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. 2026 Oct 1;4:IMAG.a.1386. doi: 10.1162/IMAG.a.1386

Iterative delay correction improves breath-hold cerebrovascular reactivity mapping in clinical populations

Rebecca G Clements 1,2,*, Fatemeh Geranmayeh 3,4, Niamh V Parkinson 3,4, Molly G Bright 1,2
PMCID: PMC13636296  PMID: 42835949

Abstract

Cerebrovascular reactivity (CVR), the ability of cerebral blood vessels to dilate or constrict in response to a vasoactive stimulus, is an important measure of cerebrovascular health. Accurate CVR estimation requires accounting for the time required for the vasoactive stimulus to reach each brain region and the time it takes for local arterioles to modulate cerebral blood flow. The temporal search range used to calculate this spatially varying offset can substantially impact CVR estimates, and the appropriate search range may vary across populations, acquisition protocols, and even brain regions. Here, we present an iterative approach for automatically determining the appropriate maximum shift, using breath-hold fMRI data acquired in a cohort of stroke survivors. This approach selectively expands the delay search range only for voxels with estimated delays at the boundary (i.e., near the minimum or maximum shift) until the estimated delay is no longer at the boundary or a predefined value is reached. In the context of stroke, among voxels initially at the boundary, this approach significantly increased the number of voxels with statistically significant CVR (i.e., having a relationship between end-tidal CO2 and the BOLD signal that is unlikely to be due to random chance). It also resulted in CVR polarity reversals in voxels originally at the early-response boundary and amplified negative CVR values in voxels originally at the late-response boundary, suggesting that using an iterative maximum shift can critically impact CVR interpretation. This approach is broadly applicable beyond stroke, but careful parameter tuning is required, as illustrated by our demonstration of the parameter tuning process for a participant with Moyamoya disease. Together, these findings suggest that iterative delay correction allows for improved CVR assessments in clinical populations.

Keywords: BOLD fMRI, cerebrovascular reactivity, delay correction, clinical, stroke, breath-hold task

1. Introduction

Cerebrovascular reactivity (CVR) is the ability of cerebral blood vessels to dilate or constrict in response to a vasoactive stimulus. CVR has numerous clinical applications, including stroke risk prediction (Papassin et al., 2021; Van Niftrik et al., 2024), presurgical planning for brain tumors (Zaca et al., 2011), and prediction of cognitive outcomes (Catchlove et al., 2018; Liu et al., 2024; Sur et al., 2020). One common method for measuring CVR involves using a breath-hold task during blood-oxygen-level-dependent functional MRI (BOLD fMRI) (Bright & Murphy, 2013; Kastrup et al., 2001). Breath holding elevates arterial CO2 levels, inducing systemic vasodilation and an increase in cerebral blood flow that can be detected using BOLD fMRI. End-tidal CO2 (PETCO2), which acts as a surrogate for arterial CO2 (Robbins et al., 1990; Young et al., 1991), is measured during the scan and is often convolved with the canonical hemodynamic response function (HRF) (Friston et al., 1998) to better model the expected BOLD signal response shape (Domingos et al., 2025; Murphy et al., 2011). Then, PETCO2 is used as a regressor in a general linear model (GLM) to calculate CVR in each voxel as %BOLD change per CO2 unit change in mmHg (Pinto et al., 2021; Sleight et al., 2021).

When calculating CVR, it is important to account for the spatially varying temporal offset between measured PETCO2 and the local BOLD response. This offset arises from measurement delays in gas sampling, the time it takes for gases to reach each brain region, and the response times of local arterioles and cerebral blood flow (Stickland et al., 2021). Recent work used a “lagged-GLM” to account for these delays while calculating CVR (Moia et al., 2020; Stickland et al., 2021). This approach involves first correcting for measurement delays and a global vascular transit delay by “bulk-shifting” PETCO2 convolved with the HRF to maximize its correlation with a reference time series such as the average time series in normal-appearing gray matter (GM). Then, local hemodynamic delays are accounted for through voxel-wise modeling of the BOLD data using a series of temporally shifted PETCO2 regressors, along with nuisance regressors. The voxel-wise PETCO2 regressor shift producing the maximum total model R2 is considered optimal and used to generate a CVR map. This approach not only improves the accuracy of CVR estimates but also provides complementary information about hemodynamic timing (Stickland et al., 2021).

When using a lagged-GLM to calculate CVR, a temporal lag range must be specified that determines the allowable temporal offsets between PETCO2 and the BOLD signal, relative to the bulk shift. In healthy participants, lag ranges of ±9 s have been successfully used to calculate CVR (Bailes et al., 2025; Moia et al., 2021; Zvolanek et al., 2025). The choice of lag range for clinical populations is uncertain, as the lagged-GLM has primarily only been validated in healthy participants. Prior studies have reported prolonged hemodynamic delays in cerebrovascular diseases (Donahue et al., 2016; Han et al., 2024; Siegel et al., 2016), suggesting that a larger maximum shift may be appropriate for some populations. However, the applicability of these estimates is unclear, since it is often not clear what the reported delays are relative to or whether they include measurement delays in gas sampling. Additionally, voxel-wise delay estimates derived from different fMRI paradigms (e.g., breath-hold versus resting-state) are not necessarily interchangeable (Gong et al., 2023), suggesting that different shift ranges may be needed for different acquisition strategies.

