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Kopylova V, Boronovskiy S, Nartsissov Y. Approaches to vascular network, blood flow, and metabolite distribution modeling in brain tissue. Biophys Rev 2023; 15:1335-1350. [PMID: 37974995 PMCID: PMC10643724 DOI: 10.1007/s12551-023-01106-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2023] [Accepted: 07/24/2023] [Indexed: 11/19/2023] Open
Abstract
The cardiovascular system plays a key role in the transport of nutrients, ensuring a continuous supply of all cells of the body with the metabolites necessary for life. The blood supply to the brain is carried out by the large arteries located on its surface, which branch into smaller arterioles that penetrate the cerebral cortex and feed the capillary bed, thereby forming an extensive branching network. The formation of blood vessels is carried out via vasculogenesis and angiogenesis, which play an important role in both embryo and adult life. The review presents approaches to modeling various aspects of both the formation of vascular networks and the construction of the formed arterial tree. In addition, a brief description of models that allows one to study the blood flow in various parts of the circulatory system and the spatiotemporal metabolite distribution in brain tissues is given. Experimental study of these issues is not always possible due to both the complexity of the cardiovascular system and the mechanisms through which the perfusion of all body cells is carried out. In this regard, mathematical models are a good tool for studying hemodynamics and can be used in clinical practice to diagnose vascular diseases and assess the need for treatment.
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Affiliation(s)
- Veronika Kopylova
- Institute of Cytochemistry and Molecular Pharmacology, Moscow, 115404 Russia
| | | | - Yaroslav Nartsissov
- Institute of Cytochemistry and Molecular Pharmacology, Moscow, 115404 Russia
- Biomedical Research Group, BiDiPharma GmbH, Siek, 22962 Germany
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2
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Otani T, Nishimura N, Yamashita H, Ii S, Yamada S, Watanabe Y, Oshima M, Wada S. Computational modeling of multiscale collateral blood supply in a whole-brain-scale arterial network. PLoS Comput Biol 2023; 19:e1011452. [PMID: 37683012 PMCID: PMC10519592 DOI: 10.1371/journal.pcbi.1011452] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2023] [Revised: 09/25/2023] [Accepted: 08/21/2023] [Indexed: 09/10/2023] Open
Abstract
The cerebral arterial network covering the brain cortex has multiscale anastomosis structures with sparse intermediate anastomoses (O[102] μm in diameter) and dense pial networks (O[101] μm in diameter). Recent studies indicate that collateral blood supply by cerebral arterial anastomoses has an essential role in the prognosis of acute ischemic stroke caused by large vessel occlusion. However, the physiological importance of these multiscale morphological properties-and especially of intermediate anastomoses-is poorly understood because of innate structural complexities. In this study, a computational model of multiscale anastomoses in whole-brain-scale cerebral arterial networks was developed and used to evaluate collateral blood supply by anastomoses during middle cerebral artery occlusion. Morphologically validated cerebral arterial networks were constructed by combining medical imaging data and mathematical modeling. Sparse intermediate anastomoses were assigned between adjacent main arterial branches; the pial arterial network was modeled as a dense network structure. Blood flow distributions in the arterial network during middle cerebral artery occlusion simulations were computed. Collateral blood supply by intermediate anastomoses increased sharply with increasing numbers of anastomoses and provided one-order-higher flow recoveries to the occluded region (15%-30%) compared with simulations using a pial network only, even with a small number of intermediate anastomoses (≤10). These findings demonstrate the importance of sparse intermediate anastomoses, which are generally considered redundant structures in cerebral infarction, and provide insights into the physiological significance of the multiscale properties of arterial anastomoses.
