Validation and Comparison of [18F]NaF PET/CT Analysis Methods and Derivation of a Semi-population Input Function for Site Specific Measurements of Bone Formation in a Population with Chronic Kidney Disease Mineral and Bone Disorder


 BackgroundMethods for assessing bone metabolism which can replace the gold standard bone biopsy are sorely needed in the clinical setting in patients with chronic kidney disease - mineral and bone disorder (CKD-MBD). The aim of the present study was implementation, validation and comparison of non-invasive dynamic and static whole-body (WB) [18F]NaF PET/CT scan methods to replace invasive bone biopsy, used for quantitative analysis of bone clearance in CKD-MBD patients.MethodsSeventeen patients with CKD-MBD underwent a 60-minute dynamic scan followed by a 30-minute static WB scan. Tracer kinetics in four thoracic vertebrae were analyzed using non-linear regression with the Hawkins model and two different Patlak-analysis methods using image-derived arterial input functions obtained from the left myocardial ventricle and the thoracic aorta. For future use in WB PET/CT scans, we validated the use of a semi-population input function. The resulting kinetic parameters (Ki, K1, k2, k3, k4, V0) were compared between the different methods of analysis using the various derived input functions.ResultsDynamic kinetic results from both standard and single-point Patlak analyses correlate well with non-linear regression analysis, but Ki results using Patlak analysis are generally lower for all tested input functions compared to regression analysis. Single-point Patlak analysis on WB scans correlates well with standard Patlak analysis on dynamic scans but show 13-21% higher Ki-values. ConclusionsOur results show good correlation between dynamic and static analysis of skeletal plasma clearance but different Ki-values depending on the analysis method and choice of input function used. Thus, WB [18F]NaF PET/CT scans can be applied in future studies, but the results should not be compared uncritically with results obtained using non-linear regression analysis.


Introduction
Fluorine-18 labelled sodium uoride ( 18 F-NaF) was introduced in the 1960s as a bone-seeking tracer in nuclear medicine [1] and widely used for gamma camera bone scintigraphy, but was later replaced by Technetium-99m labelled diphosphonates in the 1970s. In the past decades, 18 F-NaF has been reintroduced in combination with PET/CT. Chronic kidney disease (CKD) is associated with universal bone abnormalities (renal osteodystrophy) and disturbances in mineral metabolism leading to cardiovascular and extra skeletal calci cations. These processes are caused by common pathophysiological pathways and are de ned as a systemic disorder named Chronic Kidney Disease -Mineral and Bone Disorder (CKD-MBD) [2]. Even though bone-related complications have been known in CKD since 1883 [3], the key to effective treatment and prevention remains to be found, with this shortcoming possibly attributed to the lack of non-invasive methods available for diagnosing and monitoring CKD-MBD.
Today, bone biopsy is considered the gold standard for analysis [4], but it is invasive, unpleasant and not without risk to the patient. However since the 1990s, non-invasive 18 F-NaF PET/CT has shown good potential for monitoring CKD-MBD [5]. Here 18 F-NaF, administered as an intravenous bolus injection, diffuses from the plasma into the extra vascular compartment in bones from where it is further incorporated into the bone's hydroxyapatite skeleton as uoroapatite [6].
The plasma clearance of 18 F-NaF to bone [K i (ml min − 1 ml − 1 )] re ects changes in either bone blood ow or bone formation rate. Traditionally, nonlinear regression analysis with the Hawkins two-tissue, three compartmental, model ( Fig. 1) or the Patlak multiple data point graphical method (mp- Patlak), have been used to determine K i and other kinetic parameters using dynamic data acquisition [7,8]. K i -values are shown to correlate well with turnover results obtained by bone biopsies [5]. Both Hawkins and Patlak analysis require dynamic acquisition over a single eld-of-view (FOV), typically of 60-minutes duration. Due to restrictions in the axial width of a given scanner (16-25 cm), a single dynamic scan can examine only a selected region of the skeleton, with extended regions of interest requiring multiple scans and tracer injections. This is not only impractical in a clinical setting, but will result in a high radiation dose to the patient. However, modern advances in PET/CT scanner functionality, combining an initial, short duration dynamic acquisition over the heart followed by a series of fast multiple whole-body scans are now available and may soon provide a solution to the problem of extended dynamic scanning. Previously this limitation has been addressed through development of a simpli ed acquisition and analysis method in which a static, WB 18 F-NaF PET scan in combination with a standardized semi-population input function (SPIF), estimates K i values in multiple bone regions using a single-point graphical analysis (sp-Patlak) [9,10]. With this method it is possible to perform a 30 minute WB acquisition with sitespeci c bone analysis using a single tracer injection [9,11,12].
The application of a SPIF requires an a priori derived population residual curve. Ideally, a population residual curve should be derived from the relevant population as the curve re ects the tracer distribution in the body and may be subject to vascular changes caused by various diseases. Since the CKD-MBD population generally has complications with vascular calci cations, it seems possible that a population residual curve for this population may differ from one obtained in an osteoporotic population [13]. To our knowledge, a population residual curve for CKD-MBD patients has not previously been published.
The objectives of this study were threefold: 1) implementation of 18 F-NaF PET/CT using the Hawkins method and mp-Patlak analysis for dynamic studies of NaF skeletal plasma clearance, 2) derivation of a CKD-MBD population residual curve for subsequent SPIF construction in combination with venous blood samples to be used as the arterial input function (AIF) for sp-Patlak analysis in WB scans and, 3) comparison and validation of WB scan results with results from dynamic scan analysis.

