Kinetic Modeling of 3′-Deoxy-3′-¹⁸F-Fluorothymidine for Quantitative Cell Proliferation Imaging in Subcutaneous Tumor Models in Mice

Radiopharmaceutical Preparation

¹⁸F-FLT was prepared from 5′-O-(DMTr-2′-deoxy-3′-O-nosyl-β-d-threopentafuranosyl)-3-N-BOC-thymine as a precursor by the nucleophilic fluorination of ¹⁸F-fluoride with a protic solvent (t-butanol or t-amyl alcohol) (21). Typically, decay-corrected radiochemical yields ranged from 60% to 70%, and after high-performance liquid chromatography (HPLC) purification, the radiochemical purity was 98% ± 1.2% (mean ± SD). The specific activity of the ¹⁸F-FLT obtained was greater than 100 TBq/mmol.

Cell Cultures and Tumor Models

A431 and LLC cell lines were obtained from the American Type Culture Collection. Cells were routinely cultured in Dulbecco's modified Eagle medium supplemented with 10% heat-inactivated fetal bovine serum (FBS), l-glutamine (2 mM), penicillin (100 IU/mL), and streptomycin (50 g/mL) (Gibco, Invitrogen Corp.). Cells were maintained at 37°C in an atmosphere of 5% CO₂ in air.

BALB-c/nu and C57BL/6 mice (both from Charles River Laboratories) subcutaneously injected with A431 and LLC cells, respectively, were used as tumor models. The research protocol used was approved by the Institutional Animal Care and Use Committee at the Asan Institute for Life Science. Mice were also maintained in accordance with guidelines issued by this committee. Exponentially growing 7 × 10⁶ A431 and 1 × 10⁶ LLC cells suspended in 300 μL of the culture medium described earlier were injected subcutaneously into the right forelimbs of anesthetized mice. When tumor diameters reached 6–10 mm at 10–12 d after injection, mice were used for the experiments.

Thymidine Kinase Assay

Thymidine kinase activities were measured in A431 and LLC tumors excised from 3 and 4 mice, respectively, that were treated in parallel with animals used for imaging. The activities were measured with a previously described thymidine kinase assay that was slightly modified (1). In brief, tumors were lysed in lysis buffer and incubated for 30 min on ice. Lysates were centrifuged at 10,000g for 20 min at 4°C, and supernatants were recentrifuged at 100,000g for 1 h at 4°C to separate mitochondrial fractions. After protein contents were determined, cytosolic fractions were assayed for thymidine kinase activities in a reaction buffer containing 10 M ³H-thymidine (TRK120; 925 × 10⁹ Bq/mmol; Amersham Bioscience). Mixtures were then incubated at 37°C with gentle stirring, and samples were removed and added to 10 mM ethylenediaminetetraacetic acid to stop the reaction. For sequestration of labeled nucleotides, samples were spotted onto DE-81 filters (Whatman), dried, and washed in 4 mM ammonium formate and 95% ethanol. Radioactivity was measured by liquid scintillation counting with Ultima Gold F scintillation cocktail solution (Perkin-Elmer). Activities were calculated with linear time–activity curves and are presented as picomoles of phosphorylated thymidine per minute per milligram of protein. TK1 activities (mean ± SD) in A431 and LLC tumors were 0.074 ± 0.023 and 0.028 ± 0.01 pmol of phosphorylated thymidine per minute per milligram of protein, respectively; these values were significantly different (P < 0.05).

PET Scans

PET scans were performed by use of a microPET Focus120 system (Siemens Medical Solutions, Inc.) with resolutions of 1.18 mm (radial), 1.13 mm (tangential), and 1.44 mm (axial) at the center of the field of view (22). A 37-frame dynamic protocol (4 × 3 s, 6 × 1 s, 7 × 6 s, 8 × 30 s, 1 × 300 s, and 11 × 600 s) was used for the emission PET scans. Mice were maintained under isoflurane anesthesia during the scans, and body temperatures were maintained at 36°C with an electric heating pad. Animals fasted for 4 h before imaging. Transaxial images were reconstructed as 128 × 128 × 95 matrices of 0.432 × 0.432 × 0.796 mm by use of a filtered backprojection algorithm with a Hamming filter at a cutoff frequency of 0.5 cycle per pixel.

