Arrival time mapping with ¹⁵O-gas PET for cerebrovascular steno-occlusive diseases: a comparative study with CT perfusion

Abstract

Background

Positron emission tomography (PET) with ¹⁵O-gas for quantifying cerebral blood flow (CBF) and oxygen metabolism is the gold standard for assessing hemodynamics in ischemic cerebrovascular disease. However, conventional ¹⁵O-gas PET methods do not provide information on regional arrival timing, a hemodynamic parameter typically measured using computed tomography (CT) perfusion with contrast media. This study demonstrated that ¹⁵O-gas PET with a state-of-the-art clinical PET scanner and optimized analysis can generate arrival time maps. In this retrospective study of ten patients with unilateral stenosis or occlusion of the major arteries, we compared PET-derived arrival time maps with CT perfusion Tmax maps.

Results

In PET with short inhalation of [¹⁵O]-CO₂ gases, dynamic images were reconstructed with 2-sec temporal resolution, followed by weighted least-squares fitting of one-tissue compartment models, with or without the contributions from vascular components. PET arrival time maps were visually comparable to CT perfusion Tmax maps regarding the spatial extent of delayed brain regions, with less noise and higher image quality when using the model without the vascular components. Region-of-interest analyses showed good correlations between the two modalities: correlation coefficients of 0.834 for absolute values and 0.718 for ipsilateral-to-contralateral differences, respectively, indicating that ¹⁵O-gas PET can quantitatively measure the arrival time with reasonable accuracy.

Conclusions

The present method generates arrival-time maps with ¹⁵O-gas PET by applying optimized kinetic analysis to dynamic [¹⁵O]-CO₂ images acquired using a state-of-the-art, high-sensitivity clinical PET scanner. Additional arrival time information for conventional PET parameters of CBF and oxygen metabolism may facilitate a more comprehensive understanding of the hemodynamic status in cerebrovascular steno-occlusive diseases.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13550-025-01209-7.

Introduction

Positron emission tomography (PET) with oxygen-15-labeled compounds (¹⁵O-PET), the gold standard method for quantification of cerebral blood flow (CBF) and oxygen metabolism, is a valuable imaging modality for understanding brain pathophysiology, especially in ischemic cerebrovascular disease [1]. Primary hemodynamic parameters, i.e., CBF, cerebral blood volume (CBV), oxygen extraction fraction (OEF), and cerebral metabolic rate of oxygen (CMRO₂), are obtained by performing serial PET scans with three types of ¹⁵O-labeled gases, [¹⁵O]-CO, [¹⁵O]-O₂, and [¹⁵O]-CO₂ (or direct intravenous injection of [¹⁵O]-H₂O) along with arterial input function (AIF) measurements using arterial blood sampling [2, 3]. Each hemodynamic parameter reflects a different aspect of the hemodynamic status, thus enabling a comprehensive assessment of the brain pathophysiology [1, 3].

Computed tomography (CT) or magnetic resonance (MR) perfusion with bolus injection of contrast agent, a more frequently used imaging modality, can acquire information on arterial blood arrival time in addition to the traditional circulation parameters, CBF, CBV, and mean transit time (MTT), calculated as the ratio of CBV to CBF [4, 5]. In the current clinical setting, arrival time is usually calculated as Tmax, the peak time of the residue function estimated by deconvolution analysis [6–9]. This Tmax parameter helps estimate the spatial extent of delayed arrival regions, especially in patients with acute stroke [10, 11].

The arrival time parameter provides additional information to the conventional hemodynamic parameters measured by ¹⁵O-gas PET, namely CBF, CBV, OEF, and CMRO₂, and thus may contribute to a more detailed understanding of brain pathophysiology; however, the noisy dynamic PET images of ¹⁵O (approximately 2 min of half-life) with short acquisition frames (a few seconds) hinder the accurate determination of the arrival time in each imaging voxel, that is, arrival time mapping. To our knowledge, there is only one report on arrival-time mapping in ¹⁵O-gas PET [12], using a technique that leverages different error sensitivities of analysis methods to the arrival time. To establish the validity of arrival time mapping with ¹⁵O-gas PET, direct comparisons with other, more reliable modalities are desirable but have not yet been performed.

This study aimed to establish a method for arrival time mapping with ¹⁵O-gas PET and to validate its effectiveness in evaluating delayed brain regions in patients with hemodynamic ischemia. This study demonstrated that arrival time mapping is possible using a state-of-the-art clinical PET scanner [13–15] and optimized compartment model analysis. Specifically, we directly compared arrival time maps measured by ¹⁵O-gas PET with those measured by established CT perfusion using contrast media in patients with unilateral occlusion or severe stenosis of the main cerebral artery. Additionally, computer simulations were performed to confirm the validity of the proposed method, particularly its robustness against image noise.

Materials and methods

Subjects

We enrolled consecutive patients with atherosclerotic steno-occlusive disease who underwent ¹⁵O-gas PET and CT perfusion during preoperative examinations between 2019 and 2023. The inclusion criteria were (1) occlusion or severe stenosis of the unilateral internal carotid artery (ICA) or middle cerebral artery (MCA), as documented by MR or CT angiography; (2) no large cortical infarctions on MR or CT images; and (3) no evidence of any neurological event (transient ischemic attack or stroke) between ¹⁵O-gas PET and CT perfusion examinations. Details of the enrolled patients (n = 10) are summarized in Table S1 (Additional file 1). The study was approved by the Ethics Committee of the Research Institute for Brain and Blood Vessels-Akita (No. 23 − 20) and was performed in accordance with the Declaration of Helsinki. The requirement for informed consent was waived because of its retrospective design.

