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Shalom ES, Van Loo S, Khan A, Sourbron SP. Identifiability of spatiotemporal tissue perfusion models. Phys Med Biol 2024; 69:115034. [PMID: 38636525 DOI: 10.1088/1361-6560/ad4087] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2023] [Accepted: 04/18/2024] [Indexed: 04/20/2024]
Abstract
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.
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Affiliation(s)
- Eve S Shalom
- School of Physics and Astronomy, The University of Leeds, United Kingdom
| | - Sven Van Loo
- Department of Applied Physics, Ghent University, Belgium
| | - Amirul Khan
- School of Civil Engineering, The University of Leeds, United Kingdom
| | - Steven P Sourbron
- Division of Clinical Medicine, University of Sheffield, United Kingdom
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Shalom ES, Khan A, Van Loo S, Sourbron SP. Current status in spatiotemporal analysis of contrast-based perfusion MRI. Magn Reson Med 2024; 91:1136-1148. [PMID: 37929645 PMCID: PMC10962600 DOI: 10.1002/mrm.29906] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2023] [Revised: 10/05/2023] [Accepted: 10/10/2023] [Indexed: 11/07/2023]
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.
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Affiliation(s)
- Eve S. Shalom
- School of Physics and AstronomyUniversity of LeedsLeedsUK
- Division of Clinical MedicineUniversity of SheffieldSheffieldUK
| | - Amirul Khan
- School of Civil EngineeringUniversity of LeedsLeedsUK
| | - Sven Van Loo
- School of Physics and AstronomyUniversity of LeedsLeedsUK
- Department of Applied PhysicsGhent UniversityGhentBelgium
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Fisher-Rao Regularized Transport Analysis of the Glymphatic System and Waste Drainage. ACTA ACUST UNITED AC 2020; 12267:573-582. [PMID: 33415322 DOI: 10.1007/978-3-030-59728-3_56] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
In this work, a unified representation of all the time-varying dynamics is accomplished with a Lagrangian framework for analyzing Fisher-Rao regularized dynamical optimal mass transport (OMT) derived flows. While formally equivalent to the Eulerian based Schrödinger bridge OMT regularization scheme, the Fisher-Rao approach allows a simple and interpretable methodology for studying the flows of interest in the present work. The advantage of the proposed Lagrangian technique is that the time-varying particle trajectories and attributes are displayed in a single visualization. This provides a natural capability to identify and distinguish flows under different conditions. The Lagrangian analysis applied to the glymphatic system (brain waste removal pathway associated with Alzheimer's Disease) successfully captures known flows and distinguishes between flow patterns under two different anesthetics, providing deeper insights into altered states of waste drainage.
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Kaur J, Davoodi-Bojd E, Fahmy LM, Zhang L, Ding G, Hu J, Zhang Z, Chopp M, Jiang Q. Magnetic Resonance Imaging and Modeling of the Glymphatic System. Diagnostics (Basel) 2020; 10:diagnostics10060344. [PMID: 32471025 PMCID: PMC7344900 DOI: 10.3390/diagnostics10060344] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2020] [Revised: 05/22/2020] [Accepted: 05/25/2020] [Indexed: 12/20/2022] Open
Abstract
The glymphatic system is a newly discovered waste drainage pathway in the brain; it plays an important role in many neurological diseases. Ongoing research utilizing various cerebrospinal fluid tracer infusions, either directly or indirectly into the brain parenchyma, is investigating clearance pathways by using distinct imaging techniques. In the present review, we discuss the role of the glymphatic system in various neurological diseases and efflux pathways of brain waste clearance based on current evidence and controversies. We mainly focus on new magnetic resonance imaging (MRI) modeling techniques, along with traditional computational modeling, for a better understanding of the glymphatic system function. Future sophisticated modeling techniques hold the potential to generate quantitative maps for glymphatic system parameters that could contribute to the diagnosis, monitoring, and prognosis of neurological diseases. The non-invasive nature of MRI may provide a safe and effective way to translate glymphatic system measurements from bench-to-bedside.
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Affiliation(s)
- Jasleen Kaur
- Department of Neurology, Henry Ford Health System, Detroit, MI 48202, USA; (J.K.); (E.D.-B.); (L.M.F.); (L.Z.); (G.D.); (Z.Z.); (M.C.)
- Department of Physics, Oakland University, Rochester, MI 48309, USA
| | - Esmaeil Davoodi-Bojd
- Department of Neurology, Henry Ford Health System, Detroit, MI 48202, USA; (J.K.); (E.D.-B.); (L.M.F.); (L.Z.); (G.D.); (Z.Z.); (M.C.)
- Department of Radiology, Henry Ford Health System, Detroit, MI 48202, USA
| | - Lara M Fahmy
- Department of Neurology, Henry Ford Health System, Detroit, MI 48202, USA; (J.K.); (E.D.-B.); (L.M.F.); (L.Z.); (G.D.); (Z.Z.); (M.C.)
- Department of Psychiatry and Behavioral Neurosciences, Wayne State University, Detroit, MI 48201, USA
| | - Li Zhang
- Department of Neurology, Henry Ford Health System, Detroit, MI 48202, USA; (J.K.); (E.D.-B.); (L.M.F.); (L.Z.); (G.D.); (Z.Z.); (M.C.)
| | - Guangliang Ding
- Department of Neurology, Henry Ford Health System, Detroit, MI 48202, USA; (J.K.); (E.D.-B.); (L.M.F.); (L.Z.); (G.D.); (Z.Z.); (M.C.)
| | - Jiani Hu
- Department of Radiology, Wayne State University, Detroit, MI 48201, USA;
| | - Zhenggang Zhang
- Department of Neurology, Henry Ford Health System, Detroit, MI 48202, USA; (J.K.); (E.D.-B.); (L.M.F.); (L.Z.); (G.D.); (Z.Z.); (M.C.)
| | - Michael Chopp
- Department of Neurology, Henry Ford Health System, Detroit, MI 48202, USA; (J.K.); (E.D.-B.); (L.M.F.); (L.Z.); (G.D.); (Z.Z.); (M.C.)
- Department of Physics, Oakland University, Rochester, MI 48309, USA
| | - Quan Jiang
- Department of Neurology, Henry Ford Health System, Detroit, MI 48202, USA; (J.K.); (E.D.-B.); (L.M.F.); (L.Z.); (G.D.); (Z.Z.); (M.C.)
- Department of Physics, Oakland University, Rochester, MI 48309, USA
- Correspondence: ; Tel.: +1-313-916-8735; Fax: +1-313-916-1324
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