Validation of LV Input Function

Forty-four normal C57BL/6 mice were studied to verify the LV input function derived from dynamic PET data. For measurement of the equilibrium constant for plasma and whole blood over time, arterial blood samples were obtained from 16 mice by cardiac puncture at 30 s, 2 min, 5 min, and 10 min (4 mice at each sampling time point) after injection of 37 MBq of ¹⁸F-FLT. Arterial blood was collected in heparinized tubes from the LV cavity by direct cardiac puncture. Immediately after sample collection, plasma was separated from whole blood by centrifugation at 10,000g for 20 s at 4°C. The plasma samples (>15 μg) were weighed with 0.1-mg precision. Counts in the plasma and whole-blood samples were determined with a well γ-counter (COBRA II Auto Gamma; Canberra Packard). All tubes were incubated at 4°C before use. The time interval between plasma sampling after centrifugation and the sacrifice of the animal was 53 ± 11 s.

Dynamic PET scans were performed in 24 mice to compare arterial blood activities obtained by PET with activities obtained from blood data. The 24 animals were divided into 4 equal groups according to the time of arterial blood sampling (5, 10, 30, and 60 min after the initiation of scanning). Dynamic PET scans were started immediately after the injection of 37 MBq of ¹⁸F-FLT into tail veins and were completed at each group time for blood sampling by direct cardiac puncture. Arterial blood samples (20 μl) were analyzed with the well γ-counter.

Cross-calibration factors for the well γ-counter and PET scanner were independently measured with a mouse-size uniform cylindric phantom (diameter = 3 cm, length = 11.5 cm) filled with 37 MBq of ¹⁸F-FLT solution. To obtain a PET image–derived input function, cylindric volumes of interest (VOIs) (length of 3 slices) were drawn on the centers of the left ventricles on PET images. The diameters of these cylindric VOIs were varied from 1.3 to 3.0 mm (3–7 pixels in diameter) to explore the effects of VOI size on the image-derived input function. Finally, correlation analysis was performed on cross-calibrated counts from arterial blood and image-derived input functions. The ratios of cross-calibrated PET image–derived and blood sample–derived activities (recovery coefficients) were also calculated, and the reciprocal of the mean ratio of the data for the 24 imaged animals (at all time points between 5 and 60 min) was used as a partial-volume effect correction factor for the image-derived input function.

¹⁸F-FLT Metabolite Analysis

Metabolite fractions in arterial blood were measured at 1 and 2 h after the injection of 185 MBq of ¹⁸F-FLT into 4 mice as described previously (3). Plasma samples were deproteinated by the addition of ice-cold acetonitrile and centrifugation (1,800g, 10 min). Supernatants containing ¹⁸F-FLT and metabolites were passed through a sterile filter (0.2 μm) and analyzed by HPLC. Eluted material was monitored with a radioactivity detector, and unchanged phosphorylated ¹⁸F-FLT fractions were determined by HPLC with radioisotope detectors.

Metabolite fractions in tumors were also measured immediately after dynamic imaging studies as described later. Tumor samples were cut into small pieces and homogenized. Supernatants obtained by centrifugation were filtered and analyzed as described earlier.

Kinetic Modeling

For kinetic modeling studies, PET scans were performed on 19 mice bearing A431 (n = 9) and LLC (n = 10) tumors. Dynamic emission scans were acquired after the injection of 30–46 MBq of ¹⁸F-FLT into tail veins, and scanning was continued for 2 h.

To obtain time–activity curves for kinetic analysis, cylindric VOIs with a diameter of 3.0 mm and a length of 3 slices were drawn on PET images. LV time–activity curves corrected for partial-volume effects with the correction factor described earlier were used as the input function. Tissue time–activity curves were obtained from tumor-bearing regions on the right forelimbs and from normal contralateral regions.

