Gait variability, fractal dynamics, and statistical regularity of treadmill and overground walking recorded with a smartphone

BACKGROUND

The nonlinear variability present during steady-state gait may provide a signature of health and showcase one's walking adaptability. Although treadmills can capture vast amounts of walking data required for estimating variability within a small space, gait patterns may be misrepresented compared to an overground setting. Smartphones may provide a low-cost and user-friendly estimate of gait patterns among a variety of walking settings. However, no study has investigated differences in gait patterns derived from a smartphone between treadmill walking (TW) and overground walking (OW).

RESEARCH QUESTION

This study implemented a smartphone accelerometer to compare differences in temporal gait variability and gait dynamics between TW and OW.

METHODS

Sixteen healthy adults (8F; 24.7 ± 3.8 years) visited the laboratory on three separate days and completed three 8-minute OW and three TW trials, at their preferred speed, during each visit. The inter-stride interval was calculated as the time difference between right heel contact events located within the vertical accelerometery signals recorded from a smartphone while placed in participants front right pant pocket during walking trials. The inter-stride interval series was used to calculate stride time standard deviation (SD) and coefficient of variation (COV), statistical persistence (fractal scaling index), and statistical regularity (sample entropy). Two-way analysis of variance compared walking condition and laboratory visits for each measure.

RESULTS

Compared to TW, OW displayed significantly (p < 0.01) greater stride time SD (0.014 s, 0.020 s), COV (1.26 %, 1.82 %), fractal scaling index (0.70, 0.79) and sample entropy (1.43, 1.63). No differences were found between visits for all measures.

SIGNIFICANCE

Smartphone-based assessment of gait provides the ability to distinguish between OW and TW conditions, similar to previously established methodologies. Furthermore, smartphones may be a low-cost and user-friendly tool to estimate gait patterns outside the laboratory to improve ecological validity, with implications for free-living monitoring of gait among various populations.

Random number generator based on a memristive circuit

In this paper we discuss the details, limitations, and difficulties of the implementation in hardware of a memristor-based random number generator that exhibits monofractal/multifractal behavior. To do so, the components and selection criteria of a reference memristor and one proposed by the authors, the chaotic circuit leveraging them, and the processing that is performed on the chaotic signals to achieve the random discrete sequences are described. After applying the estimation tools, findings indicate that more than 60% of the proposed combinations allow generating random discrete sequences, with long-range dependence, and that both monofractal and multifractal behaviors can also be obtained. Consequently, a hardware system was achieved that can be used as a source of entropy in future synthetic biological signal generators.

Flexible liquid metal-based microfluidic strain sensors with fractal-designed microchannels for monitoring human motion and physiological signals

With the rapid advancement of wearable electronics, there is an increasing demand for high-performance flexible strain sensors. In this work, a flexible strain sensor based on liquid metal (LM)-integrated into a microfluidic device is developed with Peano-type fractal structure design. Compared with the microfluidic sensors with straight and wavy microchannels, the sensor with Peano-shaped channels shows lower hysteresis and improved stretchability. Furthermore, the increase of the fractal order can further improve the sensing performances. The third-order Peano sensor exhibits excellent mechanical and electrical properties, including high tensile capability (490.3%), minimal hysteresis (DH = 0.86%), ultra-low detection limit (0.1%), low overshoot, rapid response time (117 ms), as well as good stability and durability. By adding two independent and perpendicular straight channels to the Peano sensing unit, the feasibility of multi-directional strain recognition is demonstrated. To further improve the sensitivity of the Peano-shaped sensor, a multi-layer Peano sensor is developed, exhibiting remarkably enhanced sensitivity while maintaining low hysteresis. Overall, the developed LM-based microfluidic strain sensors enrolling Peano fractal geometry hold high potential for various wearable electronics applications.

Liver cancer: A geometric approach to fractals and scaling analysis

In the study of liver cancer, invasive techniques such as computed tomography (CT) and magnetic resonance imaging (MRI) are used. In the present work, an in vivo 3D study will be carried out using MRI and CT images, using scaling dynamics, that is, calculating critical exponents of local roughness and fractal dimension. The results obtained for stages IA, IIA, and IIIA in liver cancer correspond to what was proposed by F. Family and T. Vicsek (1991).

Fractal feature selection model for enhancing high-dimensional biological problems

The integration of biology, computer science, and statistics has given rise to the interdisciplinary field of bioinformatics, which aims to decode biological intricacies. It produces extensive and diverse features, presenting an enormous challenge in classifying bioinformatic problems. Therefore, an intelligent bioinformatics classification system must select the most relevant features to enhance machine learning performance. This paper proposes a feature selection model based on the fractal concept to improve the performance of intelligent systems in classifying high-dimensional biological problems. The proposed fractal feature selection (FFS) model divides features into blocks, measures the similarity between blocks using root mean square error (RMSE), and determines the importance of features based on low RMSE. The proposed FFS is tested and evaluated over ten high-dimensional bioinformatics datasets. The experiment results showed that the model significantly improved machine learning accuracy. The average accuracy rate was 79% with full features in machine learning algorithms, while FFS delivered promising results with an accuracy rate of 94%.

Prognostic value of right ventricular trabecular complexity in patients with arrhythmogenic cardiomyopathy

OBJECTIVES

The present study aimed to investigate the incremental prognostic value of the right ventricular fractal dimension (FD), a novel marker of myocardial trabecular complexity by cardiac magnetic resonance (CMR) in patients with arrhythmogenic cardiomyopathy (ACM).

METHODS

Consecutive patients with ACM undergoing CMR were followed up for major cardiac events, including sudden cardiac death, aborted cardiac arrest, and appropriate implantable cardioverter defibrillator intervention. Prognosis prediction was compared by Cox regression analysis. We established a multivariable model supplemented with RV FD and evaluated its discrimination by Harrell's C-statistic. We compared the category-free, continuous net reclassification improvement (cNRI) and integrated discrimination index (IDI) before and after the addition of FD.

RESULTS

A total of 105 patients were prospectively included from three centers and followed up for a median of 60 (48, 66) months; experienced 36 major cardiac events were recorded. Trabecular FD displayed a strong unadjusted association with major cardiac events (p < 0.05). In the multivariable Cox regression analysis, RV maximal apical FD maintained an independent association with major cardiac events (hazard ratio, 1.31 (1.11-1.55), p < 0.002). The Hosmer-Lemeshow goodness of fit test displayed good fit (X2 = 0.68, p = 0.99). Diagnostic performance was significantly improved after the addition of RV maximal apical FD to the multivariable baseline model, and the continuous net reclassification improvement increased 21% (p = 0.001), and the integrated discrimination index improved 16% (p = 0.045).

CONCLUSIONS

In patients with ACM, CMR-assessed myocardial trabecular complexity was independently correlated with adverse cardiovascular events and provided incremental prognostic value.

CLINICAL RELEVANCE STATEMENT

The application of FD values for assessing RV myocardial trabeculae may become an accessible and promising parameter in monitoring and early diagnosis of risk factors for adverse cardiovascular events in patients with ACM.

KEY POINTS

• Ventricular trabecular morphology, a novel quantitative marker by CMR, has been explored for the first time to determine the severity of ACM. • Patients with higher maximal apical fractal dimension of RV displayed significantly higher cumulative incidence of major cardiac events. • RV maximal apical FD was independently associated with major cardiac events and provided incremental prognostic value in patients with ACM.

