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Knüppel F, Malchow S, Sun A, Hussong J, Hartmann A, Wurm FH, Torner B. Viscosity Modeling for Blood and Blood Analog Fluids in Narrow Gap and High Reynolds Numbers Flows. MICROMACHINES 2024; 15:793. [PMID: 38930763 PMCID: PMC11205544 DOI: 10.3390/mi15060793] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2024] [Revised: 06/06/2024] [Accepted: 06/13/2024] [Indexed: 06/28/2024]
Abstract
For the optimization of ventricular assist devices (VADs), flow simulations are crucial. Typically, these simulations assume single-phase flow to represent blood flow. However, blood consists of plasma and blood cells, making it a multiphase flow. Cell migration in such flows leads to a heterogeneous cell distribution, significantly impacting flow dynamics, especially in narrow gaps of less than 300 μm found in VADs. In these areas, cells migrate away from the walls, forming a cell-free layer, a phenomenon not usually considered in current VAD simulations. This paper addresses this gap by introducing a viscosity model that accounts for cell migration in microchannels under VAD-relevant conditions. The model is based on local particle distributions measured in a microchannels with a blood analog fluid. We developed a local viscosity distribution for flows with particles/cells and a cell-free layer, applicable to both blood and analog fluids, with particle volume fractions of up to 5%, gap heights of 150 μm, and Reynolds numbers around 100. The model was validated by comparing simulation results with experimental data of blood and blood analog fluid flow on wall shear stresses and pressure losses, showing strong agreement. This model improves the accuracy of simulations by considering local viscosity changes rather than assuming a single-phase fluid. Future developments will extend the model to physiological volume fractions up to 40%.
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Affiliation(s)
- Finn Knüppel
- Institute of Turbomachinery, Faculty for Mechanical Engineering and Ship Design, University of Rostock, 18059 Rostock, Germany; (F.K.); (S.M.); (F.-H.W.)
| | - Sasha Malchow
- Institute of Turbomachinery, Faculty for Mechanical Engineering and Ship Design, University of Rostock, 18059 Rostock, Germany; (F.K.); (S.M.); (F.-H.W.)
| | - Ang Sun
- Institute for Fluid Mechanics and Aerodynamics, Technical University of Darmstadt, 64287 Darmstadt, Germany; (A.S.); (J.H.)
| | - Jeanette Hussong
- Institute for Fluid Mechanics and Aerodynamics, Technical University of Darmstadt, 64287 Darmstadt, Germany; (A.S.); (J.H.)
| | - Alexander Hartmann
- Institute of Clinical Chemistry and Laboratory Medicine, Rostock University Medical Center, 18057 Rostock, Germany;
| | - Frank-Hendrik Wurm
- Institute of Turbomachinery, Faculty for Mechanical Engineering and Ship Design, University of Rostock, 18059 Rostock, Germany; (F.K.); (S.M.); (F.-H.W.)
| | - Benjamin Torner
- Institute of Turbomachinery, Faculty for Mechanical Engineering and Ship Design, University of Rostock, 18059 Rostock, Germany; (F.K.); (S.M.); (F.-H.W.)
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Barbosa F, Dueñas-Pamplona J, Abreu CS, Oliveira MSN, Lima RA. Numerical Model Validation of the Blood Flow through a Microchannel Hyperbolic Contraction. MICROMACHINES 2023; 14:1886. [PMID: 37893323 PMCID: PMC10608998 DOI: 10.3390/mi14101886] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2023] [Revised: 09/18/2023] [Accepted: 09/28/2023] [Indexed: 10/29/2023]
Abstract
A computational fluid dynamics (CFD) model of blood flow through hyperbolic contraction with a discrete phase model (DPM) was experimentally validated. For this purpose, the positions and velocities of red blood cells (RBCs) flowing in a microchannel with hyperbolic contraction were experimentally assessed using image analysis techniques, and were subsequently compared with the numerical results. The numerically and experimentally obtained velocity fields were in good agreement, with errors smaller than 10%. Additionally, a nearly constant strain rate was observed in the contraction region, which can be attributed to the quasilinear increase in the velocity along the hyperbolic contraction. Therefore, the numerical technique used was validated due to the close similarity between the numerically and experimentally obtained results. The tested CFD model can be used to optimize the microchannel design by minimizing the need to fabricate prototypes and evaluate them experimentally.
