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Silva DPF, Coelho RCV, Pagonabarraga I, Succi S, Telo da Gama MM, Araújo NAM. Lattice Boltzmann simulation of deformable fluid-filled bodies: progress and perspectives. SOFT MATTER 2024; 20:2419-2441. [PMID: 38420837 PMCID: PMC10933750 DOI: 10.1039/d3sm01648j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2023] [Accepted: 02/20/2024] [Indexed: 03/02/2024]
Abstract
With the rapid development of studies involving droplet microfluidics, drug delivery, cell detection, and microparticle synthesis, among others, many scientists have invested significant efforts to model the flow of these fluid-filled bodies. Motivated by the intricate coupling between hydrodynamics and the interactions of fluid-filled bodies, several methods have been developed. The objective of this review is to present a compact foundation of the methods used in the literature in the context of lattice Boltzmann methods. For hydrodynamics, we focus on the lattice Boltzmann method due to its specific ability to treat time- and spatial-dependent boundary conditions and to incorporate new physical models in a computationally efficient way. We split the existing methods into two groups with regard to the interfacial boundary: fluid-structure and fluid-fluid methods. The fluid-structure methods are characterised by the coupling between fluid dynamics and mechanics of the flowing body, often used in applications involving membranes and similar flexible solid boundaries. We further divide fluid-structure-based methods into two subcategories, those which treat the fluid-structure boundary as a continuum medium and those that treat it as a discrete collection of individual springs and particles. Next, we discuss the fluid-fluid methods, particularly useful for the simulations of fluid-fluid interfaces. We focus on models for immiscible droplets and their interaction in a suspending fluid and describe benchmark tests to validate the models for fluid-filled bodies.
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Affiliation(s)
- Danilo P F Silva
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
| | - Rodrigo C V Coelho
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
| | - Ignacio Pagonabarraga
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Carrer de Martí Franqués 1, 08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
| | - Sauro Succi
- Center for Life Nano Science at La Sapienza, Istituto Italiano di Tecnologia, 295 Viale Regina Elena, I/00161 Roma, Italy
- Harvard Institute for Applied Computational Science, Cambridge, MA 02138, USA
| | - Margarida M Telo da Gama
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
| | - Nuno A M Araújo
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
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Nikfar M, Razizadeh M, Paul R, Muzykantov V, Liu Y. A numerical study on drug delivery via multiscale synergy of cellular hitchhiking onto red blood cells. NANOSCALE 2021; 13:17359-17372. [PMID: 34590654 PMCID: PMC10169096 DOI: 10.1039/d1nr04057j] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
Red blood cell (RBC)-hitchhiking, in which different nanocarriers (NCs) shuttle on the erythrocyte membrane and disassociate from RBCs to the first organ downstream of the intravenous injection spot, has recently been introduced as a solution to enhance target site uptake. Several experimental studies have already approved that cellular hitchhiking onto the RBC membrane can improve the delivery of a wide range of NCs in mice, pigs, and ex vivo human lungs. In these studies, the impact of NC size, NC surface chemistry, and shear rate on the delivery process and biodistribution has been widely explored. To shed light on the underlying physics in this type of drug delivery system, we present a computational platform in the context of the lattice Boltzmann method, spring connected network, and frictional immersed boundary method. The proposed algorithm simulates nanoparticle (NP) dislodgment from the RBC surface in shear flow and biomimetic microfluidic channels. The numerical simulations are performed for various NP sizes and RBC-NP adhesion strengths. In shear flow, NP detachment increases upon increasing the shear rate. RBC-RBC interaction can also significantly boost shear-induced particle detachment. Larger NPs have a higher propensity to be disconnected from the RBC surface. The results illustrate that changing the interaction between the NPs and RBCs can control the desorption process. All the findings agree with in vivo and in vitro experimental observations. We believe that the proposed setup can be exploited as a predictive tool to estimate optimum parameters in NP-bound RBCs for better targeting procedures in tissue microvasculature.
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Affiliation(s)
- Mehdi Nikfar
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania 18015, USA.
| | - Meghdad Razizadeh
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania 18015, USA.
| | - Ratul Paul
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania 18015, USA.
| | - Vladimir Muzykantov
- Department of Systems Pharmacology and Translational Therapeutics and Center for Translational Targeted Therapeutics and Nanomedicine, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Yaling Liu
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania 18015, USA.
