Assessing the kidney function parameters glomerular filtration rate and effective renal plasma flow with dynamic FDG-PET/MRI in healthy subjects

First, a blood sample was drawn to determine hematocrit (Hct) and creatinine. All subjects underwent a routine dynamic renal scintigraphy according to the EANM standardized protocol [7] (for details, see below). In the course of this, another blood sample was drawn 41 ± 2 min after injection of around 80 MBq MAG3, which was used to determine MAG3 clearance. For this purpose, a standard of around 20 MBq in 1 ml was measured both in the dose calibrator for syringes and, after dilution by 1:100, in a gamma counter for blood sample measurement.

Similar to renal scintigraphy, volunteers were hydrated with water (10 ml/kg body weight) for 20 min and asked to empty their bladder directly before injection of FDG (~ 3 MBq/kg body weight). The FDG is prepared in our institution on a routine basis to a well-known and established method [8] based on a GE FASTlab platform (General Electric Healthcare, USA). With a combined PET/MRI scanner (Siemens Biograph mMR, Siemens Healthcare Diagnostics GmbH, Germany), PET acquisition started immediately after tracer injection and continued for 30 min. The PET list-mode data was re-binned into a dynamic sequence: 60 × 5 s, 25 × 60s, and each PET frame was reconstructed (Siemens e7 tools) into a 172 × 172 × 127 matrix using the ordinary Poisson ordered subsect expectation maximization (OP-OSEM) 3D algorithm (3 iterations, 21 subsets, Gaussian filter). Scatter correction along with Dixon-based MR-attenuation correction was performed. The MR imaging protocol consisted of a T1 weighted MRI sequence (axial breath holding and fat suppression, VIBE SPAIR). A contrast-enhanced (Dotarem: 0.2 ml/kg body weight) TWIST dynamic MR sequence was performed on 10 subjects (group 2, see Table 1). To perform quantitative analysis, five volumes-of-interest (VOIs) were chosen with the Hermes Hybrid Viewer tool (Hermes Medical Solutions AB, Stockholm, Sweden): (1) aorta descendens (between diaphragm and arteria renalis), drawn by hand in several layers (2) left kidney, (3) right kidney, (4) left kidney cortex, and (5) right kidney cortex. VOIs (2–3) were carefully drawn by hand in each layer; VOIs (4–5) were delineated randomly in about 30% of all layers by threshold ROI selection tool in the outer part of the parenchyma. In Fig. 2, aorta, right cortex, and right total kidney ROIs are presented. VOIs were then copied to the PET images, from which the TACs, i.e., the FDG concentration in the VOIs over time, were exported in units of kilobecquerel per milliliter.

FDG TAC analysis was performed using an in-house Java-based tool (programmed with openjdk version 1.8.0_162), for which the aorta input function (AIF) along with the TACs (Fig. 3) was used as inputs. With a machine learning approach (see Additional file 1 and [9]), it was found that TACs need to be smoothed with a filter for which a Bezier curve was calculated to overcome noise and fluctuations especially appearing in the initial part of the TACs. Since we observed a hump in the total kidney TACs between 3 and 5 min p.i, which was paralleled by an increase of concentration in the renal pelvis (see Fig. 3a), we assume that FDG remains in the kidney compartment during the first minutes (irreversible process within the minimal transit time) before it was forwarded into the pelvis or re-absorbed. Therefore, a graphical analysis was performed with a Patlak plot [10, 11].

The rapid decay of the peak might be affected by several processes, such as glomerular filtration, re-absorption, and forwarding to the renal pelvis. If many processes occur, a Patlak plot results in a complicated, curved shape [11], which can be clearly observed in Fig. 3b. To calculate GFR_FDG, regression analysis was used to obtain the slope K of the Patlak plot (see Fig. 3b). To unambiguously identify the relevant linear part, a machine learning approach was used (see Additional file 1), showing that the linear part within the first 2 min, starting at the point which corresponds to the TAC peak maximum, was most suitable. Final GFR_FDG was then defined as the sum of the right and the left cortex or total kidney value V:

GFR_FDG[ml/min] = K_right[min⁻¹]V_right[ml] + K_left[min⁻¹]V_left[ml]

As reference value, GFR_ref was estimated from creatinine values with the CKD-EPI formula [12].

Initial FDG blood flush is represented by the integral of the TAC peak, while the TAC peak maximum P_max gives the largest by the kidney physically graspable quantity of fluid. The ratio between these two quantities consequently results in a time value representing the capability of the kidney to forward the maximum quantity of fluid and was therefore taken as a measure for the ERPF, i.e., ERPF_FDG. This value was then multiplied with the corresponding kidney volume V. Final cortex and total kidney ERPF_FDG were taken as sum of the corresponding left and right single kidney values.

The integral over the peak was calculated from peak rise to 1 min after peak rise, which was found with the machine learning approach.

MAG3 clearance and, from this, ERPF_ref were determined from one blood sample, drawn ~ 40 min p.i. according to [1, 13].

For reference values, GFR_ref error was set to 12% according to [14]. ERPF_ref error was estimated with 10%, because the blood sample measurement protocol was identical to [15], showing that errors, usually not higher than 10%, mainly arise from the measurement procedure.

