### Data acquisition and kinetic modeling

We used experimental TACs and blood-activity curves from a previous study [7] with C57BL/6 mice (*n* = 5) with normal glycemia (plasma glucose 11.9 ± 4.0 mmol/L (6.7 to 16.9 mmol/L)) for our analysis. In brief, animals were under isoflurane (1.5% to 2%) anesthesia, and body temperature and respiratory frequency were controlled at 36°C to 37°C and approximately 90 cycles/min, respectively. FDG (10 to 14 MBq) was administered intravenously as a constant infusion over 4.0 to 5.3 min. Blood radioactivity was recorded with a coincidence counter (Twilite, Swisstrace GmbH, Zurich, Switzerland) on a shunt volume of approximately 60 μL with 1-s temporal resolution. List mode data were acquired for 45 min on a GE Healthcare/Sedecal (Madrid, Spain) eXplore VISTA PET/CT scanner in parallel.

Calibration of the coincidence counter with respect to the PET scanner was performed daily. A syringe containing approximately 1 MBq/cm^{3} FDG solution was attached to a catheter as used for the shunt [7], and FDG solution was flushed through the catheter which was guided through the coincidence counter. The syringe and catheter were measured simultaneously with scanner and coincidence counter, respectively. FDG radioactivity (Bq/cm^{3}) was calculated from the images of the calibrated scanner and divided by the coincidence counts per cubic centimeter from the blood counter. This ratio was used to calculate blood radioactivity in the animal experiments.

If not stated otherwise, plasma radioactivity, i.e., the IF was calculated from the blood radioactivity with Equation 3 correcting for blood cell uptake kinetics in mouse [14, 15]. For comparison, IFs were in addition calculated with Equation 4, which was determined for blood cell uptake kinetics in rats [8]. Furthermore, we calculated IFs from the experimental blood data by multiplication with the constant factor 1.165, which is the equilibrium partition coefficient determined by Wu et al. [14] (Equation 3). Finally, we also used the whole blood radioactivity as IF. The four functions of plasma to blood radioactivity (*A*
_{p}/*A*
_{b}) are plotted against time in Figure 1A.

\frac{{A}_{\mathrm{p}}}{{A}_{\mathrm{b}}}=0.386\times {e}^{-0.191\times t\left(\mathrm{min}\right)}+1.165

(3)

\begin{array}{ll}\frac{{A}_{\mathrm{p}}}{{A}_{\mathrm{b}}}=& 0.51\times {e}^{-0.1447\times t\left(\mathrm{min}\right)}+0.3\times {e}^{-0.00206\times t\left(\mathrm{min}\right)}\\ +0.8\end{array}

(4)

Image data were reconstructed into 33 to 39 time frames with the shortest frames (10 s) around the infusion stop and longer frames toward the end of the scan (maximal length 240 s) and analyzed with PMOD v3.4 (PMOD Technologies Inc., Zurich, Switzerland). TACs were derived from the cortex and hypothalamus, respectively, with anatomic templates of PMOD covering the entire structures. Figure 1B shows experimental TACs and IF of one representative experiment.

Two-tissue compartment kinetic modeling was performed with PMOD. A Marquardt-Levenberg algorithm was used for fitting until convergence to unique solutions. The LC for CMR_{glc} calculation was 0.6 and *v*
_{b} 5.5% if not stated otherwise [7, 16]. *χ*^{2} was used as indicator for goodness of fit according to Equation 5:

{\chi}^{2}={\displaystyle \sum}_{i=1}^{n}\left(\frac{{\left({O}_{i}-{E}_{i}\right)}^{2}}{{E}_{i}}\right),

(5)

where *n* is the total number of observations (*O*
_{i}) and *E*
_{i} is the expected value for *O*
_{i} as calculated with the fit function.

### Influence of choice of fractional blood volume on fit parameters

The effect of different assumptions for *v*
_{b} on the fitted model parameters and *χ*^{2} for the cortex and hypothalamus was tested by systematically varying *v*
_{b} between 0 and 0.2 (i.e., 0% and 20% blood in tissue, in steps of 0.5%). Alternatively, *v*
_{b} was included as a variable parameter in the fit. In order to reduce the impact of noise in the experimental data on *χ*^{2}, smoothed TACs and IFs were generated from the whole experimental datasets with robust locally weighted regression (LOWESS) smoothing as implemented in MATLAB. Furthermore, to assess the effects of limited degrees of freedom, every second data point was deleted from the experimental TACs. Modeling was then performed as described above with fixed or variable *v*
_{b} for each of the five scans with the following five combinations: unmodified experimental IF with unmodified TAC or with TAC after deletion of every second data point or with smoothed TAC, as well as smoothed IF with unmodified TAC or with smoothed TAC. To visualize the effect of the chosen *v*
_{b} on CMR_{glc}, CMR_{glc} values were normalized to the averaged CMR_{glc} over all *v*
_{b} for each scan (CMR_{glc} at a particular *v*
_{b}/averaged value of all calculated CMR_{glc} of this scan) and plotted against *v*
_{b}. For the rate constants *K*
_{1} to *k*
_{4}, average values from the five scans were plotted against *v*
_{b}.

### Influence of time delays between IF and TAC and of miscalibration between scanner and coincidence counter

To estimate the effect of time delays between TAC and IF, we shifted the experimental unmodified IF relative to the experimental unmodified TAC within a window of −20 to 30 s and plotted *χ*^{2} of the model fits (with constant *v*
_{b} 0.055) against the timing error. To visualize the influence on CMR_{glc} and the single rate constants, the parameters were normalized to the respective value at zero time delay for each scan (e.g., CMR_{glc} (delay i)/CMR_{glc} (no delay)). To simulate a minor miscalibration by 5% between scanner and coincidence counter, the TAC was multiplied with 0.95 and 1.05, respectively. The resulting model fit parameters were compared to correctly time-matched and calibrated data fitting results.