Computational and Translational Fractal-Based Analysis in the Translational Neurosciences: An Overview

After the previous sections on "Fractals: What and Why?," the last section of this book covers the software tools necessary to perform computational fractal-based analysis, with special emphasis on its applications into the neurosciences. The use of ImageJ and MATLAB, as well as other software packages, is reviewed. The current and future applications of fractal modeling in bioengineering and biotechnology are discussed as well. Perspectives on the translation of merging fractals with artificial intelligence-based methods with the final aim of pattern discrimination in neurological diseases by means of a unified fractal model of the brain are also given. Moreover, some new translational applications of fractal analysis to the neurosciences are presented, including eye tracking analysis, cognitive neuroscience, and music.

EEG Complexity Analysis of Brain States, Tasks and ASD Risk

Autism spectrum disorder is an increasingly prevalent and debilitating neurodevelopmental condition and an electroencephalogram (EEG) diagnostic challenge. Despite large amounts of electrophysiological research over many decades, an EEG biomarker for autism spectrum disorder (ASD) has not been found. We hypothesized that reductions in complex dynamical system behaviour in the human central nervous system as part of the macroscale neuronal function during cognitive processes might be detectable in whole EEG for higher-risk ASD adults. In three studies, we compared the medians of correlation dimension, largest Lyapunov exponent, Higuchi's fractal dimension, multiscale entropy, multifractal detrended fluctuation analysis and Kolmogorov complexity during resting, cognitive and social skill tasks in 20 EEG channels of 39 adults over a range of ASD risk. We found heterogeneous complexity distribution with clusters of hierarchical sequences pointing to potential cognitive processing differences, but no clear distinction based on ASD risk. We suggest that there is indication of statistically significant differences between complexity measures of brain states and tasks. Though replication of our studies is needed with a larger sample, we believe that our electrophysiological and analytic approach has potential as a biomarker for earlier ASD diagnosis.

Analyzing Eye Paths Using Fractals

Visual patterns reflect the anatomical and cognitive background underlying process governing how we perceive information, influenced by stimulus characteristics and our own visual perception. These patterns are both spatially complex and display self-similarity seen in fractal geometry at different scales, making them challenging to measure using the traditional topological dimensions used in Euclidean geometry.However, methods for measuring eye gaze patterns using fractals have shown success in quantifying geometric complexity, matchability, and implementation into machine learning methods. This success is due to the inherent capabilities that fractals possess when reducing dimensionality using Hilbert curves, measuring temporal complexity using the Higuchi fractal dimension (HFD), and determining geometric complexity using the Minkowski-Bouligand dimension.Understanding the many applications of fractals when measuring and analyzing eye gaze patterns can extend the current growing body of knowledge by identifying markers tied to neurological pathology. Additionally, in future work, fractals can facilitate defining imaging modalities in eye tracking diagnostics by exploiting their capability to acquire multiscale information, including complementary functions, structures, and dynamics.

Local fractal dimension of collagen detects increased spatial complexity in fibrosis

Increase of collagen content and reorganization characterizes fibrosis but quantifying the latter remains challenging. Spatially complex structures are often analyzed via the fractal dimension; however, established methods for calculating this quantity either provide a single dimension for an entire object or a spatially distributed dimension that only considers binary images. These neglect valuable information related to collagen density in images of fibrotic tissue. We sought to develop a fractal analysis that can be applied to 3-dimensional (3D) images of fibrotic tissue. A fractal dimension map for each image was calculated by determining a single fractal dimension for a small area surrounding each image pixel, using fiber thickness as the third dimension. We found that this local fractal dimension increased with age and with progression of fibrosis regardless of collagen content. Our new method of distributed 3D fractal analysis can thus distinguish between changes in collagen content and organization induced by fibrosis.

Advances in Understanding Fractals in Affective and Anxiety Disorders

In this chapter, we review the research that has applied fractal measures to the study of the most common psychological disorders, that is, affective and anxiety disorders. Early studies focused on heart rate, but diverse measures have also been examined, from variations in subjective mood, or hand movements, to electroencephalogram or magnetoencephalogram data. In general, abnormal fractal dynamics in different physiological and behavioural outcomes have been observed in mental disorders. Despite the disparity of variables measured, fractal analysis has shown high sensitivity in discriminating patients from healthy controls. However, and because of this heterogeneity in measures, the results are not straightforward, and more studies are needed in this promising line.

Fractals in Neuroanatomy and Basic Neurosciences: An Overview

The introduction of fractal geometry to the neurosciences has been a major paradigm shift over the last decades as it has helped overcome approximations and limitations that occur when Euclidean and reductionist approaches are used to analyze neurons or the entire brain. Fractal geometry allows for quantitative analysis and description of the geometric complexity of the brain, from its single units to the neuronal networks.As illustrated in the second section of this book, fractal analysis provides a quantitative tool for the study of the morphology of brain cells (i.e., neurons and microglia) and its components (e.g., dendritic trees, synapses), as well as the brain structure itself (cortex, functional modules, neuronal networks). The self-similar logic which generates and shapes the different hierarchical systems of the brain and even some structures related to its "container," that is, the cranial sutures on the skull, is widely discussed in the following chapters, with a link between the applications of fractal analysis to the neuroanatomy and basic neurosciences to the clinical applications discussed in the third section.

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.

Neuronal Fractal Dynamics

Synapse formation is a unique biological phenomenon. The molecular biological perspective of this phenomenon is different from the fractal geometrical one. However, these perspectives are not mutually exclusive and supplement each other. The cornerstone of the first one is a chain of biochemical reactions with the Markov property, that is, a deterministic, conditional, memoryless process ordered in time and in space, in which the consecutive stages are determined by the expression of some regulatory proteins. The coordination of molecular and cellular events leading to synapse formation occurs in fractal time space, that is, the space that is not only the arena of events but also actively influences those events. This time space emerges owing to coupling of time and space through nonlinear dynamics. The process of synapse formation possesses fractal dynamics with non-Gaussian distribution of probability and a reduced number of molecular Markov chains ready for transfer of biologically relevant information.

Scale-free dynamics of COVID-19 in a Brazilian city

A common basis to address the dynamics of directly transmitted infectious diseases, such as COVID-19, are compartmental (or SIR) models. SIR models typically assume homogenous population mixing, a simplification that is convenient but unrealistic. Here we validate an existing model of a scale-free fractal infection process using high-resolution data on COVID-19 spread in São Caetano, Brazil. We find that transmission can be described by a network in which each infectious individual has a small number of susceptible contacts, of the order of 2-5. This model parameter correlated tightly with physical distancing measured by mobile phone data, such that in periods of greater distancing the model recovered a lower average number of contacts, and vice versa. We show that the SIR model is a special case of our scale-free fractal process model in which the parameter that reflects population structure is set at unity, indicating homogeneous mixing. Our more general framework better explained the dynamics of COVID-19 in São Caetano, used fewer parameters than a standard SIR model and accounted for geographically localized clusters of disease. Our model requires further validation in other locations and with other directly transmitted infectious agents.

