Introduction: This study reviews the historical march towards topical advancements in glioblastoma (GBM) growth and invasion modeling using diffusion MRI, laying the framework for the next era of in silico modeling for refining neurosurgical and radiotherapy treatment.
Methods: Literature review.
Results: In 1822, Joseph Fourier published on the classical heat equation and flux (the transfer of something over a surface area per unit of time). In 1827, Robert Brown noticed the microscopic, irregular transfer of pollen seeds in water – a movement later called “Brownian Motion”. In 1855, Fick published a partial differential diffusion equation, with terms and a diffusion coefficient analogous to those used in the classical heat equation, but in the context of particle diffusion rather than heat conduction. In 1905, Einstein added a statistical element for describing the “random walk” of particles undergoing Brownian Motion, explaining how a particle’s “mean-square displacement” relates to the diffusion coefficient. Then, in 1937, Fisher published a reaction-diffusion equation with a diffusion term analogous to Fick’s and Fourier’s, applied in 1995 by Tracqui and colleagues to model glioma growth. Jbabdi and colleagues later capitalized on the diffusion principles of diffusion tensor imaging (DTI) in 2005, incorporating DTI data into a glioma growth model. This is important given Scherer's findings in the 1930s-1940s, amongst others since, that GBM cells infiltrate white matter. Moreover, there have been promising advancements in the last decade, particularly DTI-related models, that integrate patient diffusion data and microenvironment variables shown to influence the directional flux of GBM cells.
Conclusion : Diffusion MRI is a powerful tool for neurosurgical preoperative planning for tumors like glioblastoma. Understanding the physics and mathematical principles of diffusion from a historical framework will inform progression modeling with the aim of refining resection margins, so that the next model may achieve more ubiquitous implementation into the neurosurgical approach to GBM.
.jpg)