In our preliminary analyses, we observed that simply using a larger maximum shift for an entire dataset can reduce the number of voxels with delay values at the boundaries of the shift range, but it can also result in widespread spurious negative CVR values (Fig. 1). This is likely related to the fact that breath-hold tasks can evoke responses resembling a sine wave (Murphy et al., 2011), which are transient in nature and can lead to artifactual negative CVR responses when estimated delays are off by half a period. This issue may be particularly relevant in participants with severely increased delays in one hemisphere and relatively normal delays in the other. This finding highlights the importance of carefully selecting the delay search range and suggests that simply using a conservatively large upper bound for all voxels in the brain may not be an appropriate strategy for breath-hold data.

Fig. 1.

Brain MRI images showing voxels at the boundary of each maximum delay value, along with corresponding CVR amplitude and delay maps for each maximum delay.

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CVR amplitude and delay maps, along with masks of voxels with delay values at the boundaries of the shift range, for one example participant with stroke. A minimum shift of −9 s was used, and the maximum shift ranged from 9 to 19 s in increments of 2 s. We did not explore expanding the minimum shift because delays are calculated relative to normal-appearing GM, and responses earlier than approximately 9 s are not expected in stroke. A combined infarct and white matter hyperintensity (“vascular lesion”) mask is outlined in white and indicated by white arrows. Increasing the maximum shift reduces the number of voxels with delay values at the boundaries of the shift range but also results in more bilateral negative CVR values.

To address these uncertainties, we aim to develop an iterative, voxel-wise approach for determining the appropriate temporal shift range for breath-hold CVR estimation. Estimating the shift range at the voxel level may be particularly advantageous in spatially localized cerebrovascular pathologies, in which hemodynamic delays can vary significantly across brain regions (Braban et al., 2023; Stickland et al., 2021). We propose selectively expanding the maximum shift only in voxels with lag estimates at the boundaries, which may help mitigate the spurious negative CVR values observed in Figure 1. Here, we describe our method and provide open-source code and then validate our method and describe its effects in a cohort of stroke participants.

2. Methods

2.1. Iterative approach for determination of the appropriate maximum shift

To automatically determine the appropriate lag range, we expanded on the code for phys2cvr, an open-source tool for generating CVR maps with a lagged-GLM (Moia et al., 2020, 2024). In addition to the standard parameters used for CVR estimation, the relevant parameters for this analysis are a minimum lag, a starting maximum lag, a final maximum lag, an increment for increasing the maximum lag, and a lag step that determines the resolution of the shifts. These values can be specified by the user and will require careful consideration, depending on the patient population. We suggest that the final maximum lag should be less than half of the breath-hold trial duration, as delays exceeding half of the breath-hold period may introduce spurious negative correlations between PETCO2 and the BOLD signal (Moia et al., 2020). Participants with severe vascular impairments may exhibit very long hemodynamic delays; to avoid underestimation of these delays, breath-hold paradigms should be designed with sufficient paced breathing and recovery time (potentially around 1 min total, though the optimal duration may vary) so that the expected maximum delay is less than half of the breath-hold trial duration. For the lag step, previous work has used a lag step that is a quarter of the imaging TR (Stickland et al., 2021).

First, the PETCO2 regressor, kept at its original sampling frequency without any downsampling, is “bulk shifted” to account for measurement delays and a global vascular transit delay (Moia et al., 2020; Stickland et al., 2021). Bulk shifting is performed by shifting the PETCO2 regressor to maximize its cross-correlation with the average time series in normal-appearing GM, up-sampled to have the same sampling frequency as PETCO2. Next, temporally shifted versions of the bulk shifted PETCO2 regressor are generated, spanning lags from the minimum lag to the final maximum lag in increments defined by the lag step, and downsampled to the imaging TR. The BOLD data are then modeled with a separate GLM for each temporally shifted PETCO2 regressor, including any nuisance regressors. Using PETCO2 regressors with shifts up to the final maximum for this step ensured that the entire range of possible delays was captured, so the lagged-GLM needed to be run only once.

