Low-order differentiator

One of the perils of any modeling analysis is the failure to obtain the input function to the system under study. For both single photon and PET imaging of the heart, the left ventricular cavity blood pool concentration-time curve gives the appropriate information when it is convoluted with the vascular transport function between the ventricular cavity and the coronary artery inflow. (Low order differential operators can be used to describe purely intravascular dispersive transport.)... 

Steady-state empirical models can be used for instrument calibration, process optimization, and specific instances of process control. Single-input, single-output (SISO) models typically consist of simple polynomials relating an output to an input. Dynamic empirical models can be employed to understand process behavior during upset conditions. They are also used to design control systems and to analyze their performance. Empirical dynamic models typically are low-order differential equations or transfer function models (e.g., first-or second-order model, perhaps with a time delay), with unspecified model parameters to be determined from experimental data. However, in some situations more complicated models are valuable in control system design, as discussed later in this chapter. 

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