Comparison of Different Quantitative Approaches to ¹⁸F-Fluoride PET Scans

MATERIALS AND METHODS

Data Analysis

PET data were analyzed by an ROI approach. Tissue time–activity curves of the graft, the contralateral normal bone, and a thoracic vertebra, if the spine was within the field of view, were generated from the ROI for each image in the dynamic dataset. These data were processed using 3 different techniques: NLR and Patlak graphical analysis, both based on a 3-compartment model, and SUV calculation.

ROIs.

The 30- to 60-min summed images were used to guide ROI placement. Circular or elliptic ROIs, ranging in size from 9 to 30 pixels equaling 1.3–4.4 cm², were placed over the contact zone between the graft and the original bone, including the area with maximum counts (Fig. 2). Each ROI was applied to 3–6 contiguous planes in each frame, creating a volume of interest (VOI). These VOIs limited to a maximum of 6 planes were chosen because we pose that the contact zone with the area of maximum counts reflects graft healing better than a VOI covering the whole graft, which is often a heterogeneous and large area that cannot be completely included within a single tomographic field of view. A same-size VOI was used on the contralateral side as a reference volume for normal bone tissue. For the thoracic vertebrae, VOIs consisting of 3 contiguous planes were created with the ROIs covering the center of the vertebra in each plane. Tissue time–activity curves for all regions were generated from application of the VOIs to the whole dynamic image set. The same VOIs were used for calculating SUV.

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FIGURE 2.

Diagram of ROI placement over femoral graft and contralateral normal femur.

SUV.

SUV was calculated according to the formula: Eq. 1 where A is the mean tissue activity (μCi/mL or μCi/g) within the VOI in summed images from 30 to 60 min of the dynamic dataset, ID is the injected dose (mCi), and m is the patient body weight (kg).

Patlak Analysis.

The fluoride bone influx rate was calculated using graphical analysis (15,16) for a 3-compartment model as described by Hawkins et al. (2). In Patlak analysis, the fluoride bone influx rate K_Pat is determined by the following equation: Eq. 2 where C_t(t) is the tissue activity concentration (μCi/mL) at time t measured using the ROI approach, C_b(t) is the blood concentration of tracer (μCi/mL), and V is the effective distribution volume of the tracer (mL/mL). K_Pat (mL/min/mL; since bone density is different from 1 mg/mL and varies within bones, values are given per milliliter of bone volume instead of per milligram of bone) is the net uptake of fluoride in bone tissue assuming that fluoride in the bound compartment is irreversibly bound to the bones (k₄ = 0). K_Pat is obtained from the slope of the linear part of the fit of C_t(t)/C_b(t) versus [∫₀^t C_b(t)dt]/C_b(t).

The period before equilibrium of the blood and the exchangeable compartment is characterized as an initial period of curvature before the linear part of the fit. Using the complete dynamic dataset, the linear portion of the curve was observed in almost all patients from 10 to 50 min after injection. These times or, if necessary, individually adjusted times were used as the boundaries for the graphical fit to estimate K_Pat. In performing the fit, the time for each point in the tissue time–activity curve was taken as the center of the time bin. Matched time points in C_b(t) were obtained using linear interpolation between neighboring time points in the measured blood curve.

NLR Analysis.

NLR was performed on the basis of a 3-compartment model consisting of the plasma space, an unbound bone compartment, and a bound bone compartment (Fig. 1) as described by Hawkins et al. (2). The rate constants K₁ to k₄ describe the transport of fluoride between the compartments: K₁ and k₂ for the forward and reverse transport from plasma to the interstitial unbound bone compartment, k₃ for binding to bone apatite, and k₄ for release from the mineral bone compartment. A fifth parameter for the fractional blood volume (fBV) was included to account for the contribution of tracer remaining in the vascular space to the measured tissue data. The delay between tracer injection and tracer accumulation in the bone tissue was estimated by χ² fitting in each patient and for each region separately. The blood input function and the time–activity curve data were fitted to this compartment model using a NLR algorithm (PMOD 2.00; PMOD Group, University Hospital Zurich, Zurich, Switzerland) to estimate the kinetic parameters K₁ to k₄ and fBV. For both fBV and K₁–k₃, a parameter range from 0 to 1 was applied, whereas k₄ was constrained to 0–0.1 min⁻¹. Parameter starting conditions for the fit were 0.1 mL/mL, 0.1 mL/min/mL, 0.15 min⁻¹, 0.1 min⁻¹, and 0.01 min⁻¹ for fBV, K₁, k₂, k₃, and k₄, respectively. The fluoride bone influx rate K_NLR (mL/min/mL) is the net forward transport parameter and was calculated as: Eq. 3

RESULTS

Metabolic measures for ¹⁸F-fluoride were obtained in a total of 98 bone sites (42 grafts, 42 normal bone sites of the contralateral limb, and 14 thoracic vertebrae). Results covered a wide range of normal and pathologic values from 0.4 to 9.9, 0.0035 to 0.0742 mL/min/mL, and 0.0027 to 0.0737 mL/min/mL for SUV, Patlak analysis, and NLR, respectively (Table 1). For the relationship between Patlak and NLR, a high linear correlation coefficient of r = 0.99 was calculated for the whole range of values, irrespective of the bone site (Fig. 3). Significant positive linear correlations were also found for SUV and Patlak and SUV and NLR (Figs. 4 and 5).

