Fractal Analysis in Pulmonary CT Images of COVID-19-Infected Patients

In this paper, we propose to quantitatively compare the loss of human lung health under the influence of the illness with COVID-19, based on the fractal-analysis interpretation of the chest-pulmonary CT pictures, in the case of small datasets, which are usually encountered in medical applications. The fractal analysis characteristics, such as fractal dimension and lacunarity measured values, have been utilized as an effective advisor to interpretation of pulmonary CT picture texture.

Forecasting the COVID-19 with Interval Type-3 Fuzzy Logic and the Fractal Dimension

In this article, the prediction of COVID-19 based on a combination of fractal theory and interval type-3 fuzzy logic is put forward. The fractal dimension is utilized to estimate the time series geometrical complexity level, which in this case is applied to the COVID-19 problem. The main aim of utilizing interval type-3 fuzzy logic is for handling uncertainty in the decision-making occurring in forecasting. The hybrid approach is formed by an interval type-3 fuzzy model structured by fuzzy if then rules that utilize as inputs the linear and non-linear values of the dimension, and the forecasts of COVID-19 cases are the outputs. The contribution is the new scheme based on the fractal dimension and interval type-3 fuzzy logic, which has not been proposed before, aimed at achieving an accurate forecasting of complex time series, in particular for the COVID-19 case. Publicly available data sets are utilized to construct the interval type-3 fuzzy system for a time series. The hybrid approach can be a helpful tool for decision maker in fighting the pandemic, as they could use the forecasts to decide immediate actions. The proposed method has been compared with previous works to show that interval type-3 fuzzy systems outperform previous methods in prediction. © 2022, The Author(s) under exclusive licence to Taiwan Fuzzy Systems Association.

Complexity and Entropy in Physiological Signals (CEPS): Resonance Breathing Rate Assessed Using Measures of Fractal Dimension, Heart Rate Asymmetry and Permutation Entropy.

BACKGROUND: As technology becomes more sophisticated, more accessible methods of interpretating Big Data become essential. We have continued to develop Complexity and Entropy in Physiological Signals (CEPS) as an open access MATLAB® GUI (graphical user interface) providing multiple methods for the modification and analysis of physiological data. METHODS: To demonstrate the functionality of the software, data were collected from 44 healthy adults for a study investigating the effects on vagal tone of breathing paced at five different rates, as well as self-paced and un-paced. Five-minute 15-s recordings were used. Results were also compared with those from shorter segments of the data. Electrocardiogram (ECG), electrodermal activity (EDA) and Respiration (RSP) data were recorded. Particular attention was paid to COVID risk mitigation, and to parameter tuning for the CEPS measures. For comparison, data were processed using Kubios HRV, RR-APET and DynamicalSystems.jl software. We also compared findings for ECG RR interval (RRi) data resampled at 4 Hz (4R) or 10 Hz (10R), and non-resampled (noR). In total, we used around 190-220 measures from CEPS at various scales, depending on the analysis undertaken, with our investigation focused on three families of measures: 22 fractal dimension (FD) measures, 40 heart rate asymmetries or measures derived from Poincaré plots (HRA), and 8 measures based on permutation entropy (PE). RESULTS: FDs for the RRi data differentiated strongly between breathing rates, whether data were resampled or not, increasing between 5 and 7 breaths per minute (BrPM). Largest effect sizes for RRi (4R and noR) differentiation between breathing rates were found for the PE-based measures. Measures that both differentiated well between breathing rates and were consistent across different RRi data lengths (1-5 min) included five PE-based (noR) and three FDs (4R). Of the top 12 measures with short-data values consistently within ± 5% of their values for the 5-min data, five were FDs, one was PE-based, and none were HRAs. Effect sizes were usually greater for CEPS measures than for those implemented in DynamicalSystems.jl. CONCLUSION: The updated CEPS software enables visualisation and analysis of multichannel physiological data using a variety of established and recently introduced complexity entropy measures. Although equal resampling is theoretically important for FD estimation, it appears that FD measures may also be usefully applied to non-resampled data.

