Calculation of Velocity Distributions

The primary results of PET-measurements are spatially resolved tracer concentration distributions. For the modelling of transfer processes we need the velocity distribution. It is necessary for the calculation of the velocity distribution to determine the tracer concentration in two neighbouring cross sections (Q and Q2) (distance SI) at two times (t and t + At) while the tracer pulse is passing the cross sections. 

Area ranges (Fq) of equal tracer concentration are selected from the tomographic images of the cross sections and the specific activities A](t) and (Bq/cm ) are determined in these area ranges. The same is done with the images, measured at time t + At (specific activities Aj(t + At), A2(t + At)). 

The following relations can be derived from the geometrical values (lenght /,, radius defined in Fig. 2.7. 

The specific activity is proportional to the part of F, which the parabolic profile covered at the measuring time in the particular cross section. Therefore, the following relations for the activity ratios can be derived  

The flow velocity can be calculated from the activity ratios in the area range Fq. It is not necessary to determine absolute values of the specific activity. 

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