Subjects
Thirty-four chronic dialysis patients (30-80 years) were included, of which 17 participants completed the study (hemodialysis n = 15, peritoneal dialysis n = 2). Exclusion criteria were: pregnancy, participants who suffered from alcohol/drug abuse, were allergic to 18 F-NaF or Tetracycline, or in the past three months had had bone fracture, acute myocardial infarction, transitory cerebral ischemia, kidney transplant or parathyroidectomy. Table 1 shows demographics and Fig. 2 shows owchart for inclusion. Normal distributed data: mean ± SD. Non-normal distributed data: median (25th percentile; 75th percentile) During data analysis one patient had to be excluded due to very poor image quality resulting from severe obesity and three patients excluded due to delayed bolus injection and problems with blood sampling.

Image acquisition
PET/CT images were acquired on a Siemens Biograph mCT-4R 64 slice PET/CT scanner with a 22 cm axial FOV. The participants were positioned with the heart and the thoracic vertebrae 7 through 10 (Th7 -Th10) centered in the FOV.
Following an intravenous bolus injection of 150 MBq 18 F-NaF ushed with 20 mL isotonic saline, a 60-minute list-mode dynamic scan was acquired followed by a WB scan from the middle of the femur to the vertex of the skull acquired in 6-7 FOVs of 3 minutes per bed position.

Image reconstruction
PET images for dynamic analysis were re-binned into 50-time frames: 20 × 3 s, 12 × 5 s, 4 × 30 s and 14 × 240 s. Reconstruction of PET scans was done using ltered back-projection with a Gaussian lter of 5 mm and matrix size of 256 × 256.
Low-dose CT scans were performed and the images reconstructed in three utilization-dependent series: 1) attenuation correction, 2) localization and identi cation of thoracic vertebrae in the dynamic scan and 3) localization of the relevant bone regions in the WB scan.
All dynamic images were automatically decay corrected to the study injection time (study reference time). Image data from the WB scan was automatically decay corrected to the start of the WB scan, on average 66 ± 2 minutes post injection, requiring additional decay correction to the study reference time for comparison with dynamic data.