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Affiliation(s)
- Filipe Barbosa
- Mechanical Engineering and Resource Sustainability Center (METRICS), University of Minho, 4800-058 Guimarães, Portugal;
| | - Jorge Dueñas-Pamplona
- Departamento de Ingeniería Energética, Universidad Politécnica de Madrid, 28040 Madrid, Spain;
| | - Cristiano S. Abreu
- Center for MicroElectromechanical Systems (CMEMS-UMinho), University of Minho, 4800-058 Guimarães, Portugal;
- LABBELS—Associate Laboratory, 4710-057 Braga, Portugal
- Physics Department, Porto Superior Engineering Institute, ISEP, 4200-072 Porto, Portugal
| | - Mónica S. N. Oliveira
- James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, UK;
| | - Rui A. Lima
- Mechanical Engineering and Resource Sustainability Center (METRICS), University of Minho, 4800-058 Guimarães, Portugal;
- CEFT—Transport Phenomena Research Center, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal
- ALiCE—Associate Laboratory in Chemical Engineering, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal
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Miranda I, Souza A, Sousa P, Ribeiro J, Castanheira EMS, Lima R, Minas G. Properties and Applications of PDMS for Biomedical Engineering: A Review. J Funct Biomater 2021; 13:2. [PMID: 35076525 PMCID: PMC8788510 DOI: 10.3390/jfb13010002] [Citation(s) in RCA: 135] [Impact Index Per Article: 45.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Revised: 12/13/2021] [Accepted: 12/16/2021] [Indexed: 12/14/2022] Open
Abstract
Polydimethylsiloxane (PDMS) is an elastomer with excellent optical, electrical and mechanical properties, which makes it well-suited for several engineering applications. Due to its biocompatibility, PDMS is widely used for biomedical purposes. This widespread use has also led to the massification of the soft-lithography technique, introduced for facilitating the rapid prototyping of micro and nanostructures using elastomeric materials, most notably PDMS. This technique has allowed advances in microfluidic, electronic and biomedical fields. In this review, an overview of the properties of PDMS and some of its commonly used treatments, aiming at the suitability to those fields' needs, are presented. Applications such as microchips in the biomedical field, replication of cardiovascular flow and medical implants are also reviewed.
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Affiliation(s)
- Inês Miranda
- Center for MicroElectromechanical Systems (CMEMS-UMinho), Campus de Azurém, University of Minho, 4800-058 Guimaraes, Portugal; (I.M.); (P.S.); (G.M.)
| | - Andrews Souza
- MEtRICs, Mechanical Engineering Department, Campus de Azurém, University of Minho, 4800-058 Guimaraes, Portugal;
| | - Paulo Sousa
- Center for MicroElectromechanical Systems (CMEMS-UMinho), Campus de Azurém, University of Minho, 4800-058 Guimaraes, Portugal; (I.M.); (P.S.); (G.M.)
| | - João Ribeiro
- Centro de Investigação de Montanha (CIMO), Campus de Santa Apolónia, Instituto Politécnico de Bragança, 5300-253 Braganca, Portugal;
| | - Elisabete M. S. Castanheira
- Centre of Physics of Minho and Porto Universities (CF-UM-UP), Campus de Gualtar, University of Minho, 4710-057 Braga, Portugal;
| | - Rui Lima
- MEtRICs, Mechanical Engineering Department, Campus de Azurém, University of Minho, 4800-058 Guimaraes, Portugal;
- CEFT, Faculdade de Engenharia da Universidade do Porto (FEUP), Rua Roberto Frias, 4200-465 Porto, Portugal
| | - Graça Minas
- Center for MicroElectromechanical Systems (CMEMS-UMinho), Campus de Azurém, University of Minho, 4800-058 Guimaraes, Portugal; (I.M.); (P.S.); (G.M.)
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Sadek SH, Rubio M, Lima R, Vega EJ. Blood Particulate Analogue Fluids: A Review. MATERIALS (BASEL, SWITZERLAND) 2021; 14:2451. [PMID: 34065125 PMCID: PMC8126041 DOI: 10.3390/ma14092451] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/05/2021] [Revised: 04/30/2021] [Accepted: 05/01/2021] [Indexed: 11/16/2022]
Abstract
Microfluidics has proven to be an extraordinary working platform to mimic and study blood flow phenomena and the dynamics of components of the human microcirculatory system. However, the use of real blood increases the complexity to perform these kinds of in vitro blood experiments due to diverse problems such as coagulation, sample storage, and handling problems. For this reason, interest in the development of fluids with rheological properties similar to those of real blood has grown over the last years. The inclusion of microparticles in blood analogue fluids is essential to reproduce multiphase effects taking place in a microcirculatory system, such as the cell-free layer (CFL) and Fähraeus-Lindqvist effect. In this review, we summarize the progress made in the last twenty years. Size, shape, mechanical properties, and even biological functionalities of microparticles produced/used to mimic red blood cells (RBCs) are critically exposed and analyzed. The methods developed to fabricate these RBC templates are also shown. The dynamic flow/rheology of blood particulate analogue fluids proposed in the literature (with different particle concentrations, in most of the cases, relatively low) is shown and discussed in-depth. Although there have been many advances, the development of a reliable blood particulate analogue fluid, with around 45% by volume of microparticles, continues to be a big challenge.
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Affiliation(s)
- Samir Hassan Sadek
- Departamento de Ingeniería Mecánica, Energética y de los Materiales and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain; (S.H.S.); (M.R.)
| | - Manuel Rubio
- Departamento de Ingeniería Mecánica, Energética y de los Materiales and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain; (S.H.S.); (M.R.)
| | - Rui Lima
- MEtRICs, Mechanical Engineering Department, Campus de Azurém, University of Minho, 4800-058 Guimarães, Portugal;
- Transport Phenomena Research Center, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
| | - Emilio José Vega
- Departamento de Ingeniería Mecánica, Energética y de los Materiales and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain; (S.H.S.); (M.R.)
