Compartmental-modelling-based measurement of murine glomerular filtration rate using 18F-fluoride PET/CT

Accurate measurement of glomerular filtration rate (GFR) is essential for optimal decision making in many clinical settings of renal failure. We aimed to show that GFR can be accurately measured using compartmental tracer kinetic analysis of 18F-fluoride dynamic PET/CT. Twenty-three male Sprague-Dawley rats of three experimental groups (cyclosporine-administered [n = 8], unilaterally nephrectomized [n = 8], and control [n = 7]) underwent simultaneous 18F-fluoride dynamic PET/CT and reference 51Cr-EDTA GFR (GFRCrEDTA) test at day 0 and post-intervention day 3. 18F-fluoride PET GFR (GFRF-PET) was calculated by multiplying the influx rate and functional kidney volume in a single-tissue-compartmental kinetic model. Within-test repeatability and between-test agreement were evaluated by intraclass correlation coefficient (ICC) and Bland-Altman analysis. In the control group, repeatability of GFRF-PET was excellent (ICC = 0.9901, repeatability coefficient = 12.5%). GFRF-PET significantly decreased in the renally impaired rats in accordance with respective GFRCrEDTA changes. In the pooled population, GFRF-PET agreed well with GFRCrEDTA with minimal bias (−2.4%) and narrow 95% limits of agreement (−25.0% to 20.1%). These data suggest that the single-compartmental kinetic analysis of 18F-fluoride dynamic PET/CT is an accurate method for GFR measurement. Further studies in humans are warranted.

imaging, allowing accurate measurement of input function and tissue concentration of radiotracers, therefore has the potential for quantitative renal imaging 7 . Several proof-of-concept studies produced promising results. 68 Ga-1,4,7-triaza-cyclononane-1,4,7-triacetic acid ( 68 Ga-NOTA) or 68 Ga-EDTA have been investigated for GFR measurement but the results are yet to be validated 8,9 . To date, there is no accepted methodological standard of PET for GFR measurement. 18 F-fluoride is an established skeletal PET radiopharmaceutical, but it could also be used for renal imaging because fluoride is not bound to plasma protein and thus is freely filtered through glomeruli 10 . However, fluoride clearance is always lower than GFR due to significant tubular reabsorption 11,12 . Therefore, the previous 18 F-fluoride dynamic PET/CT study reported a moderate correlation of fluoride clearance with a broad range of renal function parameters; the direct measurement of GFR was beyond the scope 13 .
Compartmental tracer kinetic modelling enables the measurement of rate constants as parameters of important physiological processes in vivo. Dynamic PET is suited for this purpose due to its accurate and non-invasive quantification ability. We hypothesized that because the compartmental modelling allows the separate quantification of influx and efflux rates, we might be able to quantify GFR using 18 F-fluoride influx rate despite the presence of tubular reabsorption. In this study, we showed that GFR could be accurately measured in rats via compartmental modelling of dynamic 18 F-fluoride PET/CT. Neither urine handling nor blood sampling was necessary in this imaging-based approach. Validity of the compartmental model was independently tested by calculating GFR using dynamic PET/CT scans of 68 Ga-NOTA.

Group
Number of kidneys V C (cm 3 ) vB K 1 (ml/cm 3 /min) k 2 (min −1 )  The baseline GFR F-PET and GFR CrEDTA were not significantly different among the experimental groups (P = 0.830 and 0.686, respectively; Table 2). After cyclosporine intake or nephrectomy, GFR F-PET and GFR CrEDTA were significantly decreased ( Supplementary Fig. 1), whereas in the control group, there was no such decrease ( Supplementary Fig. 2). In each of the three groups, GFR F-PET and GFR CrEDTA were in good agreement ( Supplementary Fig. 3). In the pooled population (46 measurements), GFR F-PET agreed well with GFR CrEDTA ( (Fig. 2, Supplementary Fig. 4). P 30 and P 10 (see Statistics in the Methods section) were 97.8% (45/46) and 60.9% (28/46), respectively. The accuracy statistics of the GFR F-PET were summarized in the Table 3.