Blood samples
Venous blood samples (5 mL) were collected at -5, 30, 40, 50, 60 and 90 minutes after injection and thereafter centrifuged at 3000 rpm for 10 minutes. The activity concentrations in 1 ml of whole blood and plasma were measured in a well-counter (Perkin Elmer Wizard2® − 2480 Automatic Gamma Counter, USA). The well-counter and PET/CT scanner were cross-calibrated. To convert measured activity from image-derived whole blood to plasma activity curves, plasma to whole blood activity ratios were calculated for each of the samples (Fig. 3).

Image analysis
The PMOD® version 4.003 software (PMOD Technologies LLC, Switzerland) was used for non-linear regression analysis of the dynamic data as well as analysis of the single-point WB data.
The drawing of VOIs, for generation of time activity curves (TACs) from the cardiac left ventricle (LV) or thoracic aorta (AO), was facilitated by summing the relevant time frames with highest activity into one static frame. Contours of the activity within the LV were drawn using the hot contouring tool in PMOD, de ned as a percentage of the maximum activity within a box VOI surrounding the LV (typically 45-65%). AO VOIs were drawn using box VOIs (10 × 10 × 30 mm) centered in the aortic lumen (Fig. 4).
For partial volume effect (PVE) and activity spillover correction, VOI contours within the myocardial wall and surrounding the luminal activity in the aorta, were manually drawn using the brush tool on at least 10 axial slices with a voxel-size of 3.2 × 3.2 × 1.4 mm.
Box VOIs were tted to the trabecular part of the vertebral bodies Th7-Th10, avoiding the endplates and the disk spaces using the CT images as a template. These VOIs were similar for both dynamic and WB studies.
TACs were derived in the PMOD View Module and transferred to the PMOD Kinetic Module for further analysis as described in detail below.

Input functions
Dynamic scan analysis used an image-derived arterial input function (IDAIF) from a VOI placed in the LV and AO as described above.
Errors due to PVE and activity spillover were corrected by calculation of the recovery coe cient β, as described by Cook et al. and Puri et al. [10,14] where R LV/AO is activity in the image-derived TAC obtained from the LV or AO, C Bg is the background activity concentration in the surrounding myocardium or aortic wall and C LV/AO is the corrected arterial blood activity concentration in LV or AO. C LV/AO is approximated to activity in venous blood samples 30 minutes after injection [10]. From (Eq. 1), β can be estimated as the mean value of β-coe cients calculated from each of the paired image and blood sample data.
Population residual curves β-corrected IDAIFs were scaled to a reference dose of 150 MBq and used to generate a residual curve for each participant. The residual curve represents the sum of the early fast exponentials and was derived by subtracting the terminal exponential from the entire image-derived curve. The residual curves were averaged to de ne the population residual curve in three different ways: 1) Population residual 1 -all residual curves were averaged with no time adjustment of the peak (LV: n = 12; AO: n = 11), 2) Population residual 2 -all residual curves were selected but were adjusted so that the times of peak count rate for all curves were coincident with the most frequent unadjusted peak time (LV: 16.5 s; AO: 19.5 s) and, 3) Population residual 3 -only unadjusted residual curves which peaked at the most frequent time frame were selected (n = 6).
For WB analysis we used a SPIF as previously described by Blake et al. [9]. The selected population residual curve was scaled for the patient injected activity and added to the terminal exponential of the plasma TAC to de ne the 0-60 minute and 0-90 minute SPIF for each subject.

Skeletal plasma clearance analysis
The skeletal plasma clearance [K i (ml min − 1 ml − 1 )] was calculated as the mean value of four thoracic vertebrae (Th7-Th10) for the systematic application of three different analytic methods and input functions as described below.
Hawkins model: Non-linear regression analysis PMOD software was used to perform two-tissue compartmental model dynamic analysis of NaF-turnover as described by Hawkins et al. [7]. The exchange of 18 F-NaF between the three compartments (plasma, extravascular and bone) is described by the kinetic parameters (K i , K 1 -k 4, V 0 ) ( Fig. 1), where K i is de ned as: K i was calculated for two different prede ned values of the percentage of 18 F-NaF present in the extravascular compartment V 0 : 1) previously published population mean value V 0 = 0.43 [11] and 2) the mean value for this study data V 0 = 0.51, obtained from data analysis performed without a prede ned value.
The fractional blood volume was xed at 5%.

