In the present study, we report the use of a specially designed arteriovenous shunt apparatus for use in combination with a beta microprobe system to determine input function (IF) in rats. This apparatus can be used in studies of radioligand accumulation or binding in small animals using either beta microprobe systems or microPET. The major advantages of our system are very high temporal resolution and no blood loss, while its major disadvantages are its invasive nature and low sensitivity.
The probe-derived IF closely matched that derived by manual blood sampling, the so called "gold standard", as shown by visual comparison (Figure 2) and in the comparison between areas under the curve (AUC) (Table 1). The difference in AUC observed may be attributable to statistical noise but also the difference in temporal resolution between these techniques. Although blood samples were taken with a resolution of 5 s, the probe system has a maximum resolution of 1 s. In contrast to the high degree of agreement shown between probe-derived and manual sampling derived IFs, image-derived IFs showed an underestimation and increased variability (Figure 2 and Table 1). PET-derived IF based on a volume-of-interest in the left ventricle of the heart has been described for use as a true arterial IF in a number of species [10, 16, 17, 19–21]. Fitting of the IFs to reduce noise had a negligible effect on the coefficient of variation for the AUC ratios with all methods (Table 1). In addition to AUC, the slope constants of a bi-exponential model fitted to the IF curves were compared. Although AUC is a useful method for comparing the integrated activity present in the blood over the duration of the study, a drawback of the method is that it is possible for curves with very different shapes to have similar AUCs. In the present, study it was shown that the shapes of the IF curves are very similar (Figure 2), but comparison of the slope constants of the bi-exponential fit provides an indication of the instantaneous level of radioactivity in the blood, which is of importance for kinetic modeling using the IF curves. Statistical analysis revealed that all methods differed for the first slope constant, but that there was no significant difference between the probe- and manually derived curves in the second slope constant (Table 2). Changes in the first slope constant have a limited effect on the shape of the input function, while the second constant governs the decline in activity after the peak. Thus, the similarity in the second slope constant between probe- and manually derived curves supports the result of the AUC comparison and the conclusion that these IF curves are well matched.
A partial-volume effect is likely to be involved in the difference between image-derived IF and the gold standard or probe-derived IF. It is well documented that partial-volume effects adversely affect quantitative measures from small VOIs less than two times the FWHM resolution. The Siemens Concorde Focus 120 has a measured resolution of 1.2-1.5 mm [34, 35], while the VOI used for IF determination had a diameter of 2 mm to avoid spillover. It is thus likely that a partial-volume effect leads to underestimation of the activity in the blood. Furthermore, spillover of activity from the myocardium is a serious problem in cardiac ventricular image-derived IF in rats and mice. In the present study in rats, spillover was reduced by using a small VOI located centrally in the left ventricle. While spillover can be corrected for mathematically [36, 37], a clear advantage of the probe-derived IF is the lack of spillover. Methods combining image-derived IF and later blood sampling may also help minimize spillover effects [26, 27]. Factor analysis of cardiac PET images can be used to separate the ventricular and myocardial components of the image [14, 15, 17–19, 21–23], though calibration of the IF obtained to a blood sample may still be necessary.
A further drawback of PET-derived IF in microPET studies of the brain is the need to position both the heart and region of interest (e.g., cerebral cortex) in the field-of-view. Particularly where regions of interest are of the same scale as individual voxels, such as in the brain, it is well known that positioning that organ centrally in the field-of-view offers optimal spatial resolution. In order to position the brain and heart in the field-of-view of small animal scanners such as the Focus 120 simultaneously, it is necessary to position both organs at or near the extremes of the field-of-view. This may be detrimental to the overall data. Even in the human situation, where scanner resolution is less critical, a reliable method for image-derived input function without some degree of blood sampling has not yet been achieved .
