Abstract
We present and validate a method to obtain an input function from dynamic image data and 0 or 1 blood sample for smallanimal ^{18}FFDG PET studies. The method accounts for spillover and partialvolume effects via a physiologic model to yield a modelcorrected input function (MCIF). Methods: Imagederived input functions (IDIFs) from heart ventricles and myocardial time–activity curves were obtained from 14 Sprague–Dawley rats and 17 C57BL/6 mice. Each MCIF was expressed as a mathematic equation with 7 parameters, which were estimated simultaneously with the myocardial model parameters by fitting the IDIFs and myocardium curves to a dualoutput compartment model. Zero or 1 late blood sample was used in the simultaneous estimation. MCIF was validated by comparison with input measured from blood samples. Validation included computing errors in the areas under the curves (AUCs) and in the ^{18}FFDG influx constant Ki in 3 types of tissue. Results: For the rat data, the AUC error was 5.3% ± 19.0% in the 0sample MCIF and −2.3% ± 14.8% in the 1sample MCIF. When the MCIF was used to calculate the Ki of the myocardium, brain, and muscle, the overall errors were −6.3% ± 27.0% in the 0sample method (correlation coefficient r = 0.967) and 3.1% ± 20.6% in the 1sample method (r = 0.970). The t test failed to detect a significant difference (P > 0.05) in the Ki estimates from both the 0sample and the 1sample MCIF. For the mouse data, AUC errors were 4.3% ± 25.5% in the 0sample MCIF and −1.7% ± 20.9% in the 1sample MCIF. Ki errors averaged −8.0% ± 27.6% for the 0sample method (r = 0.955) and −2.8% ± 22.7% for the 1sample method (r = 0.971). The t test detected significant differences in the brain and muscle in the Ki for the 0sample method but no significant differences with the 1sample method. In both rat and mouse, 0sample and 1sample MCIFs both showed at least a 10fold reduction in AUC and Ki errors compared with uncorrected IDIFs. Conclusion: MCIF provides a reliable, noninvasive estimate of the input function that can be used to accurately quantify the glucose metabolic rate in smallanimal ^{18}FFDG PET studies.
PET with ^{18}FFDG is widely used to quantify glucose metabolism. This entails compartment modeling to estimate kinetic rate constants and requires knowledge of the input function, which is the ^{18}FFDG plasma time–activity curve (1,2). The gold standard to determine the input function is an invasive bloodsampling procedure to measure the ^{18}FFDG activity concentration in the arterial blood. For smallanimal ^{18}FFDG PET studies, this procedure is challenging because of the small size of blood vessels and the limited blood volume. In addition, blood loss may perturb the physiology and confound the experimental outcome. To avoid these problems, various methods have been proposed to estimate the input function noninvasively. Those methods can be categorized as imagederived input functions (IDIFs), factor analysis (FA) methods, standardized input functions, and simultaneous estimation.
IDIFs are the time–activity curves obtained by drawing regions over the major vascular structures, such as the ventricular cavity, aorta, or large arteries (3). In principle, this method is relatively simple to use. However, in smallanimal imaging, hearts and arteries are small compared with the scanner spatial resolution. Consequently, vascular radioactivity is blurred into adjacent tissues and vice versa. Also, cardiac and respiratory motion creates additional crosscontamination between vascular structures and surrounding tissues. As a result, curves obtained from regions drawn over the vascular space will be a mixture of the input function and the surrounding tissue time–activity curves. Some methods have been proposed to correct for the mixing—sometimes called spillover and partialvolume effect—in IDIFs using a few blood samples in clinical studies (4,5). For smallanimal PET, Yee et al. applied the IDIF method to ^{15}Owater studies with correction for partial volume and spillover (6). However, the assumption that the blood tracer concentration achieves equilibrium with that in the tissue makes the method inappropriate for ^{18}FFDG. Green et al. presented an IDIF in mice assuming a negligible contribution of the myocardium to the cavity curve (7). In many circumstances, this assumption is not valid.
FA methods have been applied to separate the arterial blood and the myocardial tissue components in the dynamic heart images. The heart image is assumed to be a sum of 3 or more factors—typically myocardium and blood in the left and right ventricles. Principal component analysis is applied to find these components and, therefore, obtain an estimate of the input function. FA has been used to extract the input function for rats and mice using just 1 blood sample (8), showing good correlation between the measured and extracted input functions. FA is described as being robust and requiring few blood samples. However, the ambiguity still exists in this method of whether, especially in mice (8), the factors found include the blood curves without spillover and partialvolume degradation. Moreover, an analysis of the consequence of using FAderived input functions on the ^{18}FFDG influx rate constant has not been reported.