Each voxel’s hemodynamic delay value was estimated by identifying the temporal shift associated with the maximum model fit (R2). To identify this maximum, R2 values were first examined within the lag window defined by the minimum lag and the starting maximum lag. If the lag corresponding to the maximum R2 did not fall within one lag step of either boundary of this window, the lag value for this voxel was considered optimized and no further evaluation of this voxel was performed. If the lag was within 1 lag step of either the positive or negative boundary, the maximum lag was not considered optimized (Moia et al., 2020; Stickland et al., 2021). As a result, for this voxel, the maximum lag was increased by the specified increment and checked again. This process continued until the optimal lag was no longer within one lag step of the boundary or the final maximum lag was reached, whichever came first. An overview of this process for an example subject is shown in Figure 2. After determining the appropriate lag value for each voxel, CVR was calculated as the beta coefficient of the PETCO2 regressor convolved with the HRF at its optimal shift. We did not extend the minimum lag because, assuming the bulk shift is estimated from normal-appearing tissue or, in cases of pathology such as Moyamoya disease or carotid stenosis, from unaffected vascular territories, hemodynamic responses more than 9 s earlier than the bulk shift are not expected to be physiologically plausible. Rare exceptions, such as arteriovenous shunting, would require a different analytical approach.

Fig. 2.

Diagram showing brain lag-mapping method: shift range parameters, R² curves finding optimal lag, iterative maximum shift extension, with brain maps indicating earlier/later timing.

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Overview of the iterative delay correction process for 1 example subject, using parameter values shown in the top left. Using a maximum shift of +9 s produced “optimal” lag estimates of -9 and +9 s in two neighboring voxels. The optimal lag value is identified as the shift producing the maximum R2. Because the peak R2 occurred at the boundary of the search range, it is likely that the true maximum R2 was not captured. For each voxel, the maximum shift was iteratively expanded in 2-s increments until the identified optimal shift no longer occurred at the boundary. This approach yielded lag values of +14.5 and +15.5 s in neighboring voxels, which is more plausible since we expect neighboring voxels of the same tissue type to have similar delay values.

To better ground our interpretation of results in real patient data, where “ground truth” CVR values may be obscured, we applied the iterative delay correction method to two simulated fMRI datasets generated from known ground-truth CVR amplitude and delay maps (Supplementary Figs. S1 and S2). Compared with the standard delay correction approach that used a fixed 9-s maximum delay, the iterative approach produced more accurate delay estimates, particularly within simulated lesion regions containing extreme delay values. The iterative approach also improved the accuracy of CVR amplitude estimates in the simulated lesions.

2.2. Validation in a cohort of participants with stroke

2.2.1. Data collection and pre-processing

We validated our methodology using a BOLD fMRI dataset consisting of 64 participants with stroke (49 M, 61 ± 10 years) (mean ± SD) who were imaged at Imperial College London 137 ± 71 days after stroke onset. The participants were recruited as part of the IC3 study (Gruia et al., 2023) approved by the UK’s Health Research Authority (Registered under NCT05885295; IRAS:299333). Written, informed consent was obtained from all participants for being included in the study. Data collection and processing have been previously described by Clements et al. (2026).

Briefly, during a multi-band multi-echo planar imaging sequence (TR = 1.792 s, TEs = 13.6/26.97/40.34/53.71 ms, voxel size = 3 mm isotropic, MB factor = 2, 154 volumes), participants completed a breath-hold task consisting of 6 repetitions of the following paradigm: 14 s of natural breathing, 16 s of paced breathing, and a 15 s end-expiration breath-hold. Expired CO2 was measured during the scan using a sampling frequency of 1,000 Hz. A T1-weighted whole brain structural image and a fluid-attenuated inversion recovery (FLAIR) image were also acquired. As previously described (Clements et al., 2025; Zvolanek et al., 2023), 28 participants were excluded due to having low-quality PETCO2 timeseries, making the final sample size 36 participants (28 M, 10 participants with hemorrhagic stroke, 63 ± 12 years). It is important to note that this level of attrition is conservatively high. This approach would likely still be effective using surrogate measures of PETCO2, like respiration volume per time (Zvolanek et al., 2023) or deep-learning derived PETCO2 (Clements et al., 2025), but we wanted to focus on and validate this approach in participants with high-quality measured PETCO2 first.

Pre-processing of the BOLD fMRI data included volume registration, distortion correction, brain extraction, optimal combination of the 4 echoes with tedana (DuPre et al., 2021; Kundu et al., 2012, 2013), and smoothing with a 4 mm FWHM kernel (Cox, 1996; Jenkinson et al., 2012). We chose to perform smoothing to improve our signal to noise ratio, and we used a kernel size consistent with previous CVR studies (Thrippleton et al., 2018; Yeh et al., 2022). Smoothing is not required for successful implementation of this delay correction approach (Supplementary Fig. S3). Multi-echo independent component analysis (ME-ICA) was performed with tedana to produce additional nuisance regressors, using methods described by Clements et al. (2026). The expired CO2 data were processed by using in-house MATLAB code to identify end-tidal peaks, manually verifying the peaks, and linearly interpolating the peaks to create PETCO2 timeseries with the same sampling frequency as the original CO2 data. PETCO2 timeseries were then convolved with canonical HRF (Friston et al., 1998). The canonical HRF is commonly used in CVR studies (Domingos et al., 2025; Murphy et al., 2011), despite being empirically derived to estimate neurally driven hemodynamic responses. The shape of this response function should be re-evaluated in future work, since it may vary across subjects and scan sessions (Kassinopoulos & Mitsis, 2019) and in pathology (Bonakdarpour et al., 2007; Pineiro et al., 2002).