Discussion
In this study, we developed a compartmental tracer kinetic model for PET-based GFR measurement and applied it to 18 F-fluoride, which is not a GFR tracer under the conventional concept of urinary or plasma clearance measurement. According to the model, the influx rate K 1 can be considered as GFR per unit extravascular renal cortical volume for any tracer that is freely filtered through glomeruli but does not undergo tubular secretion. Previous reports suggests that 18 F-fluoride has such properties 11,12 . GFR F-PET was in good agreement with gold-standard GFR CrEDTA in conditions of nephrotoxic drug use and post-nephrectomy with minimal bias and narrow LOA. P 30 and P 10 were 97.8% and 60.9%, respectively, which suggests that GFR F-PET possesses sufficient accuracy (P 30 > 80% and P 10 > 50%) compared with other GFR markers such as iohexol, iothalamate and DTPA 15,16 . Furthermore, the accuracy of GFR F-PET was preserved with a reduction in imaging time to 15 min, which bears practical importance.
Good within-test repeatability is a prerequisite for assessing between-test agreement 17 . The repeatability of GFR F-PET was excellent with repeatability coefficient (half-width of the LOA) of 12.6%. GFR CrEDTA measured in this study showed slightly poorer repeatability coefficient of 22.2%, which is somewhat large compared to the reproducibility figures previously reported in humans (7.4-9.0%) 18 . This might have been caused by technical difficulties of the small animal experiment. We speculate that the agreement between GFR F-PET and GFR CrEDTA might be even better in humans, considering the expected increase in the precision of GFR CrEDTA .
To our knowledge, approaches of measuring GFR by using a compartmental rate constant have not been attempted in the field of nuclear medicine. In contrast, various types of compartmental modelling approach have been employed in magnetic resonance imaging (MRI) or CT studies. However, a critical literature review suggested that these MRI-or CT-based methodologies are not adequately accurate to be used as routine clinical or research tools 19 . Among the MRI-based methods, the cortical compartment model proposed by Annet et al. is similar to ours 20 . The differences are that Annet's method used two-dimensional regions of interest (ROIs) and abdominal aortic input function and that the dispersion and time delay from aorta to renal vasculature were accounted for. Many MRI-based methods use two-dimensional single-slice ROIs for better temporal resolution, and this acts as a limitation because a single slice or a slab cannot be representative of a whole kidney [20][21][22] . In this respect, the inherent 3-dimensional capability of PET is an advantage. The use of dispersion-and time-delay-corrected aortic input curves might be a merit of Annet's method in their rabbit experiment. However, we do not think that the non-correction for dispersion and time-delay caused any significant biases in our rat experiments because of smaller animal size. If this PET/CT analysis is implemented in humans, a proper selection of site for arterial input function measurement may become an important issue.
There may be a concern about the spill-out from the renal pelvic radioactivity into the renal cortical ROIs, considering small size of the rat kidneys. However, the scatter from the renal pelvic radioactivity turned out to be negligible compared with the renal cortical uptake. No significant amount of spill-out activity from the renal pelvis reached the renal cortical ROIs because the renal cortex and renal pelvis are intervened by the renal medulla and because the spatial resolution in terms of full-width half-maximum of the micro PET system used in our study was 0.7 mm that was much smaller than the thickness of the renal medulla (more than 3 mm).
We conducted another set of experiments using 68 Ga-NOTA. The results also showed good agreement with GFR CrEDTA (Supplementary Fig. 6B). However, the goodness-of-fit to the 68 Ga-NOTA data was not as good as that for 18 F-fluoride. The cause of the poor fit is unclear. We speculate that the urination process might not follow first-order (exponential) kinetics and therefore that the process might not be appropriately described by an exponential rate constant k u . For 68 Ga-NOTA, the rate constant k 2 (=k u + k reabs ) becomes k u because k reabs = 0, and according to the above speculation, k 2 also becomes an inappropriately modelled parameter. This could hamper the validity of the model equations. In contrast, 18 F-fluoride is reabsorbed through the lipid bilayer of tubular cells via passive diffusion 23 , and passive diffusion follows first-order kinetics. The reabsorption of fluoride is approximately 60% of glomerular filtrate, but it could increase up to 90% 11,12 . This implies that k reabs comprises a major portion of the efflux constant k 2 , causing the efflux process to roughly follow first-order kinetics. Therefore, the model fit becomes better for 18 F-fluoride, which would be a paradoxical advantage of nonzero reabsorption.
