by cardiac magnetic resonance whether myocardial trabecular complexity, quantified by endocardial border fractal analysis, tracks phenotype evolution in Fabry cardiomyopathy.

METHODS AND RESULTS

Study population included 20 healthy controls (12 males, age 32±9) and 45 Fabry patients divided into three groups: 15 left ventricular hypertrophy (LVH)-negative patients with normal T1 (5 males, age 28±13; Group 1); 15 LVH-negative patients with low T1 (9 males, age 33±9.6; Group 2); 15 LVH-positive patients (11 males, age 53.5±9.6; Group 3). Trabecular fractal dimensions (Dfs) (total, basal, mid-ventricular, and apical) were evaluated on cine images. Total Df was higher in all Fabry groups compared to controls, gradually increasing from controls to Group 3 (1.27±0.02 controls vs. 1.29±0.02 Group 1 vs. 1.30±0.02 Group 2 vs. 1.34±0.02 Group 3; P<0.001). Group 3 showed significantly higher values of all Dfs compared to the other Groups. Both basal and total Dfs were significantly higher in Group 1 compared with controls (basal: 1.30±0.03 vs. 1.26±0.04, P =0.010; total: 1.29±0.02 vs. 1.27±0.02, P=0.044). Total Df showed significant correlations with: (i) T1 value (r=-0.569; P<0.001); (ii) LV mass (r=0.664, P<0.001); (iii) trabecular mass (r=0.676; P <0.001); (iv) Mainz Severity Score Index (r=0.638; P<0.001).

CONCLUSION

Fabry cardiomyopathy is characterized by a progressive increase in Df of endocardial trabeculae together with shortening of T1 values. Myocardial trabeculation is increased before the presence of detectable sphingolipid storage, thus representing an early sign of cardiac involvement.

Multi-Chaotic Analysis of Inter-Beat (R-R) Intervals in Cardiac Signals for Discrimination between Normal and Pathological Classes

Cardiac signals have complex structures representing a combination of simpler structures. In this paper, we develop a new data analytic tool that can extract the complex structures of cardiac signals using the framework of multi-chaotic analysis, which is based on the p-norm for calculating the largest Lyapunov exponent (LLE). Appling the p-norm is useful for deriving the spectrum of the generalized largest Lyapunov exponents (GLLE), which is characterized by the width of the spectrum (which we denote by W). This quantity measures the degree of multi-chaos of the process and can potentially be used to discriminate between different classes of cardiac signals. We propose the joint use of the GLLE and spectrum width to investigate the multi-chaotic behavior of inter-beat (R-R) intervals of cardiac signals recorded from 54 healthy subjects (hs), 44 subjects diagnosed with congestive heart failure (chf), and 25 subjects diagnosed with atrial fibrillation (af). With the proposed approach, we build a regression model for the diagnosis of pathology. Multi-chaotic analysis showed a good performance, allowing the underlying dynamics of the system that generates the heart beat to be examined and expert systems to be built for the diagnosis of cardiac pathologies.

Investigating fractal dimension, heart rate variability, and memory during different image sequencing regimes in young adults

The goal of this study is to investigate patterns that emerge in brain and heart signals in response to external stimulating image regimes. Data were collected from 84 subjects of ages 18-22. Subjects viewed a series of both neutrally and negatively arousing pictures during 2-min and 18-s-long segments repeated nine times. Both brain [electroencephalogram (EEG)] and heart signals [electrocardiogram (EKG)] were recorded for the duration of the study (ranging from 1.5 to 2.5 h) and analyzed using nonlinear techniques. Specifically, the fractal dimension was computed from the EEG to determine how this voltage trace is related to the image sequencing. Our results showed that subjects visually stimulated by a series of mixed images (a randomized set of neutrally or negatively arousing images) had a significantly higher fractal dimension compared to subjects visually triggered by pure images (an organized set of either all neutral or all negatively arousing images). In addition, our results showed that subjects who performed better on memory recall had a higher fractal dimension computed from the EEG. Analysis of EKG also showed greater heart rate variability in subjects who viewed a series of mixed images compared to subjects visually triggered by pure images. Overall, our results show that the healthy brain and heart are responsive to environmental stimuli that promote adaptability, flexibility, and agility.

