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Estimating Input Delay and Rate Constants

This example demonstrates an approach to simultaneously estimating input function delay along with parameters of the 1-tissue compartment (e.g. blood flow) model. For the sake of generality, this could be interpreted as a dynamic contrast-enhanced (DCE) MRI or perfusion PET study.

Tissue uptake

This model has one tissue compartment. Material in the blood is assumed to rapidly exchange with that in (extravascular) tissue. The tissue model has two rate constants: K₁ and k₂ and is depicted in the diagram:

Input function

This example also demonstrates how to temporally align measured input function data to the tissue (image) data. Here the plasma concentration vs. time t is modeled as