[¹⁸F]sodium fluoride [(¹⁸F)NaF] positron emission tomography (PET) imaging is a promising technique to study the role of bone metabolism in joint diseases such as osteoarthritis (1). [¹⁸F]NaF uptake is influenced by regional bone blood flow, or perfusion, and bone metabolism. Tracer uptake kinetics may be quantified using dynamic scans of up to 60 min or longer. The rate of fluoride clearance from plasma to the bone matrix (K_i) can be estimated using the graphical Patlak model (2) or using nonlinear regression based on the Hawkins two-tissue model (3). The Hawkins method can further be used to estimate bone perfusion (K₁) as well as the fraction of [¹⁸F] extracted into the bone where it binds to the bone matrix in newly formed hydroxyapatite crystals at sites of bone formation (4) [extraction fraction, or k₃/(k₂+ k₃)]. The Hawkins K_i has good reproducibility, with a precision error of less than 15% when calculated from 50 to 60 min of dynamic PET data (5–8). However, long scan times can result in increased motion artifacts, reduced throughput, and patient discomfort (9). Methods of accurately estimating [¹⁸F]NaF uptake kinetics from shorter acquisitions could help address these concerns.

Here, we examined the impact of shortening dynamic PET acquisition duration on kinetic [¹⁸F]NaF uptake parameters in the knee, hypothesizing that the scan duration could be shortened without impacting the accuracy of kinetic uptake parameters.

Across all bone regions and participants, the mean error of the Hawkins K_i, K₁, and extraction fraction, and the Patlak K_i, was less than 6% for all scan durations with respect to parameters calculated using 50 min of scan data. Representative Hawkins model fits used to estimate kinetic parameters for shortened scan durations are shown in Figure 3C. A summary of the volumes of each bone region and y-axis intercept values from Patlak analysis (V₀) are provided in the Supplemental Material. Mean and standard deviation in values and percent errors for Patlak K_i, Hawkins K_i, K₁, and extraction fraction are presented in Tables 1, 2 respectively. The standard deviation of the error was 15% or less for scan durations of 30 min or longer.

An example qDESS MRI and maximum intensity projection (MIP) PET images of tracer uptake at 30, 50, and 75 min depict an area of focally high tracer uptake in the patella at each timepoint for a healthy knee (Figure 4). For the three healthy subjects scanned for 75 min, the mean and standard deviation of the kinetic uptake parameters at 75 min were 0.0054 ± 0.0027 ml min⁻¹ml⁻¹ for Patlak K_i, 0.0067 ± 0.0032 ml min⁻¹ml⁻¹ for Hawkins K_i, 0.0095 ± 0.0048 for K₁ ml min⁻¹ ml⁻¹, and 0.745 ± 0.180 for extraction fraction. Errors in the estimation of kinetic parameters associated with using shortened scan durations compared to parameters calculated using 75 min of scan data as a reference are presented in Table 3. Negative values represent underestimations of uptake parameters relative to those calculated using 75 min of scan data. For scan durations 30 min or longer, the mean and standard deviation of the error was less than 15% for all parameters. The errors decreased with increasing scan duration.

Error in kinetic parameters grouped by [¹⁸F]NaF uptake rates is shown in Figure 5 and Table 4. There were 14 regions with high K_i, 144 regions with medium K_i, and 442 regions with low K_i. The mean error at 50 min is 0% since parameters derived from a 50-minute scan were used as a reference. The error decreased with increasing duration of the scan data used for fitting the models, and was less than 10% for high, medium, and low uptake rates when calculated using data with a duration of at least 30 min.

We examined the impact of shorter scan durations on estimating kinetic parameters, including Hawkins parameters for bone perfusion (K₁), extraction fraction [k₃/(k₂+ k₃)], and metabolism (K_i) from [¹⁸F]NaF uptake. Retrospectively shortening the duration of the time activity curve increased errors in K_i, K₁, and extraction fraction. Trends were similar between Hawkins and Patlak techniques, though the Patlak K_i was associated with lower variability and the parameter V₀ from the graphical Patlak analysis increased in a linear fashion as scan time decreased. The mean error in Hawkins uptake parameters were, however, less than 10% for scan durations exceeding 30 min for regions with high and low uptake. Errors in kinetic uptake parameters were comparable between Hawkins and Patlak models.

Conventional techniques for kinetic quantification using [¹⁸F]NaF require data from a 60-minute dynamic scan (23). Precision error using the 60-minute scans are reported to range from 13.9–14.5% for Hawkins K_i and 11.7–13.5% for Patlak K_i (6, 7). The precision error metric from reproducibility studies, defined as the percentage of the standard deviation divided by the mean from two repeated PET scans (6), is comparable to the standard deviation of the percent error between abbreviated and full-length scans used in this study. For scan durations of 30 min or longer, the standard deviations in the error were within previously reported ranges for precision error at 60 min (23) for all kinetic uptake parameters. Further, the errors in parametric values with shortened scan durations are similar to prior literature on new techniques for quantifying [¹⁸F]NaF uptake rates from shorter acquisitions (22), including from a 12-minute dynamic scan using a Hawkins model with fixed rate constants (24). With the 12-minute technique, the Hawkins K_i had an equivalent or superior statistical power compared to the conventional scan in an osteoporotic population. However, with fixed rate constants, K₁ values were in a fixed ratio to K_i and did not represent true measurements of bone blood flow. In the current study, both K_i and associated Hawkins rate constants were freely fitted to available scan data, which may be more widely applicable to a variety of conditions where bone metabolism may vary.