Intrinsic Complexity of Sympathetic and Parasympathetic Dynamics from HRV series: a Preliminary Study on Postural Changes

The analysis of complex heartbeat dynamics has been widely used to characterize heartbeat autonomic control in healthy and pathological conditions. However, underlying physiological correlates of complexity measurements from heart rate variability (HRV) series have not been identified yet. To this extent, we investigated intrinsic irregularity and complexity of cardiac sympathetic and vagal activity time series during postural changes. We exploited our recently proposed HRV-based, time-varying Sympathetic and Parasympathetic Activity Indices (SAI and PAI) and performed Sample Entropy, Fuzzy Entropy, and Distribution Entropy calculations on publicly-available heartbeat series gathered from 10 healthy subjects undergoing resting state and passive slow tilt sessions. Results show significantly higher entropy values during the upright position than resting state in both SAI and PAI series. We conclude that an increase in HRV complexity resulting from postural changes may derive from sympathetic and vagal activities with higher complex dynamics.

Fractal properties in sensorimotor variability unveil internal adaptations of the organism before symptomatic functional decline

If health can be defined as adaptability, then measures of adaptability are crucial. Convergent findings across clinical areas established the notion that fractal properties in bio-behavioural variability characterize the healthy condition of the organism, and its adaptive capacities in general. However, ambiguities remain as to the significance of fractal properties: the literature mainly discriminated between healthy vs. pathological states, thereby loosing perspective on the progression in between, and overlooking the distinction between adaptability and effective adaptations of the organism. Here, we design an experimental tapping paradigm involving gradual feedback deprivation in groups of healthy subjects and one deafferented man as a pathological-limit case. We show that distinct types of fractal properties in sensorimotor behaviour characterize, on the one hand impaired functional ability, and on the other hand internal adaptations for maintaining performance despite the imposed constraints. Findings may prove promising for early detection of internal adaptations preceding symptomatic functional decline.

Sex differences in adolescents' cardiac reactivity and recovery under acute stress: The importance of nonlinear measures

How well adolescents can self-regulate in the face of stressors has considerable implications for long-term well-being and risk of psychopathology. This study investigated sex differences in adolescents' cardiac reactivity and recovery during a stressful task. Measures of cardiac variability (linear) and complexity (nonlinear) were obtained from N = 92 adolescents, 41 males (M age = 13.28, SD = 0.69; BMI = 21.9) and 51 females (M age = 13.36, SD = 0.67; BMI = 21.5). The adolescents underwent the Trier Social Stress Test, consisting of five conditions: baseline, anticipation, social exposure, math task, and recovery. Repeated measures ANOVAs revealed that female in comparison to male adolescents showed lower cardiac complexity revealed by higher short-term scaling exponent at baseline (p = .006) and math (p = .013) and lower entropy at exposure (p = .013) and math (p = .012). A marginal between-groups effect was found for Higuchi's fractal dimension, F(1, 90) = 3.67, p = .059, η_p ²  = .041, with females showing lower fractal dimension than males in math (p = .037). Linear measures did not reveal sex-related differences. Results suggest that adolescent females show lower cardiac complexity during stress. These findings support the importance of nonlinear cardiac measures for understanding cardiac reactivity during stress. Further research is needed to test the hypothesis that cardiac complexity is useful to detect an increased risk of emotional disorders, disorders that are more prevalent in women.

Non-invasive prediction of genotype positive-phenotype negative in hypertrophic cardiomyopathy by 3D modern shape analysis

NEW FINDINGS

What is the central question of this study? Can impaired deformational indicators for genotype positive for hypertrophic cardiomyopathy in subjects that do not exhibit a left-ventricular wall hypertrophy condition (G+LVH-) be determined using non-invasive 3D echocardiography? What is the main finding and its importance? Using 3D-STE and modern shape analysis, peculiar deformational impairments can be detected in G+LVH- subjects that can be classified with good accuracy. Moreover, the patterns of impairment are located mainly on the apical region in agreement with other evidence coming from previous biomechanical investigations.