Comparison of Texture Feature Extraction Method for COVID-19 Detection With Deep Learning

This paper describes research on texture feature extraction for COVID-19 detection. Fractal Dimension Texture Analysis (FDTA) and Gray Level Co-occurrence Matrix (GLCM) were used for feature extraction. A dense neural network is used for classification. Three classes were used for classification to classify Normal, COVID-19, and Other pneumonia. The data entered in the texture feature extraction is a chest x-ray (CXR) image that is grey scaled and resized into 400400 pixels. Performance analysis of the model uses a confusion matrix. The best performance feature extraction method for detecting COVID-19 is FDTA, with an accuracy testing of 62.5%. © 2022 IEEE.

Textural features for automatic detection and categorisation of pneumonia in chest X-ray images

Pneumonia is an acute lung infection caused by a variety of organisms, such as viruses, bacteria, or fungi, that poses a serious risk to vulnerable populations. The first step in the diagnosis and treatment of pneumonia is a prompt and accurate diagnosis, especially in the context of an epidemic outbreak such as COVID-19, where pneumonia is an important symptom. To provide tools for this purpose, this article evaluates the potential of three textural image characterisation methods, fractal dimension, radiomics, and superpixel-based histon, as biomarkers both to distinguish between healthy individuals and patients affected by pneumonia and to differentiate between potential pneumonia causes. The results show the ability of the textural characterisation methods tested to discriminate between nonpathological images and images with pneumonia, and how some of the generated models show the potential to characterise the general textural patterns that define viral and bacterial pneumonia, and the specific features associated with a COVID-19 infection. © 2022 IEEE.

Toward a fractalomic idiotype/anti-idiotypic paradigm.

The CoViD-19 pandemic has demonstrated the need for future developments in anti-viral immunology. We propose that artificial intelligence (AI) and machine learning, and in particular fractal analysis could play a crucial role in that context. Fractals - never-ending repeats of self-similar shapes whose composite tend to resemble the whole - are found in most natural biological structures including immunoglobulin and antigenic epitopes. Increased knowledge of the fractalomic properties of the idiotype/anti-idiotypic paradigm should help develop a novel and improved simplified artificial model of the immune system. Case in point, the regulation and dampening of antibodies as well as the synergetic recognition of an antigen by multiple idiotypes are both immune mechanisms that require further analysis. An enhanced understanding of these complexities could lead to better data analysis for novel vaccines to improve their sensitivity and specificity as well as open other new doors in the field of immunology.

Explainable COVID-19 detection using fractal dimension and vision transformer with Grad-CAM on cough sounds.

The polymerase chain reaction (PCR) test is not only time-intensive but also a contact method that puts healthcare personnel at risk. Thus, contactless and fast detection tests are more valuable. Cough sound is an important indicator of COVID-19, and in this paper, a novel explainable scheme is developed for cough sound-based COVID-19 detection. In the presented work, the cough sound is initially segmented into overlapping parts, and each segment is labeled as the input audio, which may contain other sounds. The deep Yet Another Mobile Network (YAMNet) model is considered in this work. After labeling, the segments labeled as cough are cropped and concatenated to reconstruct the pure cough sounds. Then, four fractal dimensions (FD) calculation methods are employed to acquire the FD coefficients on the cough sound with an overlapped sliding window that forms a matrix. The constructed matrixes are then used to form the fractal dimension images. Finally, a pretrained vision transformer (ViT) model is used to classify the constructed images into COVID-19, healthy and symptomatic classes. In this work, we demonstrate the performance of the ViT on cough sound-based COVID-19, and a visual explainability of the inner workings of the ViT model is shown. Three publically available cough sound datasets, namely COUGHVID, VIRUFY, and COSWARA, are used in this study. We have obtained 98.45%, 98.15%, and 97.59% accuracy for COUGHVID, VIRUFY, and COSWARA datasets, respectively. Our developed model obtained the highest performance compared to the state-of-the-art methods and is ready to be tested in real-world applications.

