Current status in spatiotemporal analysis of contrast-based perfusion MRI

Abstract

In perfusion MRI, image voxels form a spatially organized network of systems, all exchanging indicator with their immediate neighbors. Yet the current paradigm for perfusion MRI analysis treats all voxels or regions-of-interest as isolated systems supplied by a single global source. This simplification not only leads to long-recognized systematic errors but also fails to leverage the embedded spatial structure within the data. Since the early 2000s, a variety of models and implementations have been proposed to analyze systems with between-voxel interactions. In general, this leads to large and connected numerical inverse problems that are intractible with conventional computational methods. With recent advances in machine learning, however, these approaches are becoming practically feasible, opening up the way for a paradigm shift in the approach to perfusion MRI. This paper seeks to review the work in spatiotemporal modelling of perfusion MRI using a coherent, harmonized nomenclature and notation, with clear physical definitions and assumptions. The aim is to introduce clarity in the state-of-the-art of this promising new approach to perfusion MRI, and help to identify gaps of knowledge and priorities for future research.

Keywords: DCE-MRI; DSC-MRI; perfusion; spatiotemporal modeling; tracer kinetics.

FIGURE 1

Timeline of contributions within the literature landscape leading toward developing spatiotemporal tracer kinetics. The studies listed are grouped by the theme of the work or model applied using distinct colors as indicated by the key.

FIGURE 2

Diagrams of the nine spatiotemporal models proposed in the literature (model equations are given in Table 1). Each model is illustrated for a central voxel and four neighbors, with interstitial (green) and/or vascular compartments (red for arterial or total blood compartments, and blue for venous). Solid colored lines and double‐ended arrows show between‐voxel transport by convection and diffusion, respectively, within a given compartment. Black arrows show within‐voxel exchange between different compartments. Shown are (A) A one‐compartment system with interstitial diffusion; (B) A one‐compartment system with interstitial convection and diffusion; (C) A one‐compartment system with interstitial diffusion and a vascular input; (D) A one‐compartment system with interstitial convection and diffusion and a vascular input; (E) A one‐compartment system with vascular convection; (F) A one‐compartment system with vascular convection and diffusion; (G) A two‐compartment system with vascular convection, interstitial convection and diffusion with bidirectional exchange; (H) A two‐compartment system with vascular convection and mono‐directional exchange; (I) A three‐compartment system with interstitial convection and diffusion, vascular convection, and directional exchange.