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Bantwal AS, Bhayadia AK, Meng H. Critical role of arterial constitutive model in predicting blood pressure from pulse wave velocity. Comput Biol Med 2024; 178:108730. [PMID: 38917535 DOI: 10.1016/j.compbiomed.2024.108730] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2024] [Revised: 05/29/2024] [Accepted: 06/08/2024] [Indexed: 06/27/2024]
Abstract
BACKGROUND A promising approach to cuff-less, continuous blood pressure monitoring is to estimate blood pressure (BP) from Pulse Wave Velocity (PWV). However, most existing PWV-based methods rely on empirical BP-PWV relations and have large prediction errors, which may be caused by the implicit assumption of thin-walled, linear elastic arteries undergoing small deformations. Our objective is to understand the BP-PWV relationship in the absence of such limiting assumptions. METHOD We performed Fluid-Structure Interaction (FSI) simulations of the radial artery and the common carotid artery under physiological flow conditions. In these dynamic simulations, we employed two constitutive models for the arterial wall: the linear elastic model, implying a thin-walled linear elastic artery undergoing small deformations, and the Holzapfel-Gasser-Ogden (HGO) model, accounting for the nonlinear effects of collagen fibers and their orientations on the large arterial deformation. RESULTS Despite the changing BP, the linear elastic model predicts a constant PWV throughout a cardiac cycle, which is not physiological. The HGO model correctly predicts a positive BP-PWV correlation by capturing the nonlinear deformation of the artery, showing up to 50 % variations of PWV in a cardiac cycle. CONCLUSION Dynamic FSI simulations reveal that the BP-PWV relationship strongly depends on the arterial constitutive model, especially in the radial artery. To infer BP from PWV, one must account for the varying PWV, a consequence of the nonlinear arterial response due to collagen fibers. Future efforts should be directed towards robust measurement of time-varying PWV if it is to be used to predict BP.
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Affiliation(s)
| | - Amit Kumar Bhayadia
- Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY, 14260, USA.
| | - Hui Meng
- Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY, 14260, USA.
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Zhou B, Cheng Q, Chen Z, Chen Z, Liang D, Munro EA, Yun G, Kawai Y, Chen J, Bhowmick T, Padmanathan KK, Occhipinti LG, Matsumoto H, Gardner JW, Su BL, Hasan T. Universal Murray's law for optimised fluid transport in synthetic structures. Nat Commun 2024; 15:3652. [PMID: 38714661 PMCID: PMC11076523 DOI: 10.1038/s41467-024-47833-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2023] [Accepted: 04/09/2024] [Indexed: 05/10/2024] Open
Abstract
Materials following Murray's law are of significant interest due to their unique porous structure and optimal mass transfer ability. However, it is challenging to construct such biomimetic hierarchical channels with perfectly cylindrical pores in synthetic systems following the existing theory. Achieving superior mass transport capacity revealed by Murray's law in nanostructured materials has thus far remained out of reach. We propose a Universal Murray's law applicable to a wide range of hierarchical structures, shapes and generalised transfer processes. We experimentally demonstrate optimal flow of various fluids in hierarchically planar and tubular graphene aerogel structures to validate the proposed law. By adjusting the macroscopic pores in such aerogel-based gas sensors, we also show a significantly improved sensor response dynamics. In this work, we provide a solid framework for designing synthetic Murray materials with arbitrarily shaped channels for superior mass transfer capabilities, with future implications in catalysis, sensing and energy applications.
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Affiliation(s)
- Binghan Zhou
- Cambridge Graphene Centre, University of Cambridge, Cambridge, CB3 0FA, UK
| | - Qian Cheng
- Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, UK
| | - Zhuo Chen
- Cambridge Graphene Centre, University of Cambridge, Cambridge, CB3 0FA, UK
| | - Zesheng Chen
- Cambridge Graphene Centre, University of Cambridge, Cambridge, CB3 0FA, UK
| | - Dongfang Liang
- Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, UK
| | - Eric Anthony Munro
- Cambridge Graphene Centre, University of Cambridge, Cambridge, CB3 0FA, UK
| | - Guolin Yun
- Cambridge Graphene Centre, University of Cambridge, Cambridge, CB3 0FA, UK
| | - Yoshiki Kawai
- Department of Materials Science and Engineering, Tokyo Institute of Technology, Tokyo, 152-8552, Japan
| | - Jinrui Chen
- Cambridge Graphene Centre, University of Cambridge, Cambridge, CB3 0FA, UK
| | - Tynee Bhowmick
- Cambridge Graphene Centre, University of Cambridge, Cambridge, CB3 0FA, UK
| | | | | | - Hidetoshi Matsumoto
- Department of Materials Science and Engineering, Tokyo Institute of Technology, Tokyo, 152-8552, Japan
| | | | - Bao-Lian Su
- Laboratory of Inorganic Materials Chemistry (CMI), University of Namur, B-5000, Namur, Belgium
- State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan, 430070, China
| | - Tawfique Hasan
- Cambridge Graphene Centre, University of Cambridge, Cambridge, CB3 0FA, UK.