Measurement of haematocrit was essential for the calculation of 68 Ga-NOTA plasma input function because the fixed plasma fraction produced imprecise GFR (Supplementary Fig. 6C). In contrast, a fixed plasma fraction of 1.23 produced accurate GFR for 18 F-fluoride. It is likely that the plasma fraction of 18 F-fluoride remained relatively stable irrespective of haematocrit because 18 F-fluoride permeates into the RBC 24 , whereas the plasma fraction of 68 Ga-NOTA is more affected by haematocrit because 68 Ga-NOTA cannot enter in the RBC 8 . The high accuracy of GFR F-PET under a fixed plasma fraction is an advantage because haematocrit need not be measured, eliminating the need for blood sampling.
Given the high accuracy of the GFR measurement using dynamic 18 F-fluoride PET, translational application to humans may be promising for appropriate indications. Using the expensive PET technology for GFR measurement could only be justified in clinical situations where accurate measurement of GFR is critically necessary. Such situations might include nephron-sparing surgery for malignant lesions in patients with marginal renal function, determination of overall and split renal function before abdominal radiotherapy, and monitoring of renal function during nephrotoxic drug use 9,25 .
The present study has limitations. First, the range of the measured GFR was not sufficiently wide. The normalized GFR F-PET measured in this study fell within 41.2-140.2 mL/min/1.73 m 2 BSA. Further validation is needed for low GFR values because chronic kidney disease stage grades 4 and 5 (GFR <30 mL/min/1.73 m 2 ) were not included in the tested range 26 . Second, manual drawing of ROIs is too laborious for future clinical application. Automatic segmentation of renal cortex might have to be implemented.
In conclusion, dynamic 18 F-fluoride PET/CT in conjunction with a single-compartmental modelling approach holds promise as a reliable and accurate method for GFR measurement. The difficulties in urine handling and blood sampling in the measurement of conventional urinary and plasma clearance of ideal filtration markers may be overcome by pure image-based analysis. A quick assessment of GFR (within 15 min) is another practical advantage of this approach. Further studies in humans are warranted.

Materials and Methods
tracer kinetic modelling. The compartmental tracer kinetic modelling is a mathematical framework that originated from the field of pharmacokinetics and is a commonly used model for analysing PET data 27 . In the modelling, it is assumed that there are physiologically separate pools, or compartments, of a tracer substance 27 . Each compartment has its own influx and efflux rate constants, and the model fitting procedure allows to quantify them. We devised a compartmental tracer kinetic model in which the rate constant of a certain compartment could be interpreted as GFR.
In the model, extravascular renal cortex (EVRC), which contains Bowman's capsule, the renal tubule, and the interstitium, serves as a functional kidney volume. A tracer enters the EVRC via glomerular filtration and tubular secretion and moves out via reabsorption and urinary outflow (Fig. 3A). The rate of change in the tracer amount within the EVRC can be described by the following equation: where A EC (t) = tracer amount within EVRC, C P (t) = tracer concentration in plasma, k secr = rate constant of tubular secretion, k u = rate constant of tracer loss due to urinary outflow from the cortex, and k reabs = rate constant of tubular reabsorption. Because no tubular secretion occurs for the 18 F-fluoride 11,12 , k secr = 0 (Fig. 3A), the Equation (1) becomes as follows: where V C = renal cortical volume, vB = vascular volume fraction, C EC (t) = tracer concentration within the EVRC, K 1 = GFR/V EC and k 2 = k u + k reabs (Fig. 3B). The solution to Equation (3) can be expressed as follows: where ⊗ = convolution integral.
The model function C model (t) can be expressed as a superposition of C EC (t) and C P (t) according to their respective volume fractions in the kidney: The C model (t) is fitted to the renal cortical TAC with K 1 , k 2 , and vB as fitting parameters. Single-kidney GFR is obtained by multiplying K 1 and V C × (1 − vB), and total GFR is the sum of the GFR values of both kidneys.
We applied the above model to 18 F-fluoride dynamic PET/CT to measure the GFR and compared the values with gold-standard 51 Cr-EDTA GFR. Additionally, we tested the model using 68 Ga-NOTA. 68 Ga-NOTA was recently reported as a promising GFR tracer with no tubular reabsorption and secretion, and minimal binding to RBCs and serum protein 8 .