Patlak: multiple-point graphical analysis
Assuming the e ux rate constant k 4 to be negligibly small (k 4 ≈ 0 min − 1 ), mp-Patlak graphical analysis provides a simpler alternative analysis method for measuring K i as described by Eq. 3 [8,15].
This equation approximates a straight-line t with K i as the slope. C Bone and C Plasma are the respective concentrations of tracer bound in bone and freely diffusible in plasma. V 0 is the intercept of the ordinate and represents the extra vascular compartment in the bone.
K i was calculated from the 60-minute dynamic PET/CT scan using a bone TAC and the various image-derived AIFs with and without data from venous blood samples.

Patlak: single-point graphical analysis
For calculation of the straight-line function for analysis, the sp-Patlak model requires a single data point using activity measured in a selected bone region combined with a previously determined value of the intercept (V 0 ).
The present study compared three different values of V 0 applied in sp-Patlak: a mean value of 0.43, as previously published for mp-Patlak analysis of lumbar vertebrae [11] and two mean values obtained from this study; V 0 = 0.64 when data were analyzed by the mp-Patlak method using 30-90 min blood samples, and V 0 = 0.52 when using 30-60 min blood samples.

Statistical analysis
Normally distributed results are presented as mean ± standard deviation (SD). Non-normally distributed data are presented as median (25th percentile; 75th percentile).
K i was independently calculated for mp-Patlak by an experienced nuclear medical specialist (S) and by a medical resident (R) to determine interobserver variability. The paired t-test was used to compare mean values of K i and V 0 obtained from the various input functions, where a two-tailed pvalue of 0.05 or less was considered statistically signi cant. Correlations between K i -values obtained using different analysis models were calculated by linear regression and presented by Pearson's correlation coe cient and the chi 2 -test was used to evaluate the t of the input functions to an applied model. The percentage coe cient of variation of the population residual curves was obtained by dividing the SD by the population residual curve and the 95% con dence interval was estimated using a chi² distribution.

Results
The mean plasma to whole blood ratio was 1.17 ± 0.03. The mean recovery-coe cients β were 0.69 ± 0.15 and 1.06 ± 0.44 when the IDAIF was obtained from TACs in the LV and the AO respectively.  Table 2 shows the characteristic mean peak-and AUC-values of the various AIFs before and after β-correction and tting with the terminal plasma exponentials.

Input functions
Data are presented as mean values ± SD obtained by the same 12 scans. The mp-Patlak t was evaluated by Pearson's correlations coe cient (r 2 ). *Level of statistical signi cance is p < 0.05 Table 3 evaluates the various input curves by comparing their terminal exponentials with the terminal exponential of the plasma samples and found only small average differences in activity values at all comparable time-points. Mean differences signi cantly different from 0 and mean ratios signi cantly different from 1 were determined using the student paired t-test. *Level of statistical signi cance p < 0.05

Population residual curves
The various population residual curves are shown in Fig. 6a. The variation in the curves is illustrated by the SD of the residual curves in Fig. 6b (plotted as the percentage of the total population residual curve).
Comparison of the peak-activity values and AUCs of the SPIFs derived by the 2 observers, after combining the population residual curves with the terminal exponentials of the venous plasma samples for 30-60 minutes and 30-90 minutes, is shown in Table 4. No signi cant differences were observed between the IDAIFs' mean AUC compared to the SPIFs' mean AUC when adding the terminal exponential taken 30-60 minutes after injection.
Statistically signi cant difference was found by observer-R in peak-values for population residual 1, using the 30-90 minute plasma samples as SPIF when compared with IDAIFs using 30-90 minute plasma samples as SPIF, but this difference was not found by observer-S. However, the resulting AUC's were not signi cantly different. Skeletal plasma clearance Figure 3 shows a typical bone TAC. Initially the tracer concentration is very low and the resulting part of the curve is generally poorly de ned, making it di cult, if not impossible, to determine the exact time of arrival of the ow peak. Uptake in bone rises signi cantly after a few minutes, but with slowly declining rate.

