Spatiotemporal analysis of magnetic resonance perfusion data: The multi-compartment problem

Quantitative analysis in perfusion magnetic resonance imaging (MRI) has shown real potential for extracting clinically relevant diagnostic information. Integration of quantitative perfusion MRI into clinical care is limited, in part due to issues in parameter reproducibility between centres. An assessment of 10 typical dynamic contrast-enhanced MRI analysis software packages is presented across clinical and synthetic datasets in terms of accuracy, repeatability, and reproducibility. Results show differences in Ktrans quantification between the 10 software packages dependent on multiple methodology choices. While reduction of manual methodology steps and improved documentation is recommended, development of spatiotemporal modelling is proposed as a potential paradigm change to improve perfusion analysis. A literature review of early contributions within spatiotemporal modelling for perfusion MRI is carried out, identifying the multi-compartment problem as the most critical and open challenge.

A novel gradient descent-based algorithm is proposed which uses both one- and two-compartment toy-models to determine system identifiability. The whole 1D spatial system is fitted at once from in-silico data. Results across 3 systems for each model showed identifiability of transport and system influx for one-compartment systems. Multiple solutions were reported in two-compartment systems. The long computational times observed restricted the extension of this approach to higher dimensional systems.

The suitability of Physical Informed Neural Networks (PINNs) for spatiotemporal modelling in perfusion MRI has been investigated as a solution for decreased computational times. Implementation of PINNs reports similar outcomes in one- and two-compartment systems compared with the standard approach. Boundary condition enforcement in two-compartment systems is recommended in future developments. Results showed decreased computational time compared to standard optimisation, with straightforward extension into higher spatial dimensions.

The proposed algorithms show spatiotemporal one-compartment models are readily identifiable from 1D toy-models. This work reports multiple solutions for two-compartment systems, indicating further work on fundamental identifiability and optimisation strategies is required.