Applications of fractal analysis to physiology

BP neural network-based analysis of the applicability of NMF in side-step cutting

Background

Although the spatio-temporal structure of muscle activation in cutting have been studied extensively, including time-varying motor primitives and time-invariant motor modules under various conditions, the factorisation methods suitable for cutting are unclear, and the extent to which each factorisation method loses information about movement during dimensionality reduction is uncertain.

Research question

To clarify the extent to which NMF, PCA and ICA retain information about movement when downscaling, and to explore the factorisation method suitable for cutting.

Methods

The kinematic data during cutting was captured with a Vicon motion capture system, from which the kinematic features of the pelvic centre of mass were calculated. NMF, PCA and ICA were used to obtain muscle synergies based on sEMG of the cutting at different angles, respectively. A back propagation neural network was constructed using temporal component of synergy as input and the kinematics data of pelvic as output. Calculation of the Hurst index using fractal analysis based on the temporal component of muscle synergy.

Results

The quality of sEMG reconstruction is significantly higher with ICA (P < 0.01) than with NMF and PCA for the cutting. The NMF reconstruction has a high degree of preservation of movement, whereas the ICA loses movement information about the most of the swing phase, and the PCA loses information related to the change of direction. Hurst index less than 0.5 for all three angles of cutting.

Significance

NMF is suitable for extracting muscle synergies in all directions of cutting. Information related to movement may be lost when using PCA and ICA to extract the synergy of cutting. The high individual variability of muscle synergy in cutting may be responsible for the loss of movement information in muscle synergy.

Three-Dimensional Fractal Analysis of the Interstitial Cells of Cajal Networks of Gastrointestinal Tissue Specimens

Introduction

Several functional gastrointestinal disorders (FGIDs) have been associated with the degradation or remodeling of the network of interstitial cells of Cajal (ICC). Introducing fractal analysis to the field of gastroenterology as a promising data analytics approach to extract key structural characteristics that may provide insightful features for machine learning applications in disease diagnostics. Fractal geometry has advantages over several physically based parameters (or classical metrics) for analysis of intricate and complex microstructures that could be applied to ICC networks.

Methods

In this study, three fractal structural parameters: Fractal Dimension, Lacunarity, and Succolarity were employed to characterize scale-invariant complexity, heterogeneity, and anisotropy; respectively of three types of gastric ICC network structures from a flat-mount transgenic mouse stomach.

Results

The Fractal Dimension of ICC in the longitudinal muscle layer was found to be significantly lower than ICC in the myenteric plexus and circumferential muscle in the proximal, and distal antrum, respectively (both p < 0.0001). Conversely, the Lacunarity parameters for ICC-LM and ICC-CM were found to be significantly higher than ICC-MP in the proximal and in the distal antrum, respectively (both p < 0.0001). The Succolarity measures of ICC-LM network in the aboral direction were found to be consistently higher in the proximal than in the distal antrum (p < 0.05).

Conclusions

The fractal parameters presented here could go beyond the limitation of classical metrics to provide better understanding of the structural-functional relationship between ICC networks and the conduction of gastric bioelectrical slow waves.

Fractals in the Neurosciences: A Translational Geographical Approach

The chapter presents three new fractal indices (fractal fragmentation index, fractal tentacularity index, and fractal anisotropy index) and normalized Kolmogorov complexity with proven applicability in geographic research, developed by the authors, and the possibility of their future use in neuroscience. The research demonstrates the relevance of fractal analysis in different fields and the basic concepts and principles of fractal geometry being sufficient for the development of models relevant to the studied reality. Also, the research highlighted the need to continue interdisciplinary research based on known fractal indicators, as well as the development of new analysis methods with the translational potential between fields.

A Comprehensive Guide to Artificial Intelligence in Endoscopic Ultrasound

BACKGROUND

Endoscopic Ultrasound (EUS) is widely used for the diagnosis of bilio-pancreatic and gastrointestinal (GI) tract diseases, for the evaluation of subepithelial lesions, and for sampling of lymph nodes and solid masses located next to the GI tract. The role of Artificial Intelligence in healthcare in growing. This review aimed to provide an overview of the current state of AI in EUS from imaging to pathological diagnosis and training.

METHODS

AI algorithms can assist in lesion detection and characterization in EUS by analyzing EUS images and identifying suspicious areas that may require further clinical evaluation or biopsy sampling. Deep learning techniques, such as convolutional neural networks (CNNs), have shown great potential for tumor identification and subepithelial lesion (SEL) evaluation by extracting important features from EUS images and using them to classify or segment the images.

RESULTS

AI models with new features can increase the accuracy of diagnoses, provide faster diagnoses, identify subtle differences in disease presentation that may be missed by human eyes, and provide more information and insights into disease pathology.

CONCLUSIONS

The integration of AI in EUS images and biopsies has the potential to improve the diagnostic accuracy, leading to better patient outcomes and to a reduction in repeated procedures in case of non-diagnostic biopsies.

Power laws prevail in medical ultrasound

Major topics in medical ultrasound rest on the physics of wave propagation through tissue. These include fundamental treatments of backscatter, speed of sound, attenuation, and speckle formation. Each topic has developed its own rich history, lexicography, and particular treatments. However, there is ample evidence to suggest that power law relations are operating at a fundamental level in all the basic phenomena related to medical ultrasound. This review paper develops, from literature over the past 60 years, the accumulating theoretical basis and experimental evidence that point to power law behaviors underlying the most important tissue-wave interactions in ultrasound and in shear waves which are now employed in elastography. The common framework of power laws can be useful as a coherent overview of topics, and as a means for improved tissue characterization.

Ergodic descriptors of non-ergodic stochastic processes

The stochastic processes underlying the growth and stability of biological and psychological systems reveal themselves when far-from-equilibrium. Far-from-equilibrium, non-ergodicity reigns. Non-ergodicity implies that the average outcome for a group/ensemble (i.e. of representative organisms/minds) is not necessarily a reliable estimate of the average outcome for an individual over time. However, the scientific interest in causal inference suggests that we somehow aim at stable estimates of the cause that will generalize to new individuals in the long run. Therefore, the valid analysis must extract an ergodic stationary measure from fluctuating physiological data. So the challenge is to extract statistical estimates that may describe or quantify some of this non-ergodicity (i.e. of the raw measured data) without themselves (i.e. the estimates) being non-ergodic. We show that traditional linear statistics such as the standard deviation, coefficient of variation and root mean square can break ergodicity. Time series of statistics addressing sequential structure and its potential nonlinearity: fractality and multi-fractality, change in a time-independent way and fulfil the ergodic assumption. Complementing traditional linear indices with fractal and multi-fractal indices would empower the study of stochastic far-from-equilibrium biological and psychological dynamics.