- Department of Bioengineering, Lehigh University, Bethlehem, Pennsylvania 18015, USA
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DiNapoli KT, Robinson DN, Iglesias PA. Tools for computational analysis of moving boundary problems in cellular mechanobiology. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2020; 13:e1514. [PMID: 33305503 DOI: 10.1002/wsbm.1514] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Revised: 10/08/2020] [Accepted: 10/20/2020] [Indexed: 12/29/2022]
Abstract
A cell's ability to change shape is one of the most fundamental biological processes and is essential for maintaining healthy organisms. When the ability to control shape goes awry, it often results in a diseased system. As such, it is important to understand the mechanisms that allow a cell to sense and respond to its environment so as to maintain cellular shape homeostasis. Because of the inherent complexity of the system, computational models that are based on sound theoretical understanding of the biochemistry and biomechanics and that use experimentally measured parameters are an essential tool. These models involve an inherent feedback, whereby shape is determined by the action of regulatory signals whose spatial distribution depends on the shape. To carry out computational simulations of these moving boundary problems requires special computational techniques. A variety of alternative approaches, depending on the type and scale of question being asked, have been used to simulate various biological processes, including cell motility, division, mechanosensation, and cell engulfment. In general, these models consider the forces that act on the system (both internally generated, or externally imposed) and the mechanical properties of the cell that resist these forces. Moving forward, making these techniques more accessible to the non-expert will help improve interdisciplinary research thereby providing new insight into important biological processes that affect human health. This article is categorized under: Cancer > Cancer>Computational Models Cancer > Cancer>Molecular and Cellular Physiology.
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Affiliation(s)
- Kathleen T DiNapoli
- Department of Cell Biology, Johns Hopkins School of Medicine, Baltimore, Maryland, USA
| | - Douglas N Robinson
- Department of Cell Biology, Johns Hopkins School of Medicine, Baltimore, Maryland, USA
| | - Pablo A Iglesias
- Department of Cell Biology, Johns Hopkins School of Medicine, Baltimore, Maryland, USA
- Department of Electrical & Computer Engineering, Johns Hopkins University, Baltimore, Maryland, USA
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Jančigová I, Kovalčíková K, Weeber R, Cimrák I. PyOIF: Computational tool for modelling of multi-cell flows in complex geometries. PLoS Comput Biol 2020; 16:e1008249. [PMID: 33075044 PMCID: PMC7595628 DOI: 10.1371/journal.pcbi.1008249] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2020] [Revised: 10/29/2020] [Accepted: 08/14/2020] [Indexed: 11/28/2022] Open
Abstract
A user ready, well documented software package PyOIF contains an implementation of a robust validated computational model for cell flow modelling. The software is capable of simulating processes involving biological cells immersed in a fluid. The examples of such processes are flows in microfluidic channels with numerous applications such as cell sorting, rare cell isolation or flow fractionation. Besides the typical usage of such computational model in the design process of microfluidic devices, PyOIF has been used in the computer-aided discovery involving mechanical properties of cell membranes. With this software, single cell, many cell, as well as dense cell suspensions can be simulated. Many cell simulations include cell-cell interactions and analyse their effect on the cells. PyOIF can be used to test the influence of mechanical properties of the membrane in flows and in membrane-membrane interactions. Dense suspensions may be used to study the effect of cell volume fraction on macroscopic phenomena such as cell-free layer, apparent suspension viscosity or cell degradation. The PyOIF module is based on the official ESPResSo distribution with few modifications and is available under the terms of the GNU General Public Licence. PyOIF is based on Python objects representing the cells and on the C++ computational core for fluid and interaction dynamics. The source code is freely available at GitHub repository, runs natively under Linux and MacOS and can be used in Windows Subsystem for Linux. The communication among PyOIF users and developers is maintained using active mailing lists. This work provides a basic background to the underlying computational models and to the implementation of interactions within this framework. We provide the prospective PyOIF users with a practical example of simulation script with reference to our publicly available User Guide.