ABSTRACT

We propose a non-invasive procedure for predicting genotype positive for hypertrophic cardiomyopathy (HCM) in subjects that do not exhibit a left-ventricular wall hypertrophy condition (G+LVH-); the procedure is based on the enhanced analysis of medical imaging from 3D speckle tracking echocardiography (3D-STE). 3D-STE, due to its low quality images, has not been used so far to detect effectively the G+LVH- condition. Here, we post-processed echocardiographic images exploiting the tools of modern shape analysis, and we studied the motion of the left ventricle (LV) during an entire cycle. We enrolled 82 controls, 21 HCM patients and 11 G+LVH- subjects. We followed two steps: (i) we selected the most impaired regions of the LV by analysing its strains; and (ii) we used shape analysis on these regions to classify the subjects. The G+LVH- subjects showed different trajectories and deformational attributes. We found high classification performance in terms of area under the receiver operating characteristic curve (∼90), sensitivity (∼78) and specificity (∼79). Our results showed that (i) G+LVH- subjects present important deformational impairments relative to healthy controls and (ii) modern shape analysis can efficiently predict genotype by means of a non-invasive and inexpensive technique such as 3D-STE.

Short-time fractal analysis of biological autoluminescence

Biological systems manifest continuous weak autoluminescence, which is present even in the absence of external stimuli. Since this autoluminescence arises from internal metabolic and physiological processes, several works suggested that it could carry information in the time series of the detected photon counts. However, there is little experimental work which would show any difference of this signal from random Poisson noise and some works were prone to artifacts due to lacking or improper reference signals. Here we apply rigorous statistical methods and advanced reference signals to test the hypothesis whether time series of autoluminescence from germinating mung beans display any intrinsic correlations. Utilizing the fractional Brownian bridge that employs short samples of time series in the method kernel, we suggest that the detected autoluminescence signal from mung beans is not totally random, but it seems to involve a process with a negative memory. Our results contribute to the development of the rigorous methodology of signal analysis of photonic biosignals.

Oligogenic inheritance of a human heart disease involving a genetic modifier

Complex genetic mechanisms are thought to underlie many human diseases, yet experimental proof of this model has been elusive. Here, we show that a human cardiac anomaly can be caused by a combination of rare, inherited heterozygous mutations. Whole-exome sequencing of a nuclear family revealed that three offspring with childhood-onset cardiomyopathy had inherited three missense single-nucleotide variants in the MKL2, MYH7, and NKX2-5 genes. The MYH7 and MKL2 variants were inherited from the affected, asymptomatic father and the rare NKX2-5 variant (minor allele frequency, 0.0012) from the unaffected mother. We used CRISPR-Cas9 to generate mice encoding the orthologous variants and found that compound heterozygosity for all three variants recapitulated the human disease phenotype. Analysis of murine hearts and human induced pluripotent stem cell-derived cardiomyocytes provided histologic and molecular evidence for the NKX2-5 variant's contribution as a genetic modifier.

Increased fractal dimension of left ventricular trabeculations is associated with subclinical diastolic dysfunction in patients with type-2 diabetes mellitus

The aim of this study was to investigate the relationship among left ventricular (LV) concentric hypertrophy, endocardial remodeling, and myocardial deformation in type-2 diabetes mellitus (T2DM). Fifty-three T2DM patients with normotension and 36 healthy controls underwent cardiovascular magnetic resonance imaging to assess for LV concentric hypertrophy (LV myocardial mass index, LVMMi; LVMMi-to-LV end-diastolic volume index ratio, MVR), endocardial remodeling (fractal dimension of trabeculations, FD), and myocardial deformation (global longitudinal, radial and circumferential strain, systolic and diastolic strain rate). When compared with healthy controls, T2DM was associated with LV concentric hypertrophy (LVMMi: T2DM, 52.7 ± 8.9 g/m²; controls, 48.7 ± 8.4 g/m², p = 0.032; MVR: T2DM, 0.88 ± 0.19 g/mL; controls, 0.77 ± 0.16 g/mL, p = 0.007), endocardial remodeling (max. apical FD: T2DM, 1.265 ± 0.056; controls, 1.233 ± 0.055, p = 0.008; mean apical FD: T2DM, 1.198 ± 0.043; controls, 1.176 ± 0.043, p = 0.020), and subtle diastolic dysfunction (peak longitudinal diastolic strain rate, PDSRL: T2DM, 1.1 ± 0.2/s; controls, 1.2 ± 0.3/s, p = 0.031). In the stepwise multivariable regression model, the MVR was an independent determinant of the maximum apical FD (standardized β, sβ = 0.525, p < 0.001) and mean apical FD (sβ = 0.568, p < 0.001). The mean apical FD was an independent determinant of the PDSRL (p = 0.004). LV concentric hypertrophy is an independent determinant of endocardial remodeling, a process that may contribute to subtle LV diastolic dysfunction in T2DM patients.