2.2.2. CVR calculation and thresholding

CVR maps were generated using our modified version of phys2cvr that iteratively determines the appropriate lag range. The pre-processed BOLD data were modeled using temporally shifted variants of PETCO2 convolved with the HRF, motion parameters and their derivatives (obtained during volume registration), Legendre polynomials up to 3rd order, and ME-ICA components classified as noise that were orthogonalized to the ME-ICA components classified as signal and all other regressors in the model. Orthogonalization of the ME-ICA components was performed in alignment with the previously validated “conservative” ME-ICA approach developed by Moia et al. (2021) for CVR analyses. The lag minimum and starting lag maximum were set to [-9, +9] s and the lag step was set to 0.5 s, consistent with values used previously in healthy participants (Bailes et al., 2025; Moia et al., 2021; Zvolanek et al., 2025). The final lag maximum was set to 19 s, and the increment for increasing the lag maximum was set to 2 s. For comparison, CVR maps were also generated using the standard phys2cvr approach with a fixed lag range of [-9, +9] s and a lag step of 0.5 s.

To characterize changes in CVR for voxels initially at the delay boundary using a [-9, +9] s lag range, we identified voxels whose lag values were within one lag step (0.5 s) of the minimum or maximum shift. Specifically, voxels were classified as being at the early response (−9 s) boundary if their lag was less than or equal to −8.5 s and at the late response (+9 s) boundary if their lag was greater than or equal to +8.5 s. We also identified voxels with statistically significant CVR. CVR values were considered significant if they had absolute t-statistics greater than 1.98 (corresponding to p < 0.05). This value was further adjusted using Šidák correction to account for running 57 different models for the iterative maximum approach ([-9,19] s search range in 0.5 s increments) and 37 different models for the standard approach ([-9,9] s search range in 0.5 s increments) (Bright et al., 2017; Šidák, 1967). We note that this threshold is likely conservative for the iterative maximum approach, since we did not use a lag maximum of +19 s for all voxels.

2.2.3. Generation of region of interest masks

To evaluate the effects of our iterative maximum approach across different tissue types, we generated region of interest (ROI) masks using FSL tools (Jenkinson et al., 2012). Stroke lesions (including lacunes if present) and white matter hyperintensities, which we will refer to collectively as vascular lesions, were manually delineated using the FLAIR images and verified by neurologist FG. The T1-weighted image was brain-extracted with BET and segmented into GM, white matter (WM), and cerebrospinal fluid (CSF) with FAST using a threshold of 0.5 (Y. Zhang et al., 2001). Vascular lesion masks were transformed to T1-space using FLIRT (Jenkinson & Smith, 2001; Jenkinson et al., 2002) and subtracted from the GM, WM, and CSF masks to generate masks of normal-appearing GM, WM, and CSF, which were then transformed to functional space.

Because negative CVR values have been observed in and around the ventricles, and prior work suggests that CVR mechanisms in these regions may differ (Bright et al., 2014; Thomas, Liu, Aslan, et al., 2013); we wanted to evaluate the ventricles and peri-ventricular space separately from the remaining CSF. For each subject, we transformed a mask of the ventricles from the N27 template brain (Holmes et al., 1998) to functional space. This mask was dilated by 1 level using AFNI’s 3dmask_tool (Cox, 1996), and the original functional mask of the ventricles was subtracted to generate a mask of periventricular space. To avoid having overlapping voxels in the ROI masks, voxels in the ventricles or in periventricular space were excluded from the GM, WM, and CSF masks, and vascular lesion voxels were excluded from the masks of the ventricles and periventricular space. This analysis resulted in 5 total ROI masks in functional space: normal-appearing GM, normal-appearing WM, CSF, ventricles, peri-ventricular space, and vascular lesions.

2.3. Example of parameter tuning for a different pathology

To assess how the iterative delay correction approach generalizes beyond stroke, and to illustrate how parameters may need to be adjusted for other cerebrovascular pathologies, we applied our methods to data from a 31-year-old male with unilateral Moyamoya disease causing an occluded right middle cerebral artery (MCA). This dataset was collected at Northwestern University under a study approved by the Northwestern University Institutional Review Board. Written, informed consent was obtained from the participant for being included in the study. The participant completed a breath-hold task during a multi-band multi-echo gradient-echo echo planar imaging sequence (TR = 1.5 s, TEs = 10.6/27.83/45.06/62.29/79.52 ms, voxel size = 2.5 mm isotropic, MB factor = 4, 212 volumes). The breath-hold task consisted of 6 repetitions of the following paradigm: 24 s of paced breathing, a 15 s hold, a 2 s exhale, and 8 s of recovery. Afterward, the participant completed another 24 s of paced breathing. During the scan, expired CO2 was measured using a nasal cannula and used to calculate end-tidal CO2. The fMRI pre-processing steps were the same as those used for the stroke dataset, except that distortion correction was not performed as a field map was not acquired.

