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Lin J, Chen S, Zhang C, Liao J, Chen Y, Deng S, Mao Z, Zhang T, Tian N, Song Y, Zeng T. Recent advances in microfluidic technology of arterial thrombosis investigations. Platelets 2024; 35:2316743. [PMID: 38390892 DOI: 10.1080/09537104.2024.2316743] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2023] [Accepted: 02/05/2024] [Indexed: 02/24/2024]
Abstract
Microfluidic technology has emerged as a powerful tool in studying arterial thrombosis, allowing researchers to construct artificial blood vessels and replicate the hemodynamics of blood flow. This technology has led to significant advancements in understanding thrombosis and platelet adhesion and aggregation. Microfluidic models have various types and functions, and by studying the fabrication methods and working principles of microfluidic chips, applicable methods can be selected according to specific needs. The rapid development of microfluidic integrated system and modular microfluidic system makes arterial thrombosis research more diversified and automated, but its standardization still needs to be solved urgently. One key advantage of microfluidic technology is the ability to precisely control fluid flow in microchannels and to analyze platelet behavior under different shear forces and flow rates. This allows researchers to study the physiological and pathological processes of blood flow, shedding light on the underlying mechanisms of arterial thrombosis. In conclusion, microfluidic technology has revolutionized the study of arterial thrombosis by enabling the construction of artificial blood vessels and accurately reproducing hemodynamics. In the future, microfluidics will place greater emphasis on versatility and automation, holding great promise for advancing antithrombotic therapeutic and prophylactic measures.
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Affiliation(s)
- Jingying Lin
- Department of Laboratory Medicine, West China Hospital, Sichuan University, Chengdu, China
- Department of Laboratory Medicine, Chengdu Shangjin Nanfu Hospital/Shangjin Branch of West China Hospital, Sichuan University, Chengdu, China
| | - Si Chen
- Department of Laboratory Medicine, West China Hospital, Sichuan University, Chengdu, China
| | - Chunying Zhang
- Department of Laboratory Medicine, West China Hospital, Sichuan University, Chengdu, China
| | - Juan Liao
- Department of Laboratory Medicine, West China Hospital, Sichuan University, Chengdu, China
| | - Yuemei Chen
- Department of Laboratory Medicine, West China Hospital, Sichuan University, Chengdu, China
| | - Shanying Deng
- Department of Laboratory Medicine, West China Hospital, Sichuan University, Chengdu, China
| | - Zhigang Mao
- Department of Laboratory Medicine, West China Hospital, Sichuan University, Chengdu, China
| | - Tonghao Zhang
- Department of Statistics, University of Virginia, Charlottesville, USA
| | - Na Tian
- Anesthesiology Department, Qingdao Eighth People's Hospital, Qingdao, China
| | - Yali Song
- Department of Laboratory Medicine, West China Hospital, Sichuan University, Chengdu, China
| | - Tingting Zeng
- Department of Laboratory Medicine, West China Hospital, Sichuan University, Chengdu, China
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2
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Shayor AA, Kabir ME, Rifath MSA, Rashid AB, Oh KW. A Synergistic Overview between Microfluidics and Numerical Research for Vascular Flow and Pathological Investigations. SENSORS (BASEL, SWITZERLAND) 2024; 24:5872. [PMID: 39338617 PMCID: PMC11435959 DOI: 10.3390/s24185872] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2024] [Revised: 08/20/2024] [Accepted: 09/02/2024] [Indexed: 09/30/2024]
Abstract
Vascular diseases are widespread, and sometimes such life-threatening medical disorders cause abnormal blood flow, blood particle damage, changes to flow dynamics, restricted blood flow, and other adverse effects. The study of vascular flow is crucial in clinical practice because it can shed light on the causes of stenosis, aneurysm, blood cancer, and many other such diseases, and guide the development of novel treatments and interventions. Microfluidics and computational fluid dynamics (CFDs) are two of the most promising new tools for investigating these phenomena. When compared to conventional experimental methods, microfluidics offers many benefits, including lower costs, smaller sample quantities, and increased control over fluid flow and parameters. In this paper, we address the strengths and weaknesses of computational and experimental approaches utilizing microfluidic devices to investigate the rheological properties of blood, the forces of action causing diseases related to cardiology, provide an overview of the models and methodologies of experiments, and the fabrication of devices utilized in these types of research, and portray the results achieved and their applications. We also discuss how these results can inform clinical practice and where future research should go. Overall, it provides insights into why a combination of both CFDs, and experimental methods can give even more detailed information on disease mechanisms recreated on a microfluidic platform, replicating the original biological system and aiding in developing the device or chip itself.
