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  1. Radioactivity and heat production characterization by natural gamma ray well logging and multi-fractal techniques in banting district, Malaysia
    Asfahani J, Samuding K, Mostapa R, Othman O
    Appl Radiat Isot, 2021 Jan;167:109296.
    PMID: 33022484 DOI: 10.1016/j.apradiso.2020.109296
    Natural gamma ray well logging technique is used to characterize the radioactivity (GR) laterally and vertically in Banting district, SW of Malaysia. Seven drilled boreholes, along N-S profile with their natural gamma ray records are utilized to compute the heat production (HP) parameter, based on the Bucker and Rybach relationship.The analysis of 3467 measured points in those boreholes indicates that GR varies between 6.24 API and 358.4 API with an average of 79.95 API, while HP varies between 0.086 and 5.65 μw/m3 with an average of 1.25 μw/m3.The multi-fractal Concentration-Number (C-N) is used to characterize the radioactivity and heat production variations and to isolate different GR and HP populations in the study region. The high radioactivity and heat production ranges are mainly related to the silty clay layers, accompanied by uranium and thorium.
    Matched MeSH terms: Fractals
  2. Fulltext Fractal-Fractional Mathematical Model Addressing the Situation of Corona Virus in Pakistan
    Shah K, Arfan M, Mahariq I, Ahmadian A, Salahshour S, Ferrara M
    Results Phys, 2020 Dec;19:103560.
    PMID: 33200064 DOI: 10.1016/j.rinp.2020.103560
    This work is the consideration of a fractal fractional mathematical model on the transmission and control of corona virus (COVID-19), in which the total population of an infected area is divided into susceptible, infected and recovered classes. We consider a fractal-fractional order

    SIR

    type model for investigation of Covid-19. To realize the transmission and control of corona virus in a much better way, first we study the stability of the corresponding deterministic model using next generation matrix along with basic reproduction number. After this, we study the qualitative analysis using "fixed point theory" approach. Next, we use fractional Adams-Bashforth approach for investigation of approximate solution to the considered model. At the end numerical simulation are been given by matlab to provide the validity of mathematical system having the arbitrary order and fractal dimension.
    Matched MeSH terms: Fractals
  3. Detection of abnormality in wireless capsule endoscopy images using fractal features
    Jain S, Seal A, Ojha A, Krejcar O, Bureš J, Tachecí I, et al.
    Comput Biol Med, 2020 12;127:104094.
    PMID: 33152668 DOI: 10.1016/j.compbiomed.2020.104094
    One of the most recent non-invasive technologies to examine the gastrointestinal tract is wireless capsule endoscopy (WCE). As there are thousands of endoscopic images in an 8-15 h long video, an evaluator has to pay constant attention for a relatively long time (60-120 min). Therefore the possibility of the presence of pathological findings in a few images (displayed for evaluation for a few seconds only) brings a significant risk of missing the pathology with all negative consequences for the patient. Hence, manually reviewing a video to identify abnormal images is not only a tedious and time consuming task that overwhelms human attention but also is error prone. In this paper, a method is proposed for the automatic detection of abnormal WCE images. The differential box counting method is used for the extraction of fractal dimension (FD) of WCE images and the random forest based ensemble classifier is used for the identification of abnormal frames. The FD is a well-known technique for extraction of features related to texture, smoothness, and roughness. In this paper, FDs are extracted from pixel-blocks of WCE images and are fed to the classifier for identification of images with abnormalities. To determine a suitable pixel block size for FD feature extraction, various sizes of blocks are considered and are fed into six frequently used classifiers separately, and the block size of 7×7 giving the best performance is empirically determined. Further, the selection of the random forest ensemble classifier is also done using the same empirical study. Performance of the proposed method is evaluated on two datasets containing WCE frames. Results demonstrate that the proposed method outperforms some of the state-of-the-art methods with AUC of 85% and 99% on Dataset-I and Dataset-II respectively.
    Matched MeSH terms: Fractals
  4. Complexity-based classification of EEG signal in normal subjects and patients with epilepsy
    Namazi H, Aghasian E, Ala TS
    Technol Health Care, 2020;28(1):57-66.
