Research ArticleCLINICAL INVESTIGATIONS

Optimal Metabolite Curve Fitting for Kinetic Modeling of 11C-WAY-100635

Songmei Wu, R. Todd Ogden, J. John Mann and Ramin V. Parsey
Journal of Nuclear Medicine June 2007, 48 (6) 926-931; DOI: https://doi.org/10.2967/jnumed.106.038075

Article Figures & Data

Figures

  • FIGURE 1. 
    FIGURE 1. 

    Diagram of kinetic model. Parent compound begins in plasma and passes to tissue compartment (thought to be composed primarily of liver but could also include kidneys and other tissues). Some compound is metabolized and moves to “met” compartment; rest is excreted back to blood without being metabolized. Rate parameters k1– k4 are assumed to be nonnegative.

  • FIGURE 2. 
    FIGURE 2. 

    Fitted data for all models for 1 subject's data. Plots show fitted unmetabolized fraction vs. observed data.

  • FIGURE 3. 
    FIGURE 3. 

    Box plots of AIC values for 1-exponential, 2-exponential, Hill, and kinetic models. One- and 2-exponential models have similar results, and kinetic model has smaller values than exponential models. Compared with the others, Hill model tends to have much smaller values: Maximum AIC value is less than median for kinetic model and less than 25th percentile for other models. exp = exponential.

  • FIGURE 4. 
    FIGURE 4. 

    Graph of weighted residual for each model. For better visual display, points are spread out by adding small amount of gaussian noise in x direction. For 1- and 2-exponential models, residuals tend to fall only on one side of zero at each time point. Means of residuals are relatively far from zero, and distributions of residuals are, in general, rather asymmetric and heavily skewed. For kinetic model, similar problems exist. Residuals for Hill model look more reasonable: They are evenly scattered around zero, and their distributions are fairly symmetric. Although, at first 2 time points, residuals are skewed to one side of zero, they are all quite small relative to those of other models.

Tables

  • TABLE 1

    BP1 Measurements Using Each of the 4 Candidate Models on 4 Brain Regions, Along with VT Estimates for Cerebellum

    BP1
    ModelAmygdalaHippocampusCingulateParietal lobeVT, cerebellum
    1-exponential3.87 (2.41)3.14 (1.27)2.54 (1.01)5.91 (5.01)0.555 (0.257)
    2-exponential3.98 (2.56)3.16 (1.27)2.59 (1.09)5.43 (3.13)0.557 (0.237)
    Hill2.73 (1.21)2.47 (1.00)2.03 (0.83)3.88 (1.98)0.488 (0.211)
    Kinetic1.12 (1.31)1.07 (1.43)0.95 (1.26)2.05 (3.69)0.282 (0.237)

    • Data are means, with SDs in parentheses. SDs are substantially smaller for Hill model.

  • TABLE 2

    Paired t Tests and Signed-Rank Tests for Testing Difference Between BP1 and VT Estimates from Different Models

    BP1
    ModelTestAmygdalaHippocampusCingulateParietal lobeVT, cerebellum
    Hill vs. 1-exponentialt statistic6.628.9212.974.939.81
    Degrees of freedom8483848383
    P value<0.0001<0.0001<0.0001<0.0001<0.0001
    No. of outliers23233
    Signed-rank statistic338140138199
    P value<0.0001<0.0001<0.0001<0.0001<0.0001
    Hill vs. 2-exponentialt statistic6.2010.8811.699.0910.95
    Degrees of freedom8483848083
    P value<0.0001<0.0001<0.0001<0.0001<0.0001
    No. of outliers23263
    Signed-rank statistic9612095140246
    P value<0.0001<0.0001<0.0001<0.0001<0.0001
    Hill vs. kinetict statistic−9.79−9.57−8.25−4.07−5.52
    Degrees of freedom7577777678
    P value<0.0001<0.0001<0.0001<0.0001<0.0001
    No. of outliers1199108
    Signed-rank statistic906822791905760
    P value<0.0001<0.0001<0.0001<0.0001<0.0001

    • For Wilcoxon test, all 87 subjects are included, but several outliers (generally resulting from nonconvergence of modeling of PET data) were removed before computing summaries displayed in Table 1 and conducting paired t tests.

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