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Affiliation(s)
- Iveta Jančigová
- Cell-in-fluid Biomedical Modelling and Computation Group, University of Žilina, Žilina, Slovakia
| | - Kristína Kovalčíková
- Cell-in-fluid Biomedical Modelling and Computation Group, University of Žilina, Žilina, Slovakia
| | - Rudolf Weeber
- Institute for Computational Physics, University of Stuttgart, Stuttgart, Germany
| | - Ivan Cimrák
- Cell-in-fluid Biomedical Modelling and Computation Group, University of Žilina, Žilina, Slovakia
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Gerivani H, Nazari M. Proposing a lattice spring damper model for simulation of interaction between elastic/ viscoelastic filaments and fluid flow in immersed boundary-lattice Boltzmann framework. J Mol Liq 2019. [DOI: 10.1016/j.molliq.2019.111969] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Moon JY, Choi SB, Lee JS, Tanner RI, Lee JS. Numerical simulation of optical control for a soft particle in a microchannel. Phys Rev E 2019; 99:022607. [PMID: 30934346 DOI: 10.1103/physreve.99.022607] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2018] [Indexed: 11/07/2022]
Abstract
Technologies that use optical force to actively control particles in microchannels are a significant area of research interest in various fields. An optical force is generated by the momentum change caused by the refraction and reflection of light, which changes the particle surface as a function of the angle of incidence of light and which in turn feeds back and modifies the force on the particle. Simulating this phenomenon is a complex task. The deformation of a particle, the interaction between the surrounding fluid and the particle, and the reflection and refraction of light should be analyzed simultaneously. Herein, a deformable particle in a microchannel subjected to optical interactions is simulated using the three-dimensional lattice Boltzmann immersed-boundary method. The laser from the optical source is analyzed by dividing it into individual rays. To calculate the optical forces exerted on the particle, the intensity, momentum, and ray direction are calculated. The optical-separator problem with one optical source is analyzed by measuring the distance traveled because of the optical force. The optical-stretcher problem with two optical sources is then studied by analyzing the relation between the intensity of the optical source and particle deformation. This simulation will help the design of sorting and measuring by optical force.
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Affiliation(s)
- Ji Young Moon
- School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW 2006, Australia
| | - Se Bin Choi
- School of Mechanical Engineering, Yonsei University, Seoul, 03722, Republic of Korea
| | - Jung Shin Lee
- School of Mechanical Engineering, Yonsei University, Seoul, 03722, Republic of Korea
| | - Roger I Tanner
- School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW 2006, Australia
| | - Joon Sang Lee
- School of Mechanical Engineering, Yonsei University, Seoul, 03722, Republic of Korea
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Dissipative Coupling of Fluid and Immersed Objects for Modelling of Cells in Flow. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2018; 2018:7842857. [PMID: 30363716 PMCID: PMC6180995 DOI: 10.1155/2018/7842857] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/07/2018] [Revised: 08/18/2018] [Accepted: 09/03/2018] [Indexed: 11/29/2022]
Abstract
Modelling of cell flow for biomedical applications relies in many cases on the correct description of fluid-structure interaction between the cell membrane and the surrounding fluid. We analyse the coupling of the lattice-Boltzmann method for the fluid and the spring network model for the cells. We investigate the bare friction parameter of fluid-structure interaction that is mediated via dissipative coupling. Such coupling mimics the no-slip boundary condition at the interface between the fluid and object. It is an alternative method to the immersed boundary method. Here, the fluid-structure coupling is provided by forces penalising local differences between velocities of the object's boundaries and the surrounding fluid. The method includes a phenomenological friction coefficient that determines the strength of the coupling. This work aims at determination of proper values of such friction coefficient. We derive an explicit formula for computation of this coefficient depending on the mesh density assuming a reference friction is known. We validate this formula on spherical and ellipsoidal objects. We also provide sensitivity analysis of the formula on all parameters entering the model. We conclude that such formula may be used also for objects with irregular shapes provided that the triangular mesh covering the object's surface is in some sense uniform. Our findings are justified by two computational experiments where we simulate motion of a red blood cell in a capillary and in a shear flow. Both experiments confirm our results presented in this work.