    PMID: 31104032 DOI: 10.3233/THC-181579
    Analysis of human brain activity is an important topic in human neuroscience. Human brain activity can be studied by analyzing the electroencephalography (EEG) signal. In this way, scientists have employed several techniques that investigate nonlinear dynamics of EEG signals. Fractal theory as a promising technique has shown its capabilities to analyze the nonlinear dynamics of time series. Since EEG signals have fractal patterns, in this research we analyze the variations of fractal dynamics of EEG signals between four datasets that were collected from healthy subjects with open-eyes and close-eyes conditions, patients with epilepsy who did and patients who did not face seizures. The obtained results showed that EEG signal during seizure has greatest complexity and the EEG signal during the seizure-free interval has lowest complexity. In order to verify the obtained results in case of fractal analysis, we employ approximate entropy, which indicates the randomness of time series. The obtained results in case of approximate entropy certified the fractal analysis results. The obtained results in this research show the effectiveness of fractal theory to investigate the nonlinear structure of EEG signal between different conditions.
    Matched MeSH terms: Fractals
  5. Complexity-Based Decoding of the Coupling Among Heart Rate Variability (HRV) and Walking Path
    Mujib Kamal S, Babini MH, Krejcar O, Namazi H
    Front Physiol, 2020;11:602027.
    PMID: 33324242 DOI: 10.3389/fphys.2020.602027
    Walking is an everyday activity in our daily life. Because walking affects heart rate variability, in this research, for the first time, we analyzed the coupling among the alterations of the complexity of walking paths and heart rate. We benefited from the fractal theory and sample entropy to evaluate the influence of the complexity of paths on the complexity of heart rate variability (HRV) during walking. We calculated the fractal exponent and sample entropy of the R-R time series for nine participants who walked on four paths with various complexities. The findings showed a strong coupling among the alterations of fractal dimension (an indicator of complexity) of HRV and the walking paths. Besides, the result of the analysis of sample entropy also verified the obtained results from the fractal analysis. In further studies, we can analyze the coupling among the alterations of the complexities of other physiological signals and walking paths.
    Matched MeSH terms: Fractals
  6. Decoding of the relationship between human brain activity and walking paths
    Kamal SM, Sim S, Tee R, Nathan V, Aghasian E, Namazi H
    Technol Health Care, 2020;28(4):381-390.
    PMID: 31796717 DOI: 10.3233/THC-191965
    BACKGROUND: The human brain controls all actions of the body. Walking is one of the most important actions that deals with the movement of the body. In fact, the brain controls and regulates human walking based on different conditions. One of the conditions that affects human walking is the complexity of path of movement. Therefore, the brain activity should change when a person walks on a path with different complexities.

    OBJECTIVE: In this research we benefit from fractal analysis to study the effect of complexity of path of movement on the complexity of human brain reaction.

    METHODS: For this purpose we calculate the fractal dimension of the electroencephalography (EEG) signal when subjects walk on different paths with different fractal dimensions (complexity).

    RESULTS: The results of the analysis show that the complexity of brain activity increases with the increment of complexity of path of movement.

    CONCLUSION: The method of analysis employed in this research can also be employed to analyse the reaction of the human heart and respiration when subjects move on paths with different complexities.

    Matched MeSH terms: Fractals
  7. Fractal-based classification of electroencephalography (EEG) signals in healthy adolescents and adolescents with symptoms of schizophrenia
    Namazi H, Aghasian E, Ala TS
    Technol Health Care, 2019;27(3):233-241.
