## 4 Discussion
Other techniques have been traditionally employed for CVR assessment. The development of BOLD fMRI has positioned CO\({}_{2}\) as a valuable and increasingly popular stimulus, leveraging the inherent advantages of MRI [3; 4; 20; 21; 22]. The intended dynamic analysis of BOLD CVR using EtCO\({}_{2}\) data was not feasible in this study due to the poor signal quality of the acquired EtCO\({}_{2}\) measurements, which hindered reliable processing and interpretation. Despite this limitation, we adopted a static analysis approach to directly compare the overall magnitude and spatial patterns of CVR obtained from fMRI with the static measures from SPECT, which was the primary focus of our investigation. Typically, BOLD CVR studies employ a General Linear Model (GLM) with EtCO\({}_{2}\) as a regressor to model the dynamic relationship between EtCO\({}_{2}\) fluctuations and BOLD signal changes, allowing for the estimation of parameters such as time to peak [1; 6; 32]. However, given that our primary research question focused on comparing the spatial patterns of overall CVR as measured by SPECT and fMRI, and that SPECT provides a static measure of CBF change [21], a static analysis of our CO\({}_{2}\) BOLD CVR data allowed for a more direct comparison between the two modalities. This method, similar to approaches used in ACZ MRI studies when dynamic EtCO\({}_{2}\) data are unavailable, involved averaging the BOLD signal change within a predefined time window following CO\({}_{2}\) administration [2; 20]. While this static approach does not allow for a detailed assessment of the temporal dynamics of the BOLD response, it provided a comparable CVR metric to our SPECT data, enabling us to address our research question regarding the spatial concordance of CVR between these two imaging modalities. Moreover, by incorporating stimulus timing correction, tcMRI improves the temporal alignment between the CO\({}_{2}\) challenge and the resulting BOLD signal. This enhances model fit and the accuracy of CVR estimation, which likely explains the significantly stronger spatial agreement with SPECT observed in this study. In contrast, conventional BOLD analysis without timing correction may underestimate or mislocalize CVR effects, particularly in regions with variable hemodynamic latency. The validity of static BOLD CVR measures has been supported by comparisons with other techniques like ASL [25], and our study aimed to directly compare CO\({}_{2}\) induced CVR using a static BOLD approach with SPECT CVR also induced by CO\({}_{2}\). Future studies should prioritize incorporating EtCO\({}_{2}\) monitoring to enable more comprehensive dynamic BOLD CVR analysis and further validation of the current findings. Specifically, methodological improvements in EtCO\({}_{2}\) measurement are crucial, including the use of advanced gas control systems that ensure stable CO\({}_{2}\) delivery and accurate response, and the implementation of robust digital recording systems for accurate temporal synchronization of EtCO\({}_{2}\) data with BOLD signal acquisition. With high-quality EtCO\({}_{2}\) data, future work can employ dynamic analysis approaches. These include using GLM with EtCO\({}_{2}\) and its temporal derivatives as regressors to model the temporal characteristics of the BOLD response and estimate parameters such as time to peak [1; 4], or applying transfer function analysis between EtCO\({}_{2}\) and BOLD signals to estimate detailed hemodynamic parameters and phase delays [20]. In addition, the application of simultaneous imaging techniques such as PET-MR or SPECT-MR to address the possibility of changes in the physiological state of the sample resulting from non-simultaneous acquisition of images would provide an interesting avenue for future research in this field [33]. In summary, this study demonstrated a strong spatial agreement in CVR between the novel tcMRI technique and SPECT, particularly in high CVR regions.