Hawkins model: Non-linear regression analysis
The rate constants (K 1 -k 4 ) were determined using the Hawkins two-tissue compartmental model for the uncorrected and corrected IDAIFs from both the LV and AO. The data shown in Table 5 are calculated with no constraints on K 1 /k 2 , with K 1 /k 2 xed to a population value of 0.43 [11] and with the present study's population value of 0.51.
For all input functions, the value of k 4 never exceeds 0.011 min − 1 indicating that -at least within the 60-minute time frame of the dynamic study -the e ux of 18 F-NaF from the vertebrae is mostly negligible, an important prerequisite for proper use of the Patlak-analysis method.    Mean ± SD from 12 scans (Th7-10). The Hawkins analysis was made with an adjustable V 0 -value, with a xed population value of 0.43 and our own population value of 0.51. *Level of statistical signi cance is p < 0.05. Image-derived AIFs (IDAIFs) were obtained from: 6a) TAC of left ventricle of the heart (LV) and 6b) TAC of thoracic aorta (AO).
No signi cant inter-observer differences in the K i -values obtained with use of mp-Patlak analysis were found (Table 7). Table 7 Comparison of K i -values (ml min − 1 ml − 1 ) analyzed by a nuclear medical specialist (S) and a medical resident (R) Patlak: single-point graphical analysis Table 8 shows K i -values obtained by sp-Patlak analysis. For this analysis a SPIF constructed of population residual 2 in combination with the terminal exponential of plasma samples taken at 30-60 minutes or 30-90 minutes was used.  To some extent CKD-MBD is present in all patients suffering from severe kidney failure in need of dialysis treatment. Therefore, the present study includes chronic dialysis patients as representatives of the CKD-MBD population. The participants in the present study were mostly males (70%) and diabetic nephropathy was the most common cause of kidney failure (29%). Previous studies using 18 F-NaF PET/CT for dynamic bone examination have mostly studied female osteoporotic patients and excluded patients with CKD [16,12]. However, a recently published study of a CKD-MBD population also included 50% males with diabetic nephropathy as the most common cause of kidney failure (34%) [17].