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Hoque SZ, Anand DV, Patnaik BSV. The dynamics of a healthy and infected red blood cell in flow through constricted channels: A DPD simulation. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2018; 34:e3105. [PMID: 29790664 DOI: 10.1002/cnm.3105] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2018] [Revised: 05/02/2018] [Accepted: 05/14/2018] [Indexed: 06/08/2023]
Abstract
Understanding the dynamics of red blood cell (RBC) motion under in silico conditions is central to the development of cost-effective diagnostic tools. Specifically, unraveling the relationship between the rheological properties and the nature of shape change in the RBC (healthy or infected) can be extremely useful. In case of malarial infection, RBC progressively loses its deformability and tends to occlude the microvessel. In the present study, detailed mesoscopic simulations are performed to investigate the deformation dynamics of an RBC in flow through a constricted channel. Specifically, the manifestation of viscous forces (through flow rates) on the passage and blockage characteristics of a healthy red blood cell (hRBC) vis-á-vis an infected red blood cell (iRBC) are investigated. A finite-sized dissipative particle dynamics framework is used to model plasma in conjunction with a discrete model for the RBC. Instantaneous wall boundary method was used to model no-slip wall boundary conditions with a good control on the near-wall density fluctuations and compressibility effects. To investigate the microvascular occlusion, the RBC motion through 2 types of constricted channels, viz, (1) a tapered microchannel and (2) a stenosed-type microchannel, were simulated. It was observed that the deformation of an infected cell was much less compared with a healthy cell, with an attendant increase in the passage time. Apart from the qualitative features, deformation indices were obtained. The deformation of hRBC was sudden, while the iRBC deformed slowly as it traversed through the constriction. For higher flow rates, both hRBC and iRBC were found to undergo severe deformation. Even under low flow rates, hRBC could easily traverse past the constricted channel. However, for sufficiently slow flow rates (eg, capillary flows), the microchannel was found to be completely blocked by the iRBC.
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Affiliation(s)
- Sazid Zamal Hoque
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, 600036, India
| | - D Vijay Anand
- Department of Mechanical Engineering, Indian Institute of Science, Bangalore, 560012, India
| | - B S V Patnaik
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, 600036, India
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Sohrabi S, Tan J, Yunus DE, He R, Liu Y. Label-free sorting of soft microparticles using a bioinspired synthetic cilia array. BIOMICROFLUIDICS 2018; 12:042206. [PMID: 29861817 PMCID: PMC5962446 DOI: 10.1063/1.5022500] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2018] [Accepted: 04/10/2018] [Indexed: 05/25/2023]
Abstract
Isolating cells of interest from a heterogeneous population has been of critical importance in biological studies and clinical applications. In this study, a novel approach is proposed for utilizing an active ciliary system in microfluidic devices to separate particles based on their physical properties. In this approach, the bottom of the microchannel is covered with an equally spaced cilia array of various patterns which is actuated by an external stimuli. 3D simulations are carried out to study cilia-particle interaction and isolation dynamic in a microfluidic channel. It is observed that these elastic hair-like filaments can influence particle's trajectories differently depending on their biophysical properties. This modeling study utilizes immersed boundary method coupled with the lattice Boltzmann method. Soft particles and cilia are implemented through the spring connected network model and point-particle scheme, respectively. It is shown that cilia array with proper stimulation is able to continuously and non-destructively separate cells into subpopulations based on their size, shape, and stiffness. At the end, a design map for fabrication of a programmable microfluidic device capable of isolating various subpopulations of cells is developed. This biocompatible, label-free design can separate cells/soft microparticles with high throughput which can greatly complement existing separation technologies.
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Affiliation(s)
- Salman Sohrabi
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA
| | - Jifu Tan
- Department of Mechanical Engineering, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - Doruk Erdem Yunus
- Department of Mechanical Engineering, Bursa Technical University, Bursa, Turkey
| | - Ran He
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania 18015, USA
| | - Yaling Liu
- Author to whom correspondence should be addressed:
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Owen B, Bojdo N, Jivkov A, Keavney B, Revell A. Structural modelling of the cardiovascular system. Biomech Model Mechanobiol 2018; 17:1217-1242. [PMID: 29911296 PMCID: PMC6154127 DOI: 10.1007/s10237-018-1024-9] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2017] [Accepted: 04/25/2018] [Indexed: 02/02/2023]
Abstract
Computational modelling of the cardiovascular system offers much promise, but represents a truly interdisciplinary challenge, requiring knowledge of physiology, mechanics of materials, fluid dynamics and biochemistry. This paper aims to provide a summary of the recent advances in cardiovascular structural modelling, including the numerical methods, main constitutive models and modelling procedures developed to represent cardiovascular structures and pathologies across a broad range of length and timescales; serving as an accessible point of reference to newcomers to the field. The class of so-called hyperelastic materials provides the theoretical foundation for the modelling of how these materials deform under load, and so an overview of these models is provided; comparing classical to application-specific phenomenological models. The physiology is split into components and pathologies of the cardiovascular system and linked back to constitutive modelling developments, identifying current state of the art in modelling procedures from both clinical and engineering sources. Models which have originally been derived for one application and scale are shown to be used for an increasing range and for similar applications. The trend for such approaches is discussed in the context of increasing availability of high performance computing resources, where in some cases computer hardware can impact the choice of modelling approach used.