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Affiliation(s)
- Ahmed Abrar Shayor
- Department of Mechanical Engineering, Khulna University of Engineering & Technology, Khulna 9203, Bangladesh
| | - Md Emamul Kabir
- Department of Mechanical Engineering, Khulna University of Engineering & Technology, Khulna 9203, Bangladesh
- Sensors and MicroActuators Learning Lab (SMALL), Department of Electrical Engineering, The State University of New York at Buffalo, Buffalo, NY 14260, USA
| | - Md Sartaj Ahamed Rifath
- Department of Mechanical Engineering, Khulna University of Engineering & Technology, Khulna 9203, Bangladesh
| | - Adib Bin Rashid
- Department of Industrial and Production Engineering, Military Institute of Science and Technology, Dhaka 1216, Bangladesh
| | - Kwang W Oh
- Sensors and MicroActuators Learning Lab (SMALL), Department of Electrical Engineering, The State University of New York at Buffalo, Buffalo, NY 14260, USA
- Department of Biomedical Engineering, The State University of New York at Buffalo, Buffalo, NY 14260, USA
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3
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Sveshnikova AN, Shibeko AM, Kovalenko TA, Panteleev MA. Kinetics and regulation of coagulation factor X activation by intrinsic tenase on phospholipid membranes. J Theor Biol 2024; 582:111757. [PMID: 38336240 DOI: 10.1016/j.jtbi.2024.111757] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2023] [Revised: 12/13/2023] [Accepted: 01/31/2024] [Indexed: 02/12/2024]
Abstract
BACKGROUND Factor X activation by the phospholipid-bound intrinsic tenase complex is a critical membrane-dependent reaction of blood coagulation. Its regulation mechanisms are unclear, and a number of questions regarding diffusional limitation, pathways of assembly and substrate delivery remain open. METHODS We develop and analyze here a detailed mechanism-driven computer model of intrinsic tenase on phospholipid surfaces. Three-dimensional reaction-diffusion-advection and stochastic simulations were used where appropriate. RESULTS Dynamics of the system was predominantly non-stationary under physiological conditions. In order to describe experimental data, we had to assume both membrane-dependent and solution-dependent delivery of the substrate. The former pathway dominated at low cofactor concentration, while the latter became important at low phospholipid concentration. Factor VIIIa-factor X complex formation was the major pathway of the complex assembly, and the model predicted high affinity for their lipid-dependent interaction. Although the model predicted formation of the diffusion-limited layer of substrate for some conditions, the effects of this limitation on the fXa production were small. Flow accelerated fXa production in a flow reactor model by bringing in fIXa and fVIIIa rather than fX. CONCLUSIONS This analysis suggests a concept of intrinsic tenase that is non-stationary, employs several pathways of substrate delivery depending on the conditions, and is not particularly limited by diffusion of the substrate.