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FIGURE 3.

Positive linear correlation of K_Pat (mL/min/mL) and K_NLR (mL/min/mL) for ¹⁸F-fluoride (K_NLR = 1.0731 K_Pat; r = 0.99; P < 0.01).

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FIGURE 4.

Positive linear correlation of SUV and K_Pat (mL/min/mL) for ¹⁸F-fluoride (K_Pat = 0.0065 SUV; r = 0.95; P < 0.01).

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FIGURE 5.

Positive linear correlation of SUV and K_NLR (mL/min/mL) for ¹⁸F-fluoride (K_NLR = 0.0070 SUV; r = 0.93; P < 0.01).

In bone grafts, SUV was 5.3 ± 2.2, K_Pat was 0.0346 ± 0.0157 mL/min/mL, and K_NLR results were almost identical with 0.0370 ± 0.0165 mL/min/mL (Table 1). Nine patients have been imaged twice at approximately 6 and 12 mo after surgery. During this time period, a decrease of the metabolic bone activity was observed for all 3 parameters in 5 patients with cancellous chip grafts, whereas in 4 patients with full bone grafts the values of these parameters increased (Table 2). The changes of SUV and Patlak, and of SUV and NLR were correlated in a statistically significant positive linear manner (Table 2). The changes measured by Patlak and NLR were also highly correlated (r = 0.96).

In 14 scans of patients with humerus grafts, the thoracic spine was within the dynamic field of view, allowing calculation of metabolic activity in a vertebra. The mean values for SUV, Patlak, and NLR were 5.9 ± 1.0, 0.0387 ± 0.0069 mL/min/mL, and 0.0429 ± 0.0085 mL/min/mL, respectively (Table 1). In 3 patients imaged twice within 6 mo, metabolic measures for the thoracic spine, irrespective of the calculation method, showed no major changes over time. The relative differences between 2 measurements were 4.3% ± 4.3% for SUV, 6.5% ± 3.8% for Patlak, and 9.0% ± 9.8% for NLR, resulting in within-subjects coefficients of variation of 8.8%, 13.5%, and 13.9%, respectively. The 95% ranges of normal change were ±8.6%, ±7.6%, and ±19.6% for SUV, Patlak, and NLR, respectively.

The contralateral site of the graft was chosen in each patient as the reference normal value for the respective bone. Results for all 3 parameters are summarized in Table 3. Most of the imaged areas were either in the femur, the humerus, or the tibia. ANOVA showed significant differences between these 3 locations for SUV, Patlak, and NLR. The mean metabolic values for the humerus were significantly lower than those in the femur or the tibia for all 3 quantitation methods, whereas no significant differences were found between the femur and the tibia (Table 3). Metabolic values of all limb bones, irrespective of their location, were significantly lower than the values of the thoracic spine (Table 1). For 9 patients imaged twice, the relative changes in normal bones between 2 measurements are summarized in Table 4. The within-subjects coefficients of variation were 75.0% for SUV, 79.0% for K_Pat, and 82.5% for K_NLR; the corresponding 95% ranges of normal change were ±57.2%, ±27.6%, and ±28.8%. After exclusion of 1 patient who was imaged the second time 30 mo after the first PET scan, the respective 95% ranges of normal change within 6 mo were ±58.0%, ±23.0%, and ±20.2%. ANOVA showed no significant differences between the 3 calculation methods. Differences between 2 measurements were evenly scattered, both in the negative and in the positive direction, with a positive linear correlation between SUV and Patlak and between Patlak and NLR (Table 4). In only 1 patient, a discrepancy between the different methods was found with a decreasing K_NLR on the second scan while both SUV and K_Pat increased.

DISCUSSION

In a recent report by Cook et al. on skeletal kinetics measured by ¹⁸F-fluoride PET, the authors demanded further studies on computationally simplier methods such as SUV and Patlak graphical analysis to see whether these methods are as robust as NLR analysis (8). According to our knowledge, however, there are no publications applying SUV as the most simple semiquantitative measure for bone metabolism in ¹⁸F-fluoride PET.

