Methods for assessing skeletal health that can replace the gold standard bone biopsy are sorely needed in the clinical CKD-MBD setting; for example, effective bone treatment may be withheld if a patient is suspected of having adynamic bone disease. Access to non-invasive diagnostic methods to confirm or negate this would be an important clinical gain. The present study implements both dynamic and static 18F-NaF PET/CT imaging using various analysis methods: nonlinear regression, Patlak analysis, static graphical analysis and construction of a representative CKD-MBD SPIF.
All presented methods are found suitable for bone plasma clearance evaluation; still, the simplified static graphical analysis was found to be preferable for implementation in clinical practice due to its short time scan and its ability to examine multiple bone regions using a single tracer injection, compared to the limitation of a single FOV with dynamic acquisition. We found no difference in Ki results obtained by dynamic nonlinear regression or static scan analysis. Static WB 18F-NaF PET/CT allows a relatively easy clinical assessment of skeletal variables in CKD-MBD.
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 were mostly males (70%), and diabetic nephropathy was the most common cause of kidney failure (29%). Previous studies using
18F-NaF PET/CT for dynamic bone examination have been mostly carried out on female osteoporotic patients and excluded patients with CKD [
12,
15]. 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%) [
16].
In the present study, we evaluate different input functions. The mean AUC of a β-corrected IDAIF has previously been shown to be comparable with the AUC from direct arterial sampling [
13], and as such, the β-corrected IDAIF was chosen as our reference input function for comparison with results from other input functions. 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 find the plasma/whole blood ratio to be slightly lower. Some of the difference may be explained by renal anaemia in the CKD-MBD population. As we did not have blood samples in the time period of 0–30 min, we were unable to correct for changes in the plasma/whole blood ratio over time as done by Cook et al. [
10]. Additionally we found no time dependence of the ratio over the considered time window, as well as a low inter-subject variability, indicating that a single value of 1.17 may be used for data correction in future scans.
The recovery coefficient
β was calculated to correct the IDAIF for the combined effects of counting efficiency, PVE and spillover/spill-in of activity between activity in the lumen and background structures. We found the variation of this
β-coefficient to be dependent on image quality and blood sampling errors. Hence, optimal blood sampling is particularly important to obtain a reliable
β-correction. The present study found a much lower
β-coefficient (0.69 ± 0.15) than previously published mean
β-coefficient values (0.97 ± 0.54) in which the aorta was used for derivation of input functions [
13]. The reason for this is most probably our use of a large VOI (~ 20 cm
3) to define the LV input function with a representative sample of the inhomogeneous activity, as a VOI with borders close to the myocardial wall (3–6 mm separation) is subject to PVE and spillover of activity in combination with myocardial movement (5–8 mm motion) as reported by Cho et al., thus exposing it to activity in the myocardial wall [
17]. In future studies, this should be remedied by use of a smaller VOI placed in the middle of the LV, which is less subject to PVE and spillover but, on the other hand, more dependent on correct placement around the highest voxel in the inhomogeneous distributed activity. In spite of this, as long as the (local) quantitatively correct
β-correction value is used for the applied analysis protocol and imaging scanner, the
β-correction method is shown to define the AUC of the IDAIF as well as with direct arterial sampling [
15]. This is to be expected as the level of the terminal exponential of the input function is shown to account for 75% of the AUC of the input function in the first 60 min [
9]. Thus, a precise correction of the terminal exponential of the IDAIF is of high interest.
To enable future static scan analysis of multiple bone regions, a SPIF was derived combining the population residual curve and venous blood samples to produce an AIF. No difference was found between AUCs of the SPIFs compared with AUCs of the IDAIFs (Table
3). This suggests that 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 (Fig.
4C).
V0 is observed to vary with the choice of input function as shown in Table
5. Our Patlak analysis yields a mean
V0 value of 0.39 ± 0.17 when IDAIF is applied as input function. This value is comparable to the population value of 0.43 previously reported by Siddique et al. [
11] in a population of ten women with osteoporosis. However, when SPIFs are used as input function for Patlak analysis, mean V
0 values tend to be higher. For static analysis, Siddique et al. have previously published a
V0 of 0.46 when using a SPIF [
18]. Thus, our values are in the same range as previously published values.