Standardized input function methods assume that input functions across animals and experimental conditions have an identical curve shape that can be used to approximate the individual input function by scaling the standard curve to match the concentration measured in 1 or 2 blood samples (9). In reality, the input function curve shape varies between subjects on the basis of several factors, such as the injection technique and speed, dietary state of the animal, metabolic status, catheterization site, and animal species. Therefore, the standard curve lacks the ability to account for the range of curve shapes present, especially in animals with abnormal metabolism. Moreover, the use of standardized input functions has not been validated for mice.
Simultaneous estimation was originally proposed to estimate the input function for human brain studies (10). It is assumed that the input function can be described by a mathematic function with multiple parameters that can be estimated simultaneously with the fitting of multiple regions of interest (ROIs), typically 3. Few, usually 2, late blood samples are required in the simultaneous estimation process. The main challenge of this method is the large number of parameters (>25) that needs to be estimated, thus making the fitting especially challenging. Moreover, this method has not been validated in smallanimal PET studies.
In this article we present and validate a method that overcomes the limitations of the above methods. Our method uses simultaneous estimation to correct the spillover and partialvolume effect for an IDIF. We assume that both the IDIF from the heart ventricles and the time–activity curve of the myocardium are mixtures of the true input function and the myocardium uptake. Using a mathematic equation to express the input function, we can then determine both time–activity curves as outputs of a compartment model simultaneously with the nonvascular tissue parameters. The estimated input is denoted as a modelcorrected input function (MCIF) because it is obtained by correcting the spillover and partialvolume effects from IDIF by compartment modeling. This method is validated by comparing the MCIF estimated with 0 or 1 blood sample with the input functions measured with blood sampling in rats and mice. We also compared our MCIF with the uncorrected IDIF.
MATERIALS AND METHODS
Rat Studies
All experiments took place in the Case Center for Imaging Research in Case Western Reserve University and were performed according to a protocol approved by its Institutional Animal Care and Use Committee. Twenty datasets were acquired from 14 female Sprague–Dawley rats ranging from 206 to 253 g. Six of the 14 underwent 2 studies separated by 1 wk. For each scan, the rat was anesthetized with 2%∼2.5% isoflurane in oxygen. Each rat was cannulated in the tail artery with microrenathane tubing (0.83mm outer diameter) and in the tail vein with microrenathane tubing (0.63mm outer diameter). Each microPET study began with a 10min transmission scan using a ^{57}Co source on a microPET R4 scanner (Siemens Medical Solutions USA, Inc.). After that, a 90min emission scan in 3dimensional dataacquisition mode commenced with the intravenous bolus injection of approximately 30 MBq ^{18}FFDG. Dynamic image sequences were reconstructed with 5s (n = 12), 30s (n = 12), 60s (n = 5), and 300s (n = 17) frames. Fourier rebinning and a 2dimensional filtered backprojection (FBP) algorithm was used for image reconstruction with 256 × 256 × 63 pixels per frame. Pixel spacing was 0.42 × 0.42 × 1.25 mm and the field of view included the brain, heart, and lung. Correction for radioactive decay, attenuation, scatter, and dead time was performed during the sinogram histogramming and reconstruction.
Blood sampling was performed to provide a goldstandard reference. For the first 3 min, a continuous automatic bloodsampling device, a bloodactivity monitor (BAM), was used to acquire data with a high sampling rate to capture the initial rapid kinetics (11). During this time, the blood was continuously drawn from the arterial line using a syringe pump at 0.2 mL/min flow rate and counted by the BAM using contiguous 0.1s intervals. After the first 3 min, continuous sampling was discontinued, and 10 samples were manually taken at 3.5, 4, 4.5, 5, 7, 10, 15, 30, 60, and 90 min. For 12 of the 20 studies, a late venous sample at 92 min was taken to compare the activity concentrations in late arterial and venous blood samples. The manual samples were counted with a well counter (Wallac LKB 1282). The sample net weight was measured to obtain the activity concentration from the counts. Input functions from the BAM and manual samples were linearly interpolated to construct a single input function. Shortly after the end of the study, an extra blood sample was taken for determination of the hematocrit and plasma activity fraction (plasma ^{18}FFDG divided by wholeblood ^{18}FFDG).
