Computational Fractal-Based Analysis of Brain Arteriovenous Malformation Angioarchitecture

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Neuroimaging is the gold standard for diagnosis and follow-up of brain arteriovenous malformations (bAVMs), but no objective parameter has been validated for the assessment of the nidus angioarchitecture and for prognostication following treatment. The fractal dimension (FD), which is a mathematical parameter able to quantify the space-filling properties and roughness of natural objects, may be useful in quantifying the geometrical complexity of bAVMs nidus.


To propose FD as a neuroimaging biomarker of the nidus angioarchitecture, which might be related to radiosurgical outcome.


We retrospectively analyzed 54 patients who had undergone stereotactic radiosurgery for the treatment of bAVMs. The quantification of the geometric complexity of the vessels forming the nidus, imaged in magnetic resonance imaging, was assessed by means of the box-counting method to obtain the fractal dimension.


FD was found to be significantly associated with the size (P = .03) and volume (P < .001) of the nidus, in addition to several angioarchitectural parameters. A nonsignificant association between clinical outcome and FD was observed (area under the curve, 0.637 [95% confidence interval, 0.49-0.79]), indicative of a potential inverse relationship between FD and bAVM obliteration.


In our exploratory methodological research, we showed that the FD is an objective computer-aided parameter for quantifying the geometrical complexity and roughness of the bAVM nidus. The results suggest that more complex bAVM angioarchitecture, having higher FD values, might be related to decreased response to radiosurgery and that the FD of the bAVM nidus could be used as a morphometric neuroimaging biomarker.


AVM, arteriovenous malformation


bAVM, brain arteriovenous malformation


CTA, computed tomographic angiography


FD, fractal dimension


nrAVM, nonruptured arteriovenous malformation


ROI, region of interest

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