Compartmental Analysis

To determine the optimal compartmental model for ¹⁸F-FLT in mice, we tested a 3-compartment model suggested for human data (8,9) and its nested models. Figure 1 shows the 3-compartment model, in which the parameters K₁, k₂, k₃, and k₄ represent the rate of transport from plasma to tissue, the rate of outflow from tissue to plasma, the TK1 phosphorylation rate, and the dephosphorylation rate, respectively. The blood volume fraction (V_b) was included in the modeling, and 3-compartment models with reversible phosphorylation (k₄ ≠ 0, 3C5P) and irreversible phosphorylation (k₄ = 0, 3C4P) were examined. In addition, a 2-compartment model that combined exchangeable and phosphorylated compartments into a single tissue compartment with 3 parameters (2C3P: K₁, k₂, and V_b) was also considered.

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FIGURE 1. 

Kinetic model for ¹⁸F-FLT. C_pFLT represents concentration of ¹⁸F-FLT in arterial plasma. Tissue is composed of exchangeable tissue compartment (Q_e) and compartment of trapped phosphorylated ¹⁸F-FLT nucleotides (Q_m). Parameters K₁ and k₂ are rate constants for forward and reverse transport of ¹⁸F-FLT between plasma and tissue pool, respectively. Rate constants for precursor and phosphorylated ¹⁸F-FLT denote thymidine kinase–mediated phosphorylation (k₃) and dephosphorylation (k₄) of ¹⁸F-FLT. C_met = concentration of metabolites in arterial plasma.

The PMOD software package (version 2.65; PMOD Group (23)) was used for parameter estimation. Tissue time–activity curves were fitted to the models by use of the nonlinear least-squares method with the Levenberg–Marquardt algorithm, which minimizes the weighted sum of squared errors between PET measurements and model solutions. Inverse SDs of frame counts were used as weights. Estimated parameters were restricted to the following value ranges: 0.0–0.5 for K₁, 0.0–5.0 for K₁/k₂, 0.0–1.0 for k₃, 0.0–0.5 for k₄, and 0.0–0.2 for V_b. Initial values for these parameters were set at 0.1, 1.0, 0.1, 0.01, and 0.05 for A431 and at 0.1, 0.5, 0.01, 0.01, and 0.05 for LLC, respectively.

The net influx of ¹⁸F-FLT (K_FLT), the total distribution volume (DV_tot), and the distribution volume for phosphorylated ¹⁸F-FLT nucleotides (DV_m) were estimated as follows:

We chose an adequate compartment model on the basis of the Akaike information criterion (AIC) and the F test. We also examined the correlations between kinetic parameters (such as K_FLT, DV_tot, and DV_m) obtained with the best model and percentages of Ki-67–positive nuclei (% Ki-67). Kinetic parameters obtained with simpler methods (fewer parameters or a shorter scan duration) were compared with those obtained with the best model and data acquired over 120 min.

Nonparametric or Semiquantitative Approaches

Gjedde–Patlak graphic analysis (GPGA) was also performed to estimate K_FLT. Only the linear region on the GPGA plot (A431: 7.5–90 min; LLC: 20–120 min) was included in the linear regression analysis. The SUV at the last frame (duration of 10 min) was also calculated.

Immunohistochemical Analysis

After small-animal PET images were acquired from mice bearing tumors, animals were sacrificed for immunohistochemical analysis. Tumors were fixed with 10% neutral buffered formalin and embedded in paraffin. For Ki-67 immunostaining, 4-μm-thick sections were obtained from paraffin blocks. Paraffin sections were placed on slides, deparaffinized in xylene, and rehydrated in graded ethanol. Endogenous peroxidase was blocked with 3% hydrogen peroxide in 70% methanol for 15 min. Antigen retrieval was performed with 10 mM citrate buffer solution (pH 6.0) for 15 min in a microwave oven, and sections were cooled to room temperature for 20 min. Sections were incubated overnight at 4°C with monoclonal mouse anti–human Ki-67 antibody. Sections were treated with biotinylated Link (LSAB 2 system-HRP kit; Dakocytomation) for 30 min, incubated with streptavidin–horseradish peroxidase (LSAB 2 system-HRP kit) for 30 min at room temperature, and washed. Sections were treated with diaminobenzidine (Dakocytomation) for 5 min, washed with tap water, counterstained with hematoxylin, rewashed, and mounted. For determination of % Ki-67, more than 1,000 cells per slide were counted and scored with a ×40 optical microscope (Leica) by 2 masked observers.