The capillary fascicle in skeletal muscle: Structural and functional physiology of RBC distribution in capillary networks

KEY POINTS

The capillary module, consisting of parallel capillaries from arteriole to venule, is classically considered as the building block of complex capillary networks. In skeletal muscle, this structure fails to address how blood flow is regulated along the entire length of the synchronously contracting muscle fibres. Using intravital video microscopy of resting extensor digitorum longus muscle in rats, we demonstrated the capillary fascicle as a series of interconnected modules forming continuous columns that align naturally with the dimensions of the muscle fascicle. We observed structural heterogeneity for module topology, and functional heterogeneity in space and time for capillary-red blood cell (RBC) haemodynamics within a module and between modules. We found that module RBC haemodynamics were independent of module resistance, providing direct evidence for microvascular flow regulation at the level of the capillary module. The capillary fascicle is an updated paradigm for characterizing blood flow and RBC distribution in skeletal muscle capillary networks.

ABSTRACT

Capillary networks are the fundamental site of oxygen exchange in the microcirculation. The capillary module (CM), consisting of parallel capillaries from terminal arteriole (TA) to post-capillary venule (PCV), is classically considered as the building block of complex capillary networks. In skeletal muscle, this structure fails to address how blood flow is regulated along the entire length of the synchronously contracting muscle fibres, requiring co-ordination from numerous modules. It has previously been recognized that TAs and PCVs interact with multiple CMs, creating interconnected networks. Using label-free intravital video microscopy of resting extensor digitorum longus muscle in rats, we found that these networks form continuous columns of linked CMs spanning thousands of microns, herein denoted as the capillary fascicle (CF); this structure aligns naturally with the dimensions of the muscle fascicle. We measured capillary-red blood cell (RBC) haemodynamics and module topology (n = 9 networks, 327 modules, 1491 capillary segments). The average module had length 481 μm, width 157 μm and 9.51 parallel capillaries. We observed structural heterogeneity for CM topology, and functional heterogeneity in space and time for capillary-RBC haemodynamics within a module and between modules. There was no correlation between capillary RBC velocity and lineal density. A passive inverse relationship between module length and haemodynamics was remarkably absent, providing direct evidence for microvascular flow regulation at the level of the CM. In summary, the CF is an updated paradigm for characterizing RBC distribution in skeletal muscle, and strengthens the theory of capillary networks as major contributors to the signal that regulates capillary perfusion.

Integrative Computational Models of Lung Structure-Function Interactions

Anatomically based integrative models of the lung and their interaction with other key components of the respiratory system provide unique capabilities for investigating both normal and abnormal lung function. There is substantial regional variability in both structure and function within the normal lung, yet it remains capable of relatively efficient gas exchange by providing close matching of air delivery (ventilation) and blood delivery (perfusion) to regions of gas exchange tissue from the scale of the whole organ to the smallest continuous gas exchange units. This is despite remarkably different mechanisms of air and blood delivery, different fluid properties, and unique scale-dependent anatomical structures through which the blood and air are transported. This inherent heterogeneity can be exacerbated in the presence of disease or when the body is under stress. Current computational power and data availability allow for the construction of sophisticated data-driven integrative models that can mimic respiratory system structure, function, and response to intervention. Computational models do not have the same technical and ethical issues that can limit experimental studies and biomedical imaging, and if they are solidly grounded in physiology and physics they facilitate investigation of the underlying interaction between mechanisms that determine respiratory function and dysfunction, and to estimate otherwise difficult-to-access measures. © 2021 American Physiological Society. Compr Physiol 11:1501-1530, 2021.

Fractal genomics of SOD1 evolution

To understand the fundamental processes of gene evolution such as the impact of point mutations and segmental duplications on statistical topography, superoxide dismutase-1 (SOD1) orthologous sequences (n = 50) are studied. These demonstrate scale invariant self-similarity patterns and long-range correlations (LRCs) indicating fractal organization. Phylogenetic hierarchies change when SOD1 orthologs are grouped according to fractal measures, indicating that statistical topographies can be used to study gene evolution. Sliding window k-mer analysis show that majority of k-mers across all SOD1 orthologs are unique, with very few duplications. Orthologs from simpler species contribute minimally (< 1% of k-mers) to more complex species. Both simple and complex random processes fail to produce significant matching k-mer sequences for SOD1 orthologs. Point mutations causing amyotrophic lateral sclerosis do not impact the fractal organization of human SOD1. Hence, SOD1 did not evolve by a patchwork of repetitive sequences modified by point mutations. Moreover, fractal and other methods described here can be used to study the origin and evolution of genomes.

Functional lung imaging with synchrotron radiation: Methods and preclinical applications

Many lung disease processes are characterized by structural and functional heterogeneity that is not directly appreciable with traditional physiological measurements. Experimental methods and lung function modeling to study regional lung function are crucial for better understanding of disease mechanisms and for targeting treatment. Synchrotron radiation offers useful properties to this end: coherence, utilized in phase-contrast imaging, and high flux and a wide energy spectrum which allow the selection of very narrow energy bands of radiation, thus allowing imaging at very specific energies. K-edge subtraction imaging (KES) has thus been developed at synchrotrons for both human and small animal imaging. The unique properties of synchrotron radiation extend X-ray computed tomography (CT) capabilities to quantitatively assess lung morphology, and also to map regional lung ventilation, perfusion, inflammation and biomechanical properties, with microscopic spatial resolution. Four-dimensional imaging, allows the investigation of the dynamics of regional lung functional parameters simultaneously with structural deformation of the lung as a function of time. This review summarizes synchrotron radiation imaging methods and overviews examples of its application in the study of disease mechanisms in preclinical animal models, as well as the potential for clinical translation both through the knowledge gained using these techniques and transfer of imaging technology to laboratory X-ray sources.