Mouse Studies
In addition to rat data, our method was tested using mouse data shared on the Internet by the Crump Institute of Molecular Imaging, UCLA (12,13). Seventeen C57BL/6 male mice weighing 22–36 g were anesthetized with 1.5%–2% isoflurane in oxygen. Of these, 9 mice were pretreated with insulin. As insulin does not directly affect the spillover and partialvolume effects, these data were treated as 1 group for evaluation of the input function estimation. Into each mouse, 9–37 MBq ^{18}FFDG were bolusinjected in the tail vein. Input functions were measured using femoral artery blood samples. On average, 15 (range, 5–22) samples were collected from each mouse. Eight mice were scanned with a microPET Focus220 scanner and 9 were scanned with a microPET P4 scanner (both scanners: Siemens Medical Solutions USA, Inc.) For each PET study, a mouse underwent a CT scan for attenuation correction and then either a 60 or 90min emission scan. Herein, only the first 60 min of data were used to standardize the data analysis. The image reconstruction method was FBP with 128 × 128 × 95 pixels. Dynamic framing varies slightly among these studies but typically there were 0.5s (n = 15), 2s (n = 1), 4s (n = 1), 6s (n = 1), 15s (n = 1), 30s (n = 3), 60s (n = 1), 120s (n = 1), 180s (n = 3), and 900s (n = 4) frames.
^{18}FFDG Compartment Model
The wellestablished compartment model has been used for estimating the rate constants and the glucose metabolic rate (1,2). This model entails 2 tissue compartments: ^{18}FFDG and phosphorylated ^{18}FFDG (^{18}FFDG6P) in extravascular tissue, denoted by C_{e} and C_{m}, respectively. The state equations are:Eq. 1Eq. 2The model output equation is:Eq. 3where m_{i} is the modelpredicted activity concentration in the i^{th} frame with the frame beginning at time and ending at time F_{v} is the fraction of the pixel that is vascular space. C_{p} and C_{a} are the plasma and wholeblood time–activity curves, respectively. C_{p} is calculated from C_{a} by:Eq. 4where H is the hematocrit and F_{pa} is the fraction of blood activity attributed to that in the plasma (plasma activity divided by wholeblood activity). Although there have been studies showing that the F_{pa} varies with time (14,15), accounting for this time variation requires blood sampling. In fact, many studies use whole blood as a surrogate for plasma activity and, therefore, implicitly assume that F_{pa} is constant. Thus, to simplify the procedure and offer the possibility of avoiding blood sampling, we treat F_{pa} as a constant (We observed F_{pa} to be 0.63 ± 0.07 in rats.). The glucose metabolic rate of glucose is defined by:Eq. 5LC is the lumped constant between ^{18}FFDG and glucose, and C_{glu} is the glucose concentration in blood. The ^{18}FFDG influx constant Ki equals Often determination of Ki alone is a sufficient index of glucose metabolism, and it can be robustly estimated. In contrast, obtaining precise estimates of k_{1} to k_{4} is less frequently used because of parameter correlation and noise in the time–activity curves. Therefore, our present work focuses on the estimates of Ki in the parameter estimation results.
DualOutput Cardiac ^{18}FFDG Model
Ideally, when an ROI is drawn within the cavity of the left ventricle, the tissue time–activity curve would equal the wholeblood time–activity curve C_{a}. However, due to spillover and partialvolume effects, the modelpredicted output of an IDIF is more accurately expressed as a mixture of blood and nonvascular tissue activity:Eq. 6where is the mixing coefficient from the myocardium to the ventricular cavity, and is the mixing coefficient of the input function C_{a}. Similarly, the model output of the surrounding myocardium ^{18}FFDG concentration is:Eq. 7where is the mixing coefficient from the tissue ^{18}FFDG uptake, and is the mixing coefficient of the input function C_{a} contribution to the myocardium ROI. If there is no spillover and partialvolume effect, and would equal 1, and and would equal 0. In microPET images, those 4 mixing coefficients range between 0 and 1, with and dominant (closer to 1) and greater than and In this study, it is assumed that a single set of extravascular compartments (C_{e}, C_{m}) is adequate to predict both the ventricular () and the myocardial () activities because activities measured in these areas reflect a mixture of the same underlying myocardial extravascular and intravascular activities.