Multifractal test for nonlinearity of interactions across scales in time series

The creativity and emergence of biological and psychological behavior tend to be nonlinear, and correspondingly, biological and psychological measures contain degrees of irregularity. The linear model might fail to reduce these measurements to a sum of independent random factors (yielding a stable mean for the measurement), implying nonlinear changes over time. The present work reviews some of the concepts implicated in nonlinear changes over time and details the mathematical steps involved in their identification. It introduces multifractality as a mathematical framework helpful in determining whether and to what degree the measured series exhibits nonlinear changes over time. These mathematical steps include multifractal analysis and surrogate data production for resolving when multifractality entails nonlinear changes over time. Ultimately, when measurements fail to fit the structures of the traditional linear model, multifractal modeling allows for making those nonlinear excursions explicit, that is, to come up with a quantitative estimate of how strongly events may interact across timescales. This estimate may serve some interests as merely a potentially statistically significant indicator of independence failing to hold, but we suspect that this estimate might serve more generally as a predictor of perceptuomotor or cognitive performance.

Computer-aided Diagnosis of Polyp Classification Using Scale Invariant Features and Extreme Gradient Boosting

Aims

Analysis of colonoscopy images is an important diagnostic procedure in the identification of colorectal cancer. It has been observed that owing to advancements in technology, numerous machine-learning models now excel in the analysis of colorectal polyps classification. This work focused on developing a framework that can classify polyps using images during colonoscopy.

Materials and Methods

First, the images were corrected by removing their spectral reflection. Second, feature pools were obtained by applying Radon transform (θ=45, 90, 135, and 180). From the Radon transform, fractal dimension was calculated as a feature vector combined with Zernike moment obtained from the Zernike features. Finally, Extreme Gradient Boosting (XGBoost) algorithm was applied for the classification and to compare it with state-of-the-art methods.

Results

The experimental results obtained with the proposed framework have been reported, cross-validated, and discussed. The proposed method gives a classification accuracy of 93% for light XGBoost and 92% for XGBoost.

Conclusion

This study shows that by applying scale invariant features over a small dataset, XGBoost outperforms state-of-the-art methods when it comes to polyp classification.

Full-scale pore characteristics in coal and their influence on the adsorption capacity of coalbed methane

Coalbed methane (CBM) is primarily stored and transported through the pores in the coal matrix, making it essential to study the development of different scales of pores in coal to better understand the evaluation and exploration of CBM. In this study, four coal samples of varying ranks (R_o,max = 0.68%-2.86%) were selected, and different scale pores were obtained through low-pressure CO₂ and Ar adsorption (LP-CO₂/ArGA) and mercury intrusion porosimetry (MIP) experiments. A full-scale pore evaluation model was established, and the impact of pores on methane adsorption and restriction was analyzed and discussed through high-pressure adsorption experiments. Our results show that (1) at high pressures (> 100 MPa), the MIP technique caused pore compression and overestimated the pore size below 30 nm by up to 47.2%; (2) to obtain a comprehensive pore evaluation, we developed an accurate model that combines LP-CO₂/ArGA with NLDFT and BJH and NLDFT models to determine micropore (0.3-1.5 nm) and mesopore (1.5-30 nm) parameters. By combining this model with MIP test results, we can obtain a full-scale pore size in the range of 0.3 nm-200 μm; (3) coal rank affected the development of full-scale pore characteristics. As coal rank increased, the specific surface area (SSA) of micropores and adsorption capacity of methane first decreased, then increased. Micropores were found to be the most important storage space for CBM and control gas adsorption, with a microporous SSA and PV to total SSA and total PV ratio of 97.93% and 63.69%, respectively. (4) We also observed a significant linear relationship between the fractal dimension of micropores and the Langmuir volume (V_L) based on fractal theory. As the fractal dimension increased, V_L also increased (R² = 0.8581), indicating that V_L is controlled by the complexity of micropores, which is consistent with the comprehensive evaluation index (D_t) and V_L (R² = 0.8744). Based on our predicted model, V_L can be estimated using the SSA of micropores and D_t. Our findings shed light on the relationship between pore morphology and CBM occurrence and have practical implications for fields such as catalytic synthesis, E-CBM, and gas purification.

Statistical theory of asymmetric damage segregation in clonal cell populations

Asymmetric damage segregation (ADS) is ubiquitous among unicellular organisms: After a mother cell divides, its two daughter cells receive sometimes slightly, sometimes strongly different fractions of damaged proteins accumulated in the mother cell. Previous studies demonstrated that ADS provides a selective advantage over symmetrically dividing cells by rejuvenating and perpetuating the population as a whole. In this work we focus on the statistical properties of damage in individual lineages and the overall damage distributions in growing populations for a variety of ADS models with different rules governing damage accumulation, segregation, and the lifetime dependence on damage. We show that for a large class of deterministic ADS rules the trajectories of damage along the lineages are chaotic, and the distributions of damage in cells born at a given time asymptotically becomes fractal. By exploiting the analogy of linear ADS models with the Iterated Function Systems known in chaos theory, we derive the Frobenius-Perron equation for the stationary damage density distribution and analytically compute the damage distribution moments and fractal dimensions. We also investigate nonlinear and stochastic variants of ADS models and show the robustness of the salient features of the damage distributions.

Statistical Theory of Asymmetric Damage Segregation in Clonal Cell Populations

Asymmetric damage segregation (ADS) is ubiquitous among unicellular organisms: After a mother cell divides, its two daughter cells receive sometimes slightly, sometimes strongly different fractions of damaged proteins accumulated in the mother cell. Previous studies demonstrated that ADS provides a selective advantage over symmetrically dividing cells by rejuvenating and perpetuating the population as a whole. In this work we focus on the statistical properties of damage in individual lineages and the overall damage distributions in growing populations for a variety of ADS models with different rules governing damage accumulation, segregation, and the lifetime dependence on damage. We show that for a large class of deterministic ADS rules the trajectories of damage along the lineages are chaotic, and the distributions of damage in cells born at a given time asymptotically becomes fractal. By exploiting the analogy of linear ADS models with the Iterated Function Systems known in chaos theory, we derive the Frobenius-Perron equation for the stationary damage density distribution and analytically compute the damage distribution moments and fractal dimensions. We also investigate nonlinear and stochastic variants of ADS models and show the robustness of the salient features of the damage distributions.

Fractal analysis of impact of PM2.5 on surface O3 sensitivity regime based on field observations

Properties of PM_2.5 that can change aerosol chemistry and photolysis rates have great impacts on O₃ sensitivity regime, further affecting the production rate of surface O₃. However, responses of O₃ sensitivity regime to changes in PM_2.5 levels are difficult to be accurately determined, due to the complexity and nonlinearity of atmospheric chemistry. Here, based on long-term time series (2016-2020) of air quality variables in north and south Taiwan, fractal analysis along with Pearson correlation analysis are used to directly reveal the impacts of PM_2.5 on O₃ sensitivity regime in real atmosphere, by capturing the nonlinear dynamic relations among air pollutants. Great regional and seasonal difference in impacts of PM_2.5 on O₃ sensitivity regime may be ascribed to meteorological factors, PM_2.5 components and levels of SO₂, NO, NO₂, etc. For north Taiwan, increased PM_2.5 level can enhance the sensitivity of O₃ formation to VOC in spring and summer, whereas the opposite effect can be observed in winter. But for south Taiwan, the influence of PM_2.5 on O₃ sensitivity regime is not statistically significant, excluding spring. Furthermore, feasibility and availability of fractal analysis is tested by simulations with Empirical Kinetics Modeling Approach (EKMA). The results demonstrate the capability of fractal analysis to identify the impacts of PM_2.5 on O₃ sensitivity regime in real atmosphere, which can provide suggestions for PM_2.5-O₃ coordinated control strategies in regions suffering combined air pollution.