An exploration on the topologies of SARS-CoV-2/human protein-protein interaction network.

Network biology is an important finding that uncovers the significant elements in viral infection control. Since viruses use the proteins on their surfaces to attach and enter into the host cell, the establishment of virus-host protein interactions is a potent regulator of the global organization of the viral life cycle after virus entry into host cells. In this instance, a topological study on the SARS-CoV-2/Human Protein-Protein Interaction Network (PPIN) evacuates much information about the protein-protein interactions. By making some interruptions to the interaction between proteins and hosts, we can quickly reduce the spread of the disease and get an insight into the target protein for drug development. This paper mainly focused on the graphical and structural complexity of the SARS-CoV-2/Human PPIN. For this purpose, the various primary (distance, radius, diameter, etc…) and advanced levels of graph measures (density, modularity, clustering coefficient, etc…) as well as a few fractal (box dimension, multifractal analysis) and entropy measures have been used. In addition, several graph descriptions and distribution graphs of PPIN offered to gain a thorough understanding of the SARS-CoV-2/Human PPIN. Conclusively, based on our work, we have discovered that PPIN is moderately complex and identified that hiring Nsp8 as a target node will positively affect the PPIN and has pointed out that mathematically found target proteins are matched with already suggested target proteins in the previous survey.Communicated by Ramaswamy H. Sarma.

Modeling the multifractal dynamics of COVID-19 pandemic

We propose a mathematical model for the multifractal dynamics of COVID-19 pandemic. Within this model and the finite-difference parametric nonlinear equations of the reduced SIR (Susceptible-Infected-Removed) model we calculate the fractal dimensions of various segments of daily disease incidence in the world and the variations of COVID-19 basic reproduction number based on the COVID-19 World Statistics data. © 2022 SPIE.

Fractal Analysis Usage Areas in Healthcare

This chapter presents a brief introduction to fractal analysis usage areas and their roles in the healthcare system. The definition of fractal, the properties of fractal, what is fractal dimension, most known methods used in fractal analysis and fractal analysis usage areas in healthcare have been examined under the different titles. The comparison of Euclidean geometry and fractal geometry has been explained. Accordingly, the relationship between fractal dimension (D ) and Euclidean topological dimension (DT ) has been expressed. A range of scientific research about fractal analysis in the healthcare system have been reviewed. As a most known fractal analysis methods Box Counting method, Richardson’s method, Dilation (pixel dilation) method and Mass (mass-radius) method have been explained briefly. Moreover, a glance of some usage areas for fractal analysis in healthcare system are COVID-19 disease, oncology, cardiology, brain imaging, neuroscience, dental, osteoporosis, ophthalmology and dermatology have been given. The reviewed studies about fractal analysis in many different areas showed that it can be used to obtain information about the severity and progression of the existing disease or early detection of a potential disease. The main goal of this study can be explained as briefly that giving an opinion to researchers about the usage areas of fractal analysis in healthcare. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Automatic detection of pneumonia in chest X-ray images using textural features.

Fast and accurate diagnosis is critical for the triage and management of pneumonia, particularly in the current scenario of a COVID-19 pandemic, where this pathology is a major symptom of the infection. With the objective of providing tools for that purpose, this study assesses the potential of three textural image characterisation methods: radiomics, fractal dimension and the recently developed superpixel-based histon, as biomarkers to be used for training Artificial Intelligence (AI) models in order to detect pneumonia in chest X-ray images. Models generated from three different AI algorithms have been studied: K-Nearest Neighbors, Support Vector Machine and Random Forest. Two open-access image datasets were used in this study. In the first one, a dataset composed of paediatric chest X-ray, the best performing generated models achieved an 83.3% accuracy with 89% sensitivity for radiomics, 89.9% accuracy with 93.6% sensitivity for fractal dimension and 91.3% accuracy with 90.5% sensitivity for superpixels based histon. Second, a dataset derived from an image repository developed primarily as a tool for studying COVID-19 was used. For this dataset, the best performing generated models resulted in a 95.3% accuracy with 99.2% sensitivity for radiomics, 99% accuracy with 100% sensitivity for fractal dimension and 99% accuracy with 98.6% sensitivity for superpixel-based histons. The results confirm the validity of the tested methods as reliable and easy-to-implement automatic diagnostic tools for pneumonia.