Although studies typically use scan times of around an hour, increased scanning time, such as in the 75-minute datasets in the present study, give similar results. Kinetic uptake parameters for all abbreviated scan durations were within 5% of values calculated from 50 min of scan data and within 12% of values calculated from 75 min of scan data; for both, errors were within 5% for scan durations exceeding 30 min. PET images show similar patterns of tracer uptake at 30, 50, and 75 min. At 30 min, it can be assumed that circulating venous and arterial [¹⁸F]NaF have reached equilibrium (25). A 30-minute scan may thus represent a reasonable lower limit for abbreviated dynamic acquisitions without appreciable impacts on parametric values. Introducing errors on the order of 5% from shorter acquisitions may be an acceptable compromise to reduce overall study time and motion artifacts for exercise studies, for example, where relative changes in kinetic uptake parameters on the order of 25%–180% have been observed (26).

SUV, K_i, and K₁ have been observed to be elevated in osteoarthritic knees compared to healthy ones (1), although areas of high uptake may occur in non-osteoarthritic knees (27) and after exercise in healthy knees (26). To account for the variable uptake levels that may be found within a given knee or in situations like loading that induce high tracer uptake, differences in errors at each scan duration were examined according to tracer uptake levels. The overall error in uptake parameters decreased with increasing scan durations but was variable between bone regions with high or low uptake rates. Bone regions with moderate to high uptake rates had higher SNR contributing to lower error in K₁ with shorter scan durations but larger errors in the extraction fraction. Extraction fraction is generally associated with greater variability than K₁ due to greater uncertainties in estimating rate constants k₂ and k₃ (28). Additionally, extraction fraction in bone regions with moderate-high uptake is more variable than in bone regions with low uptake, as observed in prior work in an osteoarthritic population and exercise studies where high uptake rates were associated with [¹⁸F] delivery that outpaced clearance (1, 26, 29). Errors in kinetic parameters calculated with reference to a 75-minute PET acquisition followed similar trends. Shortening the scan duration to 30 min was sufficient to estimate kinetic parameters within 10% of parameters calculated using 50 and 75 min of scan data. Using shorter scans with fewer time points or shorter frames does change the calculus regarding signal to noise. Although regions of interest within the knee are small curved shapes where smaller voxels are advantageous for segmentation and contrast recovery (30, 31), the combined signal to noise of the volume does need to be sufficient for fitting parameters requiring an optimization of frame time, number of frames and voxel size.

One limitation of this work was the variability in the number of regions with different K_i values in this population including osteoarthritic knees. The selection of K_i ranges was based on prior work in an osteoarthritic population (1), but there were fewer bone regions with high K_i compared to regions with low K_i, which may have impacted the observed differences in mean error between groups. While it is a heterogeneous sample, the division of results by bone regions with different uptake rates attempted to represent regional and metabolic variability associated with disease and associated impacts on errors observed in shortened scans. Regions of low and high bone metabolism can be found in knees with conditions affecting bone metabolism such as osteoarthritis, so it is important to consider this variability when using abbreviated protocols. Another limitation was that only three datasets with 75 min of data were used to compare errors against datasets with 50–60 min of data. This data was used as a proof of concept to demonstrate that results were not noticeably different when longer duration scans were used as a reference. Additionally, k-loss due to k₄ was not assessed for longer scan times. As assessed by Siddique et al., k-loss due to k₄ can introduce errors underestimating K_i by approximately 20% after 2 h (32). However, in this dataset only three participants were scanned for longer than 50 min and, for these three datasets, the scan time was only 75 min which is a short time frame compared to the 120 min used previously to determine K_i loss. Moreover, we aimed to focus our analysis on the shorter scan durations, where k₄ is small (∼0.01/min) and is commonly considered negligible. Bone was not considered in the attenuation correction technique and while this may affect the accuracy of quantifying tracer uptake, this would have a similar impact at all durations studied. The same image-derived input function was used for the arterial input function (14, 15) for all retrospectively time-under sampled pharmacokinetic model fitting. Multiple plasma blood measurements were not used for validation; however, this technique has previously shown good reproducibility (14, 15). Minor discrepancies observed between the IDIF and artery TAC following peak tracer delivery may be attributed to a known bias where the IDIF underestimates measures on the order of 2%–5% (15) or may possibly reflect tracer uptake in arterial walls. Alternative input functions were beyond the scope of this work and were not explored. Finally, a limitation of techniques incorporating shorter acquisitions is that SUV will be lower with shorter uptake times. SUV could still be incorporated in population studies with shorter protocols as a relative measure compared to background uptake by standardizing the duration and starting time for SUV measurements across scans.

Overall, we observed that the duration of the dynamic [¹⁸F]NaF PET scan can be reduced while maintaining low errors in bone perfusion (K₁) and metabolism (K_i) estimation from the Hawkins model. Shorter dynamic [¹⁸F]NaF PET scans, potentially as short as 30 min, could be used without appreciable error in Hawkins uptake parameters in bone regions with both low and high tracer uptake.