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Affiliation(s)
- Tomohiro Otani
- Graduate School of Engineering Science, Osaka University, Osaka, Japan
| | - Nozomi Nishimura
- Graduate School of Engineering Science, Osaka University, Osaka, Japan
| | - Hiroshi Yamashita
- Graduate School of Integrated Sciences for Life, Hiroshima University, Hiroshima, Japan
| | - Satoshi Ii
- Graduate School of Systems Design, Tokyo Metropolitan University, Tokyo, Japan
| | - Shigeki Yamada
- Department of Neurosurgery, Nagoya City University Graduate School of Medical Science, Aichi, Japan
- Interfaculty Initiative in Information Studies, The University of Tokyo, Tokyo, Japan
| | - Yoshiyuki Watanabe
- Department of Radiology, Shiga University of Medical Science, Shiga, Japan
| | - Marie Oshima
- Interfaculty Initiative in Information Studies, The University of Tokyo, Tokyo, Japan
| | - Shigeo Wada
- Graduate School of Engineering Science, Osaka University, Osaka, Japan
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Hague JP, Keelan J, Beishon L, Swienton D, Robinson TG, Chung EML. Three-dimensional simulations of embolic stroke and an equation for sizing emboli from imaging. Sci Rep 2023; 13:3021. [PMID: 36810427 PMCID: PMC9944911 DOI: 10.1038/s41598-023-29974-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2022] [Accepted: 02/14/2023] [Indexed: 02/23/2023] Open
Abstract
Stroke simulations are needed to run in-silico trials, develop hypotheses for clinical studies and to interpret ultrasound monitoring and radiological imaging. We describe proof-of-concept three-dimensional stroke simulations, carrying out in silico trials to relate lesion volume to embolus diameter and calculate probabilistic lesion overlap maps, building on our previous Monte Carlo method. Simulated emboli were released into an in silico vasculature to simulate 1000 s of strokes. Infarct volume distributions and probabilistic lesion overlap maps were determined. Computer-generated lesions were assessed by clinicians and compared with radiological images. The key result of this study is development of a three-dimensional simulation for embolic stroke and its application to an in silico clinical trial. Probabilistic lesion overlap maps showed that the lesions from small emboli are homogeneously distributed throughout the cerebral vasculature. Mid-sized emboli were preferentially found in posterior cerebral artery (PCA) and posterior region of the middle cerebral artery (MCA) territories. For large emboli, MCA, PCA and anterior cerebral artery (ACA) lesions were comparable to clinical observations, with MCA, PCA then ACA territories identified as the most to least probable regions for lesions to occur. A power law relationship between lesion volume and embolus diameter was found. In conclusion, this article showed proof-of-concept for large in silico trials of embolic stroke including 3D information, identifying that embolus diameter could be determined from infarct volume and that embolus size is critically important to the resting place of emboli. We anticipate this work will form the basis of clinical applications including intraoperative monitoring, determining stroke origins, and in silico trials for complex situations such as multiple embolisation.
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Affiliation(s)
- James P. Hague
- grid.10837.3d0000 0000 9606 9301School of Physical Sciences, The Open University, Walton Hall, Milton Keynes, MK7 6AA UK
| | - Jonathan Keelan
- grid.10837.3d0000 0000 9606 9301School of Physical Sciences, The Open University, Walton Hall, Milton Keynes, MK7 6AA UK
| | - Lucy Beishon
- grid.9918.90000 0004 1936 8411Department of Cardiovascular Sciences, University of Leicester, Leicester, LE1 7RH UK
| | - David Swienton
- grid.269014.80000 0001 0435 9078Department of Radiology, University Hospitals of Leicester NHS Trust, Leicester, LE1 5WW UK
| | - Thompson G. Robinson
- grid.511501.1NIHR Leicester Biomedical Research Centre, British Heart Foundation Cardiovascular Research Centre, Leicester, LE3 9QP UK
| | - Emma M. L. Chung
- grid.9918.90000 0004 1936 8411Department of Cardiovascular Sciences, University of Leicester, Leicester, LE1 7RH UK ,grid.269014.80000 0001 0435 9078Department of Medical Physics, Leicester Royal Infirmary, University Hospitals of Leicester NHS Trust, Leicester, LE1 5WW UK ,grid.13097.3c0000 0001 2322 6764School of Life Course and Population Sciences, King’s College London, Guy’s Campus, London, SE1 1UL UK
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Bollmann S, Mattern H, Bernier M, Robinson SD, Park DJ, Speck O, Polimeni JR. Imaging of the pial arterial vasculature of the human brain in vivo using high-resolution 7T time-of-flight angiography. eLife 2022; 11:71186. [PMID: 35486089 PMCID: PMC9150892 DOI: 10.7554/elife.71186] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2021] [Accepted: 04/28/2022] [Indexed: 11/30/2022] Open
Abstract
The pial arterial vasculature of the human brain is the only blood supply to the neocortex, but quantitative data on the morphology and topology of these mesoscopic arteries (diameter 50–300 µm) remains scarce. Because it is commonly assumed that blood flow velocities in these vessels are prohibitively slow, non-invasive time-of-flight magnetic resonance angiography (TOF-MRA)—which is well suited to high 3D imaging resolutions—has not been applied to imaging the pial arteries. Here, we provide a theoretical framework that outlines how TOF-MRA can visualize small pial arteries in vivo, by employing extremely small voxels at the size of individual vessels. We then provide evidence for this theory by imaging the pial arteries at 140 µm isotropic resolution using a 7 Tesla (T) magnetic resonance imaging (MRI) scanner and prospective motion correction, and show that pial arteries one voxel width in diameter can be detected. We conclude that imaging pial arteries is not limited by slow blood flow, but instead by achievable image resolution. This study represents the first targeted, comprehensive account of imaging pial arteries in vivo in the human brain. This ultra-high-resolution angiography will enable the characterization of pial vascular anatomy across the brain to investigate patterns of blood supply and relationships between vascular and functional architecture.
