## 1 Introduction  
Recent advances in neuroimaging techniques have revolutionized our understanding of cerebrovascular physiology, highlighting the intricate link between cerebral blood flow (CBF) and various neurological disorders. Cerebrovascular reactivity (CVR), the dynamic capacity of cerebral arterioles to dilate and restrict in response to vasoactive stimuli, is not merely a physiological parameter but a critical homeostatic mechanism. CVR ensures adequate cerebral perfusion across a range of physiological challenges, reflecting the health and resilience of the cerebrovascular system. CVR assessment is clinically relevant for evaluating preoperative prognosis and monitoring functional recovery following neurological events [1; 2; 3; 4]. Several imaging modalities are employed for CVR measurement, including single photon emission computed tomography (SPECT), magnetic resonance imaging (MRI), and positron emission tomography (PET). These techniques typically involve administering a vasodilatory stimulus, such as acetazolamide (ACZ) or CO\({}_{2}\), to induce changes in CBF [5; 6; 7; 8; 9]. ACZ, a carbonic anhydrase inhibitor, exerts its vasodilatory effect by dilating cerebral arterioles approximately 10-30 min post administration [10; 11]. Inhaled CO\({}_{2}\), conversely, readily diffuses across the blood-brain barrier, leading to an increased hydrogen ion concentration (lowered pH) through the formation and dissociation of carbonic acid. This pH change directly relaxes cerebral arteriolar smooth muscle, resulting in rapid vasodilation and increased CBF, with the magnitude of vasodilation exhibiting a dose response relationship with CO\({}_{2}\) concentration [1; 3]. SPECT, using radiopharmaceuticals such as \({}^{99\text{m}}\)Tc-hexamethyl propyleneamine oxime (HMPAO) and ethylcysteine dimer (ECD), remains a valuable tool for assessing regional CBF due to its widespread availability and established clinical utility [9; 12; 13; 14]. The high quantitative accuracy of \({}^{15}\)O-water PET for perfusion measurement comes at the cost of requiring the administration of a radioactive tracer [5]. While MRI offers alternative techniques for assessing CBF, including perfusion MRI and arterial spin labeling (ASL), each approach presents practical considerations. Perfusion MRI, reliant on contrast agents, raises concerns about nephrogenic systemic fibrosis, especially in vulnerable renal populations. ASL, while contrast free, often grapples with inherent limitations in signal to noise ratio and extended scan times [15; 16; 17; 18]. In contrast, blood oxygenation level-dependent (BOLD) functional MRI (fMRI) with CO\({}_{2}\) challenge has become a prominent non-invasive approach for CVR assessment [19; 20; 21; 6]. Driven by neurovascular coupling, the BOLD effect arises from neuronal activity induced modulations in CBF, which in turn trigger shifts in deoxyhemoglobin and oxyhemoglobin concentrations, ultimately yielding detectable T2*-weighted signal intensity variations. Building on this mechanistic understanding, the BOLD signal, while commonly interpreted as a surrogate marker for CBF, more comprehensively reflects a multifactorial composite of localized hemodynamic and metabolic variables, prominently including CBF, cerebral blood volume, and oxygen extraction fraction [1; 18; 22; 23]. Despite the widespread clinical use of both SPECT and BOLD MRI for assessing cerebrovascular function, the vasodilatory stimuli used have typically differed; SPECT has primarily employed ACZ in clinical practice, while BOLD MRI has favored CO\({}_{2}\) due to its rapid kinetics compatible with fast MRI sequences. As a result, direct comparisons between SPECT and BOLD MRI using the same CO\({}_{2}\) stimulus--a method increasingly adopted in MRI studies--remain surprisingly scarce [9; 22; 24; 25; 26].