Input functions
Ideally, an AIF should be derived from the arteria supplying the bone region of interest by direct arterial sampling. However, an image-derived AIF is known to be a good approximation of an AIF [10]. In the past years, research in osteoporosis has frequently used 18 F-NaF PET/CT quantitative analysis, where the most common region to obtain the IDAIF has been a TAC derived from the abdominal aorta feeding the nearby bone regions. However, use of the abdominal aorta for the AIF has some limitations: the AUC is underestimated when using the abdominal aorta TAC compared with direct arterial sampling [14] and the abdominal aorta is not always close to the bone-of-interest in a whole-body scan. In addition, the aorta is often calci ed and twisted in the elderly CKD-MBD population [18], which results in VOIs placed in the aorta being more sensitive to local variable ow patterns and thus local variations in radioactive concentration. In comparison, a VOI placed in the LV allows the de nition of large VOIs which will be much less sensitive to partial-volume-effects as well as local ow and radioactive concentration variations. Thus, the LV may provide the most universal activity pool for use with extended WB anatomical regions-of-interest studies. In the present study IDAIFs are obtained from LV TACs, but the results from AO TACs have also been measured for comparison with previous results. It was observed that LV VOIs performed better than VOIs placed in the AO.
The present study evaluates several different input functions (Fig. 5). All IDAIFs were converted to plasma activity using the average plasma to whole blood ratio found by venous blood sampling as described by Cook et al. [10]. In this present study, we nd the plasma/whole blood ratio to be slightly lower, where some of the difference may be explained by renal anemia in the CKD-MBD population. As we did not have arterial plasma samples, we were unable to correct for changes in the plasma/whole blood ratio over time as done by Cook et al. [10].
The recovery coe cient β was calculated to correct the IDAIF for PVE and spillover between activity in the lumen and background structures (βcorrected IDAIF). We found the variation of this β-coe cient to be slightly dependent on image quality but even more sensitive to blood sampling errors. Hence, optimal blood sampling is particularly important to obtain a reliable β-correction. The mean AUC of a β-corrected IDAIF has previously been shown to be comparable with the AUC from direct arterial sampling [14] and as such, the β-corrected IDAIF was chosen as our reference input function for comparison with results from other input functions.
The mean β-coe cient was lower (0.69 ± 0.15) when the IDAIFs were derived from the LV as compared with the AO (1.06 ± 0.44). These ndings suggest that β-correction is required with LV derived input functions, but not for AO input functions. The higher AO β-coe cient results from a low background activity and is found to be in the same range as previously published values for correction of AO (0.97 ± 0.54) [14].
The effect of applying the various corrections to the input curves has been compared. The mean AUC and mean peak-value were signi cantly lower for uncorrected IDAIF compared with β-corrected IDAIF (Table 2). Consequently, using an IDAIF without β-correction will result in higher K i -results (0.0480 ml min − 1 ml − 1 ) compared to results from a β-corrected IDAIF (K i = 0.0415 ml min − 1 ml − 1 ) as shown in Table 6. However, the results were not signi cantly different (p = 0.06).
β-corrected IDAIF combined with blood sample adjustment results in a slightly lower mean AUC than β-corrected IDAIFs alone. This difference is statistically signi cant when the 30-90 minute blood samples are used. Nevertheless, the difference seems to be in an acceptable range (Table 2).
Likewise, K i -results are higher when β-corrected IDAIFs adjusted by venous blood samples are used, compared to β-corrected IDAIF, as the input function. Again, a statistically signi cant difference is observed for the 30-90 minute blood samples with an acceptably low (1.5%) difference. The reason for this is possibly due to steady-state NaF distribution not being reached by 60 minutes, and thus we can expect slight differences between plasma curves tted to data at 60 minutes and 90 minutes.
To enable future sp-Patlak analysis of multiple bone regions from a single static WB scan, a SPIF combining population residual 2 (having lowest SD) and venous blood samples for an AIF was derived. Once more, the AUC is found to be slightly, but insigni cantly, lower than that of the β-corrected IDAIF AUC, resulting in higher K i -results (Table 6). Table 4 compares differences in mean AUC and mean peak-values when the rst and second exponentials are obtained from image-derived or population residual curves. AUCs show no statistically signi cant differences. This suggests it is feasible for a fully dynamic IDAIF to be replaced by a generalized SPIF for estimation of dynamic information in bone clearance studies, which is necessary for investigation of extended, multiple bone regions.
V 0 is observed to vary with the choice of input function and analysis model as shown in Table 6. Using the Hawkins compartmental model with βcorrected IDAIF gives a mean V 0 value of 0.51. Correspondingly a value of 0.39 is found for mp-Patlak analysis with the same input function, or 0.43 when the AO TAC, instead of the LV TAC, is applied for the β-corrected IDAIF. This AO value is comparable to the population value previously reported by Siddique et al [11] in a population of 10 women with osteoporosis. Additionally, when SPIFs are used for the mp-Patlak analysis, mean V 0 -values tend to be comparable or even higher. For sp-Patlak, Siddique et al have previously published a V 0 of 0.46 when using a SPIF [19].
The value of V 0 is known to be skeletal site, treatment and analysis model speci c [11,19,20]. However, K i estimates have been shown to be relatively independent of the choice of V 0 . A 20% difference in V 0 resulted in only a 5% change in K i [11], making the sp-Patlak analysis robust for clinical use, despite variability in the population V 0 -value.

