The fractal geometry of the brain

Ieva, Antonio Di

doi:10.15761/fgnamb.1000138

Cited by 19 publications

(32 citation statements)

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“…SWI sequences provide information on venous vasculature, hemorrhage, iron deposits, and very small vascular structures within the central nervous system (including brain tumors) [4,[15][16][17]. Fractal geometry has been demonstrated to offer appropriate tools to quantify irregular-shaped biological objects, including microvascular and SWI patterns [8], that can be used in automated algorithms for counting microbleeds [18], quantitative susceptibility mapping [19], percentage-wise quantification of intratumoral-susceptibility signals [20], local image variance [21] and other quantitative methodologies [16]. The fractal dimension, the most used parameter in fractal geometry, has been shown as a reliable numerical index to objectively quantify geometrical complexity of microvascular patterns in brain tumors [22].…”

Section: Discussionmentioning

confidence: 99%

“…The fractal dimension, the most used parameter in fractal geometry, has been shown as a reliable numerical index to objectively quantify geometrical complexity of microvascular patterns in brain tumors [22]. The fractal dimension is a characteristic of irregularly shaped structures that maintains a constant level of complexity over a limited range of scales [8,23]. Our previous findings showed that lower FD values of the intratumoral SWI patterns are associated with tumoral microvasculature, while higher values (more "space-filling" and geometrically complex) are associated with microbleeds and necrotic areas [5].…”

Section: Discussionmentioning

confidence: 99%

“…In the field of quantitative neuroradiology and clinical neurosciences, fractal-based computational modelling has been introduced for the characterization of intrinsic features (e.g., microvascular patterns) [6][7][8]. The intratumoral patterns of magnetic susceptibility can be quantified by means of fractal analysis [9].…”

Section: Introductionmentioning

confidence: 99%

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Advanced computational and statistical multiparametric analysis of Susceptibility-Weighted Imaging to characterize gliomas and brain metastases

Ieva

Russo

Reste³

et al. 2020

Preprint

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contributed equally to this work.Abstract. Susceptibility-weighted imaging (SWI) is a technique useful for evaluation of the internal structures of brain tumors, including microvasculature and microbleeds. Intratumoral patterns of magnetic susceptibility can be quantified by means of fractal analysis. Here, we propose a radiomics methodological pipeline to merge advanced fractal-based computational modelling with statistical analysis to objectively characterize the fingerprint of gliomas and brain metastases. Forty-seven patients with glioma (grades II-IV, according to the WHO 2016 classification system) and fourteen with brain metastases underwent 3 Tesla MRI using a SWI protocol. All images underwent computational analysis aimed to quantify three Euclidean parameters (related to tumor and SWI volume) and five fractal-based parameters (related to the pixel distribution and geometrical complexity of the SWI patterns). Principal components analysis, linear and quadratic discriminant analysis, K-nearest neighbor and support vector machine methods were used to discriminate between tumor types. The combination of parameters offered an objective evaluation of the SWI pattern in gliomas and brain metastases. The model accurately predicted 88% of glioblastoma, according to the quantification of intratumoral SWI features, failing to discriminate the other types. SWI is not normally used to classify brain tumors, however fractal-based multi-parametric computational analysis can be used to characterize intratumoral SWI patterns to objectively quantify tumors-related features. Specific parameters still have to be identified to provide completely automatic computerized differential diagnosis.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Advanced computational and statistical multiparametric analysis of Susceptibility-Weighted Imaging to characterize gliomas and brain metastases

Ieva

Russo

Reste³

et al. 2020

Preprint

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“…0.5 < H is an indication for long range correlations and H < 0.5 for long-range anti-correlations (Kantelhardt et al, 2002). For some fractal processes one power-law exponent is not enough to characterize them and a multifractal formalism can be used to describe several exponents (Di Ieva, 2016). In case of multifractality, the scaling function of a signal is not linear anymore and can thus not be described by a single scaling exponent H but by a nonlinear scaling function (Zilber, 2014).…”

Section: Scale Free Approachesmentioning

confidence: 99%

“…Thus, the fractal dimension, namely D, describes the overall complexity of an object, which can be the geometrical complexity, the space filling property, the roughness of a surface, or the variation of a time series. The fractal dimension D is defined by the logarithmic ratio of change in detail with change in scale (Di Ieva, 2016). This relates to the distinct characteristic of a fractal, namely the property of self-similarity: i.e., pieces of an object are similar to larger pieces of it as well as to the whole object (Eke et al, 2002).…”