Statistical Analysis

Correlations between % Ki-67 and parameters estimated from PET data were assessed with Spearman nonparametric rank analysis. Correlations between PET kinetic parameters were also assessed with Spearman analysis. The 2-sample t test was used to compare 2-parameter estimates from different tumors. Statistical analyses were performed with SPSS for Windows (SPSS 12.0KO release 12.0.1; SPSS Inc.).

Image-Derived Input Function

¹⁸F-FLT equilibrated rapidly between plasma and whole blood, and the ratios of plasma activity to whole-blood activity converged to a constant value (mean ± SD for 30-s data = 1.0 ± 0.1) within 30 s of intravenous injection and did not change with time. Metabolite analysis in plasma revealed only one major peak of parent ¹⁸F-FLT, at 2 h after injection. Figure 2 shows the LV input function obtained for a representative mouse with a VOI with a diameter of 1.3 mm (3 pixels), which was the smallest VOI used. We obtained several samples around the initial peaks of LV input functions. Despite the short duration (1 s) of the initial frames, no counting rate fluctuation was observed for these input functions throughout the scans. Initial peak values of image-derived input functions decreased gradually with increasing VOI diameter. However, these differences were not significant up to a VOI diameter of 3 mm (7 pixels).

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FIGURE 2. 

Blood time–activity curve generated from VOI (1.3-mm diameter) placed in left ventricle to obtain input function.

Figure 3A shows the regression line for the cross-calibrated arterial blood sample data and PET data (timing difference corrected) obtained with a VOI with a 3-mm diameter. We merged the data acquired at all of the time points (5, 10, 30, and 60 min) to obtain the regression line, which had a high correlation (r > 0.96) and little bias. Regression lines for all VOIs showed a similar trend. The magnitudes of arterial blood sample data and PET data obtained at each time point with the same VOIs are compared in Figure 3B, in which the data are presented as means ± SEMs. No time-dependent difference between these data was observed.

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FIGURE 3. 

Comparison between cross-calibrated arterial blood activities measured by invasive blood sampling and by use of LV VOIs on PET images. (A) High correlation (r > 0.96) was observed between arterial blood samples and PET data (VOI diameter = 3 mm). (B) Bar plot of arterial blood samples and PET data obtained from each time point with same VOI. Bars represent means ± SEMs. (C) Mean ratios of PET data and blood sample data were 0.94, 0.94, 0.93, 0.93, and 0.92 for VOIs with diameters of 1.3, 1.7, 2.1, 2.6, and 3 mm, respectively. Input function obtained from VOI with diameter of 3 mm (7 pixels) was divided by 0.92 for kinetic analysis. Bars represent means ± SEMs.

Figure 3C shows recovery coefficients, which were defined as ratios of PET data and blood sample data (mean ± SD of 0.94 ± 0.12, 0.94 ± 0.11, 0.93 ± 0.11, 0.93 ± 0.10, and 0.92 ± 0.11 for VOIs with diameters of 1.3, 1.7, 2.1, 2.6, and 3 mm, respectively). Coefficients of variation (CVs) were less than 12.5%.

On the basis of these results, the LV time–activity curves obtained with a VOI with a 3-mm diameter (7 pixels) were used as input functions for the kinetic analysis. Input functions were scaled to compensate for differences from blood samples by dividing them by recovery coefficients.