Dispersion of the probe-derived IF due to the catheters and the shunt, and sticking of the tracer on the catheter walls are potential drawbacks of using an arteriovenous shunt. It has been shown that increasing catheter length and decreasing pumping speed increase dispersion in catheter-based blood detectors , a conclusion supported by the data in the present study (Figure 3a, b). Based on calculations for dispersion in the catheter prior to detection , Convert et al.  reported that correction of dispersion should be unnecessary for PE10 catheters where flow rate is greater than 125 μl/min (7.5 ml/h) or a length < 10 cm, or for PE50 catheters with flow rate > 250 μl/min (15 ml/h) or length < 20 cm. In the present study, PE20 catheters are used with a length < 20 cm and a measured flow rate equivalent to 477 ± 25 μl/min (15 ml/h). Thus, the effect of dispersion should be minimal, as supported by the similarity between probe-, image-, and manually derived IFs in the present study. Therefore, any dispersion effect can thus be minimized by keeping both catheters and shunt tubing to their minimum lengths, minimizing the total volume, and by maintaining a sufficient flow rate. If the circumstances of a given study do not allow optimization of these parameters, methods for the correction of dispersion have been described [40–42]. The carotid artery could also be used to obtain a probe-derived IF curve and minimize the distance from the heart to reduce dispersion. However, in the case of studies of brain function, it may be desirable to avoid possible changes in blood supply to the brain due to catheterization of the carotid artery. Furthermore, the comparison of carotid- and femoral-derived IFs in the present study indicated negligible differences (Figure 3c). The influence of a large volume shunt in the present study was clear (Figure 3a), while the difference between an extra-short shunt and a longer pump-driven shunt was minimal (see also Figure 3a), suggesting that only large increases in overall volume are significant. As above, a low pump speed is undesirable as this can increase dispersion. Indeed, halving the flow rate in the present study introduced a dispersion effect (Figure 3b). Including a pump in the shunt could be considered useful to standardize the flow rate between animals. Adsorption of the tracer can be accounted for by calibrating the shunt using a solution of known radioactivity pumped through the shunt with probe in situ, as described in the Materials and methods section. Thus, the calibration factor for the shunt probe will also be affected by tracer adsorption.
Reproducible positioning of the probe was facilitated by the shunt design (see Figure 1), and was confirmed by comparing the calculated sensitivity values. The calculated coefficient of variation was 0.04. This reproducible positioning also ensures that the minimal sensitivity of the Swisstrace probe (Swisstrace, Zurich, Switzerland) to Cerenkov radiation  is also unlikely to be of consequence to the accuracy of the measured IF, as the number of counts attributable to Cerenkov radiation was concluded to be related to the depth of the scintillating fiber in the volume of activity. In the shunt-probe apparatus, the depth of probe insertion into the blood flow is limited to approximately 1 mm, and the design allows this depth to be highly reproducible. It has been argued that beta microprobe systems can be difficult to use , particularly as many systems are highly sensitive to ambient light. The light-tight coating of the Swisstrace microprobes eliminates any influence of ambient light and removes this technical difficulty.
Recently, a method for microfluidic blood sampling has been described for IF measurement in small animals . Although this elegant approach solves a number of difficulties with blood sampling in small animals, it is still not possible to achieve the time resolution of the beta microprobe-derived IF or avoid blood loss entirely. The removal of blood is, however, often required in studies with novel radiotracers, for the determination of metabolites present in the plasma. In this case, the use of an arteriovenous shunt is no more invasive than the use of a catheter solely for blood sampling. Methods using blood sampling to determine IF may have sufficient volume to measure metabolites directly. While the present arteriovenous shunt method allows the investigator to avoid blood loss where desired, the inclusion of a T-connection for blood withdrawal facilitates sampling for metabolites. Furthermore, intravenous tracer and drug administration is also facilitated.
Coincidence counters have also been used to measure activity in flowing catheters [7, 28] with high time resolution. Due to the increased sensitivity of these counters, a lower dose of radiotracer can be used, which represents an advantage over the probe-derived system. At present, the availability and price of miniaturized coincidence counters represent disadvantages compared to beta microprobes. Furthermore, adequate shielding is required for these counters which could necessitate longer catheters and thus increased dead volume. The small size of the beta probe and lack of gamma sensitivity help to minimize these problems. Beta microprobe systems are also dual use, in that in addition to IF measurement they can be used in studies of the brain .
In those laboratories with access to a small animal PET scanner, the presently reported method allows the addition of IF with high temporal resolution at a relatively low cost, which could add value to these studies. For example, in combination with PET, the shunt allows the calculation of local cerebral glucose metabolism and kinetic rate constants in FDG studies using fully quantitative two-compartmental modeling approaches. In the case of studies into receptor occupancy and binding potential, the ability to measure IF not only allows the use of IF-reliant modeling (after the development of conversions for plasma and metabolism of the tracer) but also allows the comparison of binding data obtained using either IF or a reference region.