The Complexity and Fractal Geometry of Nuclear Medicine Images

Irregularity in shape and behavior is the main feature of every anatomical system, including human organs, tissues, cells, and sub-cellular entities. It has been shown that this property cannot be quantified by means of the classical Euclidean geometry, which is only able to describe regular geometrical objects. In contrast, fractal geometry has been widely applied in several scientific fields. This rapid growth has also produced substantial insights in the biomedical imaging. Consequently, particular attention has been given to the identification of pathognomonic patterns of "shape" in anatomical entities and their changes from natural to pathological states. Despite the advantages of fractal mathematics and several studies demonstrating its applicability to oncological research, many researchers and clinicians remain unaware of its potential. Therefore, this review aims to summarize the complexity and fractal geometry of nuclear medicine images.

Liver Backscatter and the Hepatic Vasculature’s Autocorrelation Function

Ultrasound imaging of the liver is an everyday, worldwide clinical tool. The echoes are produced by inhomogeneities within the interrogated tissue, but what are the mathematical properties of these scatterers? In theory, the spatial correlation function and the backscatter coefficient are linked by a Fourier transform relationship, however direct measures of these are relatively rare. Under the hypothesis that the fractal branching vasculature and fluid channels are the predominant source of scattering in normal tissues, we compare theory and experimental measures of the autocorrelation function, the frequency dependence of scattering, and fractal dimension estimates from high contrast 3D micro-CT data sets of rat livers. The results demonstrate a fractal dimension of approximately 2.2 with corresponding power law estimates of autocorrelation and ultrasound scattering. These results support a general framework for the analysis of ultrasound scattering from soft tissues.

The fractal geometry of bronchial trees differs by strain in mice

Fractal biological structures are pervasive throughout the plant and animal kingdoms, with the mammalian lung being a quintessential example. The lung airway and vascular trees are generated during embryogenesis from a small set of building codes similar to Turing mechanisms that create robust trees ideally suited to their functions. Whereas the blood flow pattern generated by these fractal trees has been shown to be genetically determined, the geometry of the trees has not. We explored a newly established repository providing high-resolution bronchial trees from the four most commonly studied laboratory mice (B6C3F1, BALB/c, C57BL/6 and CD-1). The data fit a fractal model well for all animals with the fractal dimensions ranging from 1.54 to 1.67, indicating that the conducting airway of mice can be considered a self-similar and space-filling structure. We determined that the fractal dimensions of these airway trees differed by strain but not sex, reinforcing the concept that airway branching patterns are encoded within the DNA. The observations also highlight that future study design and interpretations may need to consider differences in airway geometry between mouse strains.NEW & NOTEWORTHY Similar to larger mammals such as humans, the geometries of the bronchial tree in mice are fractal structures that have repeating patterns from the trachea to the terminal branches. The airway geometries of the four most commonly studied mice are different and need to be considered when comparing results that employ different mouse strains. This variability in mouse airway geometries should be incorporated into computer models exploring toxicology and aerosol deposition in mouse models.

A healthy dose of chaos: Using fractal frameworks for engineering higher-fidelity biomedical systems

Optimal levels of chaos and fractality are distinctly associated with physiological health and function in natural systems. Chaos is a type of nonlinear dynamics that tends to exhibit seemingly random structures, whereas fractality is a measure of the extent of organization underlying such structures. Growing bodies of work are demonstrating both the importance of chaotic dynamics for proper function of natural systems, as well as the suitability of fractal mathematics for characterizing these systems. Here, we review how measures of fractality that quantify the dose of chaos may reflect the state of health across various biological systems, including: brain, skeletal muscle, eyes and vision, lungs, kidneys, tumours, cell regulation, skin and wound repair, bone, vasculature, and the heart. We compare how reports of either too little or too much chaos and fractal complexity can be damaging to normal biological function, and suggest that aiming for the healthy dose of chaos may be an effective strategy for various biomedical applications. We also discuss rising examples of the implementation of fractal theory in designing novel materials, biomedical devices, diagnostics, and clinical therapies. Finally, we explain important mathematical concepts of fractals and chaos, such as fractal dimension, criticality, bifurcation, and iteration, and how they are related to biology. Overall, we promote the effectiveness of fractals in characterizing natural systems, and suggest moving towards using fractal frameworks as a basis for the research and development of better tools for the future of biomedical engineering.

Shapes and distributions of soft tissue scatterers

What causes scattering of ultrasound from normal soft tissues such as the liver, thyroid, and prostate? Commonly, the answer is formulated around the properties of spherical scatterers, related to cellular shapes and sizes. However, an alternative view is that the closely packed cells forming the tissue parenchyma create the reference media, and the long cylindrical-shaped fluid vessels serve as the scattering sites. Under a weak scattering or Born approximation for the extracellular fluid in the vessels, and assuming an isotropic distribution of cylindrical channels across a wide range of diameters, consistent with a fractal branching pattern, some simple predictions can be made about the nature of backscatter as a function of frequency in soft tissues. Specifically, a number of plausible shapes would predict that backscatter increases as a power law of frequency, where the power law is determined by the function governing the number density of the vessels versus diameter. These results are compared with some historical models developed over the last 100 years in scattering theory and point to the need for higher spatial resolution and higher bandwidths to obtain more precise measures of the key parameters in normal tissues, and to better identify the dominant structures responsible for backscatter in everyday clinical imaging.

The 3D Spatial Autocorrelation of the Branching Fractal Vasculature

The fractal branching vasculature within soft tissues and the mathematical properties of the branching system influence a wide range of important phenomena from blood velocity to ultrasound backscatter. Among the mathematical descriptors of branching networks, the spatial autocorrelation function plays an important role in statistical measures of the tissue and of wave propagation through the tissue. However, there are open questions about analytic models of the 3D autocorrelation function for the branching vasculature and few experimental validations for soft vascularized tissue. To address this, high resolution computed tomography scans of a highly vascularized placenta perfused with radiopaque contrast through the umbilical artery were examined. The spatial autocorrelation function was found to be consistent with a power law, which then, in theory, predicts the specific power law behavior of other related functions, including the backscatter of ultrasound.

