Cardiac pulsations in the human brain have received recent interest due to their possible role in the pathogenesis of neurodegenerative diseases. Further interest stems from their possible application as an endogenous signal source that can be utilized for brain imaging in general. The (pulse-)wave describing the blood flow velocity along an intracranial artery consists of a forward (anterograde) and a backward (retrograde, reflected) part, but measurements of this wave usually consist of a superposition of these components. In this paper, we provide a mathematical framework for the inverse problem of estimating the pulse wave velocity, as well as the forward and backward component of the pulse wave separately from MRI measurements on the middle cerebral artery. After a mathematical analysis of this problem, we consider possible reconstruction approaches, and derive an alternate direction approach for its solution. The resulting methods provide estimates for anterograde/retrograde wave forms and the pulse wave velocity under specified assumptions on a cerebrovascular model system.

翻译：人脑中的心脏搏动近期因可能在神经退行性疾病发病机制中发挥作用而受到关注。其另一研究价值源于可作为通用脑成像的内源性信号源。描述颅内动脉血流速度的（脉搏）波由前向（顺行）和反向（逆行/反射）分量组成，但此类波的测量通常为这些分量的叠加。本文提出一个数学框架，用于解决从大脑中动脉MRI测量数据中分别估算脉搏波速度及其前向与反向分量的逆问题。在对该问题进行数学分析后，我们探讨了可能的重构方法，并推导出一种交替方向求解方案。基于脑血管模型系统的特定假设，所提方法可提供顺行/逆行波形及脉搏波速度的估计值。