Imaging patients who had undergone resection of bony tumors of the limbs followed by bone grafting allowed us to calculate SUV and fluoride flux constants based on Patlak and NLR analysis that covered a wide range of pathologic as well as normal bone conditions of the contralateral side. K_NLR ranged from 0.0027 to 0.0737 mL/min/mL. ¹⁸F-fluoride flux values obtained by Patlak analysis were almost identical with a highly significant positive linear correlation (Fig. 3). K_NLR values were higher than K_Pat values in most patients, as already reported in literature (2,10,11). The mean difference between K_NLR and K_Pat was 7% in our study with a slope of 1.07 for the regression line. Beside other factors based on the fitting model, such as inclusion of fBV or other correction parameters, the reason for the difference is that Patlak graphical analysis does not account for the release of ¹⁸F-fluoride from the bones represented by the kinetic rate constant k₄, which was greater than zero in almost all our patients (range, 0–0.0256 min⁻¹). Therefore, the net forward constant K_NLR is expected to be higher than any net forward parameter obviating k₄ effects such as the Patlak approach. The difference between NLR and Patlak fluxes should increase with k₄ contribution. Accordingly, the mean difference between Patlak and NLR was the highest in the spine and in high-uptake grafts that also showed the highest k₄ values of all bones (data not shown).

Clinically more important is the fact that in 9 patients imaged twice, usually at 6 and 12 mo after surgery, the changes in graft metabolic values showed a strong correlation between NLR and Patlak analysis, with a correlation coefficient of 0.96. Changes of K_Pat values paralleled changes of K_NLR in all grafts (Table 2), suggesting that K_Pat is as clinically useful as K_NLR for assessing changes in bone metabolism in terms of fluoride bone influx rates. However, NLR also estimates the rate constants K₁ to k₄, information that cannot be provided by Patlak analysis. K₁, for example, is the product of regional blood flow and the extraction fraction of fluoride ion, which can be used as an indirect measure to estimate bone blood flow (10,12,17). Whether these rate constants contain relevant or even essential clinical information is not yet clear. Further studies on normal and complicated bone graft healing with repeated imaging up to 24 mo after surgery will show the clinical significance of the different methods and parameters.

For SUV, we found a similar strong positive linear correlation with NLR (r = 0.93). For any clinical application of SUV as an easy-to-obtain substitute for NLR or Patlak analysis, not only a close correlation of SUV and NLR values is necessary, but even more the correlation of changes in patients imaged repeatedly. In 9 grafts imaged twice, the percentage change of metabolic values was significantly correlated between SUV and NLR. In all patients with an increase of K_NLR, SUV increased as well, whereas in all patients with decreasing K_NLR this decrease was paralleled by SUV (Table 2). Similar findings were obtained for the changes observed in normal limb bones (Table 4) and in the thoracic spine. In 3 patients, the spine was imaged twice, and changes in K_NLR were paralleled by changes in SUV in all cases. The same was found for normal bone values. Only in 1 of 9 patients, NLR indicated a decrease of the metabolic activity while SUV increased. In this patient Patlak analysis also indicated an increasing metabolic bone activity while NLR was the only parameter revealing a decrease. The reason for this discordance was a nonoptimal fit in the NLR approach due to a low-peaking and widened blood input function in the second study. During the fitting process, k₄ hit the parameter limits and went to zero, which resulted in a lower K_NLR compared with the first study, indicating a decrease in metabolic activity over time. This shows the pitfalls of NLR with its susceptibility to noise in the data and to parameter constraints, whereas SUV as a static parameter and the more robust linear regression approach of Patlak analysis are not affected, or only little affected, by improper input functions.

For any quantitation method, reproducibility of measurements and normal fluctuations of the respective parameter over time are of special interest. Repeated dynamic PET imaging and measurements of bone metabolic parameters within a few days would be necessary to assess the reliability of measurements. Since this is not easy to achieve for radiation safety reasons, and since changes in bone metabolism are usually monitored within an interval of several months, we calculated relative changes in normal bones within 6 mo to assess the constancy of ¹⁸F-fluoride bone metabolism. For this reason we compared the results obtained in 8 contralateral normal limb bones and 3 thoracic vertebrae in 8 patients imaged twice within 5–7 mo. In these patients, no bone metabolic relevant treatment was performed between the 2 scans. In the spine, we found a within-subjects coefficient of variation ranging from 8.8% for SUV to 13.9% for NLR. The 95% range of normal change—that is, the range of spontaneous bone metabolic fluctuations—was ±8.6% for SUV, ±7.6% for K_Pat, and ±19.6% for K_NLR. This means, that changes of >20% within 6 mo would be outside the 95% range of normal change in the spine and could be considered true changes in bone metabolic activity. However, the magnitude of relative changes depends on the initial value of the parameter. For normal limb bones we observed much lower metabolic values for all 3 parameters. The 95% range of normal change within 6 mo was ±58.0% for SUV, ±23.0% for Patlak, and ±20.2% for NLR. Thus, in limb bones, changes of >25% within 6 mo could be considered true changes in the case of K_Pat and K_NLR, whereas for SUV changes of at least 50% would be required in limb bones to be judged as true changes in metabolic activity. These findings suggest that metabolic changes indicated by SUV in normal-to high-uptake areas such as the spine have clinical importance similar to the changes observed by K_NLR. The limitations of SUV, however, become eminent in low-uptake areas, where a relatively greater fraction of the measured activity within the ROI is due to blood activity and unbound ¹⁸F-fluoride and, thus, subject to non–bone-related effects that increase the variability in repeated measurements. Such effects have already been described for ¹⁸F-FDG (18).