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Affiliation(s)
- Anastasia N Sveshnikova
- National Medical and Research Center of Pediatric Hematology, Oncology and Immunology Named After Dmitry Rogachev, 1 Samory Mashela St, Moscow, 117198, Russia; Faculty of Fundamental Physico-Chemical Engineering, Lomonosov Moscow State University, 1/51 Leninskie Gory, 119991 Moscow, Russia; Department of Normal Physiology, Sechenov First Moscow State Medical University, 8/2 Trubetskaya St., 119991 Moscow, Russia; Center for Theoretical Problems of Physicochemical Pharmacology, Russian Academy of Sciences, 4 Kosygina St, Moscow, 119991, Russia
| | - Alexey M Shibeko
- National Medical and Research Center of Pediatric Hematology, Oncology and Immunology Named After Dmitry Rogachev, 1 Samory Mashela St, Moscow, 117198, Russia; Center for Theoretical Problems of Physicochemical Pharmacology, Russian Academy of Sciences, 4 Kosygina St, Moscow, 119991, Russia
| | - Tatiana A Kovalenko
- National Medical and Research Center of Pediatric Hematology, Oncology and Immunology Named After Dmitry Rogachev, 1 Samory Mashela St, Moscow, 117198, Russia; Center for Theoretical Problems of Physicochemical Pharmacology, Russian Academy of Sciences, 4 Kosygina St, Moscow, 119991, Russia
| | - Mikhail A Panteleev
- National Medical and Research Center of Pediatric Hematology, Oncology and Immunology Named After Dmitry Rogachev, 1 Samory Mashela St, Moscow, 117198, Russia; Center for Theoretical Problems of Physicochemical Pharmacology, Russian Academy of Sciences, 4 Kosygina St, Moscow, 119991, Russia; Faculty of Physics, Lomonosov Moscow State University, 1/2 Leninskie Gory, Moscow, 119991, Russia.
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4
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Zakharov A, Awan M, Cheng T, Gopinath A, Lee SJJ, Ramasubramanian AK, Dasbiswas K. Clots reveal anomalous elastic behavior of fiber networks. SCIENCE ADVANCES 2024; 10:eadh1265. [PMID: 38198546 PMCID: PMC10780871 DOI: 10.1126/sciadv.adh1265] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2023] [Accepted: 12/06/2023] [Indexed: 01/12/2024]
Abstract
The adaptive mechanical properties of soft and fibrous biological materials are relevant to their functionality. The emergence of the macroscopic response of these materials to external stress and intrinsic cell traction from local deformations of their structural components is not well understood. Here, we investigate the nonlinear elastic behavior of blood clots by combining microscopy, rheology, and an elastic network model that incorporates the stretching, bending, and buckling of constituent fibrin fibers. By inhibiting fibrin cross-linking in blood clots, we observe an anomalous softening regime in the macroscopic shear response as well as a reduction in platelet-induced clot contractility. Our model explains these observations from two independent macroscopic measurements in a unified manner, through a single mechanical parameter, the bending stiffness of individual fibers. Supported by experimental evidence, our mechanics-based model provides a framework for predicting and comprehending the nonlinear elastic behavior of blood clots and other active biopolymer networks in general.
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Affiliation(s)
- Andrei Zakharov
- Department of Physics, University of California, Merced, Merced, CA 95343, USA
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Myra Awan
- Department of Chemical and Materials Engineering, San José State University, San José, CA 95192, USA
| | - Terrence Cheng
- Department of Chemical and Materials Engineering, San José State University, San José, CA 95192, USA
| | - Arvind Gopinath
- Department of Bioengineering, University of California, Merced, Merced, CA 95343, USA
| | - Sang-Joon John Lee
- Department of Mechanical Engineering, San José State University, San José, CA 95192, USA
| | - Anand K. Ramasubramanian
- Department of Chemical and Materials Engineering, San José State University, San José, CA 95192, USA
| | - Kinjal Dasbiswas
- Department of Physics, University of California, Merced, Merced, CA 95343, USA
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5
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Ranjbar J, Yang Y, Harper AGS. Developing human tissue engineered arterial constructs to simulate human in vivo thrombus formation. Platelets 2023; 34:2153823. [PMID: 36550074 DOI: 10.1080/09537104.2022.2153823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Thrombus formation is highly dependent upon the physico-chemical environment in which it is triggered. Our ability to understand how thrombus formation is initiated, regulated, and resolved in the human body is dependent upon our ability to replicate the mechanical and biological properties of the arterial wall. Current in vitro thrombosis models principally use reductionist approaches to model the complex biochemical and cellular milieu present in the arterial wall, and so researcher have favored the use of in vivo models. The field of vascular tissue engineering has developed a range of techniques for culturing artificial human arteries for use as vascular grafts. These techniques therefore provide a basis for developing more sophisticated 3D replicas of the arterial wall that can be used in in vitro thrombosis models. In this review, we consider how tissue engineering approaches can be used to generate 3D models of the arterial wall that improve upon current in vivo and in vitro approaches. We consider the current benefits and limitations of reported 3D tissue engineered models and consider what additional evidence is required to validate them as alternatives to current in vivo models.