Tissue Time–Activity Curves

Figure 4 shows averaged PET images obtained at 110–120 min after injection and time–activity curves for tumor-bearing and normal regions. Proliferative A431 tumors showed rapid uptake and high ¹⁸F-FLT retention (Fig. 4A). On the other hand, LLC tumors had time–activity curves that resembled those of normal regions and had relatively low ¹⁸F-FLT retention and rapid clearance (Fig. 4B).

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FIGURE 4. 

Averaged PET images obtained at 110–120 min after injection (representative case for each tumor model). LV input function and tissue time–activity curves were obtained from 3-mm VOIs drawn on tumor-bearing regions (arrows at right) and on contralateral normal tissues (arrows at left) in mice bearing A431 (A) and LLC (B) tumors.

Compartmental Modeling

Time–activity curves were fitted more accurately when the V_b term, which reflected the significant amount of blood activity in VOIs, was included in the model. Means and CVs of kinetic parameters estimated with the 3C5P, 3C4P, and 2C3P models and 120 min of data and K_FLT values estimated with GPGA are summarized in Table 1. Data for 2 A431 tumors were excluded from this comparison and from further analyses because tissue time–activity curves were not properly fitted with the models within physiologically relevant ranges of kinetic parameters, possibly because of motion artifacts. For A431 and LLC tumors, the average ¹⁸F-FLT dephosphorylation rates (k₄) were estimated to be 0.011 and 0.015, respectively.

Consistent with the measurable dephosphorylation of phosphorylated ¹⁸F-FLT, both tumor cell lines showed the lowest AIC values for all mice when the 3C5P model was used for curve fitting (Table 2). The results of F tests were similar to those of AIC analysis (Table 2). AIC values from the 3C models (3C5P and 3C4P) were lower than those from the 2C3P model in all mice, and differences were significant, except for one mouse with A431 (P < 0.001). The quality of curve fitting with different models was evaluated, and the results are shown in Figure 5.

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FIGURE 5. 

Quality of curve fitting obtained with different models and 120 min of data for A431 (A) and LLC (B) tumors. Regression curves defined by 3C5P model were close to data points and did not deviate systematically from data.

Correlation matrices for the 3C5P model are shown in Table 3. K₁/k₂ and k₃ were found to be highly correlated with each other in both tumor cell lines. In LLC, k₃ and k₄ were highly correlated. Because a high level of covariance between microparameters indicates difficulties in independent estimation, K_FLT values obtained from the different compartment models were further analyzed. As was expected, K_FLT values estimated with 3C5P were much higher than those estimated with 3C4P or GPGA (Table 1). On average, K_FLT values were underestimated by approximately 33% (range, −48% to −17%) for A431 tumors and by 56% (range, −69% to −39%) for LLC tumors when k₄ was set to 0 (3C4P vs. 3C5P). K_FLT values estimated with GPGA were also consistently lower than those estimated with the 3C5P model (for A431: mean = −26% and range = −38% to −11%; for LLC: mean = −67% and range = −80% to −53%). K_FLT composed of microparameters (K₁∼k₃) was found to be better correlated with k₃ than K₁, as shown in Figure 6.

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FIGURE 6. 

Relationships between k₃ and K_FLT (r = 0.95, P < 0.0001) (A) and K₁ and K_FLT (B) for both cell lines (n = 17). K_FLT was better correlated with k₃ than with K₁ (flow-dependent parameter).

Correlation of Model Parameters with % Ki-67 and ¹⁸F-FLT Phosphorylation

A431 and LLC tumors showed markedly different levels of quantitative and semiquantitative parameters related to ¹⁸F-FLT metabolism (k₃, K_FLT, and DV_m) (P < 0.01) (Table 1). In addition, significant differences in SUVs were noted between the 2 tumor types (6.95 ± 1.14 for A431 and 0.13 ± 0.04 for LLC) and % Ki-67 (81.5 ± 4.4 for A431 and 58.7 ± 6.3 for LLC) (P < 0.01).