Analysis of Radiographic Images of Patients with COVID-19 Using Fractal Dimension and Complex Network-Based High-Level Classification

An important task in combating COVID-19 involves the quick and correct diagnosis of patients, which is not only critical to the patient’s prognosis, but can also help to optimize the configuration of hospital resources. This work aims to classify chest radiographic images to help the diagnosis and prognosis of patients with COVID-19. In comparison to images of healthy lungs, chest images infected by COVID-19 present geometrical deformations, like the formation of filaments. Therefore, fractal dimension is applied here to characterize the levels of complexity of COVID-19 images. Moreover, real data often contains complex patterns beyond physical features. Complex networks are suitable tools for characterizing data patterns due to their ability to capture the spatial, topological and functional relationship between the data. Therefore, a complex network-based high-level data classification technique, capable of capturing data patterns, is modified and applied to chest radiographic image classification. Experimental results show that the proposed method can obtain high classification precision on X-ray images. Still in this work, a comparative study between the proposed method and the state-of-the-art classification techniques is also carried out. The results show that the performance of the proposed method is competitive. We hope that the present work generates relevant contributions to combat COVID-19. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

A spatial randomness test based on the box-counting dimension.

Statistical modelling of a spatial point pattern often begins by testing the hypothesis of spatial randomness. Classical tests are based on quadrat counts and distance-based methods. Alternatively, we propose a new statistical test of spatial randomness based on the fractal dimension, calculated through the box-counting method providing an inferential perspective contrary to the more often descriptive use of this method. We also develop a graphical test based on the log-log plot to calculate the box-counting dimension. We evaluate the performance of our methodology by conducting a simulation study and analysing a COVID-19 dataset. The results reinforce the good performance of the method that arises as an alternative to the more classical distances-based strategies.

Entropy and Fractal Dimension Study of the TDP-43 Protein Low Complexity Domain Sequence in ALS Disease Severity and SARS-CoV-2 Gene Sequences in Virulence Variability.

The low complexity domain (LCD) sequence has been defined in terms of entropy using a 12 amino acid sliding window along a protein sequence in the study of disease-related genes. The amyotrophic lateral sclerosis (ALS)-related TDP-43 protein sequence with intra-LCD structural information based on cryo-EM data was published recently. An application of entropy and Higuchi fractal dimension calculations was described using the Znf521 and HAR1 sequences. A computational analysis of the intra-LCD sequence entropy and Higuchi fractal dimension values at the amino acid level and at the ATCG nucleotide level were conducted without the sliding window requirement. The computational results were consistent in predicting the intermediate entropy/fractal dimension value produced when two subsequences at two different entropy/fractal dimension values were combined. The computational method without the application of a sliding-window was extended to an analysis of the recently reported virulent genes-Orf6, Nsp6, and Orf7a-in SARS-CoV-2. The relationship between the virulence functionality and entropy values was found to have correlation coefficients between 0.84 and 0.99, using a 5% uncertainty on the cell viability data. The analysis found that the most virulent Orf6 gene sequence had the lowest nucleotide entropy and the highest protein fractal dimension, in line with extreme value theory. The Orf6 codon usage bias in relation to vaccine design was discussed.

A Novel Method for a COVID-19 Classification of Countries Based on an Intelligent Fuzzy Fractal Approach.