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Affiliation(s)
- Benjamin Owen
- School of Mechanical, Aerospace and Civil Engineering, University of Manchester, George Begg Building, Manchester, M1 3BB, UK.
| | - Nicholas Bojdo
- School of Mechanical, Aerospace and Civil Engineering, University of Manchester, George Begg Building, Manchester, M1 3BB, UK
| | - Andrey Jivkov
- School of Mechanical, Aerospace and Civil Engineering, University of Manchester, George Begg Building, Manchester, M1 3BB, UK
| | - Bernard Keavney
- Division of Cardiovascular Sciences, University of Manchester, AV Hill Building, Manchester, M13 9PT, UK
| | - Alistair Revell
- School of Mechanical, Aerospace and Civil Engineering, University of Manchester, George Begg Building, Manchester, M1 3BB, UK
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Bento D, Rodrigues RO, Faustino V, Pinho D, Fernandes CS, Pereira AI, Garcia V, Miranda JM, Lima R. Deformation of Red Blood Cells, Air Bubbles, and Droplets in Microfluidic Devices: Flow Visualizations and Measurements. MICROMACHINES 2018; 9:E151. [PMID: 30424085 PMCID: PMC6187860 DOI: 10.3390/mi9040151] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/10/2018] [Revised: 03/21/2018] [Accepted: 03/21/2018] [Indexed: 12/30/2022]
Abstract
Techniques, such as micropipette aspiration and optical tweezers, are widely used to measure cell mechanical properties, but are generally labor-intensive and time-consuming, typically involving a difficult process of manipulation. In the past two decades, a large number of microfluidic devices have been developed due to the advantages they offer over other techniques, including transparency for direct optical access, lower cost, reduced space and labor, precise control, and easy manipulation of a small volume of blood samples. This review presents recent advances in the development of microfluidic devices to evaluate the mechanical response of individual red blood cells (RBCs) and microbubbles flowing in constriction microchannels. Visualizations and measurements of the deformation of RBCs flowing through hyperbolic, smooth, and sudden-contraction microchannels were evaluated and compared. In particular, we show the potential of using hyperbolic-shaped microchannels to precisely control and assess small changes in RBC deformability in both physiological and pathological situations. Moreover, deformations of air microbubbles and droplets flowing through a microfluidic constriction were also compared with RBCs deformability.
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Affiliation(s)
- David Bento
- Instituto Politécnico de Bragança, ESTiG/IPB, C. Sta. Apolónia, 5301-857 Bragança, Portugal.
- CEFT, Faculdade de Engenharia da Universidade do Porto (FEUP) Rua Roberto Frias, 4800-058 Porto, Portugal.
| | - Raquel O Rodrigues
- Instituto Politécnico de Bragança, ESTiG/IPB, C. Sta. Apolónia, 5301-857 Bragança, Portugal.
- LCM-Laboratory of Catalysis and Materials-Associate Laboratory LSRE/LCM, Faculdade de Engenharia da Universidade do Porto (FEUP) Rua Roberto Frias, 4800-058 Porto, Portugal.
| | - Vera Faustino
- MEMS-UMinho Research Unit, Universidade do Minho, DEI, Campus de Azurém, 4800-058 Guimarães, Portugal.
| | - Diana Pinho
- Instituto Politécnico de Bragança, ESTiG/IPB, C. Sta. Apolónia, 5301-857 Bragança, Portugal.
- CEFT, Faculdade de Engenharia da Universidade do Porto (FEUP) Rua Roberto Frias, 4800-058 Porto, Portugal.
- Centro de Investigação em Digitalização e Robótica Inteligente (CeDRI), Instituto Politécnico de Bragança, Campus de Santa Apolónia, 5300-253 Bragança, Portugal.
| | - Carla S Fernandes
- Instituto Politécnico de Bragança, ESTiG/IPB, C. Sta. Apolónia, 5301-857 Bragança, Portugal.
| | - Ana I Pereira
- Instituto Politécnico de Bragança, ESTiG/IPB, C. Sta. Apolónia, 5301-857 Bragança, Portugal.
- Centro de Investigação em Digitalização e Robótica Inteligente (CeDRI), Instituto Politécnico de Bragança, Campus de Santa Apolónia, 5300-253 Bragança, Portugal.