Population residual curves
This study investigated three different population residual curves resulting in population residual 2, with the smallest variation, chosen for use in sp-Patlak analysis.
The standard deviation is generally high in all population residual curve models (Fig. 6). However, the coe cients of variation are only slightly higher at the peak than previously published data and lower at the third exponential [9]. In this study, the 18 F-NaF tracer was administered by manual bolus injection. It may be possible to produce a population residual curve with even more reduced variation through use of an automated injection system.

Skeletal plasma clearance
Greatest variability in the bone TACs occurs at initial uptake when the measured activity is low (Fig. 3), making it very di cult to accurately determine the exact time of arrival of tracer to the bone. As a consequence, attempts to correct for time delay failed to improve our data. Other published studies have used an average TAC over all vertebra to be investigated and longer time-bins for each frame, which will improve counting statistics but will lower the time resolution and as such may be counterproductive [11,12]. However, this problem did not affect the Patlak analysis, as the data was sampled at a later time between 14-60 minutes.
Hawkins model: Non-linear regression analysis The mean K i -value was 0.042 ± 0.01 ml min − 1 ml − 1 applying β-corrected IDAIFs in the Hawkins two-tissue compartment model ( Table 6).
The rst quantitative 18 F-NaF study evaluating kinetics in renal osteodystrophy, reported a mean K i -value of 0.071 ± 0.03 ml min − 1 ml − 1 [5]. A reason for such a high value may, in part, be that 72% of the population studied had untreated secondary hyperparathyroidism. Correspondingly, a new study by Aaltonen et al reported a mean value of 0.067 in dialysis patients with high turnover bone disease and 0.038 in dialysis patients with low turnover bone disease [17]. In comparison, our value of 0.042 ml min − 1 ml − 1 lies within the lower cut-off limit de ned in the Aaltonen study and above the value reported for two patients with hyperparathyroidism as found by Schiepers et al. (0.034 ml min − 1 ml − 1 ). Additionally, the latest study looking at K i related to Paget disease, has published a much higher mean value of 0.114 ml min − 1 ml − 1 [21].
Patlak: multiple-point graphical analysis This study nds a statistically signi cant correlation between the K i -values obtained using non-linear regression analysis and mp-Patlak analysis (R: 0.92, p-value: 0.001) (Fig. 7a), similar to previously published K i -values in a healthy female population and in a postmenopausal female population with osteoporosis [16,22].
The mean K i -value is 0.034 ± 0.01 ml min − 1 ml − 1 using β-corrected IDAIFs as input to the mp-Patlak analysis. This is similar to results published for a chronic dialysis population (L 1 − 4 ) with a mean value of 0.039 ml min − 1 ml − 1 and, as expected, higher than the mean value of 0.028 ml min − 1 ml − 1 found for a hemodialysis population with suspected adynamic bone disease (L 1 − 4 ) [17,23].
The mean K i -value is signi cantly lower when analyzed using the mp-Patlak method than with the Hawkins two-tissue compartmental model ( Table 6).
The mean average difference between K i -values for the two methods is 19% using β-corrected IDAIFs. This difference was reported to be 28.6% by Installé J. et al and 13% by Puri et al. [16,24].
Previously, it has been suggested that mp-Patlak results are lower than those derived from the Hawkins two-tissue compartmental model due to e ux of tracer from the bone during the scan. If such e ux is present, it may be corrected by the method described by Siddique et al [19]. Since additional investigation showed the Patlak data including later time-point data from the WB scans t very well to a straight line with regression coe cients close to 1, and taken together with k 4 -values ≤ 0.011, we found it unnecessary to correct for e ux in this study.
The mp-Patlak analysis has been reported to be superior to the Hawkins two-tissue compartmental model for research purposes; mp-Patlak analysis is computationally simpler and a lower number of participants are required to show a statistically signi cant result due to small precision error combined with a large treatment response [15,22] In addition, as the K i -values using the various input functions (Table 6) are not signi cantly different, our data strongly suggests that dynamic analysis using image derived input functions without blood sampling is feasible for clinical analysis, under the prerequisite that the scanner is accurately crosscalibrated.
Accordingly, we nd the mp-Patlak results in the present study to be very robust with no inter-observer signi cant difference (Table 7).
Patlak: single-point graphical analysis Using the sp-Patlak analysis with a SPIF as described above for the four vertebrae Th7-Th10 imaged in static WB scans, we found the K i -value to be 0.0395 ± 0.011 ml min − 1 ml − 1 . Unsurprisingly, the K i -result in the present study is higher than the K i -result from a previous published study in patients with suspected adynamic bone disease (0.028 ± 0.012 ml min − 1 ml − 1 ). For comparison, the K i -result in a study of patients with osteoporosis was in the lower range with a value of 0.025 ± 0.007 ml min − 1 ml − 1 [22,23].
Comparing K i -results from the sp-Patlak analysis with K i -results from the mp-Patlak analyses using the same input functions, resulted in 14% higher K iresults (p < 0.001). Despite this, the correlation between the methods is very good (R 2 = 0.942, P < 0.001). This however, emphasizes the importance of using the same analysis method when comparing results of tracer kinetic parameters.