For this participant with right MCA occlusion, we first evaluated two different ROIs for generating the reference timeseries used to calculate the bulk shift. These ROIs were a mask of all normal-appearing GM and a mask of normal-appearing GM excluding the affected vascular territory. The affected vascular territory was identified using a mask of the right MCA from a vascular territory atlas (Schirmer et al., 2019a, 2019b) and transformed into functional space. The GM mask that excludes the affected vascular territory is ideal, but the whole-brain GM mask can be more readily obtained and does not require a priori knowledge of pathology. The whole-brain GM mask may generate a reference timeseries that is temporally “blurred” compared to the GM mask that excluded the affected vascular territory, as it includes voxels with a large range of delay values (Tong et al., 2019). Compared to the GM mask that excluded the affected vascular territory, the timeseries in the whole-brain GM mask could also be reduced in amplitude due to averaging across regions with reduced or negative responses to the breath holds.

The increment for increasing the maximum lag was set to 2 s, equivalent to our TR rounded to the nearest whole number. Because we did not expect any voxels to exhibit responses more than 9 s earlier than the unaffected vascular territories, the minimum lag value was set to -9 s. The final maximum lag value should be less than half of the breath-hold trial length (49 s), and thus was set to 23 s. Finally, to determine the appropriate starting maximum, we experimented with using starting maximum values of 9, 11, 13, 15, 17, and 19 s.

3. Results

3.1. Validation in a cohort of participants with stroke

When using a ±9 s shift range, the median proportion of voxels at the -9 and +9 s boundaries was 4% and 5% of the brain, respectively, with some participants showing up to 18% at -9 s and 13% at +9 s. (Fig. 3A). Most of these voxels were nonsignificant. Using an iterative maximum shift, voxels at the late response boundary mostly shifted to slightly later delays, with only a minority (25%) remaining at the original boundary (Fig. 3B). The largest proportion of voxels had an appropriate maximum delay of +11 s, and progressively fewer voxels required longer delays than 11 s. Most voxels at the early response boundary (64%) retained their original early delay, while the remainder shifted from the early boundary to later delays. Using an iterative maximum significantly increased the percentage of significant voxels among voxels initially at the late response boundary and the early response boundary, as indicated using a 1-sided paired t-test (p < 0.05, Bonferroni corrected). Importantly, these significant increases occurred despite applying a stricter Šidák correction for the iterative maximum approach. This result suggests that using an iterative maximum can recover significant CVR estimates for voxels with prolonged delays.

Fig. 3.

Scientific figure with three panels (A, B, and C) showing violin plots and bar charts analyzing voxel response delays at boundaries across various ROIs.

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Effects of the iterative approach for voxels initially at the lag boundaries with a [-9,+9] shift range. The top row describes voxels initially at the late (+9 s) response boundary, and the bottom row describes voxels initially at the early (-9 s) response boundary. (A) The percentage of voxels in the brain that were initially located at each lag boundary across subjects. Significant voxels were identified using a threshold of p < 0.05 and Šidák correction. (B) The distribution of the appropriate maximum delay identified by the iterative maximum approach for voxels initially at the lag boundaries, across all the subjects. (C) The percentage of voxels in each ROI that became significant with an iterative maximum.

We also investigated the location of voxels that switched from being nonsignificant using a +9 s maximum shift to significant using an iterative maximum shift, within the predefined ROI masks (Fig. 3C). For both voxels initially at the late response boundary and voxels initially at the early response boundary, the percentages of voxels that became significant were relatively similar across ROIs. However, vascular lesions, which included both lesions and white matter hyperintensities, showed the highest percentage. This is consistent with the expectation that stroke lesions will exhibit longer hemodynamic delays (Braban et al., 2023). White matter hyperintensities have also been previously associated with delayed arterial transit times (R. Zhang et al., 2022) and thus may also exhibit prolonged hemodynamic delays. As a supplementary analysis, we examined lesions and white matter hyperintensities separately, rather than combining them in the vascular lesion mask, and found that voxels that become significant with the iterative approach were not consistently localized to either lesions or white matter hyperintensities (Supplementary Table S1).

