Identifiability of spatiotemporal tissue perfusion models.

Objective.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.

Current status in spatiotemporal analysis of contrast-based perfusion MRI.

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.

The ISMRM Open Science Initiative for Perfusion Imaging (OSIPI): Results from the OSIPI-Dynamic Contrast-Enhanced challenge.

PURPOSE: K trans $$ {K}^{\mathrm{trans}} $$ has often been proposed as a quantitative imaging biomarker for diagnosis, prognosis, and treatment response assessment for various tumors. None of the many software tools for K trans $$ {K}^{\mathrm{trans}} $$ quantification are standardized. The ISMRM Open Science Initiative for Perfusion Imaging-Dynamic Contrast-Enhanced (OSIPI-DCE) challenge was designed to benchmark methods to better help the efforts to standardize K trans $$ {K}^{\mathrm{trans}} $$ measurement. METHODS: A framework was created to evaluate K trans $$ {K}^{\mathrm{trans}} $$ values produced by DCE-MRI analysis pipelines to enable benchmarking. The perfusion MRI community was invited to apply their pipelines for K trans $$ {K}^{\mathrm{trans}} $$ quantification in glioblastoma from clinical and synthetic patients. Submissions were required to include the entrants' K trans $$ {K}^{\mathrm{trans}} $$ values, the applied software, and a standard operating procedure. These were evaluated using the proposed OSIP I gold $$ \mathrm{OSIP}{\mathrm{I}}_{\mathrm{gold}} $$ score defined with accuracy, repeatability, and reproducibility components. RESULTS: Across the 10 received submissions, the OSIP I gold $$ \mathrm{OSIP}{\mathrm{I}}_{\mathrm{gold}} $$ score ranged from 28% to 78% with a 59% median. The accuracy, repeatability, and reproducibility scores ranged from 0.54 to 0.92, 0.64 to 0.86, and 0.65 to 1.00, respectively (0-1 = lowest-highest). Manual arterial input function selection markedly affected the reproducibility and showed greater variability in K trans $$ {K}^{\mathrm{trans}} $$ analysis than automated methods. Furthermore, provision of a detailed standard operating procedure was critical for higher reproducibility. CONCLUSIONS: This study reports results from the OSIPI-DCE challenge and highlights the high inter-software variability within K trans $$ {K}^{\mathrm{trans}} $$ estimation, providing a framework for ongoing benchmarking against the scores presented. Through this challenge, the participating teams were ranked based on the performance of their software tools in the particular setting of this challenge. In a real-world clinical setting, many of these tools may perform differently with different benchmarking methodology.