Atrial Rotor Dynamics Under Complex Fractional Order Diffusion

The mechanisms of atrial fibrillation (AF) are a challenging research topic. The rotor hypothesis states that the AF is sustained by a reentrant wave that propagates around an unexcited core. Cardiac tissue heterogeneities, both structural and cellular, play an important role during fibrillatory dynamics, so that the ionic characteristics of the currents, their spatial distribution and their structural heterogeneity determine the meandering of the rotor. Several studies about rotor dynamics implement the standard diffusion equation. However, this mathematical scheme carries some limitations. It assumes the myocardium as a continuous medium, ignoring, therefore, its discrete and heterogeneous aspects. A computational model integrating both, electrical and structural properties could complement experimental and clinical results. A new mathematical model of the action potential propagation, based on complex fractional order derivatives is presented. The complex derivative order appears of considering the myocardium as discrete-scale invariant fractal. The main aim is to study the role of a myocardial, with fractal characteristics, on atrial fibrillatory dynamics. For this purpose, the degree of structural heterogeneity is described through derivatives of complex order γ = α + jβ. A set of variations for γ is tested. The real part α takes values ranging from 1.1 to 2 and the imaginary part β from 0 to 0.28. Under this scheme, the standard diffusion is recovered when α = 2 and β = 0. The effect of γ on the action potential propagation over an atrial strand is investigated. Rotors are generated in a 2D model of atrial tissue under electrical remodeling due to chronic AF. The results show that the degree of structural heterogeneity, given by γ, modulates the electrophysiological properties and the dynamics of rotor-type reentrant mechanisms. The spatial stability of the rotor and the area of its unexcited core are modulated. As the real part decreases and the imaginary part increases, simulating a higher structural heterogeneity, the vulnerable window to reentrant is increased, as the total meandering of the rotor tip. This in silico study suggests that structural heterogeneity, described by means of complex order derivatives, modulates the stability of rotors and that a wide range of rotor dynamics can be generated.

Cardiovascular assessment of supportive doctor-patient communication using multi-scale and multi-lag analysis of heartbeat dynamics

Emphatic doctor-patient communication has been associated with improved psycho-physiological well-being involving cardiovascular and neuroendocrine responses. Nevertheless, a comprehensive assessment of heartbeat linear and nonlinear dynamics throughout the communication of a life-threatening disease has not been performed yet. To this extent, we studied linear heartbeat dynamics through the extraction of time-frequency domain measurements, as well as heartbeat nonlinear and complex dynamics through novel approaches to compute multi-scale and multi-lag series analyses: namely, the multi-scale distribution entropy and lagged Poincaré plot symbolic analysis. Heart rate variability series were recorded from 54 healthy female subjects who were blind to the aim of the experiment. Participants were randomly assigned into two groups: 27 subjects watched a video where an oncologist discloses the diagnosis of a cancer metastasis to a patient, whereas the remaining 27 watched the same video including four additional supportive comments by the clinician. Considering differences between the beginning and the end of each communication video, results from non-parametric Wilcoxon tests demonstrated that, at a group level, significant differences occurred in heartbeat linear and nonlinear dynamics, with lower complexity during nonsupportive communication. Furthermore, a support vector machine algorithm, validated using a leave-one-subject-out procedure, was able to discern the supportive experience at a single-subject level with an accuracy of 83.33% when nonlinear features were considered, dropping to 51.85% when using standard HRV features only. In conclusion, heartbeat nonlinear and complex dynamics can be a viable tool for the psycho-physiological evaluation of supportive doctor-patient communication. Graphical Abstract Scheme of the three main stages of the study: signal acquisition during doctor-patient communication, ECG signal processing and pattern recognition results.