### Fit of the IFs and simulations of IFs of a bolus and two infusion protocols

For further analysis and simulations, IFs were fit with the Solver add-in in Excel 2010 (Microsoft Office) with the tri-exponential functions shown in Equations 6 and 7 [17]

\begin{array}{ll}{C}_{\mathrm{inf}}=& \left(A+B+Z\right)\\ \times \left({f}_{a}\left(1-{e}^{-\mathit{\alpha t}}\right)+{f}_{\mathrm{\beta}}\left(1-{e}^{-\mathit{\beta t}}\right)+{f}_{z}\left(1-{e}^{-\mathrm{\zeta}t}\right)\right)\end{array}

(6)

\begin{array}{ll}{C}_{\mathrm{decr}}=& \left(A+B+Z\right)\left({f}_{a},\left(1-{e}^{-\alpha {t}_{\mathrm{i}}}\right),{e}^{-\alpha \left(t-{t}_{\mathrm{i}}\right)}\right.\\ +{f}_{b}\left(1-{e}^{-\beta {t}_{\mathrm{i}}}\right){e}^{-\beta \left(t-{t}_{\mathrm{i}}\right)}\\ \left.+{f}_{z}\left(1-{e}^{-\zeta {t}_{\mathrm{i}}}\right){e}^{-\zeta \left(t-{t}_{\mathrm{i}}\right)}\right),\end{array}

(7)

where *C*
_{inf} is the arterial plasma radioactivity during the infusion and *C*
_{decr} the radioactivity after infusion stop (*t*
_{i}). The time point of infusion stop, *t*
_{i}, was determined from the curve maximum by visual inspection of the peak area of the IF. The sum of *A*, *B*, and *Z* corresponds to the extrapolated radioactivity in arterial plasma at steady state (infinite infusion duration). The fractional areas under the curves *f*
_{
a
}, *f*
_{
b
}, and *f*
_{
z
} are defined by *A*, *B*, *Z* and *α*, *β*, *ζ*, as shown in Equations 8, 9, and 10:

{f}_{a}=\frac{A}{\alpha \left(\frac{A}{\alpha}+\frac{B}{\beta}+\frac{Z}{\mathrm{\zeta}}\right)}

(8)

{f}_{b}=\frac{B}{\beta \left(\frac{A}{\alpha}+\frac{B}{\beta}+\frac{Z}{\mathrm{\zeta}}\right)}

(9)

{f}_{z}=\frac{Z}{\mathrm{\zeta}\left(\frac{A}{\alpha}+\frac{B}{\beta}+\frac{Z}{\mathrm{\zeta}}\right)}

(10)

Note that *A*, *B*, and *Z* are proportional to the infusion rate. *A*, *B*, *Z* and *α*, *β*, *ζ* were fit from the experimental IFs and kinetic analysis of the PET data was performed as described above with the fitted IF function. Fit FDG rate constants were compared to those with experimental IFs.

### Simulation of TACs and FDG kinetic modeling with different infusion protocols

IFs with bolus/infusion durations of 10 s (bolus), 300 s (similar to our experimental infusion protocol), and 900 s (for comparison) were simulated from the fit parameters *A*, *B*, *Z*, *α*, *β*, *ζ* with Equations 6 and 7 after adjusting *A*, *B*, and *Z* to the respective infusion rate (at equal FDG dose as in the experiment). The corresponding TACs were simulated with the PMOD software, applying the FDG two-tissue compartment model and *K*
_{1}, *k*
_{2}, *k*
_{3}, *k*
_{4} from the fits with the experimental IFs and TACs with *v*
_{b} 0.055. The number and minimal/maximal lengths of time frames for the simulated TACs were equal to the experimental data; however, shortest time frames were grouped around the corresponding injection/infusion stop. Blood radioactivities required for the correction with *v*
_{b} were simulated from the generated IF according to Equation 3.

Once IFs and TACs were generated, Gaussian noise was added with the Excel function NORMINV to the simulated data. The standard deviation for noise generation of the IF consisted of a constant between 25 and 40 kBq/cm^{3} plus 4% to 6% of the simulated plasma concentration. For TAC simulations, a relative standard deviation was chosen for the Gaussian noise corresponding to the simulated TAC value multiplied with 0.8 and divided by the lengths of the time interval in seconds. These standard deviations yielded similar noise levels as observed for the experimental data. For each animal and infusion protocol, one IF and ten TACs were generated as described above, and kinetic modeling was performed with these simulated, noise-containing IFs and TACs as described above. Fit parameters were compared to the experimental values, and mean values and standard deviations of the fitted parameters were compared between the bolus and infusion protocols.

Finally, to investigate the influence of sampling frequency on the fit parameters and fitting precision (parameter standard deviations), IF sampling intervals were prolonged from the experimental 1 s to 30 s and 60 s, respectively, by deleting the data between these time points from both the experimental and above simulated noise-containing IFs. Kinetic modeling was performed with the identical simulated noise-containing TACs as used for the complete IF datasets.

### Statistical analysis

Data are presented as mean ± SD; error bars in figures represent SD and are further specified in the figure legends and text. Fitted parameters with the simulated IFs and TACs were compared by two-tailed homoscedastic *t* test. The effects of data smoothing and miscalibration were assessed with paired-sample *t* test, corrected for multiple comparisons (Bonferroni). Significant differences are indicated with an asterisk (*) for *P* < 0.05 and double asterisk (**) for *P* < 0.01.