    PMID: 30829625 DOI: 10.3233/THC-181497
    Brain activity analysis is an important research area in the field of human neuroscience. Moreover, a subcategory in this field is the classification of brain activity in terms of different brain disorders. Since the Electroencephalography (EEG) signal is, in fact, a non-linear time series, employing techniques to investigate its non-linear structure is rather crucial. In this study, we evaluate the non-linear structure of the EEG signal between healthy and schizophrenic adolescents using fractal theory. The results of our analysis revealed that in terms of all recording channels, the EEG signal of healthy subjects is more complex compared to the ones suffering from schizophrenia. The statistical analysis also indicated that there is a significant difference in the complex structure of the EEG signal between these two groups of subjects. We also utilized approximate entropy in our analysis in order to verify the obtained results of the fractal analysis. The result of the entropy analysis suggested that EEG signal for healthy subjects is less random compared to the EEG signal in schizophrenic individuals. In addition, the employed methodology in this research can be further investigated in order to classify the brain activity in terms of other brain disorders, where one can explore how the complex structure of the EEG signal alters between them.
    Matched MeSH terms: Fractals*
  8. A novel automated diagnostic system for classification of myocardial infarction ECG signals using an optimal biorthogonal filter bank
    Sharma M, Tan RS, Acharya UR
    Comput Biol Med, 2018 11 01;102:341-356.
    PMID: 30049414 DOI: 10.1016/j.compbiomed.2018.07.005
    Myocardial infarction (MI), also referred to as heart attack, occurs when there is an interruption of blood flow to parts of the heart, due to the acute rupture of atherosclerotic plaque, which leads to damage of heart muscle. The heart muscle damage produces changes in the recorded surface electrocardiogram (ECG). The identification of MI by visual inspection of the ECG requires expert interpretation, and is difficult as the ECG signal changes associated with MI can be short in duration and low in magnitude. Hence, errors in diagnosis can lead to delay the initiation of appropriate medical treatment. To lessen the burden on doctors, an automated ECG based system can be installed in hospitals to help identify MI changes on ECG. In the proposed study, we develop a single-channel single lead ECG based MI diagnostic system validated using noisy and clean datasets. The raw ECG signals are taken from the Physikalisch-Technische Bundesanstalt database. We design a novel two-band optimal biorthogonal filter bank (FB) for analysis of the ECG signals. We present a method to design a novel class of two-band optimal biorthogonal FB in which not only the product filter but the analysis lowpass filter is also a halfband filter. The filter design problem has been composed as a constrained convex optimization problem in which the objective function is a convex combination of multiple quadratic functions and the regularity and perfect reconstruction conditions are imposed in the form linear equalities. ECG signals are decomposed into six subbands (SBs) using the newly designed wavelet FB. Following to this, discriminating features namely, fuzzy entropy (FE), signal-fractal-dimensions (SFD), and renyi entropy (RE) are computed from all the six SBs. The features are fed to the k-nearest neighbor (KNN). The proposed system yields an accuracy of 99.62% for the noisy dataset and an accuracy of 99.74% for the clean dataset, using 10-fold cross validation (CV) technique. Our MI identification system is robust and highly accurate. It can thus be installed in clinics for detecting MI.
    Matched MeSH terms: Fractals
  9. Automated characterization of cardiovascular diseases using relative wavelet nonlinear features extracted from ECG signals
    Adam M, Oh SL, Sudarshan VK, Koh JE, Hagiwara Y, Tan JH, et al.
    Comput Methods Programs Biomed, 2018 Jul;161:133-143.
    PMID: 29852956 DOI: 10.1016/j.cmpb.2018.04.018
    Cardiovascular diseases (CVDs) are the leading cause of deaths worldwide. The rising mortality rate can be reduced by early detection and treatment interventions. Clinically, electrocardiogram (ECG) signal provides useful information about the cardiac abnormalities and hence employed as a diagnostic modality for the detection of various CVDs. However, subtle changes in these time series indicate a particular disease. Therefore, it may be monotonous, time-consuming and stressful to inspect these ECG beats manually. In order to overcome this limitation of manual ECG signal analysis, this paper uses a novel discrete wavelet transform (DWT) method combined with nonlinear features for automated characterization of CVDs. ECG signals of normal, and dilated cardiomyopathy (DCM), hypertrophic cardiomyopathy (HCM) and myocardial infarction (MI) are subjected to five levels of DWT. Relative wavelet of four nonlinear features such as fuzzy entropy, sample entropy, fractal dimension and signal energy are extracted from the DWT coefficients. These features are fed to sequential forward selection (SFS) technique and then ranked using ReliefF method. Our proposed methodology achieved maximum classification accuracy (acc) of 99.27%, sensitivity (sen) of 99.74%, and specificity (spec) of 98.08% with K-nearest neighbor (kNN) classifier using 15 features ranked by the ReliefF method. Our proposed methodology can be used by clinical staff to make faster and accurate diagnosis of CVDs. Thus, the chances of survival can be significantly increased by early detection and treatment of CVDs.