Altered Heart Rate Regulation in Adolescent Girls and the Vulnerability for Internalizing Disorders

Background: The association between decreased heart rate variability (HRV) and increased internalizing symptoms is well documented. Adolescence is a critical period for the development of mental health problems, in particular internalizing symptoms. Previous research has illustrated sex differences in adolescent HRV, such that females have reduced short-term resting state HRV compared to males. Studies on long-term ecological recordings of HRV in adolescents are scarce. The aims of the present study were, (a) to test if adolescent females show decreased long-term HRV and cardiac complexity (CC) compared to males, and (b) to explore whether sex and HRV and CC measures, as well as their interaction, would predict internalizing symptoms. Materials and Methods: HRV was recorded in n = 166 adolescents (86 girls), on a normal school day. HRV and CC measures were calculated on the interbeat interval time series. Results: Females showed lower HRV and CC in most of the assessed indices. Internalizing symptoms were mainly predicted by HRV whereas sex only predicted symptoms of social anxiety. The interaction between sex and HRV did not predict internalizing symptoms. Conclusions: Results suggest that reduced HRV should be considered as a potential contributor to exacerbating internalizing symptoms in adolescence. Girls with reduced HRV and CC might be prone to the development of internalizing disorders. HRV is a promising tool for the early identification of vulnerability.

Fractal analysis of plaque border, a novel method for the quantification of atherosclerotic plaque contour irregularity, is associated with pro-atherogenic plasma lipid profile in subjects with non-obstructive carotid stenoses

BACKGROUND AND AIMS

Plaque border irregularity is a known imaging characteristic of vulnerable plaques, but its evaluation heavily relies on subjective evaluation and operator expertise. Aim of the present work is to propose a novel fractal-analysis based method for the quantification of atherosclerotic plaque border irregularity and assess its relation with cardiovascular risk factors.

METHODS AND RESULTS

Forty-two asymptomatic subjects with carotid stenosis underwent ultrasound evaluation and assessment of cardiovascular risk factors. Total, low-density lipoprotein (LDL), high-density lipoprotein (HDL) plasma cholesterol and triglycerides concentrations were measured for each subject. Fractal analysis was performed in all the carotid segments affected by atherosclerosis, i.e. 147 segments. The resulting fractal dimension (FD) is a measure of irregularity of plaque profile on long axis view of the plaque. FD in the severest stenosis (main plaque FD,mFD) was 1.136±0.039. Average FD per patient (global FD,gFD) was 1.145±0.039. FD was independent of other plaque characteristics. mFD significantly correlated with plasma HDL (r = -0.367,p = 0.02) and triglycerides-to-HDL ratio (r = 0.480,p = 0.002).

CONCLUSIONS

Fractal analysis is a novel, readily available, reproducible and inexpensive technique for the quantitative measurement of plaque irregularity. The correlation between low HDL levels and plaque FD suggests a role for HDL in the acquisition of morphologic features of plaque instability. Further studies are needed to validate the prognostic value of fractal analysis in carotid plaques evaluation.

Deciphering microvascular changes after myocardial infarction through 3D fully automated image analysis

The microvasculature continuously adapts in response to pathophysiological conditions to meet tissue demands. Quantitative assessment of the dynamic changes in the coronary microvasculature is therefore crucial in enhancing our knowledge regarding the impact of cardiovascular diseases in tissue perfusion and in developing efficient angiotherapies. Using confocal microscopy and thick tissue sections, we developed a 3D fully automated pipeline that allows to precisely reconstruct the microvasculature and to extract parameters that quantify all its major features, its relation to smooth muscle actin positive cells and capillary diffusion regions. The novel pipeline was applied in the analysis of the coronary microvasculature from healthy tissue and tissue at various stages after myocardial infarction (MI) in the pig model, whose coronary vasculature closely resembles that of human tissue. We unravelled alterations in the microvasculature, particularly structural changes and angioadaptation in the aftermath of MI. In addition, we evaluated the extracted knowledge's potential for the prediction of pathophysiological conditions in tissue, using different classification schemes. The high accuracy achieved in this respect, demonstrates the ability of our approach not only to quantify and identify pathology-related changes of microvascular beds, but also to predict complex and dynamic microvascular patterns.

