Newly advancing methods in MRI make it possible to measure blood flow as pulse waves in the human brain. These time dependent waves that can be measured in the brain consist of a forward travelling (outgoing from the heart) and backward travelling (reflected at vessel branches) part. The size of the reflected wave as well as the obtained pulse wave velocity are measures for abnormal conditions of the blood vessels in the human brain and play a role in aging effects and the pathogenesis of neurodegenerative diseases, and are thus of medical interest.
The goal of the inverse pulse wave splitting problem is to estimate the separated forward and backward travelling waves as well as the pulse wave velocity from the measurable waves that are obtained on several points along an artery. We work on a mathematical analysis of the inverse pulse wave splitting problem, to obtain insight on solvability and uniqueness of the solution. Further, reconstruction methods are developed to solve this non-linear ill-posed problem. These methods are numerically implemented in algorithms and tested on simulation data for accuracy and reliability. We work closely together with medical physicists in the method development and testing of our algorithms on real patients.