    Matched MeSH terms: Fractals
  10. Discrimination of stroke-related mild cognitive impairment and vascular dementia using EEG signal analysis
    Al-Qazzaz NK, Ali SHBM, Ahmad SA, Islam MS, Escudero J
    Med Biol Eng Comput, 2018 Jan;56(1):137-157.
    PMID: 29119540 DOI: 10.1007/s11517-017-1734-7
    Stroke survivors are more prone to developing cognitive impairment and dementia. Dementia detection is a challenge for supporting personalized healthcare. This study analyzes the electroencephalogram (EEG) background activity of 5 vascular dementia (VaD) patients, 15 stroke-related patients with mild cognitive impairment (MCI), and 15 control healthy subjects during a working memory (WM) task. The objective of this study is twofold. First, it aims to enhance the discrimination of VaD, stroke-related MCI patients, and control subjects using fuzzy neighborhood preserving analysis with QR-decomposition (FNPAQR); second, it aims to extract and investigate the spectral features that characterize the post-stroke dementia patients compared to the control subjects. Nineteen channels were recorded and analyzed using the independent component analysis and wavelet analysis (ICA-WT) denoising technique. Using ANOVA, linear spectral power including relative powers (RP) and power ratio were calculated to test whether the EEG dominant frequencies were slowed down in VaD and stroke-related MCI patients. Non-linear features including permutation entropy (PerEn) and fractal dimension (FD) were used to test the degree of irregularity and complexity, which was significantly lower in patients with VaD and stroke-related MCI than that in control subjects (ANOVA; p ˂ 0.05). This study is the first to use fuzzy neighborhood preserving analysis with QR-decomposition (FNPAQR) dimensionality reduction technique with EEG background activity of dementia patients. The impairment of post-stroke patients was detected using support vector machine (SVM) and k-nearest neighbors (kNN) classifiers. A comparative study has been performed to check the effectiveness of using FNPAQR dimensionality reduction technique with the SVM and kNN classifiers. FNPAQR with SVM and kNN obtained 91.48 and 89.63% accuracy, respectively, whereas without using the FNPAQR exhibited 70 and 67.78% accuracy for SVM and kNN, respectively, in classifying VaD, stroke-related MCI, and control patients, respectively. Therefore, EEG could be a reliable index for inspecting concise markers that are sensitive to VaD and stroke-related MCI patients compared to control healthy subjects.
    Matched MeSH terms: Fractals
  11. Malaysian household income distribution: a fractal point of view
    Fatimah Abdul Razak, Faridatulazna Ahmad Shahabuddin
    Sains Malaysiana, 2018;47:2187-2194.
    Malaysian Household Income Survey data provided by the Malaysian Department of Statistics is used to provide evidence
    that the upper tails of the household income distribution follows a fractal based distribution known as power-law.
    Inequality measures are then applied to ascertain the levels of inequality based on this distribution. In addition to that,
    we analyzed the data in terms of different classes of occupation, obtained power-law exponents for each class and then
    highlighted the inequality between these classes.
    Matched MeSH terms: Fractals
  12. Fulltext A Review on the Extraction of Quantitative Retinal Microvascular Image Feature
    Kipli K, Hoque ME, Lim LT, Mahmood MH, Sahari SK, Sapawi R, et al.
    Comput Math Methods Med, 2018;2018:4019538.