A perpetual switching system in pulmonary capillaries

Of the 300 billion capillaries in the human lung, a small fraction meet normal oxygen requirements at rest, with the remainder forming a large reserve. The maximum oxygen demands of the acute stress response require that the reserve capillaries are rapidly recruited. To remain primed for emergencies, the normal cardiac output must be parceled throughout the capillary bed to maintain low opening pressures. The flow-distributing system requires complex switching. Because the pulmonary microcirculation contains contractile machinery, one hypothesis posits an active switching system. The opposing hypothesis is based on passive switching that requires no regulation. Both hypotheses were tested ex vivo in canine lung lobes. The lobes were perfused first with autologous blood, and capillary switching patterns were recorded by videomicroscopy. Next, the vasculature of the lobes was saline flushed, fixed by glutaraldehyde perfusion, flushed again, and then reperfused with the original, unfixed blood. Flow patterns through the same capillaries were recorded again. The 16-min-long videos were divided into 4-s increments. Each capillary segment was recorded as being perfused if at least one red blood cell crossed the entire segment. Otherwise it was recorded as unperfused. These binary measurements were made manually for each segment during every 4 s throughout the 16-min recordings of the fresh and fixed capillaries (>60,000 measurements). Unexpectedly, the switching patterns did not change after fixation. We conclude that the pulmonary capillaries can remain primed for emergencies without requiring regulation: no detectors, no feedback loops, and no effectors-a rare system in biology. NEW & NOTEWORTHY The fluctuating flow patterns of red blood cells within the pulmonary capillary networks have been assumed to be actively controlled within the pulmonary microcirculation. Here we show that the capillary flow switching patterns in the same network are the same whether the lungs are fresh or fixed. This unexpected observation can be successfully explained by a new model of pulmonary capillary flow based on chaos theory and fractal mathematics.

Assessment of Driver's Drowsiness Based on Fractal Dimensional Analysis of Sitting and Back Pressure Measurements

The most effective way of preventing motor vehicle accidents caused by drowsy driving is through a better understanding of drowsiness itself. Prior research on the detection of symptoms of drowsy driving has offered insights on providing drivers with advance warning of an elevated risk of crash. The present study measured back and sitting pressures during a simulated driving task under both high and low arousal conditions. Fluctuation of time series of center of pressure (COP) movement of back and sitting pressure was observed to possess a fractal property. The fractal dimensions were calculated to compare the high and low arousal conditions. The results showed that under low arousal (the drowsiness state) the fractal dimension was significantly lower than what was calculated with high arousal. Accumulated drowsiness thus contributed to the loss of self-similarity and unpredictability of time series of back and sitting pressure measurement. Drowsiness further reduces the complexity of the posture control system as viewed from back and sitting pressure. Thus, fractal dimension is a necessary and sufficient condition of a decreased arousal level. It further is a necessary condition for detecting the interval or point in time with high risk of crash.

Similarity analysis between species of the genus Quercus L. (Fagaceae) in southern Italy based on the fractal dimension

The fractal dimension (FD) is calculated for seven species of the genus Quercus L. in Calabria region (southern Italy), five of which have a marcescent-deciduous and two a sclerophyllous character. The fractal analysis applied to the leaves reveals different FD values for the two groups. The difference between the means and medians is very small in the case of the marcescent-deciduous group and very large when these differences are established between both groups: all this highlights the distance between the two groups in terms of similarity. Specifically, Q.crenata, which is hybridogenic in origin and whose parental species are Q.cerris and Q.suber, is more closely related to Q.cerris than to Q.suber, as also expressed in the molecular analysis. We consider that, in combination with other morphological, physiological and genetic parameters, the fractal dimension is a useful tool for studying similarities amongst species.

Vascular amounts and dispersion of caliber-classified vessels as key parameters to quantitate 3D micro-angioarchitectures in multiple myeloma experimental tumors

Blood vessel micro-angioarchitecture plays a pivotal role in tumor progression, metastatic dissemination and response to therapy. Thus, methods able to quantify microvascular trees and their anomalies may allow a better comprehension of the neovascularization process and evaluation of vascular-targeted therapies in cancer. To this aim, the development of a restricted set of indexes able to describe the arrangement of a microvascular tree is eagerly required. We addressed this goal through 3D analysis of the functional microvascular network in sulfo-biotin-stained human multiple myeloma KMS-11 xenografts in NOD/SCID mice. Using image analysis, we show that amounts, spatial dispersion and spatial relationships of adjacent classes of caliber-filtered microvessels provide a near-linear graphical “fingerprint” of tumor micro-angioarchitecture. Position, slope and axial projections of this graphical outcome reflect biological features and summarize the properties of tumor micro-angioarchitecture. Notably, treatment of KMS-11 xenografts with anti-angiogenic drugs affected position and slope of the specific curves without degrading their near-linear properties. The possibility offered by this procedure to describe and quantify the 3D features of the tumor micro-angioarchitecture paves the way to the analysis of the microvascular tree in human tumor specimens at different stages of tumor progression and after pharmacologic interventions, with possible diagnostic and prognostic implications.

Low morphometric complexity of emphysematous lesions predicts survival in chronic obstructive pulmonary disease patients

OBJECTIVES

To investigate whether morphometric complexity in the lung can predict survival and act as a new prognostic marker in patients with chronic obstructive pulmonary disease (COPD).

METHODS

COPD (n = 302) patients were retrospectively reviewed. All patients underwent volumetric computed tomography and pulmonary function tests at enrollment (2005-2015). For complexity analysis, we applied power law exponent of the emphysema size distribution (D_size) as well as box-counting fractal dimension (D_box3D) analysis. Patients' survival at February 2017 was ascertained. Univariate and multivariate Cox proportional hazards analyses were performed, and prediction performances of various combinatorial models were compared.

RESULTS

Patients were 66 ± 6 years old, had 41 ± 28 pack-years' smoking history and variable GOLD stages (n = 20, 153, 108 and 21 in stages I-IV). The median follow-up time was 6.1 years (range: 0.2-11.6 years). Sixty-three patients (20.9%) died, of whom 35 died of lung-related causes. In univariate Cox analysis, lower D_size and D_box3D were significantly associated with both all-cause and lung-related mortality (both p < 0.001). In multivariate analysis, the backward elimination method demonstrated that D_box3D, along with age and the BODE index, was an independent predictor of survival (p = 0.014; HR, 2.08; 95% CI, 1.16-3.71). The contributions of D_size and D_box3D to the combinatorial survival model were comparable with those of the emphysema index and lung-diffusing capacity.