The radiochromatograms of A431 tumors obtained 2 h after ¹⁸F-FLT injection showed that the major radioactive component, which corresponded to phosphorylated ¹⁸F-FLT, eluted at a retention time of 2–3 min. No other radioactive peaks were identified. On the other hand, the radiochromatograms of LLC tumors did not contain well-identified peaks. In some tumors, a major peak corresponding to phosphorylated ¹⁸F-FLT and a minor peak corresponding to intact ¹⁸F-FLT were identified at retention times of 9–10 min. Although fractions of these 2 components were not measured, the results of radio-HPLC were in qualitative agreement with the percentages of intracellular metabolites of ¹⁸F-FLT (90.3% ± 2.8% for A431 and 65.5% ± 8.7% for LLC) relative to total metabolites and dephosphorylated ¹⁸F-FLT, as determined by compartmental analysis.

The correlation coefficients for the ¹⁸F-FLT PET parameters obtained with the 3C5P model and 120 min of data and % Ki-67 are summarized in Table 4. K_FLT (Fig. 7) and k₃ were found to be highly correlated with % Ki-67 (ρ > 0.8). Furthermore, the distribution volume ratio (k₃/k₄) between ¹⁸F-FLT phosphorylated nucleotides and exchangeable tissue compartment, DV_m, DV_tot, and SUV were also highly correlated (ρ > 0.6) with % Ki-67. However, K₁ and K₁/k₂ were relatively poorly correlated with % Ki-67.

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FIGURE 7. 

Relationship between K_FLT values obtained from 3C5P model and 120 min of data and % Ki-67.

Feasibility of Simple Models

We compared K_FLT values obtained with the 3C5P model and PET data obtained over 60, 90, and 120 min from the initiation of scanning. For A431 tumors, which showed a sufficiently wide K_FLT range for correlation analysis, high correlations were found for K_FLT values obtained from 120-min and shorter (60- or 90-min) scans by nonlinear regression analysis (3C5P and 3C4P models) (Table 5). However, undesirable negative correlations were obtained for 60- and 120-min scans for LLC tumors (Table 5). GPGA provided a simple estimate of K_FLT without complex nonlinear curve fitting, but it had estimation bias when compared with the 3C5P model, mainly because of the assumption of irreversible ¹⁸F-FLT metabolism (Table 1). Although K_FLT values estimated with GPGA and 60- or 90-min data showed a significant correlation with K_FLT values obtained with the 120-min 3C5P model for LLC tumors, this correlation was insignificant for A431 tumors (Table 5). SUVs at 80–90 min and 50–60 min showed lower correlations with K_FLT values obtained with the 120-min 3C5P model for both tumor types.

K_FLT values obtained with the 3C5P model and 60- or 90-min data were consistently higher than 120-min estimates for both cell lines (Table 6). K_FLT values obtained with the 90-min 3C5P model for A431 tumors showed a less than 5% mean difference from those obtained with the 120-min 3C5P model. K_FLT values obtained with 3C4P and GPGA and 60- or 90-min data were underestimated, although the 3C4P model showed a high correlation for both tumor types (Tables 5 and 6). The correlations between the K_FLT values obtained with the different models and % Ki-67 are shown in Table 7. K_FLT values obtained with 60- or 90-min data showed a high correlation with % Ki-67, as did K_FLT values obtained with the 3C5P model and 120-min data (Table 4).

Input Function

Quantitative analysis of dynamic PET images with tracer kinetic modeling requires an arterial plasma input function. However, because of small blood vessel diameters and total blood volumes, serial sampling of arterial blood to measure blood activity in mice is difficult (15). Several methods have been proposed to measure input functions in mice (24–27). Automated blood-sampling devices dedicated to small-animal imaging can be used (24), but these techniques are limited for multiple-tracer or repetitive studies in the same animals. Image-derived input functions for mouse left ventricles are an alternative to direct blood sampling. This method is attractive, especially in longitudinal studies, because of its noninvasive nature. Moreover, considerable improvements in the spatial resolution and sensitivity of state-of-the-art animal PET systems can increase the accuracy of such measurements.