PET acquisition and conventional quantification

The protocol for PET acquisition and parameter quantification was similar to that of previous studies [16, 17], except for using a different PET scanner [13–15] and applying [¹⁵O]-CO₂ inhalation instead of intravenous injection of [¹⁵O]-H₂O for CBF quantification [18].

A whole-body digital PET scanner using silicon photomultiplier (SiPM)-based detectors (Biograph Vision PET/CT system, Siemens Healthineers) was used [13–15]. Scanner specifications are as follows: transverse and axial spatial resolution at a 1-cm offset from the center of the field of view (FOV), 3.6- and 3.5-mm full width at half maximum (FWHM), respectively; axial FOV, 25.6 cm (26.1 cm including the packing spaces between the blocks [13]); sensitivity, 16.4 kcps/MBq; time-of-flight (TOF) resolution, 210 ps. All PET images were reconstructed using a 3D ordinary Poisson ordered-subset expectation–maximization (OP-OSEM) algorithm with TOF information and point-spreading-function modeling (PSF reconstruction; four iterations and five subsets), with post-reconstruction Gaussian smoothing at a 3-mm FWHM. The resulting PET images had a 440440159 matrix (0.80.81.6 mm voxel size). A standard low-dose CT scan (120 kV, 100 mAs) was acquired for attenuation correction and was subsequently used to spatially normalize all parametric maps.

Each ¹⁵O-gas PET study included three sequential scans with approximately 15-min scan intervals: (1) 1.5-min inhalation of [¹⁵O]-CO (3.0 GBq total), (2) 1-min inhalation of [¹⁵O]-O₂ (2.0 GBq total), and (3) 1-min inhalation of [¹⁵O]-CO₂ (1.5 GBq total). PET acquisition started simultaneously with ¹⁵O-gas inhalation and continued for 8 min ([¹⁵O]-CO) or 6 min ([¹⁵O]-O₂, [¹⁵O]-CO₂). The acquired list-mode PET data were dynamically reconstructed and integrated, resulting in a set of three static PET images: (1) the last 4-min [¹⁵O]-CO image (4–8 min), (2) the first 3-min [¹⁵O]-O₂ (0–3 min), and (3) the first 3-min [¹⁵O]-CO₂ images (0–3 min). An AIF was determined with a coincidence gamma-detector that continuously measured radioactivity in arterial blood taken from the radial artery (1-sec temporal sampling), corrected for global delay and dispersion effects occurring in the detector system and the internal arterial line [19, 20], and used for the parameter quantification based on a three-step autoradiographic method (3-step ARG) [2]. Specifically, CBV was calculated from the static [¹⁵O]-CO images with the cerebral-to-large vessel hematocrit ratio assumed to be 0.85 [21]. CBF is calculated using the one-tissue compartment modeling ARG method from the static [¹⁵O]-CO₂ images [18, 22]. Subsequently, OEF was calculated from the static [¹⁵O]-O₂ image in combination with CBF and CBV [2]. A brain-blood partition coefficient or distribution volume of water was fixed to 0.8 mL/mL [23]. CMRO₂ was calculated as a product of CBF, OEF, and arterial oxygen content (CaO₂) (CMRO₂ = CaO₂CBFOEF). Note that this conventional quantification considers only the global delay effect, neglecting voxel-level delay (local delay) as described in the next section.

Arrival time mapping with [¹⁵O]-CO2

To obtain the PET arrival time maps, we applied compartmental analysis to dynamic [¹⁵O]-CO₂ images using a data processing pipeline (in-house MATLAB tools) other than the clinical tools described above. The acquired 6-min list-mode data with [¹⁵O]-CO₂ inhalation were reconstructed into dynamic images with short time frames of 602 sec, 610 sec, and 630 sec, using the e7-tools offline reconstruction package (Siemens Healthineers). A timeframe of 2 s was the shortest setting for the current reconstruction tool. Although the image reconstruction parameters were the same as those described above, the image matrix was down-sampled to a 11011040 matrix (3.23.26.4 mm voxel size) to reduce the computational time for voxel-level calculations.

Compartment models and voxel-level arrival time Estimation

Inhaled [¹⁵O]-CO₂ gases are instantaneously converted to [¹⁵O]-H₂O in lung capillaries [24], which circulate into the whole body via blood flow. Thus, the inhalation of [¹⁵O]-CO₂ is treated as an intravenous injection of [¹⁵O]-H₂O, for which one-tissue compartment models are usually applied [18, 25]:

1

where C(t) and C_a(t) are the [¹⁵O]-H₂O concentrations at time t in the brain tissues and AIF (Bq/mL), respectively; K₁ is the tracer delivery rate from the blood to the tissues (mL/mL/min), corresponding to CBF under the assumption of sufficiently high first-pass extraction; and k₂ is the clearance rate (1/min), which relates to the distribution volume as V_d = K₁/k₂. Conventional analysis with Eq. (1) usually corrects only the global time delay between the AIF (C_a(t)) and the brain tissue curves (C(t)), neglecting the voxel-level arrival time. To generate arrival time maps, we explicitly included voxel-level delays in Eq. (1):