CONCLUSIONS

Low morphometric complexity in the lung is a predictor of survival in patients with COPD.

KEY POINTS

• A newly suggested method for quantifying lung morphometric complexity is feasible. • Morphometric complexity measured on chest CT images predicts COPD patients' survival. • Complexity, diffusing capacity and emphysema index contribute similarly to the survival model.

Fractal dimension and lacunarity analysis of retinal microvascular morphology in hypertension and diabetes

Hypertension and diabetes mellitus represent modifiable risk factors for vascular disease. They cause microvascular remodeling, and ultimately result in end-organ damage. Therefore, development of methods for noninvasive quantification of the effects of hypertension and diabetes mellitus on microvasculature is of paramount importance. The two goals of the study were: 1) to characterize the geometric complexity and inhomogeneity of retinal vasculature in hypertensive retinopathy (HR) and in proliferative diabetic retinopathy (PDR) by using box counting fractal dimension and lacunarity analysis, and 2) to determine if the combination of these two parameters can be used to describe differences in the vascular tree geometry between HR and PDR. The extended set of retinal images from the publicly available STARE database was manually segmented by our expert, validated, and made available for other researchers to use. The healthy retinal vascular network has a higher complexity (fractal dimension) compared to that in HR and in PDR. However, there is no difference in microvascular complexity between HR and PDR. The inhomogeneity of the retinal microvascular tree (lacunarity) was higher in PDR compared to HR. Lacunarity and fractal dimension together quantitatively characterize microvascular geometry in the retina with higher specificity than fractal analysis alone.

Systems Biology and Clinical Practice in Respiratory Medicine. The Twain Shall Meet

Respiratory diseases are highly complex, being driven by host-environment interactions and manifested by inflammatory, structural, and functional abnormalities that vary over time. Traditional reductionist approaches have contributed vastly to our knowledge of biological systems in health and disease to date; however, they are insufficient to provide an understanding of the behavior of the system as a whole. In this Pulmonary Perspective, we discuss systems biology approaches, especially but not limited to the study of the lung as a complex system. Such integrative approaches take into account the large number of dynamic subunits and their interactions found in biological systems. Borrowing methods from physics and mathematics, it is possible to study the collective behavior of these systems over time and in a multidimensional manner. We first examine the physiological basis for complexity in the respiratory system and its implications for disease. We then expand on the potential applications of systems biology methods to study complex systems, within the context of diagnosis and monitoring of respiratory diseases including asthma, chronic obstructive pulmonary disease (COPD), and critical illness. We summarize the significant advances made in recent years using systems approaches for disease phenotyping, applied to data ranging from the molecular to clinical level, obtained from large-scale asthma and COPD networks. We describe new studies using temporal complexity patterns to characterize asthma and COPD and predict exacerbations as well as predict adverse outcomes in critical care. We highlight new methods that are emerging with this approach and discuss remaining questions that merit greater attention in the field.

Aging and cardiovascular complexity: effect of the length of RR tachograms

As we age, our hearts undergo changes that result in a reduction in complexity of physiological interactions between different control mechanisms. This results in a potential risk of cardiovascular diseases which are the number one cause of death globally. Since cardiac signals are nonstationary and nonlinear in nature, complexity measures are better suited to handle such data. In this study, three complexity measures are used, namely Lempel-Ziv complexity (LZ), Sample Entropy (SampEn) and Effort-To-Compress (ETC). We determined the minimum length of RR tachogram required for characterizing complexity of healthy young and healthy old hearts. All the three measures indicated significantly lower complexity values for older subjects than younger ones. However, the minimum length of heart-beat interval data needed differs for the three measures, with LZ and ETC needing as low as 10 samples, whereas SampEn requires at least 80 samples. Our study indicates that complexity measures such as LZ and ETC are good candidates for the analysis of cardiovascular dynamics since they are able to work with very short RR tachograms.

Most suitable mother wavelet for the analysis of fractal properties of stride interval time series via the average wavelet coefficient method

Human gait is a complex interaction of many nonlinear systems and stride intervals exhibiting self-similarity over long time scales that can be modeled as a fractal process. The scaling exponent represents the fractal degree and can be interpreted as a "biomarker" of relative diseases. The previous study showed that the average wavelet method provides the most accurate results to estimate this scaling exponent when applied to stride interval time series. The purpose of this paper is to determine the most suitable mother wavelet for the average wavelet method. This paper presents a comparative numerical analysis of 16 mother wavelets using simulated and real fractal signals. Simulated fractal signals were generated under varying signal lengths and scaling exponents that indicate a range of physiologically conceivable fractal signals. The five candidates were chosen due to their good performance on the mean square error test for both short and long signals. Next, we comparatively analyzed these five mother wavelets for physiologically relevant stride time series lengths. Our analysis showed that the symlet 2 mother wavelet provides a low mean square error and low variance for long time intervals and relatively low errors for short signal lengths. It can be considered as the most suitable mother function without the burden of considering the signal length.

Intraspecific scaling laws are preserved in ventricular hypertrophy but not in heart failure

It is scientifically and clinically important to understand the structure-function scaling of coronary arterial trees in compensatory (e.g., left and right ventricular hypertrophy, LVH and RVH) and decompensatory vascular remodeling (e.g., congestive heart failure, CHF). This study hypothesizes that intraspecific scaling power laws of vascular trees are preserved in hypertrophic hearts but not in CHF swine hearts. To test the hypothesis, we carried out the scaling analysis based on morphometry and hemodynamics of coronary arterial trees in moderate LVH, severe RVH, and CHF compared with age-matched respective control hearts. The scaling exponents of volume-diameter, length-volume, and flow-diameter power laws in control hearts were consistent with the theoretical predictions (i.e., 3, 7/9, and 7/3, respectively), which remained unchanged in LVH and RVH hearts. The scaling exponents were also preserved with an increase of body weight during normal growth of control animals. In contrast, CHF increased the exponents of volume-diameter and flow-diameter scaling laws to 4.25 ± 1.50 and 3.15 ± 1.49, respectively, in the epicardial arterial trees. This study validates the predictive utility of the scaling laws to diagnose vascular structure and function in CHF hearts to identify the borderline between compensatory and decompensatory remodeling.