    PMID: 30065780 DOI: 10.1155/2018/4019538
    Digital image processing is one of the most widely used computer vision technologies in biomedical engineering. In the present modern ophthalmological practice, biomarkers analysis through digital fundus image processing analysis greatly contributes to vision science. This further facilitates developments in medical imaging, enabling this robust technology to attain extensive scopes in biomedical engineering platform. Various diagnostic techniques are used to analyze retinal microvasculature image to enable geometric features measurements such as vessel tortuosity, branching angles, branching coefficient, vessel diameter, and fractal dimension. These extracted markers or characterized fundus digital image features provide insights and relates quantitative retinal vascular topography abnormalities to various pathologies such as diabetic retinopathy, macular degeneration, hypertensive retinopathy, transient ischemic attack, neovascular glaucoma, and cardiovascular diseases. Apart from that, this noninvasive research tool is automated, allowing it to be used in large-scale screening programs, and all are described in this present review paper. This paper will also review recent research on the image processing-based extraction techniques of the quantitative retinal microvascular feature. It mainly focuses on features associated with the early symptom of transient ischemic attack or sharp stroke.
    Matched MeSH terms: Fractals
  13. Fusion of spatial gray level dependency and fractal texture features for the characterization of thyroid lesions
    Raghavendra U, Rajendra Acharya U, Gudigar A, Hong Tan J, Fujita H, Hagiwara Y, et al.
    Ultrasonics, 2017 05;77:110-120.
    PMID: 28219805 DOI: 10.1016/j.ultras.2017.02.003
    Thyroid is a small gland situated at the anterior side of the neck and one of the largest glands of the endocrine system. The abrupt cell growth or malignancy in the thyroid gland may cause thyroid cancer. Ultrasound images distinctly represent benign and malignant lesions, but accuracy may be poor due to subjective interpretation. Computer Aided Diagnosis (CAD) can minimize the errors created due to subjective interpretation and assists to make fast accurate diagnosis. In this work, fusion of Spatial Gray Level Dependence Features (SGLDF) and fractal textures are used to decipher the intrinsic structure of benign and malignant thyroid lesions. These features are subjected to graph based Marginal Fisher Analysis (MFA) to reduce the number of features. The reduced features are subjected to various ranking methods and classifiers. We have achieved an average accuracy, sensitivity and specificity of 97.52%, 90.32% and 98.57% respectively using Support Vector Machine (SVM) classifier. The achieved maximum Area Under Curve (AUC) is 0.9445. Finally, Thyroid Clinical Risk Index (TCRI) a single number is developed using two MFA features to discriminate the two classes. This prototype system is ready to be tested with huge diverse database.
    Matched MeSH terms: Fractals
  14. Fulltext Classification of Partial Discharge Measured under Different Levels of Noise Contamination
    Jee Keen Raymond W, Illias HA, Abu Bakar AH
    PLoS One, 2017;12(1):e0170111.
    PMID: 28085953 DOI: 10.1371/journal.pone.0170111
    Cable joint insulation breakdown may cause a huge loss to power companies. Therefore, it is vital to diagnose the insulation quality to detect early signs of insulation failure. It is well known that there is a correlation between Partial discharge (PD) and the insulation quality. Although many works have been done on PD pattern recognition, it is usually performed in a noise free environment. Also, works on PD pattern recognition in actual cable joint are less likely to be found in literature. Therefore, in this work, classifications of actual cable joint defect types from partial discharge data contaminated by noise were performed. Five cross-linked polyethylene (XLPE) cable joints with artificially created defects were prepared based on the defects commonly encountered on site. Three different types of input feature were extracted from the PD pattern under artificially created noisy environment. These include statistical features, fractal features and principal component analysis (PCA) features. These input features were used to train the classifiers to classify each PD defect types. Classifications were performed using three different artificial intelligence classifiers, which include Artificial Neural Networks (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS) and Support Vector Machine (SVM). It was found that the classification accuracy decreases with higher noise level but PCA features used in SVM and ANN showed the strongest tolerance against noise contamination.
    Matched MeSH terms: Fractals
  15. An integrated index for automated detection of infarcted myocardium from cross-sectional echocardiograms using texton-based features (Part 1)
    Sudarshan VK, Acharya UR, Ng EY, Tan RS, Chou SM, Ghista DN
    Comput Biol Med, 2016 Apr 1;71:231-40.
