Abstract
Arteriovenous malformations (AVMs) are cerebrovascular lesions consisting of a pathologic tangle of the vessels characterized by a core termed the nidus, which is the “nest” where the fistulous connections occur. AVMs can cause headache, stroke, and/or seizures. Their treatment can be challenging requiring surgery, endovascular embolization, and/or radiosurgery as well. AVMs’ morphology varies greatly among patients, and there is still a lack of standardization of angioarchitectural parameters, which can be used as morphometric parameters as well as potential clinical biomarkers (e.g., related to prognosis).
In search of new diagnostic and prognostic neuroimaging biomarkers of AVMs, computational fractal-based models have been proposed for describing and quantifying the angioarchitecture of the nidus. In fact, the fractal dimension (FD) can be used to quantify AVMs’ branching pattern. Higher FD values are related to AVMs characterized by an increased number and tortuosity of the intranidal vessels or to an increasing angioarchitectural complexity as a whole. Moreover, FD has been investigated in relation to the outcome after Gamma Knife radiosurgery, and an inverse relationship between FD and AVM obliteration was found.
Taken altogether, FD is able to quantify in a single and objective value what neuroradiologists describe in qualitative and/or semiquantitative way, thus confirming FD as a reliable morphometric neuroimaging biomarker of AVMs and as a potential surrogate imaging biomarker. Moreover, computational fractal-based techniques are under investigation for the automatic segmentation and extraction of the edges of the nidus in neuroimaging, which can be relevant for surgery and/or radiosurgery planning.
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References
Al-Shahi R, Warlow C. A systematic review of the frequency and prognosis of arteriovenous malformations of the brain in adults. Brain. 2001;124:1900–26.
Andrade-Souza YM, Zadeh G, Ramani M, Scora D, Tsao MN, Schwartz ML. Testing the radiosurgery-based arteriovenous malformation score and the modified spetzler-martin grading system to predict radiosurgical outcome. J Neurosurg. 2005;103:642–8.
Aoki Y, Nakagawa K, Tago M, Terahara A, Kurita H, Sasaki Y. Clinical evaluation of gamma knife radiosurgery for intracranial arteriovenous malformation. Radiat Med. 1996;14:265–8.
Babin D, Spyrantis M, Pizurica A, Philips W. Pixel profiling for extraction of arteriovenous malformation in 3-D CTA images. Conf Proc IEEE Eng Med Biol Soc. 2013;2013:5449–52.
Babin D, Pizurica A, Bellens R, De Bock J, Shang Y, Goossens B, et al. Generalized pixel profiling and comparative segmentation with application to arteriovenous malformation segmentation. Med Image Anal. 2012;16:991–1002.
Bollerslev T. Generalized autoregressive conditional heteroskedasticity. J Econ. 1986;31:307–27.
Di Ieva A, Esteban FJ, Grizzi F, Klonowski W, Martin-Landrove M. Fractals in the neurosciences, part II: clinical applications and future perspectives. Neuroscientist. 2015;21:30–43.
Di Ieva A, Boukadoum M, Lahmiri S, Cusimano MD. Computational analyses of arteriovenous malformations in neuroimaging. J Neuroimaging. 2014;25:354–60.
Di Ieva A, Niamah M, Menezes RJ, Tsao M, Krings T, Cho YB, et al. Computational fractal-based analysis of brain arteriovenous malformation angioarchitecture. Neurosurgery. 2014;75:72–9.
Di Ieva A, Matula C, Grizzi F, Grabner G, Trattnig S, Tschabitscher M. Fractal analysis of the susceptibility weighted imaging patterns in malignant brain tumors during antiangiogenic treatment: technical report on four cases serially imaged by 7 T magnetic resonance during a period of four weeks. World Neurosurg. 2012;77:785.e11–21.
Du R, Keyoung HM, Dowd CF, Young WL, Lawton MT. The effects of diffuseness and deep perforating artery supply on outcomes after microsurgical resection of brain arteriovenous malformations. Neurosurgery. 2007;60:638–46; discussion 646–8.