We outline in this article a hybrid intelligent fuzzy fractal approach for classification of countries based on a mixture of fractal theoretical concepts and fuzzy logic mathematical constructs. The mathematical definition of the fractal dimension provides a way to estimate the complexity of the non-linear dynamic behavior exhibited by the time series of the countries. Fuzzy logic offers a way to represent and handle the inherent uncertainty of the classification problem. The hybrid intelligent approach is composed of a fuzzy system formed by a set of fuzzy rules that uses the fractal dimensions of the data as inputs and produce as a final output the classification of countries. The hybrid approach calculations are based on the COVID-19 data of confirmed and death cases. The main contribution is the proposed hybrid approach composed of the fractal dimension definition and fuzzy logic concepts for achieving an accurate classification of countries based on the complexity of the COVID-19 time series data. Publicly available datasets of 11 countries have been the basis to construct the fuzzy system and 15 different countries were considered in the validation of the proposed classification approach. Simulation results show that a classification accuracy over 93% can be achieved, which can be considered good for this complex problem.

Diversity of SARS-CoV-2 isolates driven by pressure and health index.

One of the main concerns about the fast spreading coronavirus disease 2019 (Covid-19) pandemic is how to intervene. We analysed severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) isolates data using the multifractal approach and found a rich in viral genome diversity, which could be one of the root causes of the fast Covid-19 pandemic and is strongly affected by pressure and health index of the hosts inhabited regions. The calculated mutation rate (mr) is observed to be maximum at a particular pressure, beyond which mr maintains diversity. Hurst exponent and fractal dimension are found to be optimal at a critical pressure (Pm), whereas, for P > Pm and P < Pm, we found rich genome diversity relating to complicated genome organisation and virulence of the virus. The values of these complexity measurement parameters are found to be increased linearly with health index values.

Nonlinear time series and principal component analyses: Potential diagnostic tools for COVID-19 auscultation.

The development of novel digital auscultation techniques has become highly significant in the context of the outburst of the pandemic COVID 19. The present work reports the spectral, nonlinear time series, fractal, and complexity analysis of vesicular (VB) and bronchial (BB) breath signals. The analysis is carried out with 37 breath sound signals. The spectral analysis brings out the signatures of VB and BB through the power spectral density plot and wavelet scalogram. The dynamics of airflow through the respiratory tract during VB and BB are investigated using the nonlinear time series and complexity analyses in terms of the phase portrait, fractal dimension, Hurst exponent, and sample entropy. The higher degree of chaoticity in BB relative to VB is unwrapped through the maximal Lyapunov exponent. The principal component analysis helps in classifying VB and BB sound signals through the feature extraction from the power spectral density data. The method proposed in the present work is simple, cost-effective, and sensitive, with a far-reaching potential of addressing and diagnosing the current issue of COVID 19 through lung auscultation.

Forecasting of COVID-19 time series for countries in the world based on a hybrid approach combining the fractal dimension and fuzzy logic.

We describe in this paper a hybrid intelligent approach for forecasting COVID-19 time series combining fractal theory and fuzzy logic. The mathematical concept of the fractal dimension is used to measure the complexity of the dynamics in the time series of the countries in the world. Fuzzy Logic is used to represent the uncertainty in the process of making a forecast. The hybrid approach consists on a fuzzy model formed by a set of fuzzy rules that use as input values the linear and nonlinear fractal dimensions of the time series and as outputs the forecast for the countries based on the COVID-19 time series of confirmed cases and deaths. The main contribution is the proposed hybrid approach combining the fractal dimension and fuzzy logic for enabling an efficient and accurate forecasting of COVID-19 time series. Publicly available data sets of 10 countries in the world have been used to build the fuzzy model with time series in a fixed period. After that, other periods of time were used to verify the effectiveness of the proposed approach for the forecasted values of the 10 countries. Forecasting windows of 10 and 30 days ahead were used to test the proposed approach. Forecasting average accuracy is 98%, which can be considered good considering the complexity of the COVID problem. The proposed approach can help people in charge of decision making to fight the pandemic can use the information of a short window to decide immediate actions and also the longer window (like 30 days) can be beneficial in long term decisions.