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Wang X, Li K, Yuan Y, Zhang N, Zou Z, Wang Y, Yan S, Li X, Zhao P, Li Q. Nonlinear Elasticity of Blood Vessels and Vascular Grafts. ACS Biomater Sci Eng 2024; 10:3631-3654. [PMID: 38815169 DOI: 10.1021/acsbiomaterials.4c00326] [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] [Indexed: 06/01/2024]
Abstract
The transplantation of vascular grafts has emerged as a prevailing approach to address vascular disorders. However, the development of small-diameter vascular grafts is still in progress, as they serve in a more complicated mechanical environment than their counterparts with larger diameters. The biocompatibility and functional characteristics of small-diameter vascular grafts have been well developed; however, mismatch in mechanical properties between the vascular grafts and native arteries has not been accomplished, which might facilitate the long-term patency of small-diameter vascular grafts. From a point of view in mechanics, mimicking the nonlinear elastic mechanical behavior exhibited by natural blood vessels might be the state-of-the-art in designing vascular grafts. This review centers on elucidating the nonlinear elastic behavior of natural blood vessels and vascular grafts. The biological functionality and limitations associated with as-reported vascular grafts are meticulously reviewed and the future trajectory for fabricating biomimetic small-diameter grafts is discussed. This review might provide a different insight from the traditional design and fabrication of artificial vascular grafts.
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Affiliation(s)
- Xiaofeng Wang
- School of Mechanics and Safety Engineering, National Center for International Research of Micro-nano Molding Technology, Zhengzhou University, Zhengzhou 450001, China
- The State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China
| | - Kecheng Li
- School of Mechanics and Safety Engineering, National Center for International Research of Micro-nano Molding Technology, Zhengzhou University, Zhengzhou 450001, China
| | - Yuan Yuan
- School of Mechanics and Safety Engineering, National Center for International Research of Micro-nano Molding Technology, Zhengzhou University, Zhengzhou 450001, China
| | - Ning Zhang
- School of Mechanics and Safety Engineering, National Center for International Research of Micro-nano Molding Technology, Zhengzhou University, Zhengzhou 450001, China
| | - Zifan Zou
- School of Mechanics and Safety Engineering, National Center for International Research of Micro-nano Molding Technology, Zhengzhou University, Zhengzhou 450001, China
| | - Yun Wang
- School of Mechanics and Safety Engineering, National Center for International Research of Micro-nano Molding Technology, Zhengzhou University, Zhengzhou 450001, China
| | - Shujie Yan
- School of Mechanics and Safety Engineering, National Center for International Research of Micro-nano Molding Technology, Zhengzhou University, Zhengzhou 450001, China
| | - Xiaomeng Li
- School of Mechanics and Safety Engineering, National Center for International Research of Micro-nano Molding Technology, Zhengzhou University, Zhengzhou 450001, China
| | - Peng Zhao
- The State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China
| | - Qian Li
- School of Mechanics and Safety Engineering, National Center for International Research of Micro-nano Molding Technology, Zhengzhou University, Zhengzhou 450001, China
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Terragni F, Martinson WD, Carretero M, Maini PK, Bonilla LL. Soliton approximation in continuum models of leader-follower behavior. Phys Rev E 2023; 108:054407. [PMID: 38115402 DOI: 10.1103/physreve.108.054407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Accepted: 10/17/2023] [Indexed: 12/21/2023]
Abstract
Complex biological processes involve collective behavior of entities (bacteria, cells, animals) over many length and time scales and can be described by discrete models that track individuals or by continuum models involving densities and fields. We consider hybrid stochastic agent-based models of branching morphogenesis and angiogenesis (new blood vessel creation from preexisting vasculature), which treat cells as individuals that are guided by underlying continuous chemical and/or mechanical fields. In these descriptions, leader (tip) cells emerge from existing branches and follower (stalk) cells build the new sprout in their wake. Vessel branching and fusion (anastomosis) occur as a result of tip and stalk cell dynamics. Coarse graining these hybrid models in appropriate limits produces continuum partial differential equations (PDEs) for endothelial cell densities that are more analytically tractable. While these models differ in nonlinearity, they produce similar equations at leading order when chemotaxis is dominant. We analyze this leading order system in a simple quasi-one-dimensional geometry and show that the numerical solution of the leading order PDE is well described by a soliton wave that evolves from vessel to source. This wave is an attractor for intermediate times until it arrives at the hypoxic region releasing the growth factor. The mathematical techniques used here thus identify common features of discrete and continuum approaches and provide insight into general biological mechanisms governing their collective dynamics.
