<p>    </p> <p>Cerebrovascular diseases, such as stroke, constitute the most common life-threatening neurological disease in the United States. To support normal brain function, maintaining adequate brain perfusion (i.e., cerebral blood flow (CBF)) is important. Therefore, it is crucial to assess the brain perfusion so that early intervention in cerebrovascular diseases can be applied if abnormal perfusion is observed. The goal of my study is to develop metrics to measure the brain perfusion through modeling brain physiology using resting-state and task-based blood-oxygenation-level- dependent (BOLD) functional MRI (fMRI). My first and second chapters focused on deriving the blood arrival time using the resting-state BOLD signal. In the first chapters, we extracted the systemic low-frequency oscillations (sLFOs) in the fMRI signal from the internal carotid arteries (ICA) and the superior sagittal sinus (SSS). Consistent and robust results were obtained across 400 scans showing the ICA signals leading the SSS signals by about 5 seconds. This delay time could be considered as an effective perfusion biomarker that is associate with the cerebral circulation time (CCT). To further explore sLFOs in assessing dynamic blood flow changes during the scan, in my second chapter, a “carpet plot” (a 2-dimensional plot time vs. voxel) of scaled fMRI signal intensity was reconstructed and paired with a developed slope-detection algorithm. Tilted vertical edges across which a sudden signal intensity change took place were successfully detected by the algorithm and the averaged propagation time derived from the carpet plot matches the cerebral circulation time. Given that CO₂ is a vasodilator, controlling of inhaled CO₂ is able to modulate the BOLD signal, therefore, as a follow-up study, we focused on investigating the feasibility of using a CO₂ modulated sLFO signal as a “natural” bolus to track CBF with the tool developed from the second chapter. Meaningful transit times were derived from the CO₂-MRI carpet plots. Not only the timing, the BOLD signal deformation (the waveform change) under CO₂ challenge also reveals very useful perfusion information, representing how the brain react to stimulus. Therefore, my fourth chapter focused on characterizing the brain reaction to the CO₂ stimulus to better measure the brain health using BOLD fMRI. Overall, these studies deepen our understanding of fMRI signal and the derived perfusion parameters can potentially be used to assess some cerebrovascular diseases, such as stroke, ischemic brain damage, and steno-occlusive arterial disease in addition to functional activations. </p>