Identifiability of spatiotemporal tissue perfusion models

Eve S Shalom; Sven Van Loo; Amirul Khan; Steven P Sourbron

doi:10.1088/1361-6560/ad4087

Identifiability of spatiotemporal tissue perfusion models

Phys Med Biol. 2024 Apr 18. doi: 10.1088/1361-6560/ad4087. Online ahead of print.

Authors

Eve S Shalom¹, Sven Van Loo², Amirul Khan³, Steven P Sourbron⁴

Affiliations

¹ School of Physics and Astronomy, University of Leeds, Sir William Henry Bragg Building, Woodhouse Lane, Leeds, West Yorkshire, LS2 9JT, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND.
² Department of Applied Physics, University of Ghent, Faculty of engineering and architecture, Technicum blok 4, Sint Pietersnieuwstraat 41, Gent, 9000, BELGIUM.
³ School of Civil Engineering, University of Leeds, Woodhouse Lane, Woodhouse, Leeds, LS2 9LG, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND.
⁴ Division of Clinical Medicine, The University of Sheffield, 18 Claremont Crescent, Sheffield, S10 2TA, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND.

PMID: 38636525
DOI: 10.1088/1361-6560/ad4087

Abstract

Standard models for perfusion quantification in DCE-MRI produce a bias by treating voxels as isolated systems. Spatiotemporal models can remove this bias, but it is unknown whether they are fundamentally identifiable. The aim of this study is to investigate this question in-silico using one-dimensional toy systems with a one-compartment blood flow model and a two-compartment perfusion model.Approach: For each of the two models, identifiability is explored theoretically and in-silico for three systems. Concentrations over space and time are simulated by forward propagation. Different levels of noise and temporal undersampling are added to investigate sensitivity to measurement error. Model parameters are fitted using a standard gradient descent algorithm, applied iteratively with a stepwise increasing time window. Model fitting is repeated with different initial values to probe uniqueness of the solution. Reconstruction accuracy is quantified for each parameter by comparison to the ground truth. Main Results: Theoretical analysis shows that flows and volume fractions are only identifiable up to a constant, and that this degeneracy can be removed by proper choice of parameters. Simulations show that in all cases, the tissue concentrations can be reconstructed accurately. The one-compartment model shows accurate reconstruction of blood velocities and arterial input functions, independent of the initial values and robust to measurement error. The two-compartmental perfusion model was not fully identifiable, showing good reconstruction of arterial velocities and input functions, but multiple valid solutions for the perfusion parameters and venous velocities, and a strong sensitivity to measurement error in these parameters. Significance:These results support the use of one-compartment spatiotemporal flow models, but two-compartment perfusion models were not sufficiently identifiable. Future studies should investigate whether this degeneracy is resolved in more realistic 2D and 3D systems, by adding physically justified constraints, or by optimizing experimental parameters such as injection duration or temporal resolution.

Keywords: DCE-MRI; Inverse Problems; Perfusion; Spatiotemporal Modelling; Tracer Kinetics.

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