Therefore, we evaluated the validity of image-derived input functions for mouse left ventricles. Rapid equilibration of ¹⁸F-FLT between plasma and whole blood was observed at 30 s after injection, a result indicating that simple image-derived whole-blood activities from left ventricles can be used. In addition, no ¹⁸F-FLT metabolite was observed until 2 h after ¹⁸F-FLT injection. The observed low levels of ¹⁸F-FLT metabolites in mouse plasma agree with the findings of a previous study (3) and are probably explained by the relatively low uptake and glucuronidation of ¹⁸F-FLT in mouse liver (3,18,28).

In the present study, a high correlation between arterial blood sample data and PET data was observed, as shown in Figure 3, and the CVs of the ratios of PET data to blood sample data were less than 15%. Actual intersubject variations of this ratio can be expected to be small because blood sampling and PET measurement errors also contribute to these variations. Therefore, these blood activity analysis results suggest that image-derived LV input functions obtained with a state-of-the-art high-resolution rodent PET scanner can be used for kinetic modeling of ¹⁸F-FLT metabolism in mice.

For investigators who plan to use animals of different sizes or different scanners, a correction factor different from that used in the present study should be obtained because the correction factor is dependent on the spatial resolution of the scanner and the LV size of the animal. If ¹⁸F-FLT PET is used for treatment monitoring, then change over time is a primary concern, and such a correction factor can be ignored for simplicity.

Compartmental Modeling

In human PET data, phosphorylated ¹⁸F-FLT dephosphorylates more slowly than TK1 activity (29). As shown in Table 1, dephosphorylation rates (k₄) were also low in the present study and were similar for the 2 tumor cell lines. However, the phosphorylation rate (k₃) in LLC cells was not as rapid as that in A431 cells and was similar to the dephosphorylation rate. Thus, LLC had a low level of¹⁸F-FLT retention, as shown in Figure 4. This finding suggests that k₄ should not be ignored in the kinetic modeling of the LLC cell line when 120 min of data are used. K_FLT, which was calculated on the basis of the assumption that k₄ can be ignored, was underestimated by 69% in this cell line (Table 1). A significant loss of phosphorylated ¹⁸F-FLT nucleotides was also evident in kinetic studies of non–small cell lung cancer (11) and gliomas (12). However, previous ¹⁸F-FLT kinetic studies in dogs bearing non-Hodgkin's lymphoma and soft-tissue sarcoma (30) and in patients with colorectal cancer (9) demonstrated that the incorporation of k₄ ≠ 0 is not necessary to improve model accuracy. In these studies, dynamic PET scans were acquired for only up to 60 min, a length of time that might not have been sufficient to accurately estimate the effects of the k₄ parameter. Further systemic investigation of the issue of k₄ ≠ 0 in ¹⁸F-FLT kinetics is necessary because there are nonbiochemical factors that can lead to better curve fitting with k₄ ≠ 0. Heterogeneity of tissue composition is an example of such a factor.

In the present study, all compartment models had lower AIC values when the blood volume fraction term was included; this finding means that this parameter should not be neglected in ¹⁸F-FLT kinetic models. Blood volume fractions also showed wide variations in both tumor cell lines (Table 1), a result that may have been attributable, in part, to variable vasculature changes in tumors. In addition, tumor-bearing regions showed higher blood volume fractions than did normal regions, a result that is probably associated with enhanced neovascularization in these tumor models (31). With regard to the use of ¹⁸F-FLT PET for the assessment of therapeutic outcomes, considerations of blood volume fractions are important because of the possible effects of increased edema induced by treatment (13).

Model Parameters

K_FLT and k₃ showed high correlations with % Ki-67, but no correlation of K₁ and k₄ with % Ki-67 was observed (Table 4). The strong correlation of K_FLT with % Ki-67 seems to be related to the parameter k₃, which is directly associated with TK1 activity, because K_FLT is not flow-dependent (Fig. 6) and K₁ levels were similar between the 2 tumor models. Better correlations between k₃ or K_FLT and % Ki-67 than between SUVs and % Ki-67 may be attributable to a significant amount of label loss because of dephosphorylation (k₄) and better normalization of tumoral activity by input function integration rather than use of the injected dose.