Radiopharmaceutical preparation. 18  After the dynamic PET acquisition, at 60 and 100 min post 51 Cr-EDTA injection, 1 mL of blood was withdrawn via tail-tip cutting (Fig. 4A). Following each blood withdrawal, 1 mL of saline was flushed to replenish the volume. Plasma samples obtained by centrifugation (3,000 rpm for 8 min) were divided into two aliquots for www.nature.com/scientificreports www.nature.com/scientificreports/ duplication, and the radioactivity of the plasma aliquots was measured for 20 min using a well counter (Wizard 1480, Perkin Elmer) 24 h after the blood withdrawal to ensure full decay of the PET radiopharmaceuticals. The plasma clearance of 51 Cr-EDTA was calculated from the mean values of the duplicate counts after background correction using the two-sample slope-intercept method 28 . The slope-intercept plasma clearance was corrected for neglecting the fast exponential in the bi-exponential plasma curve, generating the GFR CrEDTA (please see the Supplementary Methods for details) 29 .
Animal experiment protocol. For the 18 F-fluoride PET/CT experiment, 23 male Sprague-Dawley rats (age: 8 weeks; weight: 280 ± 12 g) were used. The rats were divided into three experimental groups. Eight rats were administered with cyclosporine (Sandimmun INJ, Novartis) 30 mg/kg orally from day 0 to 2 to induce renal impairment medically. Another eight rats underwent left total nephrectomy at day 1 to form a surgical renal impairment group. The remaining seven rats were fed 1 mL/day olive oil from day 0 to 2 and served as controls. Each rat underwent two 18 F-fluoride PET/CT imaging sessions at an interval of 3 days, at baseline (day 0) and after the renal impairment or control procedures (day 3) (Fig. 4B).
For the 68 Ga-NOTA PET/CT experiment, 10 male naïve Sprague-Dawley rats (334 ± 52 g) underwent dynamic PET/CT and a 51 Cr-EDTA test. The experimental protocol was the same for the 68 Ga-NOTA experiment, except for the haematocrit measurement (please see Supplementary Methods) and 68 Ga-NOTA (3.7 MBq/100 g rat weight) injection. image analysis. We performed PET/CT data analysis and tracer kinetic modelling using PMOD software (version 3.8; PMOD Technologies). ROIs were manually drawn over the renal cortices on the coronal CT images (Fig. 5A), and the ROIs over the same kidney were integrated to form a VOI. A 3-mm-diameter spherical VOI was placed in the left ventricular cavity to obtain whole-blood input function (Fig. 5B). The ROIs was overlaid on the co-registered dynamic PET images to obtain renal cortical TACs (Fig. 5C). In order to convert whole-blood www.nature.com/scientificreports www.nature.com/scientificreports/ input function to plasma input function, we adopted a fixed plasma fraction of 1.23 for 18 F-fluoride 30 because it permeates into RBCs with its intracellular concentration stable with about half in plasma 31,32 . In contrast, we adopted a plasma fraction of 1/(1-hematocrit) for 68 Ga-NOTA because it does not distribute into RBCs 8 . To test whether the measurement of haematocrit is mandatory for the calculation of 68 Ga-NOTA plasma input function, we calculated another set of plasma input functions by assuming a fixed haematocrit of 0.45.
The single-tissue-compartmental model curve using the plasma input function was fitted to the renal cortical TACs to obtain GFR F-PET and 68 Ga-NOTA PET GFR (GFR NOTA-PET ) (Fig. 5D). Additionally, we calculated PET GFR only using the first 15 min of data (GFR F-PET-15min and GFR NOTA-PET-15min ) to test the feasibility of reducing imaging time.
Statistics. The goodness-of-fit of the model was assessed using the coefficient of determination (R 2 ). We used the control group data to test for repeatability. Within-test repeatability and between-test agreement were assessed by means of the ICC and the Bland-Altman analysis 17,33 . Accuracy of GFR F-PET was expressed by P 30 and P 10 , which are defined as the percentages of the measurements that lie within the ±30% and ±10% ranges from reference GFR CrEDTA , respectively 15,16 . The paired-samples t-test was performed to analyse the difference between paired observations. The Kruskal-Wallis test was performed for group comparisons. Two-sided P < 0.05 was considered as significant. All statistical tests were performed using MedCalc statistical software (version 18.5; MedCalc Software bvba).
Study approval. The rats were cared for in a facility accredited by the Association for Assessment and Accreditation of Laboratory Animal Care International. The study protocol was approved by the Institutional Animal Care and Use Committee of Seoul National University Bundang Hospital (IACUC No. BA1705-223/041-01). All experiments were performed in accordance with relevant guidelines and regulations.

Data Availability
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.