- Algoritmi R&D Centre, Campus de Gualtar, University of Minho, 4710-057 Braga, Portugal.
| | - Valdemar Garcia
- Instituto Politécnico de Bragança, ESTiG/IPB, C. Sta. Apolónia, 5301-857 Bragança, Portugal.
| | - João M Miranda
- CEFT, Faculdade de Engenharia da Universidade do Porto (FEUP) Rua Roberto Frias, 4800-058 Porto, Portugal.
| | - Rui Lima
- CEFT, Faculdade de Engenharia da Universidade do Porto (FEUP) Rua Roberto Frias, 4800-058 Porto, Portugal.
- MEtRiCS, Mechanical Engineering Department, Campus de Azurém, University of Minho, 4800-058 Guimarães, Portugal.
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Barns S, Balanant MA, Sauret E, Flower R, Saha S, Gu Y. Investigation of red blood cell mechanical properties using AFM indentation and coarse-grained particle method. Biomed Eng Online 2017; 16:140. [PMID: 29258590 PMCID: PMC5738115 DOI: 10.1186/s12938-017-0429-5] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2017] [Accepted: 12/08/2017] [Indexed: 12/27/2022] Open
Abstract
Background Red blood cells (RBCs) deform significantly and repeatedly when passing through narrow capillaries and delivering dioxygen throughout the body. Deformability of RBCs is a key characteristic, largely governed by the mechanical properties of the cell membrane. This study investigated RBC mechanical properties using atomic force microscopy (AFM) with the aim to develop a coarse-grained particle method model to study for the first time RBC indentation in both 2D and 3D. This new model has the potential to be applied to further investigate the local deformability of RBCs, with accurate control over adhesion, probe geometry and position of applied force. Results The model considers the linear stretch capacity of the cytoskeleton, bending resistance and areal incompressibility of the bilayer, and volumetric incompressibility of the internal fluid. The model’s performance was validated against force–deformation experiments performed on RBCs under spherical AFM indentation. The model was then used to investigate the mechanisms which absorbed energy through the indentation stroke, and the impact of varying stiffness coefficients on the measured deformability. This study found the membrane’s bending stiffness was most influential in controlling RBC physical behaviour for indentations of up to 200 nm. Conclusions As the bilayer provides bending resistance, this infers that structural changes within the bilayer are responsible for the deformability changes experienced by deteriorating RBCs. The numerical model presented here established a foundation for future investigations into changes within the membrane that cause differences in stiffness between healthy and deteriorating RBCs, which have already been measured experimentally with AFM. Electronic supplementary material The online version of this article (10.1186/s12938-017-0429-5) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Sarah Barns
- Science and Engineering Faculty, Queensland University of Technology (QUT), Brisbane, 4000, Australia
| | - Marie Anne Balanant
- Science and Engineering Faculty, Queensland University of Technology (QUT), Brisbane, 4000, Australia.,Research and Development, Australian Red Cross Blood Service, Brisbane, 4059, Australia
| | - Emilie Sauret
- Science and Engineering Faculty, Queensland University of Technology (QUT), Brisbane, 4000, Australia
| | - Robert Flower
- Research and Development, Australian Red Cross Blood Service, Brisbane, 4059, Australia.,Faculty of Health, Queensland University of Technology, Brisbane, 4000, Australia
| | - Suvash Saha
- Science and Engineering Faculty, Queensland University of Technology (QUT), Brisbane, 4000, Australia
| | - YuanTong Gu
- Science and Engineering Faculty, Queensland University of Technology (QUT), Brisbane, 4000, Australia.