2

where D_t (sec) is the arrival time or temporal delay in a tissue of interest relative to the AIF, with positive D_t values corresponding to delayed arrivals and negative values to early arrivals. In this study, the AIF (Ca(t)) was corrected for global delay and dispersion effects by matching the PET whole-brain time-activity curves (TACs) [19, 20, 26]; The D_t values are interpreted as time differences relative to the whole-brain TAC. In addition to the model in Eq. (2), we used a model with vascular components:

3

where V_a is the blood volume fraction of the voxel of interest (mL/mL). This study refers to these models as Vzero (Eq. 2) and Vfit (Eq. 3).

The decay-corrected TAC (¹⁵O half-life: 122 s) in each voxel was fitted to the model, Vzero or Vfit, using a weighted nonlinear least-squares method to minimize the residual sum of squares (RSS):

4

where is a set of fitting parameters: [K₁, k₂, D_t] for the Vzero model or [K₁, k₂, D_t, V_a] for the Vfit model; the subscript i stands for i-th time frame (N = 72 frames in total); TAC_i and C_i are their average values over each frame length; W_i is a weighting factor for each frame, as described in following subsection in details. Nonlinear least-squares fitting was performed with the Levenberg–Marquardt algorithm (MATLAB tools with default parameters) combined with a grid search for D_t values ranging from − 10 to 15 s in 1-sec increment, followed by a finer grid search with 0.1-sec increment by applying linear interpolation for the measured AIF (acquired with 1-sec temporal sampling). Figure 1 and Fig. S1 (Additional file 1) show the representative fitting results for a single voxel in the contralateral or ipsilateral hemisphere. Finally, a parameter set that minimizes RSS generates PET parametric maps. Although the parameter of interest in this study was D_t, the other parameters (K₁, k₂, V_d, and V_a) were also included as additional information. In the current implementation, the fitting was restricted for voxels with CBF values larger than 0.1 (mL/mL/min) to avoid unstable results for noisy voxels.

Fig. 1.

Representative examples of PET compartmental analysis for arrival time mapping: [Left] arterial input function (AIF) and tissue time-activity curves (TACs) from a single voxel in the ipsilateral and contralateral hemispheres of a patient (Patient No. 1), [Center] Vzero fitting results, and [Right] Vfit fitting results. Both fitting results showed a significant arrival delay in the ipsilateral TAC compared with the contralateral TAC. In the Vfit fitting, estimates in vascular components, V_a, are 0.3 and 0.2 (mL/100 mL) for the ipsilateral and contralateral hemispheres, respectively, with negligibly small contributions in these voxels. This figure uses the fitting weights based on the simple noise model (see Section “Optimization of fitting weights”). The results with constant weighting (unweighted least-squares) are presented in Fig. S1 (Additional file 1)

Optimization of fitting weights

The selection of the weighting factors in least-squares fitting (Eq. 4) affects the accuracy of PET kinetic analysis, and its impact depends on the noise levels of reconstructed PET images and the noise sensitivity of specific compartmental modeling [27]. Theoretically, a correct match between actual image noises and the weighting factors results in the best fitting, that is, the maximum likelihood estimation under the assumption of independently normally distributed noises:

5

where is a variance in the i-th time frame. However, a consensus on determining optimal fitting weights in specific dynamic PET studies has not been established because of practical difficulties in accurately estimating the voxel noises in actual reconstruction PET images. Thus, constant weighting over time frames, that is, unweighted least-squares fitting, is frequently used for simplicity. In this study, we compared two weighting factor strategies: (1) constant weighting (; unweighted least-squares) and (2) weighting factors from a simple noise model [28]:

6

where and are the midpoint time and duration of each time frame, is the radioactive decay constant for ¹⁵O, and the weighting factors are calculated from Eq. (5). This simple noise model implicitly assumes that the variance of each voxel in a PET reconstruction image is proportional to the radioactivity concentration in each voxel, considering the frame duration and radioactive decay. Although the simple noise model may be appropriate for PET images reconstructed with standard algorithms such as OP-OSEM, its validity for the specific reconstruction implementation used in the study should be explored. Here, by using a list-data bootstrap sampling technique for estimating PET reconstruction image noises [29–31], we confirmed the adequacy of the simple noise model (Eq. 6) for [¹⁵O]-CO₂ dynamic images reconstructed with the current setting (Additional file 1: Fig. S2). Four different D_t maps were generated for each patient using the two fitting weight strategies on each model (Vzero or Vfit). Fitting calculations were performed with a standard PC (CPU, Intel(R) Core(TM) i9-14900; memory, 128 GB), and computational times for generating an arrival time map ranged from approximately 20 min to 50 min depending on the patient data analyzed and the fitting models used.

CT perfusion study

Brain CT perfusion images were acquired using a dual-source CT scanner (SOMATOM Drive; Siemens Healthineers) with a kilovoltage setting of 80 kVp, a slice thickness of 1 mm for acquisition, and 5 mm for image reconstruction. The acquisition was initiated after the intravenous injection of 50 mL of iodinated contrast media at a rate of 5 mL/sec using a frame setting of 1.5 s over an acquisition duration of 45 s. Baseline non-contrast CT images were acquired.