Next, we evaluated how the iterative maximum approach impacted CVR amplitude values (Fig. 4). For this analysis, we only included voxels that were statistically significant using delay correction with an iterative maximum shift. For voxels that were initially at the late response boundary, negative CVR values became slightly more negative, and values near zero shifted toward more negative CVR amplitudes (Fig. 4A). This effect is illustrated in example CVR maps (Fig. 5, Example 1) which show a brain region where, with the iterative approach, CVR becomes more negative and statistically significant, and the estimated hemodynamic delay is increased. Negative CVR values may represent effects such as vascular steal (Poublanc et al., 2013; Venkatraghavan et al., 2018); large increases in cerebral blood volume relative to cerebral blood flow (Arteaga et al., 2014), oxygen metabolism upregulation (Arteaga et al., 2014), or fractional changes in fluid volume (Blockley et al., 2011; Bright et al., 2014; Thomas, Liu, Aslan, et al., 2013).

Fig. 4.

Two-panel scientific figure showing CVR change bar charts and histograms comparing voxel response boundaries, colored by voxel count and mean CVR polarity across shift ranges.

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Changes in CVR amplitude with an iterative maximum shift for voxels at the late response boundary (A) and the early response boundary that became delayed with an iterative maximum (B). For the top two plots, CVR values were divided into 25 bins ranging from −0.3 to 0.3, and the average change in CVR across subjects was calculated for each bin. Bins containing fewer than 100 voxels were excluded. Voxels at the late response boundary with negative or near-0 CVR values tended to have CVR values that became slightly more negative. Voxels at the early response boundary that switched to being delayed with an iterative maximum reversed in CVR polarity. This effect is illustrated in the bottom two plots: the left plot shows the original CVR distribution with a 9 s maximum shift, and the right plot shows the CVR distribution after the iterative maximum shift. Voxels are colored according to their original CVR values, and the color reversal between the two plots demonstrates the polarity change.

Fig. 5.

Brain MRI grid comparing 9s Max and Iterative Max methods across delay boundaries, delay, CVR, and thresholded CVR maps in two examples.

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Example CVR maps for 2 example subjects, generated using a 9-s maximum shift and an iterative maximum shift. The top row shows voxels with delay values at the boundaries of the tested lag range (pink). The pink circle indicates brain regions of interest, where the text description at the top applies. The remaining rows show delay maps, CVR amplitude maps, and thresholded CVR maps, generated using a threshold of p < 0.05 and Šidák correction.

For voxels that were initially at the early response boundary (-9 s) when using a ±9 s shift range, and that were recalculated as delayed (>9 s) when using an iterative maximum, we observed relatively large positive changes for CVR values that were initially negative, and large negative changes for CVR values that were initially positive (Fig. 4B). Because these voxels ultimately exhibited positive delays with an iterative maximum, their initial delay values at the early-response boundary likely reflected an artifact of the +9 s maximum positive delay being too low. Consequently, when the estimated delay shifted from the early-response boundary to a substantially delayed response, the estimated CVR value often changed drastically as well.

To determine whether these changes indicated a reversal in CVR polarity, we plotted the distribution of CVR values obtained with the 9 s maximum delay and the distribution obtained with the iterative maximum, colored by the original 9 s delay CVR values (Fig. 4B, bottom). The inversion of colors in the distribution plots indicates that extending the delay range for voxels at the early-response boundary often resulted in flipped CVR polarity. To determine whether this finding was influenced by restricting the analysis to voxels with statistically significant CVR, we repeated the analysis shown in Figure 5 using all voxels. The same overall pattern was observed (Supplementary Fig. S4). This effect is also evident in an example CVR map (Fig. 5, Example 2), in which, using an iterative maximum, negative CVR values became positive and CVR delay changed from being early to late. In Example 2, the voxels that changed CVR polarity and switched from having early to late responses were near vascular lesions, in line with previous studies reporting longer delays in these regions (Geranmayeh et al., 2015). This effect is consistent with our findings from a simulated fMRI dataset (Supplementary Fig. S2), in which, within a simulated lesion containing extremely delayed responses, using a 9-s maximum shift resulted in CVR delay being incorrectly estimated as early and CVR amplitude being incorrectly estimated as negative. In contrast, using an iterative maximum correctly identified the polarity of both the CVR delay and CVR amplitude.

These findings suggest that the iterative delay correction approach can critically impact CVR interpretation. Because delays were measured relative to normal-appearing tissue, we did not extend the early-response boundary because we did not expect any voxels to respond more than 9 s before normal-appearing tissue. A limitation of this work is that we do not validate our CVR estimates using gold-standard [15O]-water PET imaging, which is a challenging multi-modal experiment due to the invasiveness of arterial blood sampling and the need for an on-site cyclotron (Fan et al., 2016). Future work should validate our findings using controlled gas delivery with longer hypercapnic periods, where delay correction is expected to be less critical. It would be informative to determine whether regions that switched from very early to very late responses using an iterative maximum in breath-hold data also had delayed responses under sustained hypercapnia. Additionally, future validation using perfusion-weighted MRI measurements would help establish that delays measured using the iterative approach more accurately reflect underlying hemodynamics. For example, delay estimates could be compared with the time-to-maximum of the residue function (Tmax) measured using dynamic susceptibility contrast (Christen et al., 2015; Kroll et al., 2017); however, this approach requires the use of contrast agents. Future work could also assess whether the iterative approach results in stronger agreement of CVR amplitude estimates with cerebral blood flow estimates identified using arterial spin labeling (ASL) (Stickland et al., 2022). However, one caveat is that ASL signal sensitivity decreases as transit delays increase (Nael et al., 2013), making accurate estimation of cerebral blood flow in stroke challenging.

