Our proposition that the GLM may be adequate for evaluating task-specific changes in glucose metabolism is grounded in the following mathematical rationale. For irreversibly binding radiotracers such as [18F]FDG, the ratio of tracer concentration in tissue CT to that in plasma CP at a certain time point t can be characterized using the Patlak plot [11]:

$$\frac_(t)}_(t)}=_\frac_^_\left(\tau \right)d\tau }_(t)}+intercept$$

(1)

The net influx constant Ki is the estimated outcome parameter, which is determined as the slope of the Patlak plot when it approaches linearity after t* [11]. The absolute amount of CMRGlu is then determined by:

$$CMRGlu=_\frac_}*100$$

(2)

LC refers to the lumped constant and GluP represents the concentration of glucose in plasma. Rearrangement of Eq. (1) yields

$$_=\frac_\left(t\right)-}*_(t)}_^_\left(\tau \right)d\tau }$$

(3)

Assuming that intercept * CP <  < CT, the relation reduces to

$$_=\frac_\left(t\right)}_^_\left(\tau \right)d\tau }$$

(4)

This assumption is particularly true for a small bolus and after linearity of the Patlak plot has already been reached. The parameter in Eq. (4) is identical to the previously described “fractional uptake of [18F]FDG normalized by plasma activity” [12]. This normalization stems from the inherent mathematical assumptions made while deriving the relation. Furthermore, in the relationship between task effects and baseline metabolism, the integral of the plasma concentration also cancels out. This implies that the ratio between the tissue concentrations is directly proportional to the relative changes in Ki (and thus relative changes in CMRGlu, see Eq. (2))

$$\%SC\propto \frac_}_}\propto \frac_(t)}_(t)}\propto \frac_*_(t)}_*_(t)}$$

(5)

In this equation, β represents the output of the GLM when the respective regressors are used for modeling. Consequently, the ratio of the GLM’s output modeling task and baseline effects should also vary proportionally to the relative changes in CMRGlu. Since the multiplication of a beta value with its corresponding regressor represents a time course, we estimated its slope for the computation of percent signal changes (%SC, see “Surrogate parameters”). This approach was chosen because different regressors were used for task and baseline in the GLM, which implies that simple beta values cannot be directly compared.

In order to test the hypothesis, we analyzed two separate datasets with different designs (Supplementary Fig. 1), tasks, and activated regions of interest (ROIs). For both datasets, similar methods of preprocessing and statistical analysis were applied. A schematic overview of the procedure is given in Fig. 1 and further details are provided in the experimental design and tasks section of the supplement.

Schematic workflow of the preprocessing and analysis routine. After data acquisition and preprocessing, data were entered into a general linear model to separate task effects from baseline metabolism. Four different outcome parameters were then calculated: (i) the plain β-maps obtained from the general linear model and (ii) % signal change relative to baseline. Absolute quantification with the arterial input function and the Patlak plot yielded (iii) maps of cerebral rate of glucose metabolism (CMRGlu) and (iv) % signal change thereof

The first dataset (DS1) includes simultaneous fPET/fMRI examinations in 52 healthy participants performing a challenging visuo-spatial motor coordination task in two levels of difficulty (modified version of Tetris®). After an initial baseline of eight minutes, each task level was performed two times and six minutes each, followed by five minutes of rest (Supplementary Fig. 1). Detailed descriptions of the design, acquisition and analysis are provided in our previous work [13], below and in the supplement.

The second dataset (DS2) comprises data of 18 healthy participants. The fPET/fMRI scan started with a baseline of 10 min. Afterwards, participants either tapped their right thumb to their other fingers (10–20 min and 60–70 min) or opened their eyes (35–45 min and 85–95 min). Details can be found in our previous work [14], below and in the supplement.

DS1 includes 52 healthy participants (23.2 ± 3.3 years, 24 females, all right-handed), who were partly also included in previous work [13, 15,16,17]. DS2 comprises 18 healthy participants’ data (24.2 ± 4.3 years, 8 females, all right-handed), of which 15 had previously contributed to another study [3]. See supplement for details.

All fPET measurements were performed on the same fully integrated PET/MR system (Siemens mMR Biograph, Erlangen, Germany). Administration of [18F]FDG was done according to a bolus plus constant infusion protocol for DS1 and with constant infusion only for DS2. This enables the assessment of the performance of both administration protocols. Data pre-processing of both studies’ fPET data was done with SPM12 and included motion correction, spatial normalization to MNI-space and smoothing. For both datasets manual arterial blood samples were collected to construct the AIF. See supplement for details.