The CT perfusion data were processed using Siemens syngo.via CT Neuro Perfusion (VB60 version). Arterial voxels were automatically extracted from all the voxels. Subsequently, AIFs were used for delay-insensitive deconvolution analysis [6], providing a set of perfusion parametric maps: CBF, CBV, MTT, and Tmax. The parameter of interest in this study is Tmax, the peak time of a residue function derived from deconvolution analysis, which provides information on the tracer arrival timing [6–9].

Regions-of-interest analysis

Regions-of-interest (ROIs) analysis was performed in an anatomically standardized space, the Montreal Neurological Institute (MNI) space:

1. Each subject’s CT perfusion-derived CBF map was rigid-body registered to each subject’s PET CBF map, followed by the same registration to each subject’s CT perfusion Tmax map. This procedure aligned the CT perfusion Tmax maps in the native PET space for each subject.

2. All parametric maps from PET and CT perfusion were transformed into a standard brain atlas using the SPM12 software (The Wellcome Centre for Human Neuroimaging, University College London, UK). The deformation parameters for each subject were derived from CT images acquired with the PET/CT system [32]. The resultant maps of all subjects had the same anatomic format, with an isotropic voxel size of 1 mm.

3. ROIs were placed at the level of the basal ganglia (1 mm thickness 7 slices) and corona radiata (1 mm thickness 7 slices) in the MNI space according to the Alberta Stroke Program Early Computed Tomography Score (ASPECTS) system, which is frequently adopted in neuroimaging studies of stroke patients. Specifically, bilateral ROIs covered the anterior, central, and posterior parts of the cerebral cortex in the MCA territory at two levels: M1, M2, and M3 at the basal ganglia level and M4, M5, and M6 at the corona radiata level [33]. For all parameters, mean values were calculated for each ROI (120 ROIs: 10 patients, two hemispheres, 6 ROIs).

Statistical analysis

Correlation analyses were performed between the CT perfusion Tmax and PET arrival time (D_t) using data from all ROIs (n = 120). Regarding the quantitative assessment of hemodynamic abnormalities, the differences between the ipsilateral and contralateral hemispheres may be more relevant than their absolute values. Ipsilateral-to-contralateral differences in CT perfusion Tmax and PET arrival time were also analyzed (n = 60). To further investigate the inter-modality differences (CT perfusion versus PET), the ipsilateral-to-contralateral differences were examined using a paired t-test with statistical significance defined at P < 0.05 and Bland–Altman plot analysis.

For all CT perfusion and PET parameters, the mean hemispheric values for each patient were calculated using the volume-weighted averaging of all ROIs. To investigate the interhemispheric separation for each parameter, we calculated the effect size for ipsilateral-to-contralateral differences in the hemispheric values, the mean divided by the standard deviation (SD) across the subjects.

Simulation study

We performed numerical simulations to investigate the noise-induced errors in PET arrival time (D_t) estimates using different fitting models and weighting factors. Noisy TACs were generated based on the compartment model (Vzero or Vfit) by adding time-varying Gaussian random noise according to the simple noise model (Eq. 6). To achieve realistic noise levels in the simulated TACs, we determined a scaling factor for the noise model (Eq. 6) by matching the magnitudes of the voxel-level image noise between the actual data-derived bootstrap estimation and the model. Figure S2 (Additional file 1) shows that the scaled simple noise model reproduced the bootstrap-estimated noise level for the present image reconstruction setting. The AIF measured from a patient was used to generate noisy TACs with the pre-specified parameters (K₁, k₂, and V_a). We repeated the noisy TAC generation and fitting procedure 1,000 times and calculated the bias and SD of the D_t estimates with true D_t = 0 s. This simulation procedure was repeated for each patient’s AIF, and the average results for all patients were reported. The current patient study fixed the acquisition time at 360 s, but the simulations varied (from 60 to 360 s) to test the feasibility of shorter scanning.

Additional simulations were performed to investigate the effects of local dispersion. The present data analysis corrects the global delay and global dispersion for AIF and then fits the local delay (D_t) by omitting the local dispersion effect. Thus, if it exists, the local dispersion effect is not distinguished from the local delay and contributions from vascular components [34]. A simulation procedure was equivalent except for varying the local dispersion constant from 0 (i.e., the reference simulations described above) to 5 s to generate noisy TACs. A single exponential function is assumed for the local dispersion effect.

Results

PET arrival time in comparison with CT perfusion Tmax

Figure 2 shows representative PET arrival time maps with the two fitting weight strategies on both models (Vzero and Vfit) from a patient with right ICA occlusion. With both fitting models, the right hemispheres (ipsilateral to the occlusion) presented brain regions with significant arrival delays compared to the left hemispheres, with less image noise for weighted least-squares fitting. With the combination of the Vfit model and unweighted least-squares fitting, the delayed regions could hardly be defined in the ipsilateral hemisphere. This trend was observed in all cases. Unless otherwise noted, we provide only the results from the weighted least-squares fitting.

Fig. 2.