In general, macroparameters, that is, combinations of microparameters, were more stable than individual microparameters. Therefore, associations between several macroparameters (k₃/k₄, K_FLT, DV_m, and DV_tot) and ¹⁸F-FLT metabolism were explored in the present study. Although all were found to be useful for differentiating A431 tumors and LLC tumors, K_FLT values in tumor-bearing regions had the smallest variability, as shown in Table 1. In addition, K_FLT showed a strong correlation with k₃ (Fig. 6).

Simple Models

Our results show that PET parameters (k₃ and K_FLT) estimated with the 3C5P model and 120 min of PET data reflect well the metabolism of ¹⁸F-FLT in tumor cells. However, PET of mice for 120 min is inconvenient because of the time involved and the possibility of animal movement. The possible biologic effects of long-term anesthesia are also problematic.

Unfortunately, K_FLT estimates based on the 60- or 90-min 3C5P model were consistently higher than K_FLT estimates based on the 120-min model, and those obtained from the 3C4P model were lower. Only in tumor models with high uptake (A431 models) did 90-min K_FLT estimates differ from 120-min estimates by less than 5%. This result suggests that the estimation of k₄ is a vital element and that 60-min data are inappropriate in these tumor models if the absolute quantification of K_FLT is important.

If the specific aim of an ¹⁸F-FLT PET study is to monitor the therapeutic response after cancer treatment, then assessment of relative changes in a kinetic parameter over time will be sufficient. Despite the overestimation of K_FLT values, the 60- or 90-min 3C5P model had a strong correlation with the 120-min model in highly proliferative tumor cells (A431). Although K_FLT values obtained with the 60-min 3C5P model in LLC tumors had a negative correlation with those obtained with the 120-min 3C5P model and showed a high relative percentage of change, these results were mainly attributable to the fact that LLC tumors have a very low level and narrow range of K_FLT values; these conditions are not appropriate for these comparisons. In addition, K_FLT values obtained with shorter scan times (60 or 90 min) showed a high correlation with % Ki-67 (Table 7), as did K_FLT values obtained with the 3C5P model and 120 min of data. Although there is still controversy regarding the appropriateness of the incorporation of k₄ in an ¹⁸F-FLT kinetic analysis with 60 min of data, these experimental results support the notion that a dynamic ¹⁸F-FLT PET scan time shorter than 120 min can be used if the only parameter of interest is the relative change in K_FLT. In addition, the incorporation of k₄ in a kinetic analysis of shorter scan data seems to be feasible; this factor is important in the accurate estimation of K_FLT in therapeutic response monitoring with possibly varying k₄ values (11).

K_FLT estimates based on the 3C4P model (k₄ = 0) and 60 min of data correlated well with those based on the full model and data (3C5P and 120 min), as shown in Table 5, and the level of underestimation of K_FLT was not significant. Therefore, this model will also be useful in some applications in which only the relative change in K_FLT is important and in which K_FLT is insensitive to changes in k₄ or the assumption of no changes in k₄ can be justified.

Limitations

This study has several limitations. First, we used a relatively small number of mice for each tumor model. Nevertheless, consistent results were obtained with respect to model selection and parameter estimation. Second, concentrations of serum thymidine and the lumped constant for ¹⁸F-FLT were not considered. Although the consideration of a lumped constant, which accounts for differences in the transport and phosphorylation of ¹⁸F-FLT and thymidine, is required, no systematic study of this issue has been undertaken (32). Finally, 30–46 MBq of ¹⁸F-FLT were injected into mice to analyze ¹⁸F-FLT metabolites more accurately in tumors, because initial studies with 7.5 MBq of ¹⁸F-FLT did not result in a peak in LLC tumors. However, the effects of a perturbation of cellular proliferation on study results are likely to be negligible.