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He S, Joseph N, Feng S, Jellicoe M, Raston CL. Application of microfluidic technology in food processing. Food Funct 2021; 11:5726-5737. [PMID: 32584365 DOI: 10.1039/d0fo01278e] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Microfluidic technology is interdisciplinary with a diversity of applications including in food processing. The rapidly growing global population demands more advanced technologies in food processing to produce more functional and safer food, and for such processing microfluidic devices are a popular choice. This review critically critiques the state-of-the-art designs of microfluidic devices and their applications in food processing, and identifies the key research trends and future research directions for maximizing the value of microfluidic technology. Capillary, planar, and terrace droplet generation systems are currently used in the design of microfluidic devices, each with their strengths and weaknesses as applied in food processing, for emulsification, food safety measurements, and bioactive compound extraction. Conventional channel-based microfluidic devices are prone to clogging, and have high labor costs and low productivity, and their "directional pressure" restricts scaling-up capabilities. These disadvantages can be overcome by using "inside-out centrifugal force" and the new generation continuous flow thin-film microfluidic Vortex Fluidic Device (VFD) which facilitates translating laboratory processing into commercial products. Also highlighted is controlling protein-polysaccharide interactions and the applications of the produced ingredients in food formulations as targets for future development in the field.
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Affiliation(s)
- Shan He
- Department of Food Science, School of Chemistry and Chemical Engineering, Guangzhou University, Guangzhou, Guangdong 510006, China. and Flinders Institute for Nanoscale Science and Technology, College of Science and Engineering, Flinders University, Bedford Park, South Australia, 5042, Australia.
| | - Nikita Joseph
- Flinders Institute for Nanoscale Science and Technology, College of Science and Engineering, Flinders University, Bedford Park, South Australia, 5042, Australia.
| | - Shilun Feng
- School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore
| | - Matt Jellicoe
- Flinders Institute for Nanoscale Science and Technology, College of Science and Engineering, Flinders University, Bedford Park, South Australia, 5042, Australia.
| | - Colin L Raston
- Flinders Institute for Nanoscale Science and Technology, College of Science and Engineering, Flinders University, Bedford Park, South Australia, 5042, Australia.
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Carneiro J, Lima R, Campos JBLM, Miranda JM. A microparticle blood analogue suspension matching blood rheology. SOFT MATTER 2021; 17:3963-3974. [PMID: 33724275 DOI: 10.1039/d1sm00106j] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The handling of blood in vitro is demanding because of ethical, economical and safety issues. Although several Newtonian and non-Newtonian blood analogues are found in the literature, few studies have used particles to mimic red blood cells (RBCs) and built an analogue with similar rheological properties of blood. This work reports the development of a blood analogue suspension composed of polydimethylsiloxane (PDMS) microparticles with an average diameter of ∼7 μm. High throughput production of PDMS particles is possible using a multi-stage membrane emulsification process; up to ∼6 mL of microparticles are manufactured in 3 hours. PDMS particles at a concentration of around 21% (w/w) at 20 °C present steady, oscillatory and extensional rheologies very similar to those of blood under physiological conditions (37 °C and ∼41% hematocrit), making them a good candidate whole blood analogue. Also, flow studies were performed in microchannels with contraction to study the cell-free layer (CFL) formation and particle deformation, achieving good qualitative results. Using the procedure developed, it is possible to obtain blood analogue fluids with a shelf life of at least 6 months.
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Affiliation(s)
- J Carneiro
- CEFT, Transport Phenomena Research Center, Chemical Engineering Department, Faculty of Engineering, University of Porto, 4050-465 Porto, Portugal.
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Rodríguez-Villarreal AI, Carmona-Flores M, Colomer-Farrarons J. Effect of Temperature and Flow Rate on the Cell-Free Area in the Microfluidic Channel. MEMBRANES 2021; 11:membranes11020109. [PMID: 33546403 PMCID: PMC7913562 DOI: 10.3390/membranes11020109] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/23/2020] [Revised: 01/23/2021] [Accepted: 01/29/2021] [Indexed: 01/16/2023]
Abstract
Blood cell manipulation in microdevices is an interesting task for the separation of particles, by their size, density, or to remove them from the buffer, in which they are suspended, for further analysis, and more. This study highlights the cell-free area (CFA) widening based on experimental results of red blood cell (RBC) flow, suspended in a microfluidic device, while temperature and flow rate incrementally modify RBC response within the microflow. Studies of human red blood cell flow, at a concentration of 20%, suspended in its autologous plasma and phosphate-buffered saline (PBS) buffer, were carried out at a wide flow rate, varying between 10 and 230 μL/min and a temperature range of 23 °C to 50 °C. The plotted measures show an increment in a CFA near the channel wall due to cell flow inertia after a constricted channel, which becomes more significant as temperature and flow rate increase. The temperature increment widened the CFA up to three times. In comparison, flow rate increment increased the CFA up to 20 times in PBS and 11 times in plasma.