Representative PET arrival time maps at a basal ganglia level from a patient with right ICA occlusion (Patient No.8). Effect of different compartment models and least-squares fitting strategies: [Upper] Vzero model and [Lower] Vfit model; [Left] weighted least-squares (LSQ) using the simple noise model and [Right] unweighted LSQ fitting

Figure 3 compares the PET arrival time maps from Vzero fitting with the CT perfusion Tmax maps for all patients (n = 10). The ipsilateral hemispheres in all patients showed regions of arrival delays with similar spatial extent visibility for CT perfusion and PET, although the PET maps were slightly noisier. The PET arrival time maps from Vfit fitting are shown in Fig. S3 (Additional file 1). As also shown in Fig. 2, Vfit fitting provided noisier maps than Vzero fitting.

Fig. 3.

Comparisons of CT perfusion Tmax and PET arrival time (D_t) maps (Vzero model) for all patients (n = 10; Left-to-Right) at (A) basal ganglia level and (B) corona radiata level. The maps from each patient were horizontally flipped if needed, as the lesion hemispheres are shown as right hemispheres for visibility. PET maps from Vfit model fitting are provided in Fig. S3 (Additional file 1)

The results of the ROI analysis of CT perfusion Tmax and ¹⁵O-PET arrival times are summarized in Table 1. Figure 4 (left panels) shows scatter plots between the CT perfusion Tmax and ¹⁵O-PET arrival time estimated with Vzero (upper panel) and Vfit (lower panel), good correlations between the two modalities: correlation coefficients r = 0.834 (Vzero) and 0.750 (Vfit). Ipsilateral-to-contralateral differences also showed good-to-moderate correlations between the two modalities (center panels in Fig. 4): r = 0.718 (Vzero) and 0.520 (Vfit). Mean values for the ipsilateral-to-contralateral differences were slightly smaller in ¹⁵O-PET arrival time estimates both with Vzero (1.680.83 s) and Vfit (1.720.87 s) compared to CT perfusion Tmax (2.310.51 s), with statistical significances (P < 0.001 for both). The Bland–Altman plot analysis in Fig. 4 (right panels) shows weak but statistically significant upward trends in the inter-modality differences: r = 0.277 (P = 0.03; Vzero) and 0.308 (P = 0.02; Vfit). The effect size of ipsilateral-to-contralateral differences in the hemispheric values was smaller for ¹⁵O-PET, with both Vzero (2.03) and Vfit (1.98) than for CT perfusion (4.52) (Table 1).

Table 1.

Results from the regions-of-interest analysis on CT perfusion Tmax and ¹⁵O-PET arrival time

			Contralateral Hemisphere			Ipsilateral Hemisphere			Ipsilateral-to-Contralateral Difference			Effect size
CT Perfusion	Tmax (sec)		1.75	±	0.43	4.06	±	0.76	2.31	±	0.51	4.52
15O-PET	Dt (sec)	Vzero model	1.63	±	0.76	3.31	±	0.98	1.68	±	0.83	2.03
		Vfit model	2.68	±	1.04	4.40	±	0.95	1.72	±	0.87	1.98

Fig. 4.

[Left] Correlations between CT perfusion Tmax and ¹⁵O-PET arrival time (D_t) estimated with Vzero [Upper] and Vfit [Lower] fitting. Each circle corresponds to each region-of-interest measure from a patient (number of data = 6-MCA regions2-hemispheres10-patients). [Center] Correlations between ΔTmax and ΔD_t, ipsilateral-to-contralateral differences (number of data = 6-MCA regions10-patients). [Right] Bland–Altman plot (differences against means) for ΔTmax and ΔD_t. The mean difference (solid line) and ± 1.96 SD (dotted-dashed line) are shown

Results for other parameters: CBF and oxygen metabolism

Table 2 summarizes the other PET-derived parameters. In brief, CBF, CMRO₂, K₁, k₂, and V_a were lower in the ipsilateral hemisphere than in the contralateral hemisphere; CBV, OEF, and V_d showed the opposite trends. For the hemodynamic parameters (i.e., CBF, CBV, OEF, CMRO₂, K₁, k₂, and V_a), effect sizes in absolute units ranged from 0.51 (OEF) to 1.60 (CBF, k₂), smaller than the effect sizes of PET arrival time (2.03 and 1.98 in Table 1).

Table 2.

PET results other than the arrival time: clinical parameters (CBF, CBV, OEF, CMRO₂) and other fitting parameters (K₁, k₂, V_d, V_a)

		Contralateral Hemisphere			Ipsilateral Hemisphere			Ipsilateral-to-Contralateral Ratio			Effect size
Clinical PET	CBF (mL/100 mL/min)	41.2	±	7.3	33.0	±	4.8	0.811	±	0.108	-1.60
	CBV (mL/100 mL)	3.62	±	0.63	4.23	±	0.95	1.172	±	0.210	0.83
	OEF (%)	45.0	±	5.4	48.2	±	8.9	1.071	±	0.133	0.51
	CMRO2 (mL/100 mL/min)	3.32	±	0.72	2.83	±	0.55	0.854	±	0.093	-1.31
Vzero model	K1 (mL/100 mL/min)	39.0	±	5.5	31.9	±	4.5	0.822	±	0.102	-1.57
	k2 (1/100/min)	47.5	±	7.7	38.5	±	7.5	0.813	±	0.109	-1.60
	Vd (mL/mL)	0.825	±	0.105	0.838	±	0.091	1.018	±	0.050	0.28
Vfit model	K1 (mL/100 mL/min)	38.3	±	5.5	31.4	±	4.5	0.823	±	0.103	-1.51
	k2 (1/100/min)	46.4	±	7.8	37.6	±	7.3	0.813	±	0.109	-1.57
	Vd (mL/mL)	0.821	±	0.106	0.837	±	0.094	1.022	±	0.052	0.36
	Va (mL/100 mL)	1.21	±	0.54	1.04	±	0.34	0.947	±	0.386	-0.60