Migraine — New Perspectives from Chaos Theory

Converging from a number of disciplines, non-linear systems theory and in particular chaos theory offer new descriptive and prescriptive insights into physiological systems. This paper briefly reviews an approach to physiological systems from these perspectives and outlines how these concepts can be applied to the study of migraine. It suggests a wide range of potential applications including new approaches to classification, treatment and pathophysiological mechanisms. A hypothesis is developed that suggests that dysfunctional consequences can result from a mismatch between the complexity of the environment and the system that is seeking to regulate it and that the migraine phenomenon is caused by an incongruity between the complexity of mid brain sensory integration and cortical control networks. Chaos theory offers a new approach to the study of migraine that complements existing frameworks but may more accurately reflect underlying physiological mechanisms.

Nonlinear complexity analysis of brain FMRI signals in schizophrenia

We investigated the differences in brain fMRI signal complexity in patients with schizophrenia while performing the Cyberball social exclusion task, using measures of Sample entropy and Hurst exponent (H). 13 patients meeting diagnostic and Statistical Manual of Mental Disorders, 4th Edition (DSM IV) criteria for schizophrenia and 16 healthy controls underwent fMRI scanning at 1.5 T. The fMRI data of both groups of participants were pre-processed, the entropy characterized and the Hurst exponent extracted. Whole brain entropy and H maps of the groups were generated and analysed. The results after adjusting for age and sex differences together show that patients with schizophrenia exhibited higher complexity than healthy controls, at mean whole brain and regional levels. Also, both Sample entropy and Hurst exponent agree that patients with schizophrenia have more complex fMRI signals than healthy controls. These results suggest that schizophrenia is associated with more complex signal patterns when compared to healthy controls, supporting the increase in complexity hypothesis, where system complexity increases with age or disease, and also consistent with the notion that schizophrenia is characterised by a dysregulation of the nonlinear dynamics of underlying neuronal systems.

Complexity and emergent phenomena

Complex biological systems operate under non-equilibrium conditions and exhibit emergent properties associated with correlated spatial and temporal structures. These properties may be individually unpredictable, but tend to be governed by power-law probability distributions and/or correlation. This article reviews the concepts that are invoked in the treatment of complex systems through a wide range of respiratory-related examples. Following a brief historical overview, some of the tools to characterize structural variabilities and temporal fluctuations associated with complex systems are introduced. By invoking the concept of percolation, the notion of multiscale behavior and related modeling issues are discussed. Spatial complexity is then examined in the airway and parenchymal structures with implications for gas exchange followed by a short glimpse of complexity at the cellular and subcellular network levels. Variability and complexity in the time domain are then reviewed in relation to temporal fluctuations in airway function. Next, an attempt is given to link spatial and temporal complexities through examples of airway opening and lung tissue viscoelasticity. Specific examples of possible and more direct clinical implications are also offered through examples of optimal future treatment of fibrosis, exacerbation risk prediction in asthma, and a novel method in mechanical ventilation. Finally, the potential role of the science of complexity in the future of physiology, biology, and medicine is discussed.

A comparative analysis of spectral exponent estimation techniques for 1/f(β) processes with applications to the analysis of stride interval time series

BACKGROUND

The time evolution and complex interactions of many nonlinear systems, such as in the human body, result in fractal types of parameter outcomes that exhibit self similarity over long time scales by a power law in the frequency spectrum S(f)=1/f(β). The scaling exponent β is thus often interpreted as a "biomarker" of relative health and decline.

NEW METHOD

This paper presents a thorough comparative numerical analysis of fractal characterization techniques with specific consideration given to experimentally measured gait stride interval time series. The ideal fractal signals generated in the numerical analysis are constrained under varying lengths and biases indicative of a range of physiologically conceivable fractal signals. This analysis is to complement previous investigations of fractal characteristics in healthy and pathological gait stride interval time series, with which this study is compared.

RESULTS

The results of our analysis showed that the averaged wavelet coefficient method consistently yielded the most accurate results.

COMPARISON WITH EXISTING METHODS

Class dependent methods proved to be unsuitable for physiological time series. Detrended fluctuation analysis as most prevailing method in the literature exhibited large estimation variances.

CONCLUSIONS

The comparative numerical analysis and experimental applications provide a thorough basis for determining an appropriate and robust method for measuring and comparing a physiologically meaningful biomarker, the spectral index β. In consideration of the constraints of application, we note the significant drawbacks of detrended fluctuation analysis and conclude that the averaged wavelet coefficient method can provide reasonable consistency and accuracy for characterizing these fractal time series.

Spatial distribution of ventilation and perfusion: mechanisms and regulation

With increasing spatial resolution of regional ventilation and perfusion, it has become more apparent that ventilation and blood flow are quite heterogeneous in the lung. A number of mechanisms contribute to this regional variability, including hydrostatic gradients, pleural pressure gradients, lung compressibility, and the geometry of the airway and vascular trees. Despite this marked heterogeneity in both ventilation and perfusion, efficient gas exchange is possible through the close regional matching of the two. Passive mechanisms, such as the shared effect of gravity and the matched branching of vascular and airway trees, create efficient gas exchange through the strong correlation between ventilation and perfusion. Active mechanisms that match local ventilation and perfusion play little if no role in the normal healthy lung but are important under pathologic conditions.

Distribution of perfusion

Local driving pressures and resistances within the pulmonary vascular tree determine the distribution of perfusion in the lung. Unlike other organs, these local determinants are significantly influenced by regional hydrostatic and alveolar pressures. Those effects on blood flow distribution are further magnified by the large vertical height of the human lung and the relatively low intravascular pressures in the pulmonary circulation. While the distribution of perfusion is largely due to passive determinants such as vascular geometry and hydrostatic pressures, active mechanisms such as vasoconstriction induced by local hypoxia can also redistribute blood flow. This chapter reviews the determinants of regional lung perfusion with a focus on vascular tree geometry, vertical gradients induced by gravity, the interactions between vascular and surrounding alveolar pressures, and hypoxic pulmonary vasoconstriction. While each of these determinants of perfusion distribution can be examined in isolation, the distribution of blood flow is dynamically determined and each component interacts with the others so that a change in one region of the lung influences the distribution of blood flow in other lung regions.