Simultaneous Estimation
Typical parameter estimation in compartment modeling assumes that both input and output are known, so that model parameters can be estimated by fitting the model output to the experimental data. Simultaneous estimation assumes, however, that the input is unknown but can be described by a model or an equation. Then, both the parameter sets of the input function and the tracer kinetic model can be estimated simultaneously by fitting model outputs to the experimental data. This entails accounting for the dependence of the model output on the input function parameters. In ^{18}FFDG PET studies, the input function C_{a} can be approximated by a 7parameter equation (16):Eq. 8With Equation 8 and values for τ, A_{1}∼A_{3}, and L_{1}∼L_{3}, the input function can be approximated and carried into the model for solving the model output in Equation 6 with a given set of k_{1}∼k_{4}, and Model output can be solved in the same way. Model outputs and are then fit to the corresponding measurements, the PET measurement of ^{18}FFDG concentration in the ventricular cavity and in the myocardium, by minimizing the objective function:Eq. 9where p is the parameter vector [τ, A_{1}, A_{2}, A_{3}. L_{1}, L_{2}, L_{3}, k_{1}, k_{2}, k_{3}, k_{4}, ] to be optimized. n is the total number of frames. w_{1} and w_{2} are weighting coefficients. If 1 blood sample is available to incorporate into the estimation process, the objective function can be extended to:Eq. 10where b is the blood activity concentration at the sampling time t_{s}. w_{3} is the weighting associated with the blood sample. The values of the weights w_{1}∼w_{3} are estimated simultaneously with all other parameters using an extended least squares (ELS) method described by Muzic and Christian (17). The initial values and the lower and upper bounds of all parameters are summarized in Table 1. Once the simultaneous estimation is finished, the estimated values for parameters τ, A_{1}∼A_{3}, and L_{1}∼L_{3} are used in Equation 8 to calculate the MCIF.
VOI and ROI Specification
Heart and myocardium ventricular volumes of interest (VOIs) were drawn for each animal on shortaxis slices. When necessary, image volumes were rotated to obtain the shortaxis view. A ventricular VOI consisted of 2dimensional circular ROIs (n = 2–4) that were placed on the adjacent slices at the center of the heart ventricular cavity. Those ROIs were approximately 2.1 mm in diameter for rats and 1.6 mm for mice. A myocardium VOI was made of several 2dimensional doughnutlike circular ROIs with hollow centers drawn on adjacent slices. The inner diameters of the myocardial ROIs were 4.2 mm for rats and 2.4 mm for mice. The outer diameters were 9.2 mm for rats and 5.2 mm for mice. Figure 1 shows an ROI on rat images. For validation by comparison of Ki values, brain and skeletal muscle ROIs were drawn for each animal.
Software and Computation Environments
All numeric analyses were done using MATLAB R2007a (Mathworks). COmpartment Model Kinetic Analysis Tool (COMKAT) (18), a kinetic modeling toolbox free for noncommercial use, was used for implementing the compartment models and fitting experimental data. The optimization was performed with COMKAT's fitGen function that uses MATLAB function “fmincon,” which is based on an interiorreflective Newton method (17,19).
Input Function Validation
How well an estimated input function approximated the measured input function was determined by direct and indirect methods. The direct method compared input functions by calculating the difference in areas under curves (AUCs) and the root mean square error (RMSE) of estimated input functions. The indirect comparison examined the impact of an estimated input function on the estimated tissue parameter Ki. Ki values in myocardium, brain, and muscle were calculated using a measured input function (Ki_{mea}) and an MCIF (Ki_{est}). The error percentage of Ki was calculated as (Ki_{est} − Ki_{mea})/Ki_{mea} × 100 for each region and subject. These percent errors were summarized using mean and SD. Also, the correlation coefficients between Ki_{mea} and Ki_{est} were calculated. A t test with α = 0.05 was used to examine if the Ki_{mea} and Ki_{est} were significantly different in each region.
RESULTS
Results of the direct comparison between measured input functions, IDIF and MCIF, are summarized in Table 2. As shown in Figure 2, an IDIF without any correction is highly biased because of the spillover. Therefore, the AUC was highly biased and the RMSE was extremely high for the IDIF, as seen in Table 2. For example, the magnitude of AUC errors both in rats and mice exceeded 100%, meaning the AUC was more than double what it should have been. In contrast, under all conditions the MCIF had an AUC error of <6% bias for all conditions—rats and mice, 0 and 1 blood sample. With inclusion of 1 blood sample, this error was about 2%. Thus, compared with the IDIF, the MCIF reduces the AUC error by approximately 20fold in rats and 100fold in mice. In terms of RMSE, the MCIF achieved values of about 0.04 MBq/mL, which were much smaller than the 0.17 to 0.28MBq/mL values obtained with the uncorrected IDIF. To illustrate the input function estimated with 0sample MCIF compared with the measured input, Figure 3 shows a representative dataset from 1 rat. The input function is accurately estimated for both the early minutes and the whole study, as shown in Figures 3A and 3B, even when the initial guess of the input function parameters is far from the true values. Figure 3C demonstrates that the model output fits the IDIF and myocardium data very well. Figure 4 shows representative fitting results of 1 set of mouse data, indicating the close approximation of the MCIF to the measured input.