3.2. Example of parameter tuning for a different pathology

In the participant with unilateral Moyamoya disease, we calculated the bulk shift using a mask of all normal-appearing GM and a similar mask that excludes the affected vascular territory, and we found that these masks produced nearly the same results (bulk shifts of 17.1 and 17.3 s, respectively). We decided to use the mask of GM in the unaffected vascular territories, only, since it is expected to be slightly more accurate. These observations suggest that while a GM mask that excludes affected vascular territories is always preferable, if researchers do not have a priori knowledge of cerebrovascular pathology, a mask of all-normal appearing GM may be sufficient for accurately estimating the bulk shift. However, future validation in a larger cohort is needed to confirm this.

After the bulk shift is applied to account for measurement delays and a global transit delay, voxel-wise hemodynamic delays were determined using the specified shift range. Using a minimum and final maximum lag of -9 and +23 s, respectively, and increasing the maximum lag in 2-s increments, we experimented with different starting maximum values (Fig. 6). In the affected vascular territory, outlined in white, we observed that using a starting maximum of 9, 11, or 13 s resulted in a region of white matter having shorter delays (around 0–5 s) than nearby GM (around 9–14 s) (see white arrows). Although the validity of this result is uncertain, white matter typically has a slower CVR response than GM (Thomas, Liu, Park, et al., 2013), and Moyamoya is anticipated to specifically lengthen vascular transit times, suggesting that we have an insufficient initial search range to capture all voxels with longer hemodynamic delays. Using a starting maximum of at least 15 s resulted in more appropriate (i.e., longer) estimated delays in this specific white matter area relative to GM across the affected vascular territory, which is more plausible.

Fig. 6.

Brain imaging grid showing Moyamoya disease analysis across starting lags 9-19s, with delay maps, delay distribution graphs, and CVR thresholded scans.

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CVR maps generated using an iterative maximum for a participant with unilateral Moyamoya disease. Columns correspond to different starting maximum delays (9–19 s, in 2-s increments). As the starting maximum increases, delays within the affected vascular territory become longer and more spatially consistent, particularly in white matter (see white arrows in row 2). Histograms of delay values within the affected territory demonstrate that the peak at 0–5 s observed with a 9-s starting maximum diminishes with higher starting maxima and is replaced with more delay values between 10–15 s. A starting maximum of 19 s resulted in more negative CVR values outside of the affected vascular territory (see gray arrows), suggesting that a 15 or 17 s starting maximum may be most appropriate. Thresholded CVR maps were generated using a threshold of p < 0.05 and Šidák correction.

This increase in delays in white matter is also illustrated by the distribution of delays in the affected vascular territory (see row 3 of Fig. 6). Specifically, the small peak between 0–5 s observed with a 9 s starting maximum disappears when using an initial maximum shift of 15 s or 17 s and is replaced with more delays in the 10–15 s range. This shift is evident when comparing the envelope of the 9 s delay histogram with the corresponding histograms for the 15, 17, and 19 s starting maxima (see histograms in columns 4, 5, and 6 in Fig. 6). These findings suggest that when the starting maximum is too short, false negative CVR estimates may occur because the estimated delay is misaligned by approximately half of a breath-hold period. In these cases, the selected delay may not be at the boundary, so the search range would not be expanded despite the incorrect alignment. We also observed that using a starting maximum of 19 s resulted in more negative CVR values in brain areas outside of the affected vascular territory (see gray arrows), suggesting that a 19 s starting maximum also may not be appropriate, akin to our results in stroke at a 15 s starting maximum (Fig. 1). These findings suggest that using a starting maximum of 15 s or 17 s produce optimal results for this participant and may be a starting point for further work in patients with Moyamoya.

In summary, these results suggest that iterative delay correction has the flexibility to be applied to cerebrovascular pathologies other than stroke. When applying the iterative approach to a new pathology, careful consideration of parameter values is essential. For the participant with Moyamoya disease, a larger starting maximum appears necessary to accurately capture hemodynamic delays within the affected vascular territory, although a larger sample size is needed to more definitely determine this. This finding may reflect the more widespread and severe delays characteristic of Moyamoya disease, which involve an entire vascular territory, in contrast to the more localized effects we observed in stroke. In the future, leaving more time between breath-hold trials may also be helpful for patient populations with longer delays and may make successful delay correction less dependent on specific parameter values.