In order to analyze task activation within the two datasets, a general linear model (GLM) was applied. Both models included one regressor for baseline, one for movement artifacts and two regressors associated with task activation. For DS1, these regressors referred to the two levels of task difficulty. For DS2, they represented the separate tasks of eyes-open and right finger-tapping (see supplement).

For the calculation of the respective influx constants (Ki), the relevant Patlak plots were constructed and their respective slopes were identified as in Eq. (1). The start of the linear fit for the Patlak plot was set to approximately a third of the total scan time for both datasets, t* = 15 min for DS1 and t* = 30 min for DS2. The absolute quantification of CMRGlu was conducted in accordance with Eq. (2) and a value for the LC of 0.89, in both cases [18, 19]. The amount of CMRGlu was quantified in units of µmol/100 g/min.

Our primary goal was to obtain a metric that enables the identification of task-specific changes in glucose metabolism without invasive blood sampling. Thus, we compared four different parameters of interest: (i) the absolutely quantified values for CMRGlu (see Eq. (2)), used as the gold standard, (ii) the plain beta values calculated by the GLM, and (iii–iv) the percent signal change (%SC) of both quantities in relation to the baseline condition (see Eq. (5)). Thereby, we established a relationship between the beta values and CMRGlu as well as %SC of betas with %SC of CMRGlu. The %SC of CMRGlu was calculated as the ratio of task effects to baseline metabolism multiplied by 100. The %SC for the beta values cannot be directly retrieved from the GLM output since the betas are associated with different regressors. Consequently, the slopes of the time activity curves were estimated (in kBq/frame), represented by beta*regressor separately for task and baseline metabolism (see Eq. (5)). For the extraction of the slope of the baseline TAC, a linear fitting procedure was performed. The fit was applied for a similar time interval as for the Patlak plots. Specifically, for DS1 the linear fit started from minute 16 after the beginning of the radiotracer application until the end of the PET scan. For DS2, the interval began later due to the absence of an initial bolus, specifically from 30 min after the beginning until the end. Since the task regressors were modeled as ramp functions with a slope of 1 kBq/frame, the beta values for the tasks are already equivalent to the slope we aimed to extract. Hence, %SC of betas was then calculated as the ratio of the task and baseline slopes multiplied by 100.

Furthermore, two different baseline metrics (BL, BL2) were considered. Notably, for BL and BL2, no %SC data could be calculated, as the percent signal change inherently refers to the baseline condition itself. BL simply represents the beta value of the baseline condition as calculated by the GLM. BL2 was determined by calculating the slope of the curve given by multiplying the baseline regressor with the corresponding baseline beta values, i.e., a linear fit to the baseline beta * baseline regressor. We opted for the second baseline metric because this calculation also enters the determination of %SC of the beta values, allowing for a direct comparison. Furthermore, BL2 takes the individual variation in the baseline regressor into account and is therefore comparable across participants. It is worth noting that BL is also identical to standardized uptake value ratios (SUVR) with reference to global tracer uptake. That is, regional tracer uptake is represented by regional baseline beta * baseline regressor [3] and since the baseline regressor represents the global tracer uptake, this cancels out when computing the ratio.

The ROI analysis focused on the respective regions of significant activation (all p < 0.05 FWE corrected) for each dataset as obtained by group-level statistical analysis in our previous work. More precisely, for DS1, the regions selected for further investigation were the frontal eye field (FEF), the intraparietal sulcus (IPS), and the secondary occipital cortex (Occ). These were identified to be active in our previous work across three different functional approaches (fPET, BOLD, ASL) [16]. For DS2, the relevant ROIs were the primary occipital cortex (V1) as well as the primary motor cortex (M1), since these displayed significant task activation in our previous study [14]. Outcome parameters were then extracted for these ROIs and linear regression analysis was then performed for each pair of parameters using MATLAB R2018b.

For the voxel-wise analysis, group-level statistics were computed in SPM12 and a one-sample t-test was performed for each of the four parameters. Activation maps were extracted (all p < 0.05 FWE corrected cluster level following p < 0.001 uncorrected voxel level) and activation patterns across different approaches were compared using the Dice coefficient. For DS1, we extracted respective activation maps for the hard task difficulty and for DS2 for both open eyes and right finger-tapping tasks.