    PMID: 26898671 DOI: 10.1016/j.compbiomed.2016.01.028
    Cross-sectional view echocardiography is an efficient non-invasive diagnostic tool for characterizing Myocardial Infarction (MI) and stages of expansion leading to heart failure. An automated computer-aided technique of cross-sectional echocardiography feature assessment can aid clinicians in early and more reliable detection of MI patients before subsequent catastrophic post-MI medical conditions. Therefore, this paper proposes a novel Myocardial Infarction Index (MII) to discriminate infarcted and normal myocardium using features extracted from apical cross-sectional views of echocardiograms. The cross-sectional view of normal and MI echocardiography images are represented as textons using Maximum Responses (MR8) filter banks. Fractal Dimension (FD), Higher-Order Statistics (HOS), Hu's moments, Gabor Transform features, Fuzzy Entropy (FEnt), Energy, Local binary Pattern (LBP), Renyi's Entropy (REnt), Shannon's Entropy (ShEnt), and Kapur's Entropy (KEnt) features are extracted from textons. These features are ranked using t-test and fuzzy Max-Relevancy and Min-Redundancy (mRMR) ranking methods. Then, combinations of highly ranked features are used in the formulation and development of an integrated MII. This calculated novel MII is used to accurately and quickly detect infarcted myocardium by using one numerical value. Also, the highly ranked features are subjected to classification using different classifiers for the characterization of normal and MI LV ultrasound images using a minimum number of features. Our current technique is able to characterize MI with an average accuracy of 94.37%, sensitivity of 91.25% and specificity of 97.50% with 8 apical four chambers view features extracted from only single frame per patient making this a more reliable and accurate classification.
    Matched MeSH terms: Fractals
  16. Fulltext A signal processing based analysis and prediction of seizure onset in patients with epilepsy
    Namazi H, Kulish VV, Hussaini J, Hussaini J, Delaviz A, Delaviz F, et al.
    Oncotarget, 2016 Jan 5;7(1):342-50.
    PMID: 26586477 DOI: 10.18632/oncotarget.6341
    One of the main areas of behavioural neuroscience is forecasting the human behaviour. Epilepsy is a central nervous system disorder in which nerve cell activity in the brain becomes disrupted, causing seizures or periods of unusual behaviour, sensations and sometimes loss of consciousness. An estimated 5% of the world population has epileptic seizure but there is not any method to cure it. More than 30% of people with epilepsy cannot control seizure. Epileptic seizure prediction, refers to forecasting the occurrence of epileptic seizures, is one of the most important but challenging problems in biomedical sciences, across the world. In this research we propose a new methodology which is based on studying the EEG signals using two measures, the Hurst exponent and fractal dimension. In order to validate the proposed method, it is applied to epileptic EEG signals of patients by computing the Hurst exponent and fractal dimension, and then the results are validated versus the reference data. The results of these analyses show that we are able to forecast the onset of a seizure on average of 25.76 seconds before the time of occurrence.
    Matched MeSH terms: Fractals
  17. Detection of Voice Pathology using Fractal Dimension in a Multiresolution Analysis of Normal and Disordered Speech Signals
    Ali Z, Elamvazuthi I, Alsulaiman M, Muhammad G
    J Med Syst, 2016 Jan;40(1):20.
    PMID: 26531753 DOI: 10.1007/s10916-015-0392-2
    Voice disorders are associated with irregular vibrations of vocal folds. Based on the source filter theory of speech production, these irregular vibrations can be detected in a non-invasive way by analyzing the speech signal. In this paper we present a multiband approach for the detection of voice disorders given that the voice source generally interacts with the vocal tract in a non-linear way. In normal phonation, and assuming sustained phonation of a vowel, the lower frequencies of speech are heavily source dependent due to the low frequency glottal formant, while the higher frequencies are less dependent on the source signal. During abnormal phonation, this is still a valid, but turbulent noise of source, because of the irregular vibration, affects also higher frequencies. Motivated by such a model, we suggest a multiband approach based on a three-level discrete wavelet transformation (DWT) and in each band the fractal dimension (FD) of the estimated power spectrum is estimated. The experiments suggest that frequency band 1-1562 Hz, lower frequencies after level 3, exhibits a significant difference in the spectrum of a normal and pathological subject. With this band, a detection rate of 91.28 % is obtained with one feature, and the obtained result is higher than all other frequency bands. Moreover, an accuracy of 92.45 % and an area under receiver operating characteristic curve (AUC) of 95.06 % is acquired when the FD of all levels is fused. Likewise, when the FD of all levels is combined with 22 Multi-Dimensional Voice Program (MDVP) parameters, an improvement of 2.26 % in accuracy and 1.45 % in AUC is observed.