Section: Introductionmentioning

confidence: 99%

Evaluating Complexity of Fetal MEG Signals: A Comparison of Different Metrics and Their Applicability

Moser

Bensaid

Kroupi

et al. 2019

Preprint

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In this work, we aim to investigate whether information based metrics of neural activity are a useful tool for the search for consciousness before and shortly after birth. Neural activity is measured using fetal magnetoencephalography (fMEG) in human fetuses and neonates. Based on recent theories on consciousness, information-based metrics are established to measure brain complexity and to assess different levels of consciousness. Different metrics (measures of entropy, compressibility and fractality) are, thus, explored in a reference population and their usability is evaluated. For comparative analysis, two fMEG channels were selected: one where brain activity was previously detected and one at least 15cm away, that represented a control channel. The usability of each metric was evaluated and results from the brain and control channel were compared. Concerning the ease of use with fMEG data, Lempel-Ziv-Welch (LZW) compression was evaluated as best, as it is unequivocal and needs low computational effort. The fractality measures have a high parameter space and therefore forfeit comparability, while entropy measures require a higher computational effort and more parameters to adjust compared to LZW. Comparison of a channel with brain activity and a control channel in neonatal recordings showed significant differences in most complexity metrics. This clear difference can be seen as proof of concept for the usability of complexity metrics in fMEG. For fetal data, this comparison produced less clear results which can be related to leftover maternal signals included in the control channel. Further work is necessary to conclusively interpret results from the analysis of fetal recordings. Yet this study shows that complexity metrics can be used for fMEG data on early consciousness and the evaluation gives a guidance for future work. The inconsistency of results from different metrics highlights the challenges of working with complexity metrics as neural correlates of consciousness, as well as the caution one should apply to interpret them.

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Evaluation of the 3D fractal dimension as a marker of structural brain complexity in multiple‐acquisition MRI

Krohn

Froeling

Leemans

et al. 2019

Human Brain Mapping

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Fractal analysis represents a promising new approach to structural neuroimaging data, yet systematic evaluation of the fractal dimension (FD) as a marker of structural brain complexity is scarce. Here we present in-depth methodological assessment of FD estimation in structural brain MRI. On the computational side, we show that spatial scale optimization can significantly improve FD estimation accuracy, as suggested by simulation studies with known FD values. For empirical evaluation, we analyzed two recent open-access neuroimaging data sets (MASSIVE and Midnight Scan Club), stratified by fundamental image characteristics including registration, sequence weighting, spatial resolution, segmentation procedures, tissue type, and image complexity. Deviation analyses showed high repeated-acquisition stability of the FD estimates across both data sets, with differential deviation susceptibility according to image characteristics. While less frequently studied in the literature, FD estimation in T2-weighted images yielded robust outcomes. Importantly, we observed a significant impact of image registration on absolute FD estimates. Applying different registration schemes, we found that unbalanced registration induced (a) repeated-measurement deviation clusters around the registration target, (b) strong bidirectional correlations among image analysis groups, and (c) spurious associations between the FD and an index of structural similarity, and these effects were strongly attenuated by reregistration in both data sets. Indeed, differences in FD between scans did not simply track differences in structure per se, suggesting that structural complexity and structural similarity represent distinct aspects of structural brain MRI. In conclusion, scale optimization can improve FD estimation accuracy, and empirical FD estimates are reliable yet sensitive to image characteristics. K E Y W O R D S fractal analysis, MRI biomarker, structural brain complexity, structural similarity, imaging validation Carsten Finke and Francisco J. Esteban contributed equally to the manuscript.

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The fractal geometry of the brain

Cited by 19 publications

References 0 publications

Advanced computational and statistical multiparametric analysis of Susceptibility-Weighted Imaging to characterize gliomas and brain metastases

Advanced computational and statistical multiparametric analysis of Susceptibility-Weighted Imaging to characterize gliomas and brain metastases

Evaluating Complexity of Fetal MEG Signals: A Comparison of Different Metrics and Their Applicability

Evaluation of the 3D fractal dimension as a marker of structural brain complexity in multiple‐acquisition MRI

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