Falconer K. Fractal geometry: mathematical foundations and applications. New Jersey: Wiley; 2003.
Flickinger JC, Pollock BE, Kondziolka D, Lunsford LD. A dose-response analysis of arteriovenous malformation obliteration after radiosurgery. Int J Radiat Oncol Biol Phys. 1996;36:873–9.
Forkert ND, Illies T, Goebell E, Fiehler J, Saring D, Handels H. Computer-aided nidus segmentation and angiographic characterization of arteriovenous malformations. Int J Comput Assist Radiol Surg. 2013;8:775–86.
Forkert ND, Schmidt-Richberg A, Fiehler J, Illies T, Moller D, Saring D, et al. 3D cerebrovascular segmentation combining fuzzy vessel enhancement and level-sets with anisotropic energy weights. Magn Reson Imaging. 2013;31:262–71.
Jenkinson M, Smith S. A global optimisation method for robust affine registration of brain images. Med Image Anal. 2001;5:143–56.
Kanmani S, Rao CB, Raj B. On the computation of the minkowski dimension using morphological operations. J Microsc. 1993;170:81–5.
Lahmiri S, Boukadoum M, Di Ieva A. Detrended fluctuation analysis of brain hemisphere magnetic resonance imaging to detect cerebral arteriovenous malformations. In: Circuits and Systems (ISCAS), IEEE International Symposium. 2014;2409–2412.
Lopes R, Betrouni N. Fractal and multifractal analysis: a review. Med Image Anal. 2009;13:634–49.
Matsumoto M, Kodama N, Endo Y, Sakuma J, Suzuki K, Sasaki T, et al. Dynamic 3D-CT angiography. AJNR Am J Neuroradiol. 2007;28:299–304.
McGee KP, Ivanovic V, Felmlee JP, Meyer FB, Pollock BE, Huston J 3rd. MR angiography fusion technique for treatment planning of intracranial arteriovenous malformations. J Magn Reson Imaging. 2006;23:361–9.
Ondra SL, Troupp H, George ED, Schwab K. The natural history of symptomatic arteriovenous malformations of the brain: a 24-year follow-up assessment. J Neurosurg. 1990;73:387–91.
Pollock BE, Lunsford LD, Kondziolka D, Maitz A, Flickinger JC. Patient outcomes after stereotactic radiosurgery for “operable” arteriovenous malformations. Neurosurgery. 1994;35:1–7; discussion 7–8.
Pruess SA. Some remarks on the numerical estimation of fractal dimension. In: Barton CC, La Pointe PR, editors. Fractals in the earth sciences. New York: Plenum Press; 1995. p. 10.
Reishofer G, Koschutnig K, Enzinger C, Ebner F, Ahammer H. Fractal dimension and vessel complexity in patients with cerebral arteriovenous malformations. PLoS One. 2012;7:e41148.
Russo C. Brightness progressive normalization. 2012. Webpage: http://www.fractal-lab.org/Downloads/bpn_algorithm.html. Accessed on Feb 2016.
Spetzler RF, Ponce FA. A 3-tier classification of cerebral arteriovenous malformations. Clinical article. J Neurosurg. 2011;114:842–9.
Spetzler RF, Martin NA. A proposed grading system for arteriovenous malformations. J Neurosurg. 1986;65:476–83.
Wu Y, Chang W, Johnson KM, Velikina J, Rowley H, Mistretta C, et al. Fast whole-brain 4D contrast-enhanced MR angiography with velocity encoding using undersampled radial acquisition and highly constrained projection reconstruction: image-quality assessment in volunteer subjects. AJNR Am J Neuroradiol. 2011;32:E47–50.
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Di Ieva, A., Reishofer, G. (2024). Fractal-Based Analysis of Arteriovenous Malformations (AVMs). In: Di Ieva, A. (eds) The Fractal Geometry of the Brain. Advances in Neurobiology, vol 36. Springer, Cham. https://doi.org/10.1007/978-3-031-47606-8_21
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