Growth models of fractal interfaces in the description of microorganism colony growth: effect of photodynamic inactivation

Candida albicans is responsible for most of the nosocomial infections that affect immunocompromised individuals. We investigated the application of eosin in photodynamic inactivation as a strategy in the inhibition of the growth of C. albicans and the morphological variation and growth dynamics in light of fractal theory. The damage caused to fungal structures alters the roughness of the colony, and these changes were described by parameters that were defined by mathematical models. Proliferation of the fungi should be inhibited in the center of the colonies and the analysis of the edges gives an indication about the dynamics of growth and cell reproduction.

Knee extensor force control as a predictor of dynamic balance in healthy adults

BACKGROUND

Previous research has demonstrated that force control in various muscles of the lower limb (measured according to the magnitude of force fluctuations) explains significant variance in static balance. Given the dynamic nature of many functional activities and sports, assessment of balance and its determinants under dynamic conditions is of importance.

RESEARCH QUESTION

Does muscle force control explain significant variance in dynamic balance, as measured using the Y balance test (YBT)?

METHODS

YBT performance and knee extensor muscle force control were measured in 28 healthy participants. The YBT involved stance on the right leg and attempting maximal reach with the left leg in the anterior, posteromedial, and posterolateral directions. Force control was assessed during isometric knee extension contractions of the right leg at 10%, 20% and 40% maximal voluntary contraction (MVC) and was quantified according to the magnitude (using the coefficient of variation [CV]), and the temporal structure (using sample entropy, SampEn; and detrended fluctuation analysis α), of force fluctuations.

RESULTS

Significant correlations were observed for YBT anterior reach and muscle force CV (r = -0.44, P = 0.02) and SampEn (r = 0.47, P = 0.012) during contractions at 40% MVC. A subsequent regression model demonstrated that muscle force CV and SampEn at 40% MVC significantly explained 54% of variance in YBT anterior reach. Significant correlations were also observed for YBT posteromedial reach and MVC (r = 0.39, P = 0.043) and muscle force CV during contractions at 40% MVC (r = -0.51, P = 0.006). The regression model demonstrated that MVC and muscle force CV at 40% MVC significantly explained 53.9% of variance in YBT posteromedial reach.

SIGNIFICANCE

These results are the first to indicate that a moderate amount of variance in dynamic balance can be explained by measures of isometric force control.

Alternative stable state and its evaluation in wetland reconstruction based on landscape design

An alternative stable state is closely related to the health and sustainable development of ecosystems; however, knowledge of the alternative stable state and its quantitative evaluation in wetland reconstruction remains incomplete. In this study, we used landscape design to reconstruct an optimized ecological polder wetland and a lake wetland in the Yunmeng Marsh area, China, and the alternative stable states of the two wetland ecosystems were assessed from an ecosystem perspective via emergy/eco-exergy and fractal dimensions. The emergy densities for the optimized ecological polder wetland and the lake wetland were 2.35E+13 sej yr^-1 m^-3 and 2.18E+13 sej m^-3, and the emergy sustainability index (ESI) values were 216.57 and 193.31, respectively, indicating that the reconstructed wetland ecosystems were dominated by renewable energy flows and were highly sustainable. The eco-exergy density and emergy/eco-exergy ratio results showed that natural selection self-organized the reconstructed wetland ecosystems to tolerate environmental stresses and changes. In addition, the fractal dimensions of the morphology and contour of the polder wetland, which reflect the space occupation capacity of geometric and physical constraints in the wetland, were 1.57 and 1.75, and those of the lake wetland were 1.03 and 1.47, respectively. The synthetic evaluation results showed that the alternative stable states of both the optimized ecological polder wetland ecosystem and the lake wetland ecosystem were ecofriendly modes of wetland reconstruction, which can be implemented together to create a "lake-polder" ecosystem. Our study on the alternative stable states of wetland ecosystems is helpful for exploring the synergistic symbiosis between traditional culture and the ecological environment in China and other wetland-rich regions and countries with severe disturbances.

Systems biology of human aging: A Fibonacci time series model

Fractals are everywhere in nature, particularly at the interfaces where matter or energy must be transferred, since they maximize surface area while minimizing energy losses. Temporal fractals have been well studied at micro scales in human biology, but have received comparatively little attention at broader macro scales. In this paper, we describe a fractal time series model of human aging from a systems biology perspective. This model examines how intrinsic aging rates are shaped by entropy and Fibonacci fractal dynamics, with implications for the emergence of key life cycle traits. This proposition is supported by research findings. The finding of an intrinsic aging rate rooted in Fibonacci fractal dynamics represents a new predictive paradigm in evolutionary biology.

A Numerical Study of Elastic Wave Arrival Behavior in a Naturally Fractured Rock Based on a Combined Displacement Discontinuity-Discrete Fracture Network Model

The arrival behavior of elastic waves in a naturally fractured rock is studied based on numerical simulations. We use the discrete fracture network method to represent the distribution of a natural fracture system and employ the displacement discontinuity method to compute the propagation of elastic waves across individual fractures. We analyze macroscopic wavefield arrival properties collectively arising from the interaction between elastic waves and numerous fractures in the system. We show that the dimensionless angular frequency ῶ = ωZ/κ exerts a fundamental control on the arrival behavior of a plane wave traveling through the fractured rock, where ω, Z, and κ are the angular frequency, seismic impedance, and fracture stiffness, respectively. An asynchronous arrival phenomenon of the wave energy occurs and becomes more significant with an increased ῶ. Two regimes are identified according to the two-branch dependency of the fractal dimension D of the FFAW on ῶ, where the wave arrival behavior is within a non-fractal regime for ῶ smaller than the critical frequency ῶ _c ≈ 1.0, and enters the fractal regime for ῶ ≥ ῶ _c. The self-affine properties of the FFAW, i.e., the roughness exponent α and the correlation length l _c, both linearly decrease as a function of the exponent ξ (with ῶ = 10 ^ξ ) in the fractal regime. Early breakthrough of wave transport occurs in regions with relatively low fracture density, while late-time arrival happens in regions of high fracture density.

Fractal methods applied to the seminiferous lumen images can quantify testicular changes induced by heat stress

Male infertility affects many couples around the world and can be related to environmental factors such as exposure to high temperatures. Even so, automated methods evaluating the seminiferous tubules to detect testicular damage are still scarce. In search of new approaches to automation in the microscopic analysis of the testis; the present study used the fractal dimension, lacunarity, multifractality and quantitative morphometry to quantify changes in microphotographs of the seminiferous lumen in testicles reversibly damaged by heat stress (43 °C, 12 min). The parameters fractal dimension, lacunarity, multifractality (Dq and α), perimeter, feret and circularity were able to detect changes in the seminiferous lumen at 7, 15 and 30 days after the testicular damage. These methods also detected the recovery of spermatogenesis at 60 days after heat stress. Area, f(α), centroid X and Y, roundness, rectangle height and width were unable to detect changes caused by heat stress. In conclusion, computer assisted methods applied to the seminiferous lumen images can be a useful new viewpoint to analyze microscopic changes in the testicles, a fast low-cost tool to assist in the automated quantification of testicular damage.