Temporal fractals in seabird foraging behaviour: diving through the scales of time

Animal behaviour exhibits fractal structure in space and time. Fractal properties in animal space-use have been explored extensively under the Lévy flight foraging hypothesis, but studies of behaviour change itself through time are rarer, have typically used shorter sequences generated in the laboratory, and generally lack critical assessment of their results. We thus performed an in-depth analysis of fractal time in binary dive sequences collected via bio-logging from free-ranging little penguins (Eudyptula minor) across full-day foraging trips (2(16) data points; 4 orders of temporal magnitude). Results from 4 fractal methods show that dive sequences are long-range dependent and persistent across ca. 2 orders of magnitude. This fractal structure correlated with trip length and time spent underwater, but individual traits had little effect. Fractal time is a fundamental characteristic of penguin foraging behaviour, and its investigation is thus a promising avenue for research on interactions between animals and their environments.

The effect of single-pulse transcranial magnetic stimulation and peripheral nerve stimulation on complexity of EMG signal: fractal analysis

The aim of this study was to examine whether single-pulse transcranial magnetic stimulation (spTMS) affects the pattern of corticospinal activity once voluntary drive has been restored after spTMS-induced EMG silence. We used fractal dimension (FD) to explore the 'complexity' of the electromyography (EMG) signal, and median frequency of the spectra (MDF) to examine changes in EMG spectral characteristics. FD and MDF of the raw EMG epochs immediately before were compared with those obtained from epochs after the EMG silence. Changes in FD and MDF after spTMS were examined with three levels of muscle contraction corresponding to weak (20-40%), moderate (40-60%) and strong (60-80% of maximal voluntary contraction) and three intensities of stimulation set at 10, 20 and 30% above the resting motor threshold. FD was calculated using the Higuchi fractal dimension algorithm. Finally, to discern the origin of FD changes between the CNS and muscle, we compared the effects of spTMS with the effects of peripheral nerve stimulation (PNS) on FD and MDF. The results show that spTMS induced significant decrease in both FD and MDF of EMG signal after stimulation. PNS did not have any significant effects on FD nor MDF. Changes in TMS intensity did not have any significant effect on FD or MDF after stimulation nor had the strength of muscle contraction. However, increase in contraction strength decreased FD before stimulation but only between weak and moderate contraction. The results suggest that the effects of spTMS on corticospinal activity, underlying voluntary motor output, outlast the TMS stimulus. It appears that the complexity of the EMG signal is reduced after spTMS, suggesting that TMS alters the dynamics of the ongoing corticospinal activity most likely temporarily synchronizing the neural network activity. Further studies are needed to confirm whether observed changes after TMS occur at the cortical level.

Pulmonary blood flow and its distribution in highly trained endurance athletes and healthy control subjects

Pulmonary blood flow (PBF) is an important determinant of endurance sports performance, yet studies investigating adaptations of the pulmonary circulation in athletes are scarce. In the present study, we investigated PBF, its distribution, and heterogeneity at baseline and during intravenous systemic adenosine infusion in 10 highly trained male endurance athletes and 10 untrained but fit healthy controls, using positron emission tomography and [15O]water at rest and during adenosine infusion at supine body posture. Our results indicate that PBF at rest and during adenosine stimulation was similar in both groups (213 ± 55 and 563 ± 138 ml·100 ml−1·min−1 in athletes and 206 ± 83 and 473 ± 212 ml·100 ml−1·min−1 in controls, respectively). Although the PBF response to adenosine was thus unchanged in athletes, overall PBF heterogeneity was reduced from rest to adenosine infusion (from 84 ± 18 to 70 ± 19%, P < 0.05), while remaining unchanged in healthy controls (77 ± 16 to 85 ± 33%, P = 0.4). Additionally, there was a marked gravitational influence on general PBF distribution so that clear dorsal dominance was observed both at rest and during adenosine infusion, but training status did not have an effect on this distribution. Regional blood flow heterogeneity was markedly lower in the high-perfusion dorsal areas, both at rest and during adenosine, in all subjects, but flow heterogeneity in dorsal area tended to further decrease in response to adenosine in athletes. In conclusion, reduced blood flow heterogeneity in response to adenosine in endurance athletes may be a reflection of capillary reserve, which is more extensively recruitable in athletes than in matched healthy control subjects.

Training to walk amid uncertainty with Re-Step: measurements and changes with perturbation training for hemiparesis and cerebral palsy

PURPOSE

To describe Re-Step™, a novel mechatronic shoe system that measures center of pressure (COP) gait parameters and complexity of COP dispersion while walking, and to demonstrate these measurements in healthy controls and individuals with hemiparesis and cerebral palsy (CP) before and after perturbation training.

METHOD

The Re-Step™ was used to induce programmed chaotic perturbations to the feet while walking for 30 min for 36 sessions over 12-weeks of training in two subjects with hemiparesis and two with CP.

RESULTS

Baseline measurements of complexity indices (fractal dimension and approximate entropy) tended to be higher in controls than in those with disabilities, while COP variability, mean and variability of step time and COP dispersion were lower. After training the disabled subjects these measurement values tended toward those of the controls, along with a decrease in step time, 10 m walk time, average step time, percentage of double support and increased Berg balance score.

CONCLUSIONS

This pilot trial reveals the feasibility and applicability of this unique measurement and perturbation system for evaluating functional disabilities and changes with interventions to improve walking. Implication for Rehabilitation Walking, of individuals with cerebral palsy and hemiparesis following stroke, can be viewed in terms of a rigid motor behavior that prevents adaptation to changing environmental conditions. Re-Step system (a) measures and records linear and non-linear gait parameters during free walking to provide a detailed evaluation of walking disabilities, (b) is an intervention training modality that applies unexpected perturbations during walking. This perturbation intervention may improve gait and motor functions of individuals with hemiparesis and cerebral plasy.

