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. 2011:2011:234679.
doi: 10.1155/2011/234679. Epub 2010 Nov 28.

Propagation of Blood Function Errors to the Estimates of Kinetic Parameters with Dynamic PET

Yafang Cheng  1 , Imam Şamil Yetik
Affiliations

Propagation of Blood Function Errors to the Estimates of Kinetic Parameters with Dynamic PET

Yafang Cheng et al. Int J Biomed Imaging. 2011.

Abstract

Dynamic PET, in contrast to static PET, can identify temporal variations in the radiotracer concentration. Mathematical modeling of the tissue of interest in dynamic PET can be simplified using compartment models as a linear system where the time activity curve of a specific tissue is the convolution of the tracer concentration in the plasma and the impulse response of the tissue containing kinetic parameters. Since the arterial sampling of blood to acquire the value of tracer concentration is invasive, blind methods to estimate both blood input function and kinetic parameters have recently drawn attention. Several methods have been developed, but the effect of accuracy of the estimated blood function on the estimation of the kinetic parameters is not studied. In this paper, we present a method to compute the error in the kinetic parameter estimates caused by the error in the blood input function. Computer simulations show that analytical expressions we derive are sufficiently close to results obtained from numerical methods. Our findings are important to observe the effect of the blood function on kinetic parameter estimation, but also useful to evaluate various blind methods and observe the dependence of kinetic parameter estimates to certain parts of the blood function.

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Figures

Figure 1
Figure 1
Three compartments used to model the transfer of the tracer between physical compartments and chemical states.
Figure 2
Figure 2
The input blood function.
Figure 3
Figure 3
The observed noisy TAC for background, liver, and tumor.
Figure 4
Figure 4
Comparison between the estimated k 1, k 2, k 3, and k 4 of liver using the derived expressions and numerical method for a range of erroneous blood functions. A single sample out of 19 samples of C pn has an error. The results are given for two random samples.
Figure 5
Figure 5
Three compartments used to model the transfer of the tracer between physical compartments and chemical states.
Figure 6
Figure 6
Comparison between the estimated k 1, k 2, k 3, and k 4 of liver using the derived expressions and numerical approximation for a range of erroneous blood functions. Top two figures show results when all samples of the blood are erroneous, (a,b)/(c,d) when the initial peak is erroneous, and (e,f) when the tail part is erroneous.
Figure 7
Figure 7
Comparison between the estimated k 1, k 2, k 3, and k 4 of tumor using the derived expressions and numerical approximation for a range of erroneous blood functions. Top two figures show results when all samples of the blood are erroneous, middle two when the initial peak is erroneous, and the bottom two when the tail part is erroneous.
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