Conclusion
Three different methods for analysis of skeletal plasma clearance in a population of CKD-MBD patients for both experimental and clinical use using 18 F-NaF PET/CT scan have successfully been implemented.
A dynamic scan protocol using the Hawkins two-tissue compartmental model with reliable mean K i -and K 1-4 -values has been established. As expected, the K i -values are lower using mp-Patlak analysis compared with Hawkins two-tissue compartmental model analysis.
A CKD-MBD population residual curve and SPIF have been developed for use with WB PET/CT scans, allowing site-speci c measurements of bone formation in multiple regions. Variation in a constructed population curve can be minimized using LV as IDAIF and with adjustment of individual peak Title: Flowchart of participant recruitment. Legend: Patients were additionally screened to participate in a bone biopsy as part of the complete study.
Concerns regarding the bone biopsy contributed largely to the large withdrawal of consent seen in this study.

Figure 3
Title: Example data curves obtained in the present study (participant no.32). Legend: 3a) Green line: plasma corrected image-derived AIF (IDAIF). Red line: The terminal exponential obtained from venous blood samples at 30, 40, 50 and 60 minutes. Blue line: β-corrected IDAIF. 3b) Bone TAC obtained from a VOI in vertebra Th7. Noise in the initial part of the curve is caused by low activity in the early time-frames of the study Figure 4 Title: PET-images from dynamic and WB 18F NaF PET/CT scans Legend: a) FOV from a dynamic 18F NaF PET/CT showing VOIs to obtain bone TACs in vertebrae th7-10 and a VOI in the left ventricle of the heart (LV) to obtain the image-derived input function. b) The whole-body 18F NaF PET/CT with the possibility to make bone VOIs in the entire skeleton. c) A VOI placed in LV and a myocardial VOI for β-correction Title: Various input functions Legend: a) Various estimates of the AIFs obtained from example participant (no. 32). b) X-axis is scaled for better visualization of the two rst exponentials. c) Y-axis is scaled for better visualization of the terminal exponentials Title: Population residual curves Legend: a) Population residuals 1-3 (red lines) ± 1SD (blue lines). All curves are normalized to a reference activity of 150 MBq. b) The corresponding population SDs (red lines) plotted as the percentage coe cient of variation obtained by dividing the SD by the population residual curve with 95% con dence intervals (blue lines) estimated using the chi² distribution