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Zhong F, Guan L, Lin H, Zhao M, Qin Y, Li Q, Yuan Z, Yang G, Gao L, Zhao J. Red Blood Cell Count: An Unrecognized Risk Factor for Nonalcoholic Fatty Liver Disease. Front Endocrinol (Lausanne) 2021; 12:760981. [PMID: 34950103 PMCID: PMC8688742 DOI: 10.3389/fendo.2021.760981] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/19/2021] [Accepted: 11/08/2021] [Indexed: 12/12/2022] Open
Abstract
OBJECTIVE Nonalcoholic fatty liver disease (NAFLD) is becoming a global public health challenge. A convenient NAFLD indicator will greatly facilitate risk appraisal and prevention. As a readily available and inexpensive hematological index in routine clinical examinations, red blood cells (RBCs) are gaining increasing attention in many diseases, such as metabolic syndrome, but their association with NAFLD is unknown. METHODS This health management cohort study included 27,112 subjects (17,383 non-NAFLD and 9,729 NAFLD) with up to 5 years of follow-up (median 2.8 years). NAFLD was diagnosed by ultrasonography. NAFLD severity was categorized as mild, moderate, or severe. The generalized estimation equation (GEE), an extension of generalized linear models that allows for analysis of repeated measurements, was used to analyze the association between RBC count and NAFLD. RESULTS Overall, 4,332 of 17,383 (24.9%) subjects without NAFLD at baseline developed NAFLD. Incident NAFLD risk was positively associated with RBC count. After adjustment for hemoglobin and other confounders, the risk of incident NAFLD was 21%, 32%, and 51% higher in the second, third, and fourth RBC count quartiles, respectively, than in the lowest quartile. In 1,798 of 9,476 (19.0%) subjects with NAFLD at baseline, the severity of NAFLD increased. NAFLD progression risk increased progressively as RBC count increased (P for trend < 0.001). Every one-unit (1012 cells/L) increase in RBC count was associated with a 53% [OR 1.53 (95% CI 1.32-1.77)] increased risk for NAFLD progression. CONCLUSIONS Elevated RBC count was independently associated with a high risk of NAFLD incidence and progression. This finding revealed a convenient NAFLD risk indicator.
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Affiliation(s)
- Fang Zhong
- Department of Endocrinology, Shandong Provincial Hospital, Cheeloo College of Medicine, Shandong University, Jinan, China
- Shandong Clinical Medical Center of Endocrinology and Metabolism, Jinan, China
- Shandong Institute of Endocrine and Metabolic Disease, Jinan, China
| | - Liying Guan
- Health Management Center, Shandong Provincial Hospital Affiliated to Shandong First Medical University, Jinan, China
| | - Haiyan Lin
- Health Management Center, Shandong Provincial Hospital Affiliated to Shandong First Medical University, Jinan, China
| | - Meng Zhao
- Shandong Clinical Medical Center of Endocrinology and Metabolism, Jinan, China
- Shandong Institute of Endocrine and Metabolic Disease, Jinan, China
- Department of Endocrinology, Shandong Provincial Hospital Affiliated to Shandong First Medical University, Jinan, China
| | - Yiming Qin
- College of Chemical Engineering and Materials Science, Shandong Normal University, Jinan, China
| | - Qihang Li
- Department of Endocrinology, Shandong Provincial Hospital, Cheeloo College of Medicine, Shandong University, Jinan, China
- Shandong Clinical Medical Center of Endocrinology and Metabolism, Jinan, China
- Shandong Institute of Endocrine and Metabolic Disease, Jinan, China
| | - Zhongshang Yuan
- Department of Biostatistics, School of Public Health, Shandong University, Jinan, China
| | - Guang Yang
- Beijing Institute of Pharmacology and Toxicology, Beijing, China
| | - Ling Gao
- Department of Endocrinology, Shandong Provincial Hospital, Cheeloo College of Medicine, Shandong University, Jinan, China
- Shandong Clinical Medical Center of Endocrinology and Metabolism, Jinan, China
- Shandong Institute of Endocrine and Metabolic Disease, Jinan, China
- Department of Endocrinology, Shandong Provincial Hospital Affiliated to Shandong First Medical University, Jinan, China
| | - Jiajun Zhao
- Department of Endocrinology, Shandong Provincial Hospital, Cheeloo College of Medicine, Shandong University, Jinan, China
- Shandong Clinical Medical Center of Endocrinology and Metabolism, Jinan, China
- Shandong Institute of Endocrine and Metabolic Disease, Jinan, China
- Department of Endocrinology, Shandong Provincial Hospital Affiliated to Shandong First Medical University, Jinan, China
- *Correspondence: Jiajun Zhao,
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Carvalho V, Maia I, Souza A, Ribeiro J, Costa P, Puga H, Teixeira S, Lima RA. In vitro
Biomodels in Stenotic Arteries to Perform Blood Analogues Flow Visualizations and Measurements: A Review. Open Biomed Eng J 2020. [DOI: 10.2174/1874120702014010087] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Cardiovascular diseases are one of the leading causes of death globally and the most common pathological process is atherosclerosis. Over the years, these cardiovascular complications have been extensively studied by applying in vivo, in vitro and numerical methods (in silico). In vivo studies represent more accurately the physiological conditions and provide the most realistic data. Nevertheless, these approaches are expensive, and it is complex to control several physiological variables. Hence, the continuous effort to find reliable alternative methods has been growing. In the last decades, numerical simulations have been widely used to assess the blood flow behavior in stenotic arteries and, consequently, providing insights into the cardiovascular disease condition, its progression and therapeutic optimization. However, it is necessary to ensure its accuracy and reliability by comparing the numerical simulations with clinical and experimental data. For this reason, with the progress of the in vitro flow measurement techniques and rapid prototyping, experimental investigation of hemodynamics has gained widespread attention. The present work reviews state-of-the-art in vitro macro-scale arterial stenotic biomodels for flow measurements, summarizing the different fabrication methods, blood analogues and highlighting advantages and limitations of the most used techniques.