Figure 5 shows parametric maps of two representative patients with distinct appearances of hemodynamic compromise on each map. The ipsilateral hemispheres presented significant arrival delays in the CT perfusion Tmax and PET arrival time maps, accompanied by typical alterations in each PET parameter: decreased CBF and increased OEF, resulting in slight decreases in CMRO₂. The OEF elevations in the ipsilateral hemispheres were more severe in case (B) (lower in Fig. 5) than in case (A) (upper in Fig. 5), and arrival delays were more severe in case (A) than in case (B). For all patients, the K₁ maps were very similar to the CBF maps based on the clinical ARG method, albeit with slight differences in the absolute values (Table 2), as shown in Fig. S4 (Additional file 1) for the same two patients.

Fig. 5.

CT perfusion Tmax and ¹⁵O-gas PET maps acquired from representative patients: (A) a patient with right ICA stenosis and (B) a patient with right ICA occlusion. PET arrival time (D_t) maps presented are based on Vzero fitting. ROIs used in the analysis are overlaid on the non-contrast CT images. Mean hemispheric values of ipsilateral-to-contralateral differences () or ratios (R) are also provided. Display color scales: Tmax/D_t = -2 to 8 (sec); CBF = 0 to 80 (mL/100 mL/min); CBV = 0 to 10 (mL/100 mL); OEF = 0 to 80 (%); CMRO₂ = 0 to 6 (mL/100 mL/min)

Simulation study

Overall, weighted least-squares fitting reduced the SDs in the D_t estimates to approximately 50% compared with unweighted least-squares fitting (Additional file 1: Fig. S5). When the tissue dispersion effect was not present (upper panels), the biases in D_t estimates were relatively small both with Vzero (~ 0 s) and Vfit models (< 1 s) over the wide range of acquisition times, irrespective of the fitting weight strategies. The SDs of the D_t estimates were significantly smaller for the Vzero model than for the Vfit model, relatively constant with acquisition times longer than 180 s, and gradually increased with the shortening of the acquisition time. The local dispersion effects increased the biases in the D_t estimates; a local dispersion effect with a time constant of 3 s induced positive biases of approximately 2 s in the D_t estimates.

Discussion

This study presents a practical method for arrival-time mapping in clinical ¹⁵O-gas PET. The regional differences in arrival time stemming from occlusion or stenosis of the major cerebral arteries are typically only a few seconds, and arrival time mapping with sufficient accuracy is not a simple task, primarily due to image noise problems caused by the extremely short half-life of ¹⁵O (approximately 2 min). This study showed that arrival time mapping is possible with ¹⁵O-gas PET by applying optimized kinetic analysis to dynamic PET images acquired using a state-of-the-art, high-sensitivity clinical PET scanner. Importantly, this is the first study to validate the method through direct comparison with another more reliable modality, namely, CT perfusion with contrast media. The proposed method, particularly with the Vzero model, visualizes delayed-arrival brain regions in close contrast to CT perfusion-derived Tmax maps. Additionally, ROI analysis confirmed a good correspondence between the two methods, demonstrating the visual and quantitative validity of the arrival time maps obtained by the proposed method.

The present method enables us to obtain arrival time maps in addition to conventional PET parameter maps, that is, CBF, OEF, CBV, and CMRO₂, leading to a more multifaceted understanding of brain pathophysiology. Due to cerebral autoregulation, CBF is maintained by the compensatory dilation of resistance vessels (stage I) in response to decreased perfusion pressure. In contrast, when perfusion pressure is further reduced beyond the threshold, CBF is reduced, and OEF is increased (stage II), resulting in a relatively preserved CMRO₂. The ¹⁵O-gas PET can accurately identify this hemodynamic status [1, 3]. The arrival time parameter obtained with the present technique reflects blood flow velocity; thus, unlike CBF and OEF, it may provide a continuous measure of perfusion pressure. In other words, the arrival time parameter may depict a mildly reduced perfusion pressure (stage I) without a significant decrease in CBF or an increase in OEF. The effect size of each parameter as a measure of contrast between the ipsilateral and contralateral sides was higher for the arrival time than for CBF or OEF (Tables 1 and 2), indicating that the arrival time parameter is more sensitive to perfusion abnormalities than the other parameters, which supports the above speculation.

Even if the actual hemodynamics do not necessarily follow the autoregulation theory discussed above, the arrival time parameter provides information different from CBF and OEF. In the PET parameter maps of the two patients (Fig. 5), delayed arrival in the ipsilateral hemisphere was more severe in case (A), while decreased CBF and increased OEF were more pronounced in case (B). Future studies should investigate the clinical utility of arrival-time mapping in ¹⁵O-gas PET in more patients. The arrival time is governed by blood flow velocity and path length; therefore, including information on collateral pathways using MR/CT angiography or digital subtraction angiography would be helpful [35].