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Affiliation(s)
- Saskia Bollmann
- Centre for Advanced Imaging, The University of Queensland, Brisbane, Australia
| | - Hendrik Mattern
- Department of Biomedical Magnetic Resonance, Otto-von-Guericke University Magdeburg, Magdeburg, Germany
| | - Michaël Bernier
- Athinoula A Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, United States
| | - Simon D Robinson
- Centre for Advanced Imaging, The University of Queensland, Brisbane, Australia
| | - Daniel J Park
- Athinoula A Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, United States
| | - Oliver Speck
- German Center for Neurodegenerative Diseases, Magdeburg, Germany
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Keelan J, Hague JP. The role of vascular complexity on optimal junction exponents. Sci Rep 2021; 11:5408. [PMID: 33686129 PMCID: PMC7940437 DOI: 10.1038/s41598-021-84432-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2020] [Accepted: 01/28/2021] [Indexed: 11/25/2022] Open
Abstract
We examine the role of complexity on arterial tree structures, determining globally optimal vessel arrangements using the Simulated AnneaLing Vascular Optimization algorithm, a computational method which we have previously used to reproduce features of cardiac and cerebral vasculatures. In order to progress computational methods for growing arterial networks, deeper understanding of the stability of computational arterial growth algorithms to complexity, variations in physiological parameters (such as metabolic costs for maintaining and pumping blood), and underlying assumptions regarding the value of junction exponents is needed. We determine the globally optimal structure of two-dimensional arterial trees; analysing how physiological parameters affect tree morphology and optimal bifurcation exponent. We find that considering the full complexity of arterial trees is essential for determining the fundamental properties of vasculatures. We conclude that optimisation-based arterial growth algorithms are stable against uncertainties in physiological parameters, while optimal bifurcation exponents (a key parameter for many arterial growth algorithms) are affected by the complexity of vascular networks and the boundary conditions dictated by organs.
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Affiliation(s)
- Jonathan Keelan
- School of Physical Science, The Open University, Milton Keynes, MK7 6AA, UK
| | - James P Hague
- School of Physical Science, The Open University, Milton Keynes, MK7 6AA, UK.
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Multiscale modeling of human cerebrovasculature: A hybrid approach using image-based geometry and a mathematical algorithm. PLoS Comput Biol 2020; 16:e1007943. [PMID: 32569287 PMCID: PMC7332106 DOI: 10.1371/journal.pcbi.1007943] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2019] [Revised: 07/02/2020] [Accepted: 05/11/2020] [Indexed: 11/25/2022] Open
Abstract
The cerebral vasculature has a complex and hierarchical network, ranging from vessels of a few millimeters to superficial cortical vessels with diameters of a few hundred micrometers, and to the microvasculature (arteriole/venule) and capillary beds in the cortex. In standard imaging techniques, it is difficult to segment all vessels in the network, especially in the case of the human brain. This study proposes a hybrid modeling approach that determines these networks by explicitly segmenting the large vessels from medical images and employing a novel vascular generation algorithm. The framework enables vasculatures to be generated at coarse and fine scales for individual arteries and veins with vascular subregions, following the personalized anatomy of the brain and macroscale vasculatures. In this study, the vascular structures of superficial cortical (pial) vessels before they penetrate the cortex are modeled as a mesoscale vasculature. The validity of the present approach is demonstrated through comparisons with partially observed data from existing measurements of the vessel distributions on the brain surface, pathway fractal features, and vascular territories of the major cerebral arteries. Additionally, this validation provides some biological insights: (i) vascular pathways may form to ensure a reasonable supply of blood to the local surface area; (ii) fractal features of vascular pathways are not sensitive to overall and local brain geometries; and (iii) whole pathways connecting the upstream and downstream entire-scale cerebral circulation are highly dependent on the local curvature of the cerebral sulci. Cerebral autoregulation in the complex vascular networks of the brain is an amazing achievement. We believe that numerical analysis of the cerebral blood circulation using an anatomically precise vascular model provides a powerful tool for evaluating the direct relationships between local- and global-scale blood flows. However, there is a lack of information about the overall vascular pathways in the human brain, preventing a monolithic model of the human cerebrovasculature from being established. This paper presents a multiscale model of human cerebrovasculature based on a hybrid approach that uses image-based geometries and a newly developed mathematical algorithm. One important argument of this paper is the validity of the cerebrovasculature represented in the model, which reflects anatomical features of major cerebral vasculatures and brain shape, and has strong similarities with available data for human superficial cortical vessels. Investigations of the reconstructed model allow us to derive some biological insights and associated hypotheses for the cerebral vasculature. The authors believe the present cerebrovascular model can be applied to numerical simulations of the entire-scale cerebral blood flow.
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