As the purpose to estimate the input function is for its use in compartment modeling, evaluating how much error is introduced in the estimates of Ki is especially important. Table 3 lists the comparison of Ki values obtained from various input functions. When an IDIF without any correction was used in estimating Ki, the estimation of Ki was highly biased compared with the reference Ki values obtained using the measured input. This is due to the IDIF itself being highly biased, as shown in the direct comparison described earlier. In contrast, the MCIF greatly reduced the bias in the Ki estimates. For rats, the overall error percentage of Ki of all 3 regions averaged 6.3% ± 27.0% for 0sample MCIF and −3.1% ± 20.6% for 1sample MCIF, with correlation coefficients of 0.967 and 0.970, respectively. The t test failed to detect a significant difference in all 3 types of tissue using either 0sample or 1sample MCIF (P > 0.05). Comparing the 0sample and 1sample MCIF methods, the 1sample MCIF methods reduced Ki bias in both the brain and the muscle but slightly increased it in the myocardium. The precision was also greatly improved in the brain and muscle. Correlation coefficients increased in all 3 regions with the 1sample MCIF. Figure 5 shows a box plot of the Ki error in 0 and 1sample MCIF. Including 1 blood sample brought the median value closer to 0 and reduced the interquartile range (IQR). Taken together, these results show that the MCIF performs well in the tasks of estimating the input function and Ki, greatly reducing the error for IDIFs.
Similar results can be seen in the mouse data as listed in Table 4. Ki was again highly biased when using the IDIF without correction. With the MCIF, the overall error percentage of Ki of all 3 types of tissue was 8.0% ± 27.6% for the 0sample and 2.8% ± 22.7% for the 1sample MCIF method, with correlation coefficients of 0.955 and 0.971, respectively. Considering the individual tissue types, myocardium had the least bias and the best precision in Ki estimates. Although the correlation was high (r > 0.84) in all 3 types of tissue with the 0sample MCIF, the t test detected significant biases in Ki estimates in brain and muscle (P < 0.05). These biases were resolved by the use of the 1sample MCIF: The significant difference was not detected in any of the 3 regions. Moreover, use of 1 sample reduced the bias and improved the precision in brain and muscle and increased the correlation coefficients of all 3 regions to >0.9. The advantages of using the blood sample are visually evident in the box plot shown in Figure 6. In summary, with Ki analysis for MCIF in mice, bias and precision are better than that with IDIF. Inclusion of 1 blood sample improves MCIF such that no statistically significant bias was detected.
As a less invasive alternative to using 1 late arterial blood sample, we considered substituting activity concentration in a venous sample as an approximation to that in an arterial sample. In rats, venous activity concentration differed from arterial activity concentration by −5.8% ± 13.0%. Regression analysis showed a correlation coefficient of 0.944 (y = 0.942·x + 0.019, where y is the arterial activity concentration and x is the venous activity concentration), indicating that the late venous activity concentration is very close to the arterial concentration.
DISCUSSION
The ability to quantify physiologic function with measurable and testable results in a reliable and practical manner is crucial to research. In this regard, compartment modeling has long been regarded as one of the best ways to analyze PET images. However, the bloodsampling procedure to measure the input function in small animals has been a major barrier because of its invasive nature, the small size of blood vessels, and the animals' limited blood volume. Although new and advanced devices have been proposed to measure the blood activity—such as microfluidic bloodsampling devices (15) and bloodactivity monitors (20)—an invasive surgery procedure is required, making it difficult for imaging centers to include the technically demanding procedure in routine PET studies. Obtaining the input function from images using IDIFs or FA is a popular alternative as it can be done without blood sampling. IDIFs have the advantage of simplicity over FA methods but the spillover and partialvolume effects make the IDIF a highly biased estimate. Therefore, we sought to find a practical and robust method to correct for the spillover and partialvolume effect in IDIF by using simultaneous estimation to determine and correct the crosscontamination between ventricular and myocardial activities.