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Gharahi H, Filonova V, Mullagura HN, Nama N, Baek S, Figueroa CA. A multiscale framework for defining homeostasis in distal vascular trees: applications to the pulmonary circulation. Biomech Model Mechanobiol 2023; 22:971-986. [PMID: 36917305 DOI: 10.1007/s10237-023-01693-7] [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: 08/10/2021] [Accepted: 01/11/2023] [Indexed: 03/16/2023]
Abstract
Pulmonary arteries constitute a low-pressure network of vessels, often characterized as a bifurcating tree with heterogeneous vessel mechanics. Understanding the vascular complexity and establishing homeostasis is important to study diseases such as pulmonary arterial hypertension (PAH). The onset and early progression of PAH can be traced to changes in the morphometry and structure of the distal vasculature. Coupling hemodynamics with vessel wall growth and remodeling (G&R) is crucial for understanding pathology at distal vasculature. Accordingly, the goal of this study is to provide a multiscale modeling framework that embeds the essential features of arterial wall constituents coupled with the hemodynamics within an arterial network characterized by an extension of Murray's law. This framework will be used to establish the homeostatic baseline characteristics of a pulmonary arterial tree, including important parameters such as vessel radius, wall thickness and shear stress. To define the vascular homeostasis and hemodynamics in the tree, we consider two timescales: a cardiac cycle and a longer period of vascular adaptations. An iterative homeostatic optimization, which integrates a metabolic cost function minimization, the stress equilibrium, and hemodynamics, is performed at the slow timescale. In the fast timescale, the pulsatile blood flow dynamics is described by a Womersley's deformable wall analytical solution. Illustrative examples for symmetric and asymmetric trees are presented that provide baseline characteristics for the normal pulmonary arterial vasculature. The results are compared with diverse literature data on morphometry, structure, and mechanics of pulmonary arteries. The developed framework demonstrates a potential for advanced parametric studies and future G&R and hemodynamics modeling of PAH.
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Affiliation(s)
- Hamidreza Gharahi
- Section of Vascular Surgery, Department of Surgery, University of Michigan, Ann Arbor, MI, USA.
| | - Vasilina Filonova
- Section of Vascular Surgery, Department of Surgery, University of Michigan, Ann Arbor, MI, USA
| | - Haritha N Mullagura
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA
| | - Nitesh Nama
- Department of Mechanical & Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE, USA
| | - Seungik Baek
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA
| | - C Alberto Figueroa
- Section of Vascular Surgery, Department of Surgery, University of Michigan, Ann Arbor, MI, USA
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA
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Satha G, Lindström SB, Klarbring A. A goal function approach to remodeling of arteries uncovers mechanisms for growth instability. Biomech Model Mechanobiol 2014; 13:1243-59. [PMID: 24633569 PMCID: PMC4186995 DOI: 10.1007/s10237-014-0569-5] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2013] [Accepted: 02/27/2014] [Indexed: 01/12/2023]
Abstract
A novel, goal function-based formulation for the growth dynamics of arteries is introduced and used for investigating the development of growth instability in blood vessels. Such instabilities would lead to abnormal growth of the vessel, reminiscent of an aneurysm. The blood vessel is modeled as a thin-walled cylindrical tube, and the constituents that form the vessel wall are assumed to deform together as a constrained mixture. The growth dynamics of the composite material of the vessel wall are described by an evolution equation, where the effective area of each constituent changes in the direction of steepest descent of a goal function. This goal function is formulated in such way that the constituents grow toward a target potential energy and a target composition. The convergence of the simulated response of the evolution equation toward a target homeostatic state is investigated for a range of isotropic and orthotropic material models. These simulations suggest that elastin-deficient vessels are more prone to growth instability. Increased stiffness of the vessel wall, on the other hand, gives a more stable growth process. Another important finding is that an increased rate of degradation of materials impairs growth stability.
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Affiliation(s)
- Ganarupan Satha
- Mechanics, Department of Management and Engineering, The Institute of Technology, Linköping University, Linköping , 581 83, Sweden,
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