Investigation of a new input function validation approach for dynamic mouse microPET studies
Introduction
In dynamic micro positron emission tomography (PET) studies,1., 2. a valid time-activity curve (TAC) of the injected tracer in blood, called the input function, is required for reliable quantification of tissue biological function in terms of absolute biological units.3 Image-based methods for deriving input function if validated can make the quantification reliable and practical.4., 5. Even though a multiple of such methods have been validated and used for human studies,4., 5., 6., 7., 8., 9., 10., 11., their applicability to mouse microPET studies that have unique characteristics has not been demonstrated. For example, using factor analysis with positivity constraint,6., 12., 13., 14. we have obtained a blood curve in a dynamic mouse microPET study, as shown in Figure 1. Even though the curve appears reasonable, experimental evidence is needed to characterize the curve’s accuracy/limitation, so one can use the method with full confidence that it will give reliable input functions. Experimental validation of results obtained from such derivation methods for mouse studies is thus critically needed. The conventional validation method, commonly used for studies in humans and large animals, is not applicable for mouse studies, because it uses serial blood samples taken during a dynamic study as a gold standard.4., 6., 7., 8., 9., 10., 11., 15. The procedure of taking serial blood samples is technically difficult due to the small total blood volume in mouse and long time delays in drawing consecutive samples. While, eventually, the difficulty will be solved by some future technical advancement, we have sought alternative approaches that are applicable today.
We have conceived a novel validation approach to address the problem. The approach involves taking only a few blood samples per mouse and measuring their radioactivity concentrations during a dynamic microPET study. After a multiple of separate mouse studies, a large set of deviations between the blood sample measurements and image-derived input function are obtained. The accuracy/adequacy of the derived input functions can then be assessed statistically based on these deviations. In this paper, we present the theoretical basis of the approach, the associated physical, biological, and statistical issues involved, as well as computer simulations that demonstrate the capability of the new approach for discriminating inaccurate input functions. Implication of the approach in terms of the ultimate goal of quantitating tissue biological function will also be discussed.
Section snippets
Theoretical foundation of the new approach
Let Cm(ti) denote a measurement at time ti of a blood TAC (Cb(t)). If the measurement is unbiased, deviation of the measurement from the true blood TAC at the corresponding time point (i.e., Cm(ti)−Cb(ti)) will be a random variate of zero mean value. Let Cd(t) denote the image-derived input function. The deviation of the measurement from the image-derived input function (i.e., ed(ti) = Cm(ti)−Cd(ti)) would have a zero mean value if the derived input function matches the true blood TAC, regardless
Methods
Computer simulation was performed to evaluate the capability of the new approach. For each condition, three to six blood samples (ns) from each of 10 to 20 animals (na) were simulated. In order to have a high statistical confidence of the evaluation results, each experimental condition was repeated 500 times. Details of the computer simulation are described below.
Results
In Figure 2A, a set of 20 simulated input functions in one computer simulation study is shown. The spread among the different curves demonstrated that interanimal and interstudy variability in real studies was considered in the simulation study. Figure 2B shows a derived curve with an inaccuracy simulating a 5% contamination (i.e., r2 = 0.05) from uptake kinetics in tissue. The curve without inaccuracy is also shown as a comparison. The curves show visually the amount of inaccuracy of the derived
Discussions
Using serial blood samples as a gold standard for validating blood curves in a mouse microPET study is hindered by the small blood volume in mouse and the long time delays in drawing consecutive blood samples in mouse studies. At the same time, due to biological and experimental variability (variable injections), it is unrealistic to assume a common input function for different animals or studies, and one cannot simply group together all blood samples from different animals as a single input
Conclusions
The study has shown that the new approach that needs only a few blood samples per mouse can detect small systematic errors in image-derived input functions with high discriminating power. The approach is thus expected to be useful for certifying the accuracy of input functions derived with image-based methods from dynamic mouse microPET studies. The approach can also provide useful information for improvement/refinement of image-based input function methods. The ability to estimate an effective
Acknowledgements
This research was partially supported by the Office of Science (BER), U.S. Department of Energy, Cooperative Agreement No. DE-FC03-02ER63420, and by University of California Biotechnology STAR Grants 01-10184 and 01-10186.
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