Summary

The basic question in DC-MRI is this: given signals measured on a tissue, what are the values of tissue parameters such as perfusion, vascularity or capillary permeability?

By default, dcmri uses a forward-type approach to solve the problem. The approach involves building a forward model that predicts the measured signal for given values of the unknown parameters. The parameters are then adjusted until the forward model correctly predicts the measured signals.

The forward model must be well-defined, i.e. one and only one set of tissue parameters can correctly predict any given signal. This means the model should have enough freedom to predict the variety of signals that can be measured in any given context, but not so much freedom that there are multiple ways of predicting any given signal.

Building a suitable forward model in DC-MRI involves three different different layer of physics. They are described in more detail in the following sections:

• Pharmacokinetics models the concentration of indicator (usually an MRI contrast agent) in terms of parameters such as volume fractions of tissue compartments and the exchange rates between them.

• Relaxation theory models the effect of indicator concentration on electromagnetic tissue proprerties, in particular the longitudinal and transverse relaxation rates.

• MRI signal theory models the effect of MRI pulse sequences and gradients on the magnetisation and the measured signal.

The process of adjusting the model parameters until the signals are correctly predicted is called optimization and is described in more detail in the section on optimization methods. An alternative to the forward-type approach is to perform a stepwwise direct inversion of the model (section inversion).