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Visualization and Measurements of Blood Cells Flowing in Microfluidic Systems and Blood Rheology: A Personalized Medicine Perspective. J Pers Med 2020; 10:jpm10040249. [PMID: 33256123 PMCID: PMC7712771 DOI: 10.3390/jpm10040249] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2020] [Revised: 11/21/2020] [Accepted: 11/23/2020] [Indexed: 02/08/2023] Open
Abstract
Hemorheological alterations in the majority of metabolic diseases are always connected with blood rheology disturbances, such as the increase of blood and plasma viscosity, cell aggregation enhancement, and reduction of the red blood cells (RBCs) deformability. Thus, the visualizations and measurements of blood cells deformability flowing in microfluidic devices (point-of-care devices) can provide vital information to diagnose early symptoms of blood diseases and consequently to be used as a fast clinical tool for early detection of biomarkers. For instance, RBCs rigidity has been correlated with myocardial infarction, diabetes mellitus, hypertension, among other blood diseases. In order to better understand the blood cells behavior in microfluidic devices, rheological properties analysis is gaining interest by the biomedical committee, since it is strongly dependent on the interactions and mechanical cells proprieties. In addition, the development of blood analogue fluids capable of reproducing the rheological properties of blood and mimic the RBCs behavior at in vitro conditions is crucial for the design, performance and optimization of the microfluidic devices frequently used for personalized medicine. By combining the unique features of the hemorheology and microfluidic technology for single-cell analysis, valuable advances in personalized medicine for new treatments and diagnosis approach can be achieved.
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Carvalho V, Rodrigues N, Ribeiro R, Costa PF, Teixeira JCF, Lima RA, Teixeira SFCF. Hemodynamic study in 3D printed stenotic coronary artery models: experimental validation and transient simulation. Comput Methods Biomech Biomed Engin 2020; 24:623-636. [PMID: 33225743 DOI: 10.1080/10255842.2020.1842377] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
Atherosclerosis is a progressive disease that can significantly reduce blood supply to vital organs, being one of the main causes of death worldwide. In this work, a numerical and experimental study in 3D printed stenotic coronary arteries, considering both steady and pulsatile blood flow conditions, is presented. The results revealed that a degree of stenosis superior to 50% creates disturbed flows downstream of the contraction, with an accented increase in the wall shear stress measurements at the stenosis throat. Finally, the multiphase mixture was investigated and compared with a single-phase modelling, and only slight differences were observed right after the stenosis throat.
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Affiliation(s)
- Violeta Carvalho
- MEtRICs Research Center, University of Minho, Guimarães, Portugal
| | - Nelson Rodrigues
- ALGORITMI Research Center, University of Minho, Guimarães, Portugal
| | | | | | | | - Rui A Lima
- MEtRICs Research Center, University of Minho, Guimarães, Portugal.,CEFT, Faculty of Engineering, University of Porto, Porto, Portugal
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3D Printed Biomodels for Flow Visualization in Stenotic Vessels: An Experimental and Numerical Study. MICROMACHINES 2020; 11:mi11060549. [PMID: 32485816 PMCID: PMC7344925 DOI: 10.3390/mi11060549] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/24/2020] [Revised: 05/17/2020] [Accepted: 05/25/2020] [Indexed: 12/13/2022]
Abstract
Atherosclerosis is one of the most serious and common forms of cardiovascular disease and a major cause of death and disability worldwide. It is a multifactorial and complex disease that promoted several hemodynamic studies. Although in vivo studies more accurately represent the physiological conditions, in vitro experiments more reliably control several physiological variables and most adequately validate numerical flow studies. Here, a hemodynamic study in idealized stenotic and healthy coronary arteries is presented by applying both numerical and in vitro approaches through computational fluid dynamics simulations and a high-speed video microscopy technique, respectively. By means of stereolithography 3D printing technology, biomodels with three different resolutions were used to perform experimental flow studies. The results showed that the biomodel printed with a resolution of 50 μm was able to most accurately visualize flow due to its lowest roughness values (Ra = 1.8 μm). The flow experimental results showed a qualitatively good agreement with the blood flow numerical data, providing a clear observation of recirculation regions when the diameter reduction reached 60%.