Fractal organization of the human T cell repertoire in health and after stem cell transplantation

T cell repertoire diversity is generated in part by recombination of variable (V), diversity (D), and joining (J) segments in the T cell receptor β (TCR) locus. T cell clonal frequency distribution determined by high-throughput sequencing of TCR β in 10 stem cell transplantation (SCT) donors revealed a fractal, self-similar frequency distribution of unique TCR bearing clones with respect to V, D, and J segment usage in the T cell repertoire of these individuals. Further, ranking of T cell clones by frequency of gene segment usage in the observed sequences revealed an ordered distribution of dominant clones conforming to a power law, with a fractal dimension of 1.6 and 1.8 in TCR β DJ and VDJ containing clones in healthy stem cell donors. This self-similar distribution was perturbed in the recipients after SCT, with patients demonstrating a lower level of complexity in their TCR repertoire at day 100 followed by a modest improvement by 1 year post-SCT. A large shift was observed in the frequency distribution of the dominant T cell clones compared to the donor, with fewer than one third of the VDJ-containing clones shared in the top 4 ranks. In conclusion, the normal T cell repertoire is highly ordered with a TCR gene segment usage that results in a fractal self-similar motif of pattern repetition across levels of organization. Fractal analysis of high-throughput TCR β sequencing data provides a comprehensive measure of immune reconstitution after SCT.

c-Myc is required for proper coronary vascular formation via cell- and gene-specific signaling

OBJECTIVE

Although significant research has detailed angiogenesis during development and cancer, little is known about cardiac angiogenesis, yet it is critical for survival following pathological insult. The transcription factor c-Myc is a target of anticancer therapies because of its mitogenic and proangiogenic induction. In the current study, we investigate its role in cardiac angiogenesis in a cell-dependent and gene-specific context.

METHODS AND RESULTS

Angiogenesis assays using c-Myc-deficient cardiac endothelial cells and fibroblasts demonstrate that c-Myc is essential to vessel formation, and fibroblast-mediated vessel formation is dependent on c-Myc expression in fibroblasts. Gene analyses revealed that c-Myc-mediated gene expression is unique in cardiac angiogenesis and varies in a cell-dependent manner. In vitro 3-dimensional cultures demonstrated c-Myc's role in the expression of secreted angiogenic factors, while also providing evidence for c-Myc-mediated cell-cell interactions. Additional in vivo vascular analyses support c-Myc's critical role in capillary formation and vessel patterning during development and also in response to a pathological stimulus where its expression in myocytes is required for angiogenic remodeling.

CONCLUSIONS

These data demonstrate that proper c-Myc expression in cardiac fibroblasts and myocytes is essential to cardiac angiogenesis. These results have the potential for novel therapeutic applications involving the angiogenic response during cardiac remodeling.

The interdependent contributions of gravitational and structural features to perfusion distribution in a multiscale model of the pulmonary circulation

Recent experimental and imaging studies suggest that the influence of gravity on the measured distribution of blood flow in the lung is largely through deformation of the parenchymal tissue. To study the contribution of hydrostatic effects to regional perfusion in the presence of tissue deformation, we have developed an anatomically structured computational model of the pulmonary circulation (arteries, capillaries, veins), coupled to a continuum model of tissue deformation, and including scale-appropriate fluid dynamics for blood flow in each vessel type. The model demonstrates that both structural and the multiple effects of gravity on the pulmonary circulation make a distinct contribution to the distribution of blood. It shows that postural differences in perfusion gradients can be explained by the combined effect of tissue deformation and extra-acinar blood vessel resistance to flow in the dependent tissue. However, gravitational perfusion gradients persist when the effect of tissue deformation is eliminated, highlighting the importance of the hydrostatic effects of gravity on blood distribution in the pulmonary circulation. Coupling of large- and small-scale models reveals variation in microcirculatory driving pressures within isogravitational planes due to extra-acinar vessel resistance. Variation in driving pressures is due to heterogeneous large-vessel resistance as a consequence of geometric asymmetry in the vascular trees and is amplified by the complex balance of pressures, distension, and flow at the microcirculatory level.

Prompt prediction of successful defibrillation from 1-s ventricular fibrillation waveform in patients with out-of-hospital sudden cardiac arrest

PURPOSE

Ventricular fibrillation (VF) is a common cardiac arrest rhythm that can be terminated by electrical defibrillation. During cardiopulmonary resuscitation, there is a strong need for a prompt and reliable predictor of successful defibrillation because myocardial damage can result from repeated futile defibrillation attempts. Continuous wavelet transform (CWT) provides excellent time and frequency resolution of signals. The purpose of this study was to evaluate whether features based on CWT could predict successful defibrillation.

METHODS

VF electrocardiogram (ECG) waveforms stored in ambulance-located defibrillators were collected. Predefibrillation waveforms were divided into 1.0- or 5.12-s VF waveforms. Indices in frequency domain or nonlinear analysis were calculated on the 5.12-s waveform. Simultaneously, CWT was performed on the 1.0-s waveform, and total low-band (1-3 Hz), mid-band (3-10 Hz), and high-band (10-32 Hz) energy were calculated.

RESULTS

In 152 patients with out-of-hospital cardiac arrest, a total of 233 ECG predefibrillation recordings, consisting of 164 unsuccessful and 69 successful episodes, were analyzed. Indices of frequency domain analysis (peak frequency, centroid frequency, and amplitude spectral area), nonlinear analysis (approximate entropy and Hurst exponent, detrended fluctuation analysis), and CWT analysis (mid-band and high-band energy) were significantly different between unsuccessful and successful episodes (P < 0.01 for all). However, logistic regression analysis showed that centroid frequency and total mid-band energy were effective predictors (P < 0.01 for both).

CONCLUSIONS

Energy spectrum analysis based on CWT as short as a 1.0-s VF ECG waveform enables prompt and reliable prediction of successful defibrillation.

Fractals for physicians

There is increasing interest in the study of fractals in medicine. In this review, we provide an overview of fractals, of techniques available to describe fractals in physiological data, and we propose some reasons why a physician might benefit from an understanding of fractals and fractal analysis, with an emphasis on paediatric respiratory medicine where possible. Among these reasons are the ubiquity of fractal organisation in nature and in the body, and how changes in this organisation over the lifespan provide insight into development and senescence. Fractal properties have also been shown to be altered in disease and even to predict the risk of worsening of disease. Finally, implications of a fractal organisation include robustness to errors during development, ability to adapt to surroundings, and the restoration of such organisation as targets for intervention and treatment.