A common approach to produce simplified modelbased methods is the use of single-scan techniques. Here, based on a good understanding of the relationship between tissue radioactivity and the underlying physiological parameters, tissue radioactivity information is acquired during one scan interval. This single measurement permits the estimation of a single unknown physiological parameter. Since most models have multiple rate constants, some corrections must be applied to account for these other unknowns. Careful design of a single-scan technique ensures that variation in these nuisance parameters produces only minor errors in the parameter of interest.
For the measurement of cerebral blood flow with [15O]water or comparable diffusible tracers, two approaches have been taken to produce single-scan methods. Some of the earliest studies used continuous inhalation of [15O]CO2 , which is rapidly converted to [15O]water in the lungs. By achieving constant radioactivity levels, the derivative in the differential equation of uptake of the tracer (Eq. 15 with additional terms for radioactive decay) can be set to zero, and K1 can be determined from an algebraic formula in terms of tissue and blood radioactivity. A different approach uses a bolus injection followed by a single short scan [129, 130]. This autoradiographic method uses the explicit solution of the model (Eq. 27) to determine K1 from the integrated tissue radioactivity and a measured input function. Both of these methods treat the estimated K1 values as equal to blood flow, assuming a large permeability-surface (PS) area product for the tracer (Eq. 5). Both methods also require the use of an assumed value for the tracer distribution volume V in order to specify k2 as K1/V. As only one tissue measurement is made, only one unknown parameter can be determined. The short scan of the autoradiographic method was designed in part to minimize the sensitivity of this method to errors in the assumed value of the distribution volume.
Another example of single-scan, model-based techniques is the autoradiographic method for measurement of glucose metabolism, which was developed in rats with [14C]deoxyglucose  and extended to PET using [18F]2-fluoro-2-deoxy-D-glucose [2-4]. These methods take advantage of the fact that most of the radioactivity in the tissue by 45 min post-injection has been phosphorylated, so that the total tissue radioactivity can be used to estimate the net flux into tissue of deoxyglucose, K. This is the same rate constant as determined from the slope of the Patlak plot. Effectively, these methods estimate the slope of a Patlak plot by using the measured tissue value at one data point and by using population values of the model rate constants to estimate the y-intercept of the straight line. A number of other formulations of this approach have been developed [131-133], each with different sensitivities to errors in the assumed rate constants. Finally, since FDG is an analog of glucose, the metabolic rate of glucose is estimated from the measured net flux of FDG using the measured plasma glucose level and an assumed scaling factor, the lumped constant [1,5-9].
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