Efficient calculation of fractal properties via the Higuchi method

Higuchi's method of determining fractal dimension is an important, well-used, research tool that, compared to many other methods, gives rapid, efficient, and robust estimations for the range of possible fractal dimensions. One major shortcoming in applying the method is the correct choice of tuning parameter (k _max); a poor choice can generate spurious results, and there is no agreed upon methodology to solve this issue. We analyze multiple instances of synthetic fractal signals to minimize an error metric. This allows us to offer a new and general method that allows determination, a priori, of the best value for the tuning parameter, for a particular length data set. We demonstrate its use on physical data, by calculating fractal dimensions for a shell model of the nonlinear dynamics of MHD turbulence, and severe acute respiratory syndrome coronavirus 2 isolate Wuhan-Hu-1 from the family Coronaviridae.

Unraveling agglomeration and deagglomeration in aqueous colloidal dispersions of very small tin dioxide nanoparticles

HYPOTHESIS

Understanding deagglomeration, agglomerate formation and structure for very small nanoparticles (NPs), due to their more facile agglomeration, is critical for processing or tailoring agglomerates for nanostructured materials. We propose that by controlling and fine-tuning the interplay of agglomeration (colloidal interaction) and deagglomeration (hydrodynamic forces), the design of agglomerate size, microstructure and morphology is possible even for very small NPs.

EXPERIMENTS

Here, we investigate very small SnO₂ NPs (10 nm) generated in the gas phase as model system. Small-angle X-ray scattering (SAXS) and dynamic light scattering (DLS) are used to study dispersions in aqueous media across the entire pH range (2-12) at various NaCl concentrations treated with ultrasound. Parallel to size and size distribution, agglomerate morphology and microstructure are analyzed by means of the mass fractal dimension, d_m and modeled with ab initio shape simulations. The critical coagulation concentration (CCC) is determined for the alkaline region where the SnO₂ NPs are highly charged.

FINDINGS

Quantitative analysis of SAXS and DLS data reveals that size and size distribution of the agglomerates depend similarly on the electrostatic interaction influenced by pH and salinity as observed by the zeta potential. In contrast d_m is mainly influenced by the salt concentration. Ab initio shape simulations support these experimental findings.

Parametric Cortical Representations of Complexity and Preference for Artistic and Computer-Generated Fractal Patterns Revealed by Single-Trial EEG Power Spectral Analysis

Fractals are self-similar patterns that repeat at different scales, the complexity of which are expressed as a fractional Euclidean dimension D between 0 (a point) and 2 (a filled plane). The drip paintings of American painter Jackson Pollock (JP) are fractal in nature, and Pollock's most illustrious works are of the high-D (~1.7) category. This would imply that people prefer more complex fractal patterns, but some research has instead suggested people prefer lower-D fractals. Furthermore, research has suggested that parietal and frontal brain activity tracks the complexity of fractal patterns, but previous research has artificially binned fractals depending on fractal dimension, rather than treating fractal dimension as a parametrically varying value. We used white layers extracted from JP artwork as stimuli, and constructed statistically matched 2-dimensional random Cantor sets as control stimuli. We recorded the electroencephalogram (EEG) while participants viewed the JP and matched random Cantor fractal patterns. Participants then rated their subjective preference for each pattern. We used a single-trial analysis to construct within-subject models relating subjective preference to fractal dimension D, as well as relating D and subjective preference to single-trial EEG power spectra. Results indicated that participants preferred higher-D images for both JP and Cantor stimuli. Power spectral analysis showed that, for artistic fractal images, parietal alpha and beta power parametrically tracked complexity of fractal patterns, while for matched mathematical fractals, parietal power tracked complexity of patterns over a range of frequencies, but most prominently in alpha band. Furthermore, parietal alpha power parametrically tracked aesthetic preference for both artistic and matched Cantor patterns. Overall, our results suggest that perception of complexity for artistic and computer-generated fractal images is reflected in parietal-occipital alpha and beta activity, and neural substrates of preference for complex stimuli are reflected in parietal alpha band activity.

Retrospective fractal analyses of one-year follow-up data obtained after single-visit nonsurgical endodontic retreatment on periapical radiographs

OBJECTIVES

The aim of retrospective study was to evaluate the changes to the periapical bone sites after non-surgical endodontic retreatment by using fractal analysis on periapical radiographs.

MATERIALS AND METHODS

Thirty patients whose teeth had periapical lesions and underwent primary endodontic treatment were selected for nonsurgical single-visit endodontic retreatment. Two radiographs were taken, the first immediately after retreatment and the second at the 1-year follow-up. An identical region of interest close to the infected root apex was selected from each radiograph. FD was measured using the box-counting method. Periapical status was evaluated using the periapical index (PAI). Treatment outcomes were categorized into healed (PAI < 3), or not healed (PAI ≥ 3) based on radiographic criteria.

RESULTS

The mean FD value significantly increased at the 1-year follow-up compared to baseline. No significant sex biases were apparent. According to the PAI, retreatment after 1 year resulted in a 63.3% healed.

CONCLUSION

The extent of periapical trabecular bone evident radiographically increased, as revealed by FD data, 1 year after endodontic retreatment. Clinical relevance The use of fractal analysis as a quantitative method to evaluate changes in periapical trabecular bone (such as healing and inflammation) after endodontic retreatment can be an important marker in determining the prognosis of endodontic retreatment.

Preserved fractal character of structural brain networks is associated with covert consciousness after severe brain injury

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We study structural brain networks in patients with disorders of consciousness (DOC)

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Structural brain networks are less fractal (self-similar) in patients than controls.

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Preserved fractal dimension is associated with covert consciousness in DOC patients.

Self-similarity is ubiquitous throughout natural phenomena, including the human brain. Recent evidence indicates that fractal dimension of functional brain networks, a measure of self-similarity, is diminished in patients diagnosed with disorders of consciousness arising from severe brain injury. Here, we set out to investigate whether loss of self-similarity is observed in the structural connectome of patients with disorders of consciousness. Using diffusion MRI tractography from N = 11 patients in a minimally conscious state (MCS), N = 10 patients diagnosed with unresponsive wakefulness syndrome (UWS), and N = 20 healthy controls, we show that fractal dimension of structural brain networks is diminished in DOC patients. Remarkably, we also show that fractal dimension of structural brain networks is preserved in patients who exhibit evidence of covert consciousness by performing mental imagery tasks during functional MRI scanning. These results demonstrate that differences in fractal dimension of structural brain networks are quantitatively associated with chronic loss of consciousness induced by severe brain injury, highlighting the close connection between structural organisation of the human brain and its ability to support cognitive function.

[Complexity theory and the hypertensive patient]

Hypertension is the main cause of death worldwide and the approach that the Family Physician makes of hypertensive patients, given his or her key role as a gateway to the health system, is a crucial determinant in their evolution. On the other hand, Complexity theory contributes to the understanding on how systems grow, adapt and evolve. The hypertensive patient, given his character of biological and social being, can be understood and approached as a complex system. Understanding the characteristics of these systems contributes to considering the patient from another perspective, more satisfactory both for himself and for the professional who assists him. This review analyzes the characteristics of the complex system «hypertensive patient» and the tools that allow us to account for and interact with this complexity. An approach from multiple perspectives, migrating from the classic reductionist models to others that take into account the dynamic interrelationships that are at stake, would be a useful strategy for the Family Physician in the challenge of achieving adequate control of blood pressure in his or her patients.