This study used CT perfusion-derived Tmax [6], a more widespread clinical method, as a reference. However, its validity as an arrival-time parameter may be controversial. Tmax is primarily governed by the local arrival time but is also known to be affected by MTT, the time required to pass through capillaries in the tissue of interest [7–9], and the reduced blood flow velocity due to decreased perfusion pressure inevitably leads to delayed arrival and prolonged MTT. Thus, the Tmax, affected by both, should show a more prolonged value than the actual local arrival time in the affected brain regions. This indicates that Tmax should show a more significant difference between the ipsilateral and contralateral hemispheres than the PET-derived arrival time parameter, which is consistent with the present results (Table 1). Nevertheless, the good correlation between the arrival time parameters obtained from ¹⁵O-gas PET and CT perfusion indicates that both methods can depict perfusion abnormalities equally.

This study included a small number of patients (n = 10), which is a limitation. One of the difficulties with ¹⁵O-gas PET examinations is that, unlike the intravenous administration usually used in other PET scans, ¹⁵O-gases are administered via an inhalation mask. Thus, the wearing condition of the inhalation mask and the patient’s respiratory function and status can lead to variations in the net ¹⁵O-gas intake, resulting in inter-examination variability in PET image noise levels. Nevertheless, in this study, the arrival time maps were obtained for all patients at a level with visible delayed brain regions. Further studies with more patients should determine whether arrival time maps can be obtained with reasonable image quality. Another limitation is the computational time to generate the arrival time map. Although a relatively long time, over 20 min with the current implementation, may be acceptable for research purposes, a routine clinical use will need future research to shorten the computational time, which includes parallel computation or GPU utilization and the modification of kinetic analysis such as introducing the basis function method and the fixed parameter strategy [12].

Technical considerations in PET arrival time mapping

Due to its technical difficulty, primarily stemming from high noises of reconstructed PET images with short time frames, PET arrival time mapping is not trivial; reports on PET arrival time mapping have been scarce, with only a few reports using intravenous bolus injection of [¹⁵O]-H₂O [36–38] and one report using short inhalation of [¹⁵O]-CO₂ [12]. The advantage of using the short inhalation of [¹⁵O]-CO₂ is that it can be performed as part of a series of clinical PET measurements using ¹⁵O-gas inhalation, i.e., the 3-step ARG protocol, and does not require a separate synthesizing of [¹⁵O]-H₂O. However, the typical duration of the short inhalation of [¹⁵O]-CO₂ is 60–120 s, resulting in a slower rise in tissue TACs compared to the bolus injection of [¹⁵O]-H₂O, which makes it more challenging to estimate the arrival time with reasonable accuracy. Kudomi et al. proposed a method for arrival time mapping with short inhalation of [¹⁵O]-CO₂ [12]. This method indirectly estimates the arrival time by exploiting the difference in sensitivity to arrival time among three analysis methods: a conventional ARG and two dynamic fitting methods. In contrast, the present method, which is more straightforward, combines the standard compartment model analysis and grid search for arrival time, which is achieved by using a state-of-the-art clinical PET scanner and optimizing the dynamic analysis. The quality of the arrival time maps obtained using the proposed method was superior to that reported by Kudomi et al. This allowed the delayed arrival regions to be clearly defined for each patient. The clinical use of arrival time mapping may be facilitated by the adoption of state-of-the-art clinical PET scanners, such as this one, as well as ultra-sensitive total-body PET and brain-dedicated PET scanners [38–40].

The present method for estimating the arrival time relies on optimizing the weight coefficients in the least-squares fitting of the PET dynamic data. The patient data showed that the weighted least-squares fitting yielded less noisy arrival time maps than the unweighted least-squares fitting (Fig. 2), and the simulation results showed that the application of ideal weighting significantly reduced the variability of arrival time estimates (Additional file 1: Fig. S5), highlighting its importance. Additionally, unweighted least-squares fitting resulted in a lower correlation with Tmax (Additional file 1: Fig. S6). Theoretically, optimal results are obtained when the fitting weights are consistent with the actual image noise, that is, the maximum likelihood estimation under the assumption of a normal distribution. Using the list-mode bootstrap method, we confirmed that the simplified noise model reproduced image noise with the current reconstruction algorithm (3D OP-OSEM with PSF modeling) (Additional file 1: Fig. S2). An alternative method of weighting optimization is to directly apply the weights estimated by the list-mode bootstrap method instead of using noise models. This method may be particularly effective for image reconstruction and image processing algorithms that are highly nonlinear and for which simple noise models cannot be applied, such as deep learning-based methods [41, 42].

In the dynamic analysis of the [¹⁵O]-CO₂ data, K₁ simultaneously estimated with the arrival time parameter is theoretically different from the ARG CBF value, which does not consider the local arrival time. However, the image contrasts of the K₁ and ARG CBF maps obtained in this study were very similar (Additional file 1: Fig. S4), and the difference in the hemispheric ratio was less than 2% (Table 2). Based on these results and a previous simulation study showing that the effect of local arrival time on ARG CBF is small (<5% CBF variability for a local arrival time difference of a few seconds) [12, 43], the ARG CBF map should be sufficient for clinical applications. OEF and CMRO₂ in this study were calculated using ARG CBF (not K₁). The absolute K₁ values in this study were approximately 5% lower than the ARG CBF absolute values, which may be because the actual V_d values were slightly higher than the assumed value in the ARG method (0.8 mL/mL) in addition to the fitting interval (360 s) was different from the integration time in the ARG method (180 s).