Additional validation in larger datasets is important for confirming that the iterative approach can translate to pathologies beyond stroke and identifying robust iterative delay correction parameters tailored to different patient populations. For example, future work should investigate whether parameters should be adapted for participants after bypass surgery; we would expect that the parameters used prior to surgery may remain appropriate and delay values may decrease, with fewer voxels at the boundary of starting maximum lag (Shiino et al., 2025).

4. Conclusion

Accounting for voxel-wise hemodynamic delays is critical for accurate CVR estimation, particularly in clinical populations with prolonged vascular responses. The choice of maximum temporal shift can greatly impact calculated hemodynamic delay values and may need to vary across populations and acquisition protocols. We presented an approach for determining the appropriate maximum delay value that involves iteratively extending the delay range only for voxels with lag values at the boundary of the initial search window for the optimal lag. In participants with stroke, this approach significantly increased the number of voxels with statistically significant CVR among those initially at the boundary. For voxels initially at the late-response boundary, voxels with 0 or negative CVR values became slightly more negative, increasing confidence that these values reflect physiological signals rather than noise. In contrast, for voxels at the early response boundary, an iterative maximum resulted in a reversal of CVR polarity, greatly altering interpretation of these responses.

Importantly, our approach can be readily applied across different populations, although our choice of parameter values has only been validated in stroke. Careful consideration of parameter values, such as the starting and final maximum lag and the reference timeseries for calculating the bulk shift, is necessary when moving to other cohorts. To guide future work, we demonstrated the parameter tuning process for unilateral Moyamoya disease and showed that certain parameter values may need to be altered to account for more extreme or widespread hemodynamic delays. Future studies should use larger datasets spanning additional cerebrovascular disorders and more diverse breath-hold paradigms to further validate this method and better characterize how parameter choices should be tuned. Additionally, while this approach is designed for breath-hold data with short hypercapnic periods, future work should evaluate whether the iterative approach influences results in datasets containing longer hypercapnic periods achieved using CO2 inhalation.

Overall, the findings of this study highlight the importance of appropriately accounting for hemodynamic delays in CVR analysis and demonstrate that an iterative, data-driven approach for determining the delay search range can improve the accuracy and interpretation of CVR estimates.

Supplementary Material

Supplementary Material
IMAG.a.1386_supp.pdf (1.2MB, pdf)

Acknowledgments

We are grateful to all the participants for their time and involvement in the study. We thank all the research assistants and students for their help with data collection and manual stroke lesion segmentation.

Data and Code Availability

Code for calculating CVR using the iterative delay correction approach is available at https://github.com/BrightLab-ANVIL/phys2cvr_Iterative and has been submitted as a pull request on GitHub to be incorporated into the main phys2cvr code (https://github.com/smoia/phys2cvr). Imaging data are not publicly available as they are part of a study that is still ongoing. Access may be considered subject to inter-institutional agreements once the study objectives have been achieved.

Author Contributions

Rebecca G. Clements: Conceptualization, Methodology, Software, Formal analysis, Investigation, Data curation, Writing—original draft, Writing—reviewing and editing, Visualization, and Project administration. Fatemeh Geranmayeh: Methodology, Resources, Data Curation, Writing—reviewing and editing, Supervision, and Funding acquisition. Niamh V. Parkinson: Investigation, Project administration. Molly G. Bright: Conceptualization, Methodology, Resources, Writing—review & editing, Supervision, and Project administration.

Funding

This work was supported by the National Science Foundation (DGE-2234667 to R.G.C.), the National Institutes of Health National Institute of Neurological Disorders and Stroke (R01NS126509), and the UK Medical Research Council (MR/T001402/1). Infrastructure support was provided by the NIHR Imperial Biomedical Research Centre and the NIHR Imperial Clinical Research Facility. The views expressed are those of the authors and not necessarily those of the NSF, NIH, NHS, the NIHR, or the Department of Health and Social Care.

Declaration of Competing Interests

The authors declare no competing financial interests.

Supplementary Materials

Supplementary material for this article is available here: https://doi.org/10.1162/IMAG.a.1386#supplementary-data.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary Material
IMAG.a.1386_supp.pdf (1.2MB, pdf)

Data Availability Statement

Code for calculating CVR using the iterative delay correction approach is available at https://github.com/BrightLab-ANVIL/phys2cvr_Iterative and has been submitted as a pull request on GitHub to be incorporated into the main phys2cvr code (https://github.com/smoia/phys2cvr). Imaging data are not publicly available as they are part of a study that is still ongoing. Access may be considered subject to inter-institutional agreements once the study objectives have been achieved.

Articles from Imaging Neuroscience are provided here courtesy of MIT Press

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