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C. Arciero J, Causin P, Malgaroli F. Mathematical methods for modeling the microcirculation. AIMS BIOPHYSICS 2017. [DOI: 10.3934/biophy.2017.3.362] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
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Polwaththe-Gallage HN, Saha SC, Sauret E, Flower R, Senadeera W, Gu Y. SPH-DEM approach to numerically simulate the deformation of three-dimensional RBCs in non-uniform capillaries. Biomed Eng Online 2016; 15:161. [PMID: 28155717 PMCID: PMC5260140 DOI: 10.1186/s12938-016-0256-0] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Background Blood continuously flows through the blood vessels in the human body. When blood flows through the smallest blood vessels, red blood cells (RBCs) in the blood exhibit various types of motion and deformed shapes. Computational modelling techniques can be used to successfully predict the behaviour of the RBCs in capillaries. In this study, we report the application of a meshfree particle approach to model and predict the motion and deformation of three-dimensional RBCs in capillaries. Methods An elastic spring network based on the discrete element method (DEM) is employed to model the three-dimensional RBC membrane. The haemoglobin in the RBC and the plasma in the blood are modelled as smoothed particle hydrodynamics (SPH) particles. For validation purposes, the behaviour of a single RBC in a simple shear flow is examined and compared against experimental results. Then simulations are carried out to predict the behaviour of RBCs in a capillary; (i) the motion of five identical RBCs in a uniform capillary, (ii) the motion of five identical RBCs with different bending stiffness (Kb) values in a stenosed capillary, (iii) the motion of three RBCs in a narrow capillary. Finally five identical RBCs are employed to determine the critical diameter of a stenosed capillary. Results Validation results showed a good agreement with less than 10% difference. From the above simulations, the following results are obtained; (i) RBCs exhibit different deformation behaviours due to the hydrodynamic interaction between them. (ii) Asymmetrical deformation behaviours of the RBCs are clearly observed when the bending stiffness (Kb) of the RBCs is changed. (iii) The model predicts the ability of the RBCs to squeeze through smaller blood vessels. Finally, from the simulations, the critical diameter of the stenosed section to stop the motion of blood flow is predicted. Conclusions A three-dimensional spring network model based on DEM in combination with the SPH method is successfully used to model the motion and deformation of RBCs in capillaries. Simulation results reveal that the condition of blood flow stopping depends on the pressure gradient of the capillary and the severity of stenosis of the capillary. In addition, this model is capable of predicting the critical diameter which prevents motion of RBCs for different blood pressures.
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Affiliation(s)
- Hasitha-Nayanajith Polwaththe-Gallage
- School of Chemistry, Physics and Mechanical Engineering, Faculty of Science and Engineering, Queensland University of Technology, 2-George Street, Brisbane, QLD, 4001, Australia
| | - Suvash C Saha
- School of Chemistry, Physics and Mechanical Engineering, Faculty of Science and Engineering, Queensland University of Technology, 2-George Street, Brisbane, QLD, 4001, Australia
| | - Emilie Sauret
- School of Chemistry, Physics and Mechanical Engineering, Faculty of Science and Engineering, Queensland University of Technology, 2-George Street, Brisbane, QLD, 4001, Australia
| | - Robert Flower
- Research and Development, Australian Red Cross Blood Service, Kelvin Grove, QLD, 4059, Australia
| | - Wijitha Senadeera
- School of Chemistry, Physics and Mechanical Engineering, Faculty of Science and Engineering, Queensland University of Technology, 2-George Street, Brisbane, QLD, 4001, Australia
| | - YuanTong Gu
- School of Chemistry, Physics and Mechanical Engineering, Faculty of Science and Engineering, Queensland University of Technology, 2-George Street, Brisbane, QLD, 4001, Australia.
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Jančigová I, Cimrák I. Non-uniform force allocation for area preservation in spring network models. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2016; 32:e02757. [PMID: 26575301 DOI: 10.1002/cnm.2757] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2014] [Revised: 10/28/2015] [Accepted: 11/08/2015] [Indexed: 06/05/2023]
Abstract
In modeling of elastic objects in a flow such as red blood cells, white blood cells, or tumor cells, several elastic moduli are involved. One of them is the area conservation modulus. In this paper, we focus on spring network models, and we introduce a new way of modeling the area preservation modulus. We take into account the current shape of the individual triangles and find the proportional allocation of area conservation forces, which would for individual triangles preserve their shapes. The analysis shows that this approach tends to regularize the triangulation. We demonstrate this effect on individual triangles as well as on the complete triangulations. Copyright © 2015 John Wiley & Sons, Ltd.
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Affiliation(s)
- Iveta Jančigová
- Cell-in-fluid Research Group, http://cell-in-fluid.fri.uniza.sk, Faculty of Management Science and Informatics, University of Žilina, Univerzitná 8215/1, Žilina, 010 26, Slovakia.
| | - Ivan Cimrák
- Cell-in-fluid Research Group, http://cell-in-fluid.fri.uniza.sk, Faculty of Management Science and Informatics, University of Žilina, Univerzitná 8215/1, Žilina, 010 26, Slovakia
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Moon JY, Tanner RI, Lee JS. A numerical study on the elastic modulus of volume and area dilation for a deformable cell in a microchannel. BIOMICROFLUIDICS 2016; 10:044110. [PMID: 27570575 PMCID: PMC4975752 DOI: 10.1063/1.4960205] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2016] [Accepted: 07/21/2016] [Indexed: 05/31/2023]
Abstract
A red blood cell (RBC) in a microfluidic channel is highly interesting for scientists in various fields of research on biological systems. This system has been studied extensively by empirical, analytical, and numerical methods. Nonetheless, research of predicting the behavior of an RBC in a microchannel is still an interesting area. The complications arise from deformation of an RBC and interactions among the surrounding fluid, wall, and RBCs. In this study, a pressure-driven RBC in a microchannel was simulated with a three-dimensional lattice Boltzmann method of an immersed boundary. First, the effect of boundary thickness on the interaction between the wall and cell was analyzed by measuring the time of passage through the narrow channel. Second, the effect of volume conservation stiffness was studied. Finally, the effect of global area stiffness was analyzed.
