The Euclidean geometry that we learned in our primary education concerns man-made shapes such as rectangles, triangles, and perfect circles. However the shapes of molecules, cells, and organ systems (and their dynamic changes over time) are more complex. Some biological structures exhibit fractal geometry which is defined as “shapes and patterns that appear similar at different scales” (recursive iteration). Examples of biological structures exhibiting fractal geometry include the branches and roots of trees, blood vessels, lung airways, and the dendritic arbors of neurons. In this episode I talk with Antonio Di leva a neurosurgeon and neuroscientist at Macquarie University School of Medicine about fractal geometry and its applications to basic and clinical neuroscience. Fractal structures of neural networks optimize the energy efficiency of the brain. Dr. Di leva talks about emerging applications of fractals to diagnosis and monitoring of neurological disorders, neurosurgery, neuroimaging, and computational intelligence. Fractal analyses are not limited to structures and can also be applied to studies of recursive features dynamic processes including neural network activity.

LINKS

Dr. Di leva’s webpage: https://mqneurosurgery.com.au/prof-antonio-di-ieva/

Book ‘The Fractal Geometry of the Brain’: https://link.springer.com/book/10.1007/978-3-031-47606-8

Review articles:

https://journals-sagepub-com.proxy1.library.jhu.edu/doi/full/10.1177/1073858413513927

https://journals-sagepub-com.proxy1.library.jhu.edu/doi/full/10.1177/1073858413513928