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13
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Kim CM, Choi HJ, Kim GM. 512-Channel Geometric Droplet-Splitting Microfluidic Device by Injection of Premixed Emulsion for Microsphere Production. Polymers (Basel) 2020; 12:polym12040776. [PMID: 32244738 PMCID: PMC7240624 DOI: 10.3390/polym12040776] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2020] [Revised: 03/24/2020] [Accepted: 03/25/2020] [Indexed: 11/16/2022] Open
Abstract
We present a 512-channel geometric droplet-splitting microfluidic device that involves the injection of a premixed emulsion for microsphere production. The presented microfluidic device was fabricated using conventional photolithography and polydimethylsiloxane casting. The fabricated microfluidic device consisted of 512 channels with 256 T-junctions in the last branch. Five hundred and twelve microdroplets with a narrow size distribution were produced from a single liquid droplet. The diameter and size distribution of prepared micro water droplets were 35.29 µm and 8.8% at 10 mL/h, respectively. Moreover, we attempted to prepare biocompatible microspheres for demonstrating the presented approach. The diameter and size distribution of the prepared poly (lactic-co-glycolic acid) microspheres were 6.56 µm and 8.66% at 10 mL/h, respectively. To improve the monodispersity of the microspheres, we designed an additional post array part in the 512-channel geometric droplet-splitting microfluidic device. The monodispersity of the microdroplets prepared with the microfluidic device combined with the post array part exhibited a significant improvement.
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Affiliation(s)
- Chul Min Kim
- Department of Mechanical Engineering, Korea Polytechnic University, Siheung-Si 15073, Korea;
| | - Hye Jin Choi
- School of Mechanical Engineering, Kyungpook National University, Daegu 41566, Korea;
| | - Gyu Man Kim
- School of Mechanical Engineering, Kyungpook National University, Daegu 41566, Korea;
- Correspondence: ; Tel.: +82-053-950-7570
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14
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Bento D, Lopes S, Maia I, Lima R, Miranda JM. Bubbles Moving in Blood Flow in a Microchannel Network: The Effect on the Local Hematocrit. MICROMACHINES 2020; 11:mi11040344. [PMID: 32224993 PMCID: PMC7230880 DOI: 10.3390/mi11040344] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/07/2020] [Revised: 03/23/2020] [Accepted: 03/23/2020] [Indexed: 01/07/2023]
Abstract
Air inside of blood vessels is a phenomenon known as gas embolism. During the past years, studies have been performed to assess the influence of air bubbles in microcirculation. In this study, we investigated the flow of bubbles in a microchannel network with several bifurcations, mimicking part of a capillary system. Thus, two working fluids were used, composed by sheep red blood cells (RBCs) suspended in a Dextran 40 solution with different hematocrits (5% and 10%). The experiments were carried out in a polydimethylsiloxane (PDMS) microchannel network fabricated by a soft lithography. A high-speed video microscopy system was used to obtain the results for a blood flow rate of 10 µL/min. This system enables the visualization of bubble formation and flow along the network. The results showed that the passage of air bubbles strongly influences the cell's local concentration, since a higher concentration of cells was observed upstream of the bubble, whereas a lower local hematocrit was visualized at the region downstream of the bubble. In bifurcations, bubbles may split asymmetrically, leading to an uneven distribution of RBCs between the outflow branches.
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Affiliation(s)
- David Bento
- CEFT, Faculdade de Engenharia da Universidade do Porto (FEUP) Rua Dr. Roberto Frias, 4200-465 Porto, Portugal; (D.B.); (R.L.)
- Polytechnic Institute of Bragança, ESTiG/IPB, C. Sta. Apolónia, 5300-857 Bragança, Portugal;
| | - Sara Lopes
- Polytechnic Institute of Bragança, ESTiG/IPB, C. Sta. Apolónia, 5300-857 Bragança, Portugal;
| | - Inês Maia
- Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal;
| | - Rui Lima
- CEFT, Faculdade de Engenharia da Universidade do Porto (FEUP) Rua Dr. Roberto Frias, 4200-465 Porto, Portugal; (D.B.); (R.L.)
- MEtRICS, Mechanical Eng. Dep., University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal
| | - João M. Miranda
- CEFT, Faculdade de Engenharia da Universidade do Porto (FEUP) Rua Dr. Roberto Frias, 4200-465 Porto, Portugal; (D.B.); (R.L.)
- Correspondence:
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15
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Advances in Computational Fluid Mechanics in Cellular Flow Manipulation: A Review. APPLIED SCIENCES-BASEL 2019. [DOI: 10.3390/app9194041] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
Recently, remarkable developments have taken place, leading to significant improvements in microfluidic methods to capture subtle biological effects down to single cells. As microfluidic devices are getting sophisticated, design optimization through experimentations is becoming more challenging. As a result, numerical simulations have contributed to this trend by offering a better understanding of cellular microenvironments hydrodynamics and optimizing the functionality of the current/emerging designs. The need for new marketable designs with advantageous hydrodynamics invokes easier access to efficient as well as time-conservative numerical simulations to provide screening over cellular microenvironments, and to emulate physiological conditions with high accuracy. Therefore, an excerpt overview on how each numerical methodology and associated handling software works, and how they differ in handling underlying hydrodynamic of lab-on-chip microfluidic is crucial. These numerical means rely on molecular and continuum levels of numerical simulations. The current review aims to serve as a guideline for researchers in this area by presenting a comprehensive characterization of various relevant simulation techniques.