To estimate errors of GFR_FDG and ERPF_FDG, the reproducibility of the VOI choice for FDG TAC analysis was assessed with data from subject group 1 (Table 1), having high differences between their reference values, age, and gender. For each subject, the above described procedure for calculating GFR_FDG and ERPF_FDG was repeated using three different VOIs for each aorta, cortex, and total kidney, leading to seven different combinations of cortex/total kidney TACs and AIF. Different layers, VOI sizes, and regions have been chosen to alter the aorta and cortex VOIs. Note that the aorta VOIs were still located between diaphragm and arteria renalis. Either total kidney VOIs were delineated more inaccurately or every second layer was used for manual delineation, and a Hermes Hybrid Viewer tool was used to automatically fill up the missing layers. For each subject, the deviations from the mean GFR_FDG and ERPF_FDG were then calculated from all different VOIs and averaged over all three subjects.

In the case of GFR_FDG, total error was taken as square root of the squared sum of all contributing errors, which was the standard error from just described reproducibility checks as well as the standard error from the linear fit of the Patlak plot.

After image fusion, it was observable that the FDG distribution in the PET images was blurred, i.e., it exceeded the border of the aorta region in the MRI scans, in particular during the first frames (see Fig. 4), mainly due to motion and partial volume effects. Due to these effects, FDG concentration was falsely spread over a larger volume, leading to an underestimation of concentration. The effect was studied on the basis of a method described by Khalighi et al. [16, 17] with the dataset of the subjects from subject group 2, who additionally had contrast-enhanced MRI examination. The active contour algorithm from ITK snap (version 3.6.0) was used to extract the aorta volume V_A from the contrast-enhanced MR data. Spill-out region was defined by summing up the early PET frames and segmenting the aorta from the summed PET images. Using Matlab R2016a (MathWorks, USA), a background sampling region was defined by radially dilating the spill-out mask by three voxels (12 mm); the activity C_B and the volume V_B in this region were measured. Similarly, the volume of the aorta, V_A, was also determined. The total area comprises of the spill-out and background region with activity C_T and volume V_T. The activity balance in these three volumes can be then modeled by C_TV_T = C_AV_A + C_BV_B. Finally, this equation was solved for C_A, the FDG tracer concentration in the aorta (AIF), and was repeated for all frames. GFR_FDG from cortex and total kidney TACs of each subject was then re-calculated with the corrected AIF. The deviation of the GFR_FDG obtained from the corrected AIF to the uncorrected AIF was calculated, averaged over all subjects and expressed in percent.

Statistical analysis was performed with Gnumeric (open source software, version 1.12.20) and LibreOffice Calculator (open source software, version 4.3.7.2). First, reference values, values from FDG TACs, and basic subject data were tested for normal distribution with Kolmogorov-Smirnov test. Correlations have been calculated with Pearson product-moment correlation coefficient r from which p value was derived. The significance of the differences between reference and FDG value was assessed by a paired Student’s t test (p < 0.05 was considered as a statistically significant difference).

As shown in Fig. 5, cortex GFR_FDG showed an excellent correlation with GFR_ref (r = 0.85; p < 0.0001) and total kidney GFR_FDG showed an excellent correlation with GFR_ref (r = 0.88; p < 0.0001). ERPF_FDG correlated with cortex ERPF_ref by r = 0.81 (p < 0.0001) and with total kidney by r = 0.82 (p < 0.0001) (see Fig. 5).

The linear part of the Patlak plot below 2 min was used for the linear regression to obtain GFR_FDG. It should be noted that using more fit points of the Patlak plot up to 4 min did not change the correlation significantly (r > 0.84), but the differences between the means of GFR_FDG and GFR_ref were higher (+ 65 ml/min in average).

All results as well as differences from the Bland-Altman analysis are summarized in Table 2 and Figs. 5 and 6. Paired Student’s t test showed no significant difference between FDG and reference values, neither for cortex and total kidney values nor for GFR and ERPF.

Total errors are also summarized in Table 2 and presented as error bars in Fig. 5. Note that total error of GFR_FDG, in contrary to ERPF_FDG, arises not only from reproducibility checks but also from Patlak fit errors, leading to an individual error for each value which is indicated as range in Table 2. Reproducibility checks showed a variation of 7% in case of total kidney and 11% in case of cortex GFR_FDG and a variation of 7% in case of total kidney and 9% in case of cortex ERPF_FDG. Furthermore, no significant difference was found within subject group 1. Accuracy of kidney volume determination was found to be 6%.

The effect of the observed blurring of the FDG distribution in the aorta region was estimated with a corrected AIF. GFR_FDG varied in the case of cortex by (6 ± 17) % in case of total kidney by (− 1 ± 7) %. Note that ERPF_FDG is not affected by this correction because its calculation does not depend on the AIF.

There are several limitations of the present study, which have to be mentioned.

Firstly, the reference value GFR_ref was estimated from creatinine level in the blood to keep the subject comfort in mind [19]. Clearance of MAG3 is usually connected to the so-called tubular extraction rate, but it can be used as a reliable estimator of ERPF after a conversion [13, 20].

Secondly, FDG physiology is complex, a simple approach as the presented one therefore has obvious shortcomings, especially if one of the initial processes forming the peak shape is affected, e.g., in the case of chronic kidney diseases or in the case of diabetes where renal glucose re-absorption is changed [21]. The current study was based on healthy subjects; the efficiency of the method needs to be evaluated in the context of patients with pathology.

Thirdly, the method according to [16] used to correct partial volume effects in the aorta might only be applicable to PET/MRI scans, for which this method was proven to be reliable [16, 17] with even thinner cervical arteries used for the AIF.

Regarding a possible transfer of our method to different PET modalities, we focused in the present study on an evaluation of PET data in comparison to reference values. Due to this reason, the MRI part of our PET/MRI system was only used to separate renal cortex from other renal parts, even if several methods exist to obtain reliable values for kidney function parameters such as renal blood flow [22] or in particular GFR [22‐25] with different sequences, with contrast agents, based on Patlak plots or kinetic models.