| Magnetic resonance imaging (MRI) is a medical imaging technology with the advantages of noninvasion and high temporal and spatial resolutions. It is of great clinical value to study the mechanism in our brain and diagnose some related diseases. A large number of researchers have made great efforts in this field and obtained many exciting progresses. However, most of the existing researches are limited in the linear field and the employed linear analysis methods are based on the hypothesis of temporally stationary. As we know, our brain is a huge complex and nonlinear system. Employing the nonlinear methods can hence describe the brain activities more accurately and explore the essential characteristics of the brain. Meanwhile, it has reported that our brain signals show the self-similarity structure, which is suitable for fractal analysis. Moreover, comparing with monofractal, multifractal analysis can capture more comprehensive brain activity processes, and thus have more advantages. Therefore, multifractal analysis is adopted in our study and applied to both functional and structural MRI data. Our work mainly includes the following aspects:(1) Multifractal analysis was applied to resting state functional MRI (rs-fMRI) data and we conducted the normal aging study through extracting the signals in default mode network (DMN) of the brain, (i) In this study, we proposed a new way to construct the rs-fMRI series for the first time. That is, in order to obtain the longer series, we constructed the rs-fMRI series along the scanned slices and the mean value in each slice was taken as one point. Multifractal characteristics were then verified in the series. (ii) In order to explore the differences between different groups with different ages, we introduced a new multifractal feature, △asa, which can describe the asymmetry of the multifractal spectrum. Moreover, we interpreted its physiological significance from the aspect of the scale properties of a signal, indicating its potential usefulness in exploring normal aging. In this study, we mainly discussed the characteristics along the changes with age for the normal controls, and we found the slight differences between the young vs. the middle-aged and the young vs. the elderly groups can be successfully detected by the proposed △asa feature.In addition, the greater A^a values in the middle-aged and the elderly may suggest the greater averaged scale index and stronger long range correlation, which were also deduced to be associated with decreased fractal complexity and suboptimal neurophysiological dynamics, while the situation is on the contrary for the smaller △asα in the young. Our results expanded the previous findings, and further highlighted the potential usefulness of multifractal analysis in rs-fMRI series of a certain brain region. By exploring the normal aging effects in the default mode network on rs-fMRI series from the multifractal aspect, it can provide insights into understanding the inherent dynamics mechanism of the brain.(2) Multifractal analysis was applied to rs-fMRI data for early Alzheimer’s disease (AD) study.In this study, we addressed two issues for the first time:(Issue-I) if and what multifractal features are sufficiently discriminative to detect early AD from the healthy; and (Issue-II) if the discriminative performance could be further improved by combining multifractal features with the traditional features in this field. After verifying the multifractal characteristics in the extracted rs-fMRI series, we systematically investigated the discriminative power of a set of multifractal features in distinguishing early AD from the healthy. And then we also compared the performances between the multifractal features and the other traditional features such as the monofractal feature, the linear features and the network-based feature. By our study, we identified a multifractal feature, △f, which has the strongest discriminative power among all the features in our study. Furthermore, we employed the multiple kernel learning algorithm to combine the multifractal features and the traditional features, and found the classification accuracy could be further significantly improved. Our work demonstrated the potential usefulness of multifractal analysis for early AD study, especially when combining with the traditional rs-fMRI features. It contributes to distinguishing early AD from the healthy subjects.(3) Multifractal analysis was applied to structural MRI (sMRI) data for early AD study. The contributions in this study include:(i) we extended the box-counting based multifractal analysis (BCMA) into the three-dimension case; (ii) we proposed a new method called the integer ratio based BCMA (IRBCMA) algorithm, which can compensate for the rigid division rule in BCMA. Next, we explored the white matter structural changes on three-dimension sMRI volumes between the normal aging controls (NC) and the early AD subjects with the aforementioned two methods, BCMA and IRBCMA. After verifying the multifractal characteristics, we extracted two canonical multifractal features, △a and △f, based on their corresponding multifractal spectrums. The two features were demonstrated to be effective to distinguish early AD from NC groups with two-tail t test. Generally, the larger values of △f and △f in the NC group may suggest more complexity in their white matter structures than the early AD counterpart. Furthermore, through performing the Pearson’s correlation analysis, we found strong positive correlations with statistical significance between the two multifractal features and the clinical Mini-Mental State Examination (MMSE) scores, which ensured the potential physiological meaning for the two multifractal features, and smaller values of △a and △f are related to the worse adaptation and more severe of the dementia degree. In this study, both BCMA and IRBCMA achieved good performances, which suggest both of them are effective. Previously, only Aa feature was used in such studies. Hence, we highlighted that △f is also found to be an alternative feature for multifractal analysis on sMRI data. To be noted, more accurate and effective △f values can be obtained by IRBCMA method, which is supported by the finding of the stronger correlation between △f and MMSE. Therefore, we made an important step towards finding practically effective marker for AD detection. Meawhile, our findings also highlighted the potential usefulness of multifractal analysis on three-dimensional sMRI data, which may contribute to clarifying some aspects of the etiology of AD through detection of structural changes in white matter. |
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