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Affiliation(s)
| | - Ying Yang
- School of Pharmacy & Bioengineering, Keele University, Keele, UK
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6
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Mankame AR, Schriner JB, Skibber MA, George MJ, Cardenas JC, Cox CS, Gill BS. Design and Development of a Clot Burst Pressure Device to Investigate Resuscitation Strategies. J Surg Res 2023; 291:646-652. [PMID: 37549450 PMCID: PMC10626576 DOI: 10.1016/j.jss.2023.07.016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Revised: 07/04/2023] [Accepted: 07/06/2023] [Indexed: 08/09/2023]
Abstract
INTRODUCTION A reduction in clot strength is a hallmark feature of trauma-induced coagulopathy. A better understanding of clot integrity can optimize resuscitation strategies. We designed a device to gauge clot strength by pressurizing fluids over a formed clot and measuring the pressure needed to dislodge the clot. We hypothesized that this device could distinguish between clots formed in hypocoagulable and hypercoagulable states by observing differences in the clot burst pressure. METHODS Whole blood from healthy volunteers was collected into sodium citrate tubes and was treated with heparin or fibrinogen to generate clots in a hypocoagulable or hypercoagulable state, respectively. Small bore holes were drilled into polystyrene plates, and recalcified blood was pipetted into the holes. Plates were incubated at 37°C for 30 min to form clots. A pressure cap with an inlet for fluid from a syringe pump and an outlet leading to a measurement column was secured in the wells with a watertight seal. RESULTS Clot burst pressure was normalized to individual baseline values to account for inherent differences in clot strength. The 1.0 g/L and 2.0 g/L fibrinogen groups were 1.65 ± 0.07 (P = 0.0078) and 2.26 ± 0.16 (P = 0.0078) times as strong as baseline, respectively. The 0.10, 0.15, or 0.20 USP units/mL groups were 0.388 ± 0.07 (P = 0.125), 0.31 ± 0.07 (P = 0.125), 0.21 ± 0.07 (P = 0.125) times as strong as baseline, respectively. Data were analyzed using Wilcoxon matched pairs signed rank testing. CONCLUSIONS This device tests clot strength using burst pressure, an easily interpreted clinical parameter not measured in existing devices. Future work can test blood from trauma patients to better understand trauma pathophysiology.
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Affiliation(s)
- Atharwa R Mankame
- Center for Translational Injury Research and Department of Surgery, McGovern Medical School at UTHealth Science Center at Houston, Houston, Texas.