It is important to keep in mind that our data on repeated measurements are not estimates for the mere methodologic reproducibility of the different methods comparing 2 single measurements within a few days—and, thus under almost identical conditions—but also reflect normal fluctuations in bone metabolism within a time period of 5–7 mo. Furthermore, the 95% ranges of normal change provided in this study represent only rough estimates based on repeated measurements in 3 vertebrae and 8 limb bones. In the current ¹⁸F-fluoride literature there are no patient data for comparison. Only Piert et al. (12) reported on phantom measurements for the hip with ¹⁸F-fluoride, in which they found coefficients of variation increasing from 5% to 16% with decreasing activities. These values are in a range similar to our values for the spine, and they confirm the observation of higher coefficients of variation with decreasing ¹⁸F-fluoride activity—that is, lower metabolic values. Similar findings were reported by Weber et al. for ¹⁸F-FDG PET. In patients without treatment, changes in SUV of >20% were outside the 95% range of spontaneous normal change for a mean SUV of 5 (comparable to our values of spine and grafts), whereas for lower SUV a sharp incline of the 95% range up to ±50% and more for SUV values < 1.5 (comparable to our values of normal bones) was observed (19).

Whether the findings for normal changes of bone metabolic activity in limb bones are also applicable in limb grafts is not yet clear. Grafts usually had a much higher initial metabolic activity than limb bones, with the mean graft values of SUV, Patlak, and NLR quite similar to those of the spine. Thus, coefficients of variation in grafts may be comparable to the spine rather than to limb bones. According to the findings in the spine, a 20% change of metabolic bone activity might be indicative of true changes in graft metabolism.

Although venous blood sampling tends to overestimate fluoride bone flux by approximately 5% due to a systematic underestimation of blood activity (20), mean Patlak and NLR flux values of the thoracic spine were exactly within the range reported in the literature (8,10). For limb bones we found significantly lower values than those for the spine (Table 1). For all 3 metabolic parameters, mean values of the humerus, tibia, and femur were only about 15%–25% of the values of the spine. This primarily reflects bone physiology: Since bone turnover in cortical bones is much lower than that in trabecular bones, fluoride uptake values are expected to be low in limb bones due to their relative small portion of trabecular bone (21,22). This will be even more pronounced in the predominantly cortical shaft section of limb bones (23), as measured in our patients in whom the ROIs were usually placed at the midbone end of the graft and the respective location on the contralateral normal side. However, to some extent, partial-volume effects also account for the low values in the limb bones since we did not correct for these effects. According to the partial-volume recovery data of our PET scanner, object or ROI sizes of >1.3 cm, as used in this study, result in a recovery coefficient of ≥60% (unpublished data).

CONCLUSION

¹⁸F-Fluoride bone metabolic values and percentage changes over time, obtained by SUV and Patlak graphical analysis, were both strongly correlated with NLR values, suggesting that metabolic changes indicated by these 2 parameters have an importance similar to changes in bone metabolism observed by NLR. However, in low-uptake areas such as limb bones, SUV measurements are less reliable than Patlak or NLR analysis, requiring at least changes of >50% to be assessed as true metabolic changes rather than spontaneous fluctuations. Thus, SUV seems to be limited to high-uptake areas such as the spine while it does not seem to be an appropriate tool to monitor metabolic changes in limb bones. Patlak analysis was highly linked to NLR over the whole range of physiologic and pathologic metabolic bone activity. Since it is computationally simplier than NLR, it might be the tool of choice to monitor fluoride bone metabolism irrespective of location. Its use would be greatly encouraged by implementing ready-to-use software to calculate Patlak flux values on standard PET systems. NLR, on the other side, provides the most quantitative information due to the possibility to calculate single rate constants and estimate bone blood flow, though the clinical value of these rate constants is still unclear. The 95% ranges of normal change in fluoride metabolic rates provided in this study may be used as an estimate for assessing changes in bone metabolic activity—for example, in healing bone grafts. Furthermore, the normal values for various bones of the limbs provide a basis for further studies on ¹⁸F-fluoride bone metabolism.