The brain's vascular network dynamically affects its development and core functions. It rapidly responds to abnormal conditions by adjusting properties of the network, aiding stabilization and regulation of brain activities. Tracking prominent arterial changes has clear clinical and surgical advantages. However, the arterial network functions as a system; thus, local changes may imply global compensatory effects that could impact the dynamic progression of a disease. We developed automated personalized system-level analysis methods of the compensatory arterial changes and mean blood flow behavior from a patient's clinical images. By applying our approach to data from a patient with aggressive brain cancer compared with healthy individuals, we found unique spatiotemporal patterns of the arterial network that could assist in predicting the evolution of glioblastoma over time. Our personalized approach provides a valuable analysis tool that could augment current clinical assessments of the progression of glioblastoma and other neurological disorders affecting the brain.