Multifractal roots of suprapostural dexterity

Visually guided postural control emerges in response to task constraints. Task constraints generate physiological fluctuations that foster the exploration of available sensory information at many scales. Temporally correlated fluctuations quantified using fractal and multifractal metrics have been shown to carry perceptual information across the body. The risk of temporally correlated fluctuations is that stable sway appears to depend on a healthy balance of standard deviation (SD): too much or too little SD entails destabilization of posture. This study presses on the visual guidance of posture by prompting participants to quietly stand and fixate at distances within, less than, and beyond comfortable viewing distance. Manipulations of the visual precision demands associated with fixating nearer and farther than comfortable viewing distance reveals an adaptive relationship between SD and temporal correlations in postural fluctuations. Changing the viewing distance of the fixation target shows that increases in temporal correlations and SD predict subsequent reductions in each other. These findings indicate that the balance of SD within stable bounds may depend on a tendency for temporal correlations to self-correct across time. Notably, these relationships became stronger with greater distance from the most comfortable viewing and reaching distance, suggesting that this self-correcting relationship allows the visual layout to press the postural system into a poise for engaging with objects and events. Incorporating multifractal analysis showed that all effects attributable to monofractal evidence were better attributed to multifractal evidence of nonlinear interactions across scales. These results offer a glimpse of how current nonlinear dynamical models of self-correction may play out in biological goal-oriented behavior. We interpret these findings as part of the growing evidence that multifractal nonlinearity is a modeling strategy that resonates strongly with ecological-psychological approaches to perception and action.

Social modulation of on-screen looking behaviour

While passive social information (e.g. pictures of people) routinely draws one's eyes, our willingness to look at live others is more nuanced. People tend not to stare at strangers and will modify their gaze behaviour to avoid sending undesirable social signals; yet they often continue to monitor others covertly "out of the corner of their eyes." What this means for looks that are being made near to live others is unknown. Will the eyes be drawn towards the other person, or pushed away? We evaluate changes in two elements of gaze control: image-independent principles guiding how people look (e.g. biases to make eye movements along the cardinal directions) and image-dependent principles guiding what people look at (e.g. a preference for meaningful content within a scene). Participants were asked to freely view semantically unstructured (fractals) and semantically structured (rotated landscape) images, half of which were located in the space near to a live other. We found that eye movements were horizontally displaced away from a visible other starting at 1032 ms after stimulus onset when fractals but not landscapes were viewed. We suggest that the avoidance of looking towards live others extends to the near space around them, at least in the absence of semantically meaningful gaze targets.

Pore-scale model and dewatering performance of municipal sludge by ultrahigh pressurized electro-dewatering with constant voltage gradient

The disposal of huge municipal sludge with high moisture content has led to numerous energy consumption and brought extensive concerns in the world. In this paper, three dewatering modes, ultrahigh-pressure mechanical dewatering mode (UMDW), pressurized electro-dewatering (PEDW) with constant voltage mode (U-PEDW) and constant voltage gradient mode (G-PEDW) were performed on a self-designed pressurized electro-dewatering apparatus for municipal sludge. The pore structures and moisture distributions were detected by low-field nuclear magnetic resonance technology. Meanwhile, the moisture distributions and quantitative bound strength were analyzed by the thermogravimetric differential scanning calorimetry test. Moreover, a pore-scale electro-osmosis model was accordingly developed based on the fractal characteristics of pore size distribution. Finally, the effect of dewatering modes and operating parameters on moisture content and energy consumption were examined in detail. The results indicate that the pore-scale electro-osmosis model show good consistency with experimental data. The electric field can drive the middle-layers-water to overcome the capillary pressure, and make G-PEDW removing more water than UMDW. The moisture content of dewatered municipal sludge by G-PEDW and U-PEDW reaches to 28.41% and 27.33%, respectively. Furthermore, the energy consumption of G-PEDW is 189.62Wh/kg._H2O, it is much lower than that of U-PEDW. Therefore, the G-PEDW mode with low moisture content and less energy consumption indicates best dewatering performance compared with UMDW and U-PEDW modes. The present work is helpful to understand the dewatering mechanisms of G-PEDW and provides useful guidelines for G-PEDW dewatering technology.

Air-encapsulating elastic mechanism of submerged Taraxacum blowballs

In this article, we report the observation of an air-encapsulating elastic mechanism of Dandelion spherical seed heads, namely blowballs, when submerged underwater. This peculiarity seems to be fortuitous since Taraxacum is living outside water; nevertheless, it could become beneficial for a better survival under critical conditions, e.g. of temporary flooding. The scaling of the volume of the air entrapped suggests its fractal nature with a dimension of 2.782 and a fractal air volume fraction of 4.82 × 10⁻² m^0.218, resulting in nominal air volume fractions in the range of 14–23%. This aspect is essential for the optimal design of bioinspired materials made up of Dandelion-like components. The miniaturization of such components leads to an increase in the efficiency of the air encapsulation up to the threshold (efficiency = 1) achieved for an optimal critical size. Thus, the optimal design is accomplished using small elements, with the optimal size, rather than using larger elements in a lower number. The described phenomenon, interesting per se, also brings bioinspired insights toward new related technological solutions for underwater air-trapping and air-bubbles transportation, e.g. the body surface of a man could allow an apnea (air consumption of 5–10 l/min) of about 10 min if it is covered by a material made up of a periodic repetition of Dandelion components of diameter ≅18 μm and having a total thickness of about 3–6 cm.

Multifractality in postural sway supports quiet eye training in aiming tasks: A study of golf putting

The 'quiet eye' (QE) approach to visually-guided aiming behavior invests fully in perceptual information's potential to organize coordinated action. Sports psychologists refer to QE as the stillness of the eyes during aiming tasks and increasingly into self- and externally-paced tasks. Amidst the 'noisy' fluctuations of the athlete's body, quiet eyes might leave fewer saccadic interruptions to the coupling between postural sway and optic flow. Postural sway exhibits fluctuations whose multifractal structure serves as a robust predictor of visual and haptic perceptual responses. Postural sway generates optic flow centered on an individual's eye height. We predicted that perturbing the eye height by attaching wooden blocks below the feet would perturb the putting more so in QE-trained participants than participants trained technically. We also predicted that QE's efficacy and responses to perturbation would depend on multifractality in postural sway. Specifically, we predicted that less multifractality would predict more adaptive responses to the perturbation and higher putting accuracy. Results showed that lower multifractality led to more accurate putts, and the perturbation of eye height led to less accurate putts, particularly for QE-trained participants. Models of radial error (i.e., the distance between the ball's final position and the hole) indicated that lower estimates of multifractality due to nonlinearity coincided with a more adaptive response to the perturbation. These results suggest that reduced multifractality may act in a context-sensitive manner to restrain motoric degrees of freedom to achieve the task goal.

The emergence of a fractal structure of formal logic via the spatiotemporal reflexive self-identification

In this paper, we aim to analyze the structure of formal logic in relation to its emergence as a universal tool for understanding and description of reality. There are some extended variations of logic that treat time and/or space (e.g. temporal logic), however in general, formal logic is regarded as universal. This universality makes formal logic neither spatial nor temporal. Nevertheless, the emergence of formal logic takes place in time and space and its operation is characterized by the simultaneous temporal and spatial features. We realize these aspects of formal logic along the line of the previously developed model of the Double Homunculus (Sawa K., Igamberdiev A.U., 2016, BioSystems 144, 1-7) which can be seen as an emergence of logic. A diagrammatic representation of this concept reveals fractal structures. At the same time, we present actual logical connectives on these fractal figures with the transformations over time and space. This can provide the basis for understanding the relationships between time, space, and logic.