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Affiliation(s)
| | - Roger I Tanner
- School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney , Sydney, New South Wales 2006, Australia
| | - Joon Sang Lee
- School of Mechanical Engineering, Yonsei University , Seoul, South Korea
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Tan J, Keller W, Sohrabi S, Yang J, Liu Y. Characterization of Nanoparticle Dispersion in Red Blood Cell Suspension by the Lattice Boltzmann-Immersed Boundary Method. NANOMATERIALS (BASEL, SWITZERLAND) 2016; 6:E30. [PMID: 28344287 PMCID: PMC5302481 DOI: 10.3390/nano6020030] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/16/2015] [Revised: 01/21/2016] [Accepted: 01/25/2016] [Indexed: 11/18/2022]
Abstract
Nanodrug-carrier delivery in the blood stream is strongly influenced by nanoparticle (NP) dispersion. This paper presents a numerical study on NP transport and dispersion in red blood cell (RBC) suspensions under shear and channel flow conditions, utilizing an immersed boundary fluid-structure interaction model with a lattice Boltzmann fluid solver, an elastic cell membrane model and a particle motion model driven by both hydrodynamic loading and Brownian dynamics. The model can capture the multiphase features of the blood flow. Simulations were performed to obtain an empirical formula to predict NP dispersion rate for a range of shear rates and cell concentrations. NP dispersion rate predictions from the formula were then compared to observations from previous experimental and numerical studies. The proposed formula is shown to accurately predict the NP dispersion rate. The simulation results also confirm previous findings that the NP dispersion rate is strongly influenced by local disturbances in the flow due to RBC motion and deformation. The proposed formula provides an efficient method for estimating the NP dispersion rate in modeling NP transport in large-scale vascular networks without explicit RBC and NP models.
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Affiliation(s)
- Jifu Tan
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA.
| | - Wesley Keller
- Department of Civil and Environmental Engineering, Lehigh University, Bethlehem, PA 18015, USA.
| | - Salman Sohrabi
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA.
| | - Jie Yang
- School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China.
| | - Yaling Liu
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA.
- Bioengineering Program, Lehigh University, Bethlehem, PA 18015, USA.
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18
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Xu Y, Green MJ. Brownian dynamics simulations of nanosheet solutions under shear. J Chem Phys 2014; 141:024905. [DOI: 10.1063/1.4884821] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yueyi Xu
- Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409, USA
| | - Micah J. Green
- Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409, USA
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Nakamura M, Bessho S, Wada S. Analysis of red blood cell deformation under fast shear flow for better estimation of hemolysis. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2014; 30:42-54. [PMID: 23949912 DOI: 10.1002/cnm.2587] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2012] [Revised: 05/31/2013] [Accepted: 07/19/2013] [Indexed: 06/02/2023]
Abstract
We examined the deformation behavior of a red blood cell (RBC) in various flow fields to determine whether the extent of RBC deformation is correlated with the shear stress used as a hemolysis index. The RBC model was introduced to a simple shear flow (Couette flow) and to slightly complex flows (unsteady shear flows and stenosed flows). The RBC deformation was assessed by the maximum first principal strain over the RBC membrane and compared with the shear stress. Although the results were consistent under steady Couette flow, this was not the case under unsteady Couette flow or stenosed flow due to the viscoelastic nature of the RBC deformation caused by fluid forces. These results suggest that there is a limitation in accurately estimating the mechanical damage of RBCs solely from a macroscopic flow field, indicating the necessity of taking into account the dynamic deformation of RBCs to provide a better estimation of hemolysis.
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Affiliation(s)
- Masanori Nakamura
- Department of Mechanical Engineering, Saitama University, Saitama, Saitama Prefecture 338-8570, Japan
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Tavares JMRS, Jorge RN. Special issue on computational methods for biomedical image processing and analysis. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2013; 29:885-886. [PMID: 23926084 DOI: 10.1002/cnm.2574] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2013] [Accepted: 06/06/2013] [Indexed: 06/02/2023]
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