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16
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Catarino SO, Rodrigues RO, Pinho D, Miranda JM, Minas G, Lima R. Blood Cells Separation and Sorting Techniques of Passive Microfluidic Devices: From Fabrication to Applications. MICROMACHINES 2019; 10:mi10090593. [PMID: 31510012 PMCID: PMC6780402 DOI: 10.3390/mi10090593] [Citation(s) in RCA: 60] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/02/2019] [Revised: 09/03/2019] [Accepted: 09/06/2019] [Indexed: 01/23/2023]
Abstract
Since the first microfluidic device was developed more than three decades ago, microfluidics is seen as a technology that exhibits unique features to provide a significant change in the way that modern biology is performed. Blood and blood cells are recognized as important biomarkers of many diseases. Taken advantage of microfluidics assets, changes on blood cell physicochemical properties can be used for fast and accurate clinical diagnosis. In this review, an overview of the microfabrication techniques is given, especially for biomedical applications, as well as a synopsis of some design considerations regarding microfluidic devices. The blood cells separation and sorting techniques were also reviewed, highlighting the main achievements and breakthroughs in the last decades.
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Affiliation(s)
- Susana O Catarino
- Center for MicroElectromechanical Systems (CMEMS-UMinho), University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal
| | - Raquel O Rodrigues
- Center for MicroElectromechanical Systems (CMEMS-UMinho), University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal
| | - Diana Pinho
- Research Centre in Digitalization and Intelligent Robotics (CeDRI), Instituto Politécnico de Bragança, Campus de Santa Apolónia, 5300-253 Bragança, Portugal
- CEFT, Faculdade de Engenharia da Universidade do Porto (FEUP), Rua Roberto Frias, 4200-465 Porto, Portugal
| | - João M Miranda
- CEFT, Faculdade de Engenharia da Universidade do Porto (FEUP), Rua Roberto Frias, 4200-465 Porto, Portugal
| | - Graça Minas
- Center for MicroElectromechanical Systems (CMEMS-UMinho), University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal
| | - Rui Lima
- CEFT, Faculdade de Engenharia da Universidade do Porto (FEUP), Rua Roberto Frias, 4200-465 Porto, Portugal.
- MEtRICs, Mechanical Engineering Department, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal.
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17
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Cho M, Hong SO, Lee SH, Hyun K, Kim JM. Effects of Ionic Strength on Lateral Particle Migration in Shear-Thinning Xanthan Gum Solutions. MICROMACHINES 2019; 10:E535. [PMID: 31443169 PMCID: PMC6723194 DOI: 10.3390/mi10080535] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/21/2019] [Revised: 08/08/2019] [Accepted: 08/12/2019] [Indexed: 01/22/2023]
Abstract
Viscoelastic fluids, including particulate systems, are found in various biological and industrial systems including blood flow, food, cosmetics, and electronic materials. Particles suspended in viscoelastic fluids such as polymer solutions migrate laterally, forming spatially segregated streams in pressure-driven flow. Viscoelastic particle migration was recently applied to microfluidic technologies including particle counting and sorting and the micromechanical measurement of living cells. Understanding the effects on equilibrium particle positions of rheological properties of suspending viscoelastic fluid is essential for designing microfluidic applications. It has been considered that the shear-thinning behavior of viscoelastic fluid is a critical factor in determining the equilibrium particle positions. This work presents the lateral particle migration in two different xanthan gum-based viscoelastic fluids with similar shear-thinning viscosities and the linear viscoelastic properties. The flexibility and contour length of the xanthan gum molecules were tuned by varying the ionic strength of the solvent. Particles suspended in flexible and short xanthan gum solution, dissolved at high ionic strength, migrated toward the corners in a square channel, whereas particles in the rigid and long xanthan gum solutions in deionized water migrated toward the centerline. This work suggests that the structural properties of polymer molecules play significant roles in determining the equilibrium positions in shear-thinning fluids, despite similar bulk rheological properties. The current results are expected to be used in a wide range of applications such as cell counting and sorting.
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Affiliation(s)
- Mira Cho
- Department of Energy Systems Research, Ajou University, Suwon 16499, Korea
| | - Sun Ok Hong
- Department of Energy Systems Research, Ajou University, Suwon 16499, Korea
| | - Seung Hak Lee
- School of Chemical and Biomolecular Engineering, Pusan National University, Busan 46241, Korea
| | - Kyu Hyun
- School of Chemical and Biomolecular Engineering, Pusan National University, Busan 46241, Korea.
| | - Ju Min Kim
- Department of Energy Systems Research, Ajou University, Suwon 16499, Korea.
- Department of Chemical Engineering, Ajou University, Suwon 16499, Korea.