Test-retest reliability of multiscale fractal dimension measurements of plantar pressure maps during dynamic tasks

The tools used to evaluate foot types are divergent since they adopt classic linear analyzes, based on anthropometric or image measurements, which do not dynamically contemplate the variability of foot shape. The use of newer techniques such as multiscale fractal dimension (MFD) may be a key to this type of problem. However, for these measures to be used safely and consistently, it is essential to evaluate their reliability. The aim of this study was to evaluate the test-retest reliability of MFD measurements of adult plantar pressure maps during gait, as well as the standard error of measurement (SEM), and minimal detectable change (MDC₉₀). Seventy-two subjects were included in the test-retest, with a one week interval. The plantar pressure maps were constructed using a pressure platform. The data were processed in a routine for extracting the MFD curve measurements (maximum and integral values). The Intraclass Correlation Coefficient results (ICC_3,k) were excellent for both measurements (maximum value 0.96, 95% confidence interval [0.93-0.97], and integral 0.95 [0.92-0.97]) with low SEM and MDC₉₀ values below 10% of the mean. The application of MFD to the plantar pressure data generated by the pressure platform is reliable and could allow exploration of the complexity of foot shapes, enabling their classification.

Complexus cordis

The science-based study of the heart has allowed us to know its structure and function deeply, through the fragmentation and analysis of its parts, following the guidelines that so many achievements have given to us. However, at the time of reassembling those analyzed fragments, we realize that something is missing; the simply sum of the parts is not equal to everything. Thus, for decades, numerous scientists have studied novel strategies that allow us understanding, every natural phenomena from a more inclusive, open and integrative models, which closely address to interactions rather than components. In this way, we can observe how, the behavior of many variables usually transgress the conventional plane and moves towards non-linearity and fractality, making a complex tissue that will maintain its structure while thermodynamically viable. Thus, this document shows the way how, the non-linear study of complex cardiovascular dynamics, begins to give us answers to many questions that the clinical cardiologist poses every day.

Effect of a laser-ablated micron-scale modification of dental implant collar surface on changes in the vertical and fractal dimensions of peri-implant trabecular bone

BACKGROUND

Marginal bone loss (MBL) represents an important indicator of peri-implant health and the measure of its level is considered a determining factor in the evaluation of the quality of survival. Aim of this study is to compare radiographic changes in the fractal and mesial/distal vertical dimensions of peri-implant trabecular bone of dental implants with a laser-ablated micron-scale modication (LAM) of collar surface after a 5-year follow-up period.

MATERIALS AND METHODS

Thirty-four implants with LAM of collar surface (test group = TG) and 31 implants without LAM of collar surface (control group = CG) were placed in 45 non-smoking, periodontally healthy patients. Fractal and vertical dimensions of peri-implant trabecular bone were measured by comparing radiographs taken immediately after prosthesis delivery with those taken 3 years and 5 years after functional loading.

RESULT

At the end of the 5-year follow-up, the MBL in the TG was 0.87±0.21 and 0.75±0.25 mm at the mesial and distal aspects, respectively, while a MBL of 2.05±0.25 mm at the mesial aspect and 2.01±0.34 mm at the distal site was recorded in the CG. A statistically significant difference was noted. In the TG the mean fractal dimension before loading was 1.4213±0.0525. It increased significantly to 1.4329±0.0479 at 3 years after loading and remained almost stable at 5 years after loading (1.4327±0.0291). In the CG the mean fractal dimension before loading was 1.4119±0.0414. It increased significantly to 1.4282±0.0324 at 3 years after loading and decreased significantly to 1.4111±0.0624 at 5 years after loading. At the end of the follow-up, differences between both study groups were statistically significant.

CONCLUSION

The increased fractal dimension and the reduced MBL around TG implants after 5 years of functional loading indicates a positive effect of a laser-ablated micron-scale modication of collar surface on peri-implant trabecular bone remodeling.

Revealing the variations in physicochemical, morphological, fractal, and rheological properties of digestate during the mesophilic anaerobic digestion of iron-rich waste activated sludge

Dosing of iron (Fe)-salts in sewers to control odour and corrosion problems have proven to be effective on phosphate and sulfide removal in downstream treatment units. However, the interaction of Fe with sludge may impact the sludge properties during wastewater treatment and sludge digestion. Herein, we investigated the downstream impacts of sewer-dosed Fe-salt on key digestate properties including digestate dewaterability. For this, Fe-salt was dosed to a sewer reactor and resultant iron-rich waste activated sludge (Fe-WAS) was digested in an anaerobic digester (AD) in the experimental line of integrated laboratory system running in parallel to a control system. Iron containing and non-iron containing digestates were sourced from the respective AD reactors of experimental and control lines. Results showed improved dewaterability in iron containing digestate than non-iron containing digestate, which was attributed to the variations in key digestate properties. Compared to non-iron containing digestate, iron containing digestate exhibited the decreased contents of bound water, soluble extracellular polymeric substances (S-EPS), protein, polysaccharide, and monovalent-to-divalent (M⁺/D⁺⁺) cations ratio. Likewise, we observed the increased mean particle size (D_v50) for iron containing digestate than the non-iron containing digestate, but fractal dimension (D_f) values were comparable. Besides, iron containing digestate exhibited a reduced degree of thixotropy, relative sludge network strength, viscosity, yield stress, flow stress, and storage/loss/complex (G'/G''/G∗) moduli but increased creep compliance and shear strain (%) than non-iron containing digestate. The combined synergistic effects of such favorable changes amongst the key properties of iron containing digestate, might have been responsible for improving it's dewaterability.

Treadmill-belt width, but not feedback from the lower visual field, influences the noise characteristics of step width time series

Step kinematic variability, which has been associated with gait-related fall risk, is thought to be attributed to neuromotor noise. Altered neuromotor control of step kinematics would be expected to manifest as changes in the noise-related characteristics of the step kinematic time series. This study determined the effects of eliminating feedback from the lower visual field and reducing treadmill-belt width on the noise characteristics of step width time series and statistical measures of step width variability during treadmill walking. We hypothesized that eliminating feedback from the lower visual field and reducing treadmill-belt width would both alter the noise characteristics of step width time series, reflected by decreased fractal scaling, and increase statistical measures of step width variability. Eighteen young adults performed four randomly ordered walking trials during which we manipulated visual feedback from the lower visual field (normal and obstructed) and treadmill-belt width (wide and narrow). Reducing treadmill-belt width, but not eliminating feedback from the lower visual field, significantly reduced the fractal scaling of step width time series, indicating a shift towards white, uncorrelated noise. These results suggest that accounting for the influence of treadmill-belt width on step width time series may be an important consideration in both laboratory and clinical settings. Further work is needed to clarify the effects of vision on measures of step width, identify the mechanism(s) underlying the observed shift towards white, uncorrelated noise associated with reduced treadmill-belt width, and to assess the potential relationship between the noise characteristics of step width time series and fall risk.

