  Tracer-kinetic models allow for the quantification of kinetic parameters such
as blood flow from dynamic contrast-enhanced magnetic resonance (MR) images.
Fitting the observed data with multi-compartment exchange models is desirable,
as they are physiologically plausible and resolve directly for blood flow and
microvascular function. However, the reliability of model fitting is limited by
the low signal-to-noise ratio, temporal resolution, and acquisition length.
This may result in inaccurate parameter estimates.
  This study introduces physics-informed neural networks (PINNs) as a means to
perform myocardial perfusion MR quantification, which provides a versatile
scheme for the inference of kinetic parameters. These neural networks can be
trained to fit the observed perfusion MR data while respecting the underlying
physical conservation laws described by a multi-compartment exchange model.
Here, we provide a framework for the implementation of PINNs in myocardial
perfusion MR.
  The approach is validated both in silico and in vivo. In the in silico study,
an overall reduction in mean-squared error with the ground-truth parameters was
observed compared to a standard non-linear least squares fitting approach. The
in vivo study demonstrates that the method produces parameter values comparable
to those previously found in literature, as well as providing parameter maps
which match the clinical diagnosis of patients.