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18
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Microfluidic Deformability Study of an Innovative Blood Analogue Fluid Based on Giant Unilamellar Vesicles. J Funct Biomater 2018; 9:jfb9040070. [PMID: 30518160 PMCID: PMC6306889 DOI: 10.3390/jfb9040070] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2018] [Revised: 11/12/2018] [Accepted: 11/27/2018] [Indexed: 11/16/2022] Open
Abstract
Blood analogues have long been a topic of interest in biofluid mechanics due to the safety and ethical issues involved in the collection and handling of blood samples. Although the current blood analogue fluids can adequately mimic the rheological properties of blood from a macroscopic point of view, at the microscopic level blood analogues need further development and improvement. In this work, an innovative blood analogue containing giant unilamellar vesicles (GUVs) was developed to mimic the flow behavior of red blood cells (RBCs). A natural lipid mixture, soybean lecithin, was used for the GUVs preparation, and three different lipid concentrations were tested (1 × 10-3 M, 2 × 10-3 M and 4 × 10-3 M). GUV solutions were prepared by thin film hydration with a buffer, followed by extrusion. It was found that GUVs present diameters between 5 and 7 µm which are close to the size of human RBCs. Experimental flow studies of three different GUV solutions were performed in a hyperbolic-shaped microchannel in order to measure the GUVs deformability when subjected to a homogeneous extensional flow. The result of the deformation index (DI) of the GUVs was about 0.5, which is in good agreement with the human RBC's DI. Hence, the GUVs developed in this study are a promising way to mimic the mechanical properties of the RBCs and to further develop particulate blood analogues with flow properties closer to those of real blood.
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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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20
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Pinho D, Campo-Deaño L, Lima R, Pinho FT. In vitro particulate analogue fluids for experimental studies of rheological and hemorheological behavior of glucose-rich RBC suspensions. BIOMICROFLUIDICS 2017; 11:054105. [PMID: 28966701 PMCID: PMC5608610 DOI: 10.1063/1.4998190] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2017] [Accepted: 07/28/2017] [Indexed: 05/09/2023]
Abstract
Suspensions of healthy and pathological red blood cells (RBC) flowing in microfluidic devices are frequently used to perform in vitro blood experiments for a better understanding of human microcirculation hemodynamic phenomena. This work reports the development of particulate viscoelastic analogue fluids able to mimic the rheological and hemorheological behavior of pathological RBC suspensions flowing in microfluidic systems. The pathological RBCs were obtained by an incubation of healthy RBCs at a high concentration of glucose, representing the pathological stage of hyperglycaemia in diabetic complications, and analyses of their deformability and aggregation were carried out. Overall, the developed in vitro analogue fluids were composed of a suspension of semi-rigid microbeads in a carrier viscoelastic fluid made of dextran 40 and xanthan gum. All suspensions of healthy and pathological RBCs, as well as their particulate analogue fluids, were extensively characterized in steady shear flow, as well as in small and large amplitude oscillatory shear flow. In addition, the well-known cell-free layer (CFL) phenomenon occurring in microchannels was investigated in detail to provide comparisons between healthy and pathological in vitro RBC suspensions and their corresponding analogue fluids at different volume concentrations (5% and 20%). The experimental results have shown a similar rheological behavior between the samples containing a suspension of pathological RBCs and the proposed analogue fluids. Moreover, this work shows that the particulate in vitro analogue fluids used have the ability to mimic well the CFL phenomenon occurring downstream of a microchannel contraction for pathological RBC suspensions. The proposed particulate fluids provide a more realistic behavior of the flow properties of suspended RBCs when compared with existing non-particulate blood analogues, and consequently, they are advantageous for detailed investigations of microcirculation.
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Affiliation(s)
| | - Laura Campo-Deaño
- CEFT, DEMec, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
| | | | - Fernando T Pinho
- CEFT, DEMec, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
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21
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Muñoz-Sánchez BN, Silva SF, Pinho D, Vega EJ, Lima R. Generation of micro-sized PDMS particles by a flow focusing technique for biomicrofluidics applications. BIOMICROFLUIDICS 2016; 10:014122. [PMID: 27042245 PMCID: PMC4807564 DOI: 10.1063/1.4943007] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2016] [Accepted: 02/17/2016] [Indexed: 05/24/2023]
Abstract
Polydimethylsiloxane (PDMS), due to its remarkable properties, is one of the most widely used polymers in many industrial and medical applications. In this work, a technique based on a flow focusing technique is used to produce PDMS spherical particles with sizes of a few microns. PDMS precursor is injected through a hypodermic needle to form a film/reservoir over the needle's outer surface. This film flows towards the needle tip until a liquid ligament is steadily ejected thanks to the action of a coflowing viscous liquid stream. The outcome is a capillary jet which breaks up into PDMS precursor droplets due to the growth of capillary waves producing a micrometer emulsion. The PDMS liquid droplets in the solution are thermally cured into solid microparticles. The size distribution of the particles is analyzed before and after curing, showing an acceptable degree of monodispersity. The PDMS liquid droplets suffer shrinkage while curing. These microparticles can be used in very varied technological fields, such as biomedicine, biotechnology, pharmacy, and industrial engineering.
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Affiliation(s)
- B N Muñoz-Sánchez
- Depto. de Mecánica de Fluidos e Ingeniería Aeroespacial, Universidad de Sevilla , E-41092 Sevilla, Spain
| | - S F Silva
- Polytechnic Institute of Bragança , Campus de Santa Apolónia, Bragança, Portugal
| | | | - E J Vega
- Depto. de Ingeniería Mecánica, Energética y de los Materiales and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura , E-06006 Badajoz, Spain
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