Mortality Prediction in Severe Congestive Heart Failure Patients with Multifractal Point-Process Modeling of Heartbeat Dynamics

Multifractal analysis of human heartbeat dynamics has been demonstrated to provide promising markers of Congestive Heart Failure (CHF). Yet, it crucially builds on the interpolation of RR intervals series, which has been generically performed with limited links to CHF pathophysiology. We devise a novel methodology estimating multifractal autonomic dynamics from heartbeat-derived series defined in the continuous time. We hypothesize that markers estimated from our novel framework are also effective for mortality prediction in severe CHF. We merge multifractal analysis within a methodological framework based on inhomogeneous point process models of heartbeat dynamics. Specifically, wavelet coefficients and wavelet leaders are computed over measures extracted from instantaneous statistics of probability density functions characterizing and predicting the time until the next heartbeat event occurs. The proposed approach is tested on data from 94 CHF patients, aiming at predicting survivor and non-survivor individuals as determined after a 4 years follow up. Instantaneous markers of vagal and sympatho-vagal dynamics display power-law scaling for a large range of scales, from s to s. Using standard SVM algorithms, the proposed inhomogeneous point-process representation based multifractal analysis achieved the best CHF mortality prediction accuracy of 79.11 % (sensitivity 90.48%, specificity 67.74%). Our results suggest that heartbeat scaling and multifractal properties in CHF patients are not generated at the sinus-node level, but rather by the intrinsic action of vagal short-term control and of sympatho-vagal fluctuations associated with circadian cardiovascular control, especially within the VLF band. These markers might provide critical information in devising a clinical tool for individualized prediction of survivor and non-survivor CHF patients.

Multiscale properties of instantaneous parasympathetic activity in severe congestive heart failure: A survivor vs non-survivor study

Multifractal analysis of cardiovascular variability series is an effective tool for the characterization of pathological states associated with congestive heart failure (CHF). Consequently, variations of heartbeat scaling properties have been associated with the dynamical balancing of nonlinear sympathetic/vagal activity. Nevertheless, whether vagal dynamics has multifractal properties yet alone is currently unknown. In this study, we answer this question by conducting multifractal analysis through wavelet leader-based multiscale representations of instantaneous series of vagal activity as estimated from inhomogeneous point process models. Experimental tests were performed on data gathered from 57 CHF patients, aiming to investigate the automatic recognition accuracy in predicting survivor and non-survivor patients after a 4 years follow up. Results clearly indicate that, on both CHF groups, the instantaneous vagal activity displays power-law scaling for a large range of scales, from ≃ 0.5s to ≃ 100s. Using standard SVM algorithms, this information also allows for a prediction of mortality at a single-subject level with an accuracy of 72.72%.

Instantaneous Transfer Entropy for the Study of Cardiovascular and Cardiorespiratory Nonstationary Dynamics

OBJECTIVE

Measures of transfer entropy (TE) quantify the direction and strength of coupling between two complex systems. Standard approaches assume stationarity of the observations, and therefore are unable to track time-varying changes in nonlinear information transfer with high temporal resolution. In this study, we aim to define and validate novel instantaneous measures of TE to provide an improved assessment of complex nonstationary cardiorespiratory interactions.

METHODS

We here propose a novel instantaneous point-process TE (ipTE) and validate its assessment as applied to cardiovascular and cardiorespiratory dynamics. In particular, heartbeat and respiratory dynamics are characterized through discrete time series, and modeled with probability density functions predicting the time of the next physiological event as a function of the past history. Likewise, nonstationary interactions between heartbeat and blood pressure dynamics are characterized as well. Furthermore, we propose a new measure of information transfer, the instantaneous point-process information transfer (ipInfTr), which is directly derived from point-process-based definitions of the Kolmogorov-Smirnov distance.

RESULTS AND CONCLUSION

Analysis on synthetic data, as well as on experimental data gathered from healthy subjects undergoing postural changes confirms that ipTE, as well as ipInfTr measures are able to dynamically track changes in physiological systems coupling.

SIGNIFICANCE

This novel approach opens new avenues in the study of hidden, transient, nonstationary physiological states involving multivariate autonomic dynamics in cardiovascular health and disease. The proposed method can also be tailored for the study of complex multisystem physiology (e.g., brain-heart or, more in general, brain-body interactions).