Computational Fractal-Based Neurosurgery

Abstract

Fractal geometry is a branch of mathematics used to characterize and quantify the geometrical complexity of natural objects, with many applications in different fields, including physics, astronomy, geology, meteorology, finances, social sciences, and computer graphics. In the biomedical sciences, the use of fractal parameters has allowed the introduction of novel morphometric parameters, which have been shown to be useful to characterize any biomedical images as well as any time series within different domains of applications. Specifically, in the neurosciences and neurosurgery, the use of the fractal dimension and other computationally inferred fractal parameters has offered robust morphometric quantitators to characterize the brain in its wholeness, from neurons to the cortical structure and connections, and introduced new prognostic, diagnostic, and eventually therapeutic markers of many diseases of neurosurgical interest, including brain tumors and cerebrovascular malformations, as summarized in this chapter.

Keywords: Fractal; Fractal analysis; Fractal dimension; Hurst index; Lacunarity; Multifractal; Neurology; Neuroscience; Neurosurgery; Time series.