We compared the estimated input functions from MCIF with the inputs measured from blood samples. Our results show that the 1sample MCIF is validated as a reliable method to estimate input functions and Ki constants. Using the extensive bloodsampling method as the reference, the AUC error of the 1sample MCIF is <3% on average. Ki bias in both rats and mice is <10% and correlation coefficients are high. Most important, no significant difference was found by the t test in the 1sample MCIF in both rats and mice, indicating that the 1sample MCIF can be used as a replacement for input functions measured with extensive blood sampling. To use the 1sample MCIF, a late venous sample, which is easy to collect, can be substituted for the arterial blood sample because late arterial and venous concentrations are very similar, as our results demonstrate. In addition, as the estimated MCIF is the wholeblood time–activity curve C_{a}, at least 1 blood sample must be taken to measure the hematocrit and activity fraction for conversion between C_{p} and C_{a}. This could provide the wholeblood concentration used for the simultaneous estimation in MCIF. Therefore, because 1 blood sample is simple to obtain and is necessary for hematocrit determination, we recommend using the 1sample MCIF. On the other hand, although the 0sample MCIF is not as accurate as 1sample MCIF, its small bias did not reach statistical significance; thus, it may be applied in rat studies when blood sampling is infeasible or in retrospective analyses of data for which no blood samples were taken.
Compared with currently available methods for estimating input functions, MCIF has advantages. First, compared with IDIF, MCIF greatly reduces the bias by correcting for spillover and partialvolume effects. Second, compared with simultaneous estimation, MCIF has fewer parameters to estimate. Whereas the simultaneous estimation method first proposed by Wong et al. (10) models each tissue ROI according to an independent set of compartments, the MCIF method assumes that the measured heart ventricle and myocardium curves can be expressed as a weighted sum of the blood activity and the same underlying extravascular (C_{e}) and metabolized (C_{m}) activity concentrations. Consequently, only 2 VOIs and 1 set of k_{1}∼k_{4} need to be estimated for MCIF with a total number of parameters to estimate 15, which is 10 fewer than the 25 required by the simultaneous estimation method of Wong et al. (10).
We speculate that MCIF will be improved with technologic advances. For example, cardiac and respiratory gating could reduce the spillover and partialvolume effects in the IDIF (21), therefore making MCIF more robust. Similarly, image reconstruction techniques, such as a maximum a posteriori (MAP) algorithm, that accurately model the γray transport can produce images with better resolution, therefore reducing the spillover in the IDIF (22). Those methods can be used in combination with MCIF without any conflicts. When MCIF is applied to an IDIF with less severe spillover and partial volume, MCIF should be able to estimate the input function even more accurately.
Although the MCIF method is developed and validated using ^{18}FFDG, the methodology should be applicable to other PET tracers. In particular, the output equation of the heart ventricles and myocardium would remain the same, and the configuration of the tracer kinetic model and parameter values, including initial values and bounds, would be adjusted. However, for tracers that require precise measurement of metabolites and for which a standard metabolite correction is not available, blood samples are inevitable. Otherwise, for other tracers it would be necessary to validate the adjustments in a study of a limited number of subjects wherein blood samples are collected and used for validation, as we have done here. Moreover, the MCIF should be applicable to human studies with similar adjustments and validation.
CONCLUSION
Herein, we show that the MCIF accurately accounts for spillover and partialvolume effect for IDIF and yields an input function suitable for use in quantifying glucose metabolic rate using the ^{18}FFDG model. Specifically, we show that either 0sample or the 1sample MCIF has AUC error, RMSE, and Ki estimation errors that are much lower than those obtained using the uncorrected IDIF. Furthermore, the use of 1 blood sample achieves a bias of Ki estimates to a level that is not statistically significant and that is lower than the uncertainty in the Ki estimates. Therefore, MCIF can be applied to ^{18}FFDG PET smallanimal imaging for modeling analysis with a minimum bloodsampling requirement. The MCIF method is incorporated into the COMKAT toolbox and is available online at http://comkat.case.edu, free for noncommercial research use.
Acknowledgments
This work was supported by National Institute of Health grants R33CA101073 and R24CA110943. The authors thank Dr. Henry S.C. Huang and the Crump Institute of Molecular Imaging for the courtesy of sharing mouse data with us. We thank Chandra Spring Robinson and Deborah Barkauskas for assisting with the experiments and Dr. Mark Schluchter for discussions on statistics.
Footnotes

COPYRIGHT © 2008 by the Society of Nuclear Medicine, Inc.
References
 Received for publication September 27, 2007.
 Accepted for publication December 20, 2007.