Serotonergic psychedelics LSD & psilocybin increase the fractal dimension of cortical brain activity in spatial and temporal domains

Psychedelic drugs, such as psilocybin and LSD, represent unique tools for researchers investigating the neural origins of consciousness. Currently, the most compelling theories of how psychedelics exert their effects is by increasing the complexity of brain activity and moving the system towards a critical point between order and disorder, creating more dynamic and complex patterns of neural activity. While the concept of criticality is of central importance to this theory, few of the published studies on psychedelics investigate it directly, testing instead related measures such as algorithmic complexity or Shannon entropy. We propose using the fractal dimension of functional activity in the brain as a measure of complexity since findings from physics suggest that as a system organizes towards criticality, it tends to take on a fractal structure. We tested two different measures of fractal dimension, one spatial and one temporal, using fMRI data from volunteers under the influence of both LSD and psilocybin. The first was the fractal dimension of cortical functional connectivity networks and the second was the fractal dimension of BOLD time-series. In addition to the fractal measures, we used a well-established, non-fractal measure of signal complexity and show that they behave similarly. We were able to show that both psychedelic drugs significantly increased the fractal dimension of functional connectivity networks, and that LSD significantly increased the fractal dimension of BOLD signals, with psilocybin showing a non-significant trend in the same direction. With both LSD and psilocybin, we were able to localize changes in the fractal dimension of BOLD signals to brain areas assigned to the dorsal-attenion network. These results show that psychedelic drugs increase the fractal dimension of activity in the brain and we see this as an indicator that the changes in consciousness triggered by psychedelics are associated with evolution towards a critical zone.

Global Effects of Focal Brain Tumors on Functional Complexity and Network Robustness: A Prospective Cohort Study

BACKGROUND

Neurosurgical management of brain tumors has entered a paradigm of supramarginal resections that demands thorough understanding of peritumoral functional effects. Historically, the effects of tumors have been believed to be local, and long-range effects have not been considered.

OBJECTIVE

To test the hypothesis that tumors affect the brain globally, producing long-range gradients in cortical function.

METHODS

Resting-state functional magnetic resonance imaging (fMRI) data were acquired from 11 participants with glioblastoma and split into discovery and validation datasets in a single-center prospective cohort study. Fractal complexity was computed with a wavelet-based estimator of the Hurst exponent. Distance-related effects of the tumors were tested with a tumor mask-dilation technique and parcellation of the underlying Hurst maps.

RESULTS

Fractal complexity demonstrates a penumbra of suppression in the peritumoral region. At a global level, as distance from the tumor increases, this initial suppression is balanced by a subsequent overactivity before finally normalizing. These effects were best fit by a quadratic model and were consistent across different network construction pipelines. The Hurst exponent was correlated with graph theory measures of centrality including network robustness, but graph theory measures did not demonstrate distance-dependent effects.

CONCLUSION

This work provides evidence supporting the theory that focal brain tumors produce long-range gradients in function. Consequently, the effects of focal lesions need to be interpreted in terms of the global changes on functional complexity and network architecture rather than purely in terms of functional localization. Determining whether peritumoral changes represent potential plasticity may facilitate extended resection of tumors without functional cost.

Connections, Tracts, Fractals, and the Rest: A Working Guide to Network and Connectivity Studies in Neurosurgery

Brain mapping and connectomics can probe networks that span the entire brain, producing a diverse range of outputs for probing specific clinically relevant questions. The potential for understanding the effect of focal lesions on brain function, cognition, and plasticity abounds, any one of which would likely yield more effective and safer neurosurgical strategies. However, the possibilities of advanced magnetic resonance imaging and connectomics have been somewhat underused in neurosurgery, arising from actual or perceived difficulties in either application or analysis. The present review builds on previous work describing the theoretical attractions of connectomics to deliberate on the practical details of performing high-quality connectomics studies in neurosurgery. First, the data and methods involved in deriving connectomics models will be considered, specifically for the purpose of determining the nature of inferences that can be made subsequently. Next, a selection of key analysis methods will be explored using practical examples that illustrate their effective implementation and the insights that can be gleaned. The principles of study design will be introduced, including analysis tips and methods for making efficient use of available resources. Finally, a review of the best research practices for neuroimaging studies will be discussed, including principles of open access data sharing, study preregistration, and methods for improving replicability. Ultimately, we hope readers will be better placed to appraise the current connectomics studies in neurosurgery and empowered to develop their own high-quality studies, both of which are key steps in realizing the true potential of connectomics and advanced neuroimaging analyses in general.

Fractal lenses based on Cantor binary sequences for ultrasound focusing applications

In this work, we demonstrate the application of Cantor fractal lenses in acoustics. The Cantor Zone Plate (CZP), previously introduced in optics, is designed from a conventional Fresnel Zone Plate (FZP) using a binary sequence governed by the distribution of a generalized Cantor set. The CZP maintains its main focus at the same focal distance than its associated FZP, providing a softer multi-foci focusing profile which is very useful in certain ultrasound therapeutic applications. Experimental measurements are in good agreement with the theoretical model, demonstrating that CZPs are suitable for the ultrasound field.

Data on optical microscopy and vibrational modes in Diphenyl Dinaphthothienothiophene thin films

The thin-films of 2,9-diphenyl-dinaphtho[2,3-b:2′,3′-f]thieno[3,2-b]thiophene (DPh-DNTT) prepared by vacuum deposition was observed by the optical microsope. By applying the dark-field mode in observation and/or image processing after imaging appropriately, morphological structure with a resolution of a few nanometers height was visualized easily and quickly. The technique can be used in a similar to atomic force microscopy, which is commonly used for imaging surface morphology. Moreover, the vibrational modes of a DPh-DNTT molecule calculated by quantum chemistry program is described as well as the comparison of the experimental Raman spectra for identification. The presented data are produced as part of the main work entitled “The Growth Mechanism and Characterization of Few-layer Diphenyl Dinaphthothienothiophene Films Prepared by Vacuum Deposition” (Hattori et al., 2019).

Fractal properties and short-term correlations in motor control in cycling: influence of a cognitive challenge

Fluctuations in cyclic tasks periods is a known characteristic of human motor control. Specifically, long-range fractal fluctuations have been evidenced in the temporal structure of these variations in human locomotion and thought to be the outcome of a multicomponent physiologic system in which control is distributed across intricate cortical, spinal and neuromuscular regulation loops. Combined with long-range correlation analyses, short-range autocorrelations have proven their use to describe control distribution across central and motor components. We used relevant tools to characterize long- and short-range correlations in revolution time series during cycling on an ergometer in 19 healthy young adults. We evaluated the impact of introducing a cognitive task (PASAT) to assess the role of central structures in control organization. Autocorrelation function and detrending fluctuation analysis (DFA) demonstrated the presence of fractal scaling. PSD in the short range revealed a singular behavior which cannot be explained by the usual models of even-based and emergent timing. The main outcomes are that (1) timing in cycling is a fractal process, (2) this long-range fractal behavior increases in persistence with dual-task condition, which has not been previously observed, (3) short-range behavior is highly persistent and unaffected by dual-task. Relying on the inertia of the oscillator may be a way to distribute more control to the periphery, thereby allocating less resources to central process and better managing additional cognitive demands. This original behavior in cycling may explain the high short-range persistence unaffected by dual-task, and the increase in long-range persistence with dual-task.