The value of
V0 is known to be specific to the skeletal site, treatment and analysis model [
11,
18,
19]. However,
Ki estimates have been shown to be relatively independent of the choice of
V0. A 20% difference in
V0 resulted in only a 5% change in
Ki [
11], making the static analysis robust for clinical use despite variability in the population
V0 value.
The rationale for using an average population curve calibrated by the individual patient’s plasma activity is the assumption that the shape of each patient's input curves is similar, but the actual plasma values may differ due to, for example, disease or treatment of the disease [
12]. The authors show standard uptake value (SUV) analysis is less sensitive to changes in actual bone metabolism as negative changes in arterial activity may almost cancel out positive changes in bone uptake due to treatment in the calculation of SUV, as well as being dependent on factors other than bone uptake (e.g. renal clearance). Previously, two methods have been applied to relate bone uptake to actual plasma activity: either by using the fractional uptake rate (FUR), which is comparable to the standard uptake ratio used in studies of glucose metabolism, or by using a SPIF as in the present study [
9,
16,
20]. Furthermore, using a SPIF, instead of a fully obtained IDAIF for each examination, can reduce the effective scan time remarkably.
The standard deviation is generally high in the obtained population residual curve (Fig.
6). The highest SD was at the peak time of the population residual curve with a SD of 30% (95% CI 21–52%) and an average SD of the entire curve of 15.8%. These SDs are comparable with the values of 26.4% (19.0–42.3%) previously published by Blake et al. [
9]. However, in the present study, the
18F-NaF tracer was administered by manual bolus injection. It may be possible to produce a population residual curve with less variation using an automated injection system.
In the present study, time adjustment to the common peak position of the residual curves to make the average population curve was performed by time shifting the curves so that the frames with maximum activity coincide. This could be suboptimal since the temporal sampling is low and the actual peak position does not coincide with the exact frame position having the maximum activity, potentially resulting in an artificial elevation of the averaged peak. However, the actual peak value of the input function seems to have little importance when calculating Ki, which is instead highly dependent on a reliable input function AUC. The semi-population residual curves and IDAIF show similar AUCs.
Overall, we found the CKD-MBD population residual curve comparable with the previously published population residual curve for osteoporotic patients.
Bone plasma clearance
The greatest variability in the bone TACs occurs in the initial portion of the curves due to a combination of initial low activity and short time frames (Fig.
5B). Other published studies have used an average TAC over all the vertebra to be investigated with longer time bins for each frame; this improves counting statistics but lowers the time resolution and may, as such, be counterproductive [
11,
12]. However, this problem does not affect Patlak analysis, as the data are sampled at later time points between 14 and 60 min.
Nonlinear regression analysis
The mean
Ki value was 0.042 ± 0.01 ml min
−1 ml
−1 applying IDAIFs in a two-tissue compartment model (Table
5).
The first quantitative
18F-NaF study evaluating kinetics in renal osteodystrophy reported a mean
Ki value of 0.071 ± 0.03 ml min
−1 ml
−1 [
5]. The reason for this high value may 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 [
16].
In comparison, our value of 0.042 ml min
−1 ml
−1 lies within the lower cutoff limit defined 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, which studied
Ki related to Paget disease, published a much higher mean value of 0.114 ml min
−1 ml
−1 [
21].
Patlak analysis
The present study found a statistically significant correlation between the
Ki values obtained using nonlinear regression analysis and Patlak analysis (
R: 0.92,
p value: 0.001) (Fig.
8A), as for previously published values in a healthy female population and a postmenopausal female population with osteoporosis [
15,
22].
The mean
Ki value was 0.034 ± 0.01 ml min
−1 ml
−1 using IDAIFs as input to the Patlak analysis. This is comparable to results published for a chronic dialysis population (
L1–4) with a mean value of 0.039 ml min
−1 ml
−1, and as expected, it is higher than the mean value of 0.028 ml min
−1 ml
−1 found for a haemodialysis population with suspected adynamic bone disease (
L1–4) [
16,
23].
