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

¹ New York City Department of Health and Mental Hygiene, New York, New York; ² Department of Biostatistics, Columbia University School of Public Health, New York, New York; ³ Department of Psychiatry, Columbia University College of Physicians and Surgeons, New York, New York; ⁴ Department of Neuroscience, New York State Psychiatric Institute, New York, New York; and ⁵ Department of Radiology, Columbia University College of Physicians and Surgeons, New York, New York

View larger version (5K): [in this window] [in a new window]   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.

View larger version (19K): [in this window] [in a new window]   FIGURE 2.  Fitted data for all models for 1 subject's data. Plots show fitted unmetabolized fraction vs. observed data.

View larger version (9K): [in this window] [in a new window]   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.

View larger version (17K): [in this window] [in a new window]   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.