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Affiliation(s)
- F Terragni
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - W D Martinson
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - M Carretero
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - P K Maini
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - L L Bonilla
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
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Uçar MC, Kamenev D, Sunadome K, Fachet D, Lallemend F, Adameyko I, Hadjab S, Hannezo E. Theory of branching morphogenesis by local interactions and global guidance. Nat Commun 2021; 12:6830. [PMID: 34819507 PMCID: PMC8613190 DOI: 10.1038/s41467-021-27135-5] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2021] [Accepted: 11/03/2021] [Indexed: 12/14/2022] Open
Abstract
Branching morphogenesis governs the formation of many organs such as lung, kidney, and the neurovascular system. Many studies have explored system-specific molecular and cellular regulatory mechanisms, as well as self-organizing rules underlying branching morphogenesis. However, in addition to local cues, branched tissue growth can also be influenced by global guidance. Here, we develop a theoretical framework for a stochastic self-organized branching process in the presence of external cues. Combining analytical theory with numerical simulations, we predict differential signatures of global vs. local regulatory mechanisms on the branching pattern, such as angle distributions, domain size, and space-filling efficiency. We find that branch alignment follows a generic scaling law determined by the strength of global guidance, while local interactions influence the tissue density but not its overall territory. Finally, using zebrafish innervation as a model system, we test these key features of the model experimentally. Our work thus provides quantitative predictions to disentangle the role of different types of cues in shaping branched structures across scales.
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Affiliation(s)
- Mehmet Can Uçar
- Institute of Science and Technology Austria, Am Campus 1, 3400, Klosterneuburg, Austria.
| | - Dmitrii Kamenev
- Department of Neuroscience, Karolinska Institutet, 17177, Stockholm, Sweden
| | - Kazunori Sunadome
- Department of Physiology and Pharmacology, Karolinska Institutet, 17177, Stockholm, Sweden
| | - Dominik Fachet
- Institute of Science and Technology Austria, Am Campus 1, 3400, Klosterneuburg, Austria
- IRI Life Sciences, Humboldt-Universität zu Berlin, 10115, Berlin, Germany
| | - Francois Lallemend
- Department of Neuroscience, Karolinska Institutet, 17177, Stockholm, Sweden
- Ming-Wai Lau Centre for Reparative Medicine, Stockholm node, Karolinska Institutet, Stockholm, Sweden
| | - Igor Adameyko
- Department of Physiology and Pharmacology, Karolinska Institutet, 17177, Stockholm, Sweden
- Department of Neuroimmunology, Center for Brain Research, Medical University of Vienna, 1090, Vienna, Austria
| | - Saida Hadjab
- Department of Neuroscience, Karolinska Institutet, 17177, Stockholm, Sweden.
| | - Edouard Hannezo
- Institute of Science and Technology Austria, Am Campus 1, 3400, Klosterneuburg, Austria.
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Bonilla LL, Carretero M, Terragni F. Solitonlike attractor for blood vessel tip density in angiogenesis. Phys Rev E 2016; 94:062415. [PMID: 28085400 DOI: 10.1103/physreve.94.062415] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2016] [Indexed: 12/31/2022]
Abstract
Recently, numerical simulations of a stochastic model have shown that the density of vessel tips in tumor-induced angiogenesis adopts a solitonlike profile [Sci. Rep. 6, 31296 (2016)2045-232210.1038/srep31296]. In this work, we derive and solve the equations for the soliton collective coordinates that indicate how the soliton adapts its shape and velocity to varying chemotaxis and diffusion. The vessel tip density can be reconstructed from the soliton formulas. While the stochastic model exhibits large fluctuations, we show that the location of the maximum vessel tip density for different replicas follows closely the soliton peak position calculated either by ensemble averages or by solving an alternative deterministic description of the density. The simple soliton collective coordinate equations may also be used to ascertain the response of the vessel network to changes in the parameters and thus to control it.
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Affiliation(s)
- L L Bonilla
- G. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - M Carretero
- G. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - F Terragni
- G. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
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