The mean
Ki value was significantly lower when analysed using the Patlak analysis than with nonlinear regression analysis (Table
5). The average paired difference between
Ki values for the two methods is − 17.4 ± 10%. This difference varies and was previously reported to be − 7% by Brenner et al., − 13% by Installé et al. and − 23.7% by Puri et al. [
14,
15,
24].
It has been suggested that Patlak analysis results are lower than those derived from the two-tissue compartment model due to efflux of tracer from the bone during the scan. In previous studies, the Patlak plots often showed a small but obvious curvature with the slope decreasing slightly as time advanced, which has been related to tracer efflux. If such efflux is present, it may be corrected by the method described by Siddique et al. [
18].
However, in the present study this curvature of the Patlak plot was barely visible and all plots fitted very well to a straight line with regression coefficients close to 1 (Fig.
7). Combined with the small
k4 values of 0.005 with a high standard deviation of ± 0.005, a small tracer efflux can only partly explain the discrepancy between our NLR and Patlak results and we found it disproportionate to correct for such a small efflux in this study.
The Patlak analysis has been reported to be superior to the two-tissue compartment model for research purposes as it is computationally simpler and requires a lower number of participants to show a statistically significant result due to its small precision error [
14,
22].
Static scan analysis
Using the static scan analysis with a SPIF as described above for the four vertebrae Th7–Th10 imaged in WB scans, we found the
Ki value to be 0.0395 ± 0.011 ml min
−1 ml
−1. Thus, no difference was found between the static
Ki results and the dynamic
Ki results obtained by linear regression. Unsurprisingly, the
Ki result in the present study was higher than the
Ki 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
Ki 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].
In the present study, comparing Ki results from the static scan analysis with Ki results from the Patlak analyses using the same input functions resulted in 14% lower Ki results (p < 0.001) than with the static Ki results. Despite this, the correlation between the methods is very good (R2 = 0.942, p < 0.001). However, this emphasizes the importance of using the same analysis method when comparing results of tracer kinetic parameters.
The calculation of Ki in the static scan analysis is dependent on an accurate estimate of the blood/plasma activity at the same time point as which the bone region in question is scanned during the WB acquisition. Neither in the present 18F-NaF study, nor in future studies, would we want to exceed a study period of 90 min for the WB scan. However, as we included a venous sample taken immediately after the WB examination (90 < t < 100 min, where “t” is the time for scanning the bone region in question as obtained from the PMOD analysis tool (see “Methods”), we were able to use a less error prone interpolation, rather than an extrapolation of data, to obtain Cpl(t)/AUC(t) values for calculation of the Ki value in the study interval between 60 and 90–100 min: We chose to use a standard mono-exponential fit of the terminal data at 40, 50, 60 and 90–100 mpi for interpolation.
However, we could just as well have used a hyperbolic fit of all curve data from 1 mpi and later, providing an even better fit as shown by van den Hoff et al. [
25]. This method might be especially important if one is required to extrapolate to data values later than 60 mpi without the benefit of later blood samples.
Limitations of the study
The limitations of the present study include not having AIF data from direct arterial sampling as a gold standard to evaluate the validity of the IDAIFs and SPIFs; however, as described above, venous blood samples can complement the arterial sampling curve at least after 30 min [
10]. Additionally, the averaging of the residual curves for construction of a population residual curve presented here is not optimal and should be refined in future studies.
In this study design, the static scan sequentially followed a 60-min dynamic scan with the static scan analysis including a 90-min blood sample for construction of an input function ending at time point 90–100 mpi. For this reason, even a small efflux might influence the Patlak plot/static scan analysis presented here, and correction for efflux may be necessary. Thus, in order to minimize effects of possible efflux, our recommendation would be to make the static scan between 30 and 60 min after tracer injection in future studies.
Dynamic scanning in the clinical setting is generally restricted to a single bed position but may change in the future with the advent of new dynamic total body PET scanning combining an initial, short-duration dynamic acquisition over the heart followed by a series of fast, multiple whole-body scans. However, a low, effective scan time ensured by a SPIF and acquisition of a simple static scan may still be a valuable tool with the use of older scanners. Furthermore, a short effective scan time is important in the very sick CKD-MBD population to enable successful completion of an entire WB scan or the static scan time can be reduced to about 5–10 min if only a single bone region, e.g. the lumbar vertebrae, needs to be examined.