    Matched MeSH terms: Fractals*
  18. Rheological and fractal hydrodynamics of aerobic granules
    Tijani HI, Abdullah N, Yuzir A, Ujang Z
    Bioresour Technol, 2015 Jun;186:276-85.
    PMID: 25836036 DOI: 10.1016/j.biortech.2015.02.107
    The structural and hydrodynamic features for granules were characterized using settling experiments, predefined mathematical simulations and ImageJ-particle analyses. This study describes the rheological characterization of these biologically immobilized aggregates under non-Newtonian flows. The second order dimensional analysis defined as D2=1.795 for native clusters and D2=1.099 for dewatered clusters and a characteristic three-dimensional fractal dimension of 2.46 depicts that these relatively porous and differentially permeable fractals had a structural configuration in close proximity with that described for a compact sphere formed via cluster-cluster aggregation. The three-dimensional fractal dimension calculated via settling-fractal correlation, U∝l(D) to characterize immobilized granules validates the quantitative measurements used for describing its structural integrity and aggregate complexity. These results suggest that scaling relationships based on fractal geometry are vital for quantifying the effects of different laminar conditions on the aggregates' morphology and characteristics such as density, porosity, and projected surface area.
    Matched MeSH terms: Fractals
  19. Fulltext Diagnosis of Lung Cancer by Fractal Analysis of Damaged DNA
    Namazi H, Kiminezhadmalaie M
    Comput Math Methods Med, 2015;2015:242695.
    PMID: 26539245 DOI: 10.1155/2015/242695
    Cancer starts when cells in a part of the body start to grow out of control. In fact cells become cancer cells because of DNA damage. A DNA walk of a genome represents how the frequency of each nucleotide of a pairing nucleotide couple changes locally. In this research in order to study the cancer genes, DNA walk plots of genomes of patients with lung cancer were generated using a program written in MATLAB language. The data so obtained was checked for fractal property by computing the fractal dimension using a program written in MATLAB. Also, the correlation of damaged DNA was studied using the Hurst exponent measure. We have found that the damaged DNA sequences are exhibiting higher degree of fractality and less correlation compared with normal DNA sequences. So we confirmed this method can be used for early detection of lung cancer. The method introduced in this research not only is useful for diagnosis of lung cancer but also can be applied for detection and growth analysis of different types of cancers.
    Matched MeSH terms: Fractals
  20. Fulltext Mathematical Modelling and Prediction of the Effect of Chemotherapy on Cancer Cells
    Namazi H, Kulish VV, Wong A
    Sci Rep, 2015;5:13583.
    PMID: 26316014 DOI: 10.1038/srep13583
    Cancer is a class of diseases characterized by out-of-control cells' growth which affect DNAs and make them damaged. Many treatment options for cancer exist, with the primary ones including surgery, chemotherapy, radiation therapy, hormonal therapy, targeted therapy and palliative care. Which treatments are used depends on the type, location, and grade of the cancer as well as the person's health and wishes. Chemotherapy is the use of medication (chemicals) to treat disease. More specifically, chemotherapy typically refers to the destruction of cancer cells. Considering the diffusion of drugs in cancer cells and fractality of DNA walks, in this research we worked on modelling and prediction of the effect of chemotherapy on cancer cells using Fractional Diffusion Equation (FDE). The employed methodology is useful not only for analysis of the effect of special drug and cancer considered in this research but can be expanded in case of different drugs and cancers.
    Matched MeSH terms: Fractals
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