The end of the fitting interval in the dynamic analysis for [¹⁵O]-CO₂ data was set to the maximum, i.e., 360 s, the PET acquisition time, to obtain the maximum statistical counts. However, since the initial phase is more critical in the dynamic analysis, it may be possible to shorten the fitting intervals. The simulation results show that the accuracy of arrival time estimation is almost unchanged after the end of the fitting interval is 180 s (Additional file 1: Fig. S5), suggesting that the PET acquisition time can be reduced to 180 s, which is the integration time in the ARG method for CBF derivation. The arrival time maps when the end of the fitting interval is reduced from 360 s to 180 s are provided in Supplementary information (Additional file 1: Fig. S7), and results with image quality very close to 360 s are obtained.

The kinetic model used in this study did not consider the effect of local dispersion, which could be an error factor in the local arrival time estimates (D_t). When arterial blood flow is delayed due to decreased perfusion pressure, it is expected to cause temporal-shaped dispersion simultaneously. This indicates that the actual AIFs in the delayed-arrival regions deviate from the global AIF used in the kinetic analysis. According to the simulations, local dispersion effects lead to positive biases in arrival time estimates (Additional file 1: Fig. S5). Although it is difficult to quantitatively evaluate the magnitude of biases owing to the lack of real in vivo data on local dispersion [44, 45], the arrival time estimates in the present study may have been overestimated because of the local dispersion effect. The local dispersion effect is also an error factor for the CT perfusion Tmax [7, 9]. The effect may be insignificant in comparisons between ¹⁵O-PET and CT perfusion because they are in the same direction.

Relative advantages and disadvantages of the Vfit model in comparison with the Vzero model should be discussed. Based on the present results that both fitting models provided similar ipsilateral-to-contralateral differences in arrival times and the Vfit model was inferior regarding the noise level in arrival time maps, the Vzero model is the method of choice for ¹⁵O-PET arrival time mapping. In contrast, the Vfit model has the advantage of providing the V_a parameter, which is the arterial-to-capillary blood volume in the voxel of interest. In the present study, the mean V_a value in the ipsilateral hemisphere was 14% lower than that in the contralateral hemisphere (Table 2), consistent with two studies using [¹⁵O]-H₂O injection that reported approximately 20% lower values [36, 37]. The authors have attributed the lower V_a in the ipsilateral hemisphere to a decrease in the functional arterial part due to a long-term reduction in perfusion pressure and a concomitant increase in inactive vascular volume, characterized by the increased CBV (total vascular volume). However, it may be challenging to separate the contribution of V_a from the local dispersion effects. The simulation results (Additional file 1: Fig. S8) show that local dispersion effects can lead to an underestimation of V_a. Thus, the lower V_a in the ipsilateral hemisphere in the present study may be explained by local dispersion effects in the ipsilateral hemisphere. Again, there are no reliable data on the degree of local dispersion [44, 45], which makes the quantitative evaluation of dispersion-induced errors difficult. Future studies should use other imaging modalities, such as arterial spin labeling MR, which enables a detailed analysis of tracer dynamics in arterial vessels [46, 47].

Conclusion

The present method generates arrival-time maps with ¹⁵O-gas PET by applying optimized kinetic analysis to dynamic [¹⁵O]-CO₂ images acquired using a state-of-the-art, high-sensitivity clinical PET scanner. Additional arrival time information for conventional PET parameters, including CBF, OEF, CBV, and CMRO₂, may lead to a more multifaceted understanding of cerebral pathophysiology and is expected to be applied clinically in the future.

Electronic supplementary material

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Abbreviations

AIF

Arterial input function

ARG

Autoradiography

CBF

Cerebral blood flow

CBV

Cerebral blood volume

CMRO₂

Cerebral metabolic rate of oxygen

CT

Computed tomography

D_t

Arrival time

FOV

Field of view

FWHM

Full width at half maximum

ICA

Internal carotid artery

MCA

Middle cerebral artery

MR

Magnetic resonance

MTT

Mean transit time

OEF

Oxygen extraction fraction

OP-OSEM

Ordinary Poisson ordered-subset expectation–maximization

PET

Positron emission tomography

PSF

Point spreading function

ROI

Region of interest

RSS

Residual sum of squares

SD

Standard deviation

TAC

Time activity curve

Tmax

Peak time of residue function

TOF

Time of flight

Author contributions

Concept and design: MI; Data acquisition: MI, YS, AW, KS, TO, HY; Analysis and interpretation of data: MI, YS, TO, TK; Drafting of the manuscript: MI; Revision of the manuscript: All authors; Approval of the final version: All authors.

Funding

This work was supported by JSPS KAKENHI Grant Number 23K07146.

Data availability

The datasets used during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

The study was approved by the Ethics Committee of the Research Institute for Brain and Blood Vessels-Akita (No. 23 − 20) and was performed in accordance with the Declaration of Helsinki. The requirement for informed consent was waived because of its retrospective design.

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no competing interests.