| | - Jacob B Schriner
- Center for Translational Injury Research and Department of Surgery, McGovern Medical School at UTHealth Science Center at Houston, Houston, Texas
| | - Max A Skibber
- Center for Translational Injury Research and Department of Surgery, McGovern Medical School at UTHealth Science Center at Houston, Houston, Texas
| | - Mitchell J George
- Department of Cardiovascular Surgery, McGovern Medical School at UTHealth, Houston, Texas
| | - Jessica C Cardenas
- Center for Translational Injury Research and Department of Surgery, McGovern Medical School at UTHealth Science Center at Houston, Houston, Texas
| | - Charles S Cox
- Center for Translational Injury Research and Department of Pediatric Surgery, McGovern Medical School at UTHealth Science Center at Houston, Houston, Texas
| | - Brijesh S Gill
- Center for Translational Injury Research and Department of Surgery, McGovern Medical School at UTHealth Science Center at Houston, Houston, Texas
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7
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Montgomery D, Municchi F, Leiderman K. clotFoam: An Open-Source Framework to Simulate Blood Clot Formation Under Arterial Flow. ARXIV 2023:arXiv:2304.09180v3. [PMID: 37131873 PMCID: PMC10153289] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
Blood clotting involves the coupled processes of platelet aggregation and coagulation. Simulating clotting under flow in complex geometries is challenging due to multiple temporal and spatial scales and high computational cost. clotFoam is an open-source software developed in OpenFOAM that employs a continuum model of platelet advection, diffusion, and aggregation in a dynamic fluid environment and a simplified coagulation model with proteins that advect, diffuse, and react within the fluid and with wall-bound species through reactive boundary conditions. Our framework provides the foundation on which one can build more complex models and perform reliable simulations in almost any computational domain.
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Affiliation(s)
- David Montgomery
- Department of Applied Mathematics and Statistics, Colorado School of Mines, 1500 Illinois St, Golden, CO 80401, United States of America
| | - Federico Municchi
- Department of Mechanical Engineering, Colorado School of Mines, 1500 Illinois St, Golden, CO 80401, United States of America
| | - Karin Leiderman
- Department of Mathematics, University of North Carolina at Chapel Hill, 216 Lenoir Dr, Chapel Hill, NC 27599, United States of America
- Computational Medicine Program, University of North Carolina at Chapel Hill, 216 Lenoir Dr, Chapel Hill, NC 27599, United States of America
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8
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Satpute AV, Chaturvedi SS, Kashyap L, Soni R, Ghosh S, Bhatnagar T. Liver Clot after Periodontal Surgery: A Rare Case Report. JOURNAL OF PHARMACY AND BIOALLIED SCIENCES 2023; 15:S1332-S1334. [PMID: 37694041 PMCID: PMC10485469 DOI: 10.4103/jpbs.jpbs_94_23] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Revised: 02/04/2023] [Accepted: 02/06/2023] [Indexed: 09/12/2023] Open
Abstract
Due to the primary closure of the fragile tissues, large postoperative drainage is unexpected following a periodontal medical procedure. This case study elaborately illustrates the formation of a "liver coagulation" or "currant jam clot" following a periodontal fold surgical operation. Contamination, internal damage, and the presence of foreign particles such as bone splinters or bits of dental restorative dressing can all increase the risk of an incident happening.
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Affiliation(s)
- Aishwarya Virendra Satpute
- Department of Periodontology, New Horizon Dental College and Research Institute, Bilaspur, Chhattisgarh, India
| | - Shailendra Singh Chaturvedi
- Department of Periodontology, New Horizon Dental College and Research Institute, Bilaspur, Chhattisgarh, India
| | - Laxmikant Kashyap
- Department of Periodontology, New Horizon Dental College and Research Institute, Bilaspur, Chhattisgarh, India
| | - Ravindra Soni
- Department of Periodontology, New Horizon Dental College and Research Institute, Bilaspur, Chhattisgarh, India
| | - Sanghamitra Ghosh
- Department of Periodontology, New Horizon Dental College and Research Institute, Bilaspur, Chhattisgarh, India
| | - Tarun Bhatnagar
- Department of Periodontology, New Horizon Dental College and Research Institute, Bilaspur, Chhattisgarh, India
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9
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Montgomery D, Municchi F, Leiderman K. clotFoam: An open-source framework to simulate blood clot formation under arterial flow. SOFTWAREX 2023; 23:101483. [PMID: 37799564 PMCID: PMC10552559 DOI: 10.1016/j.softx.2023.101483] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 10/07/2023]
Abstract
Blood clotting involves the coupled processes of platelet aggregation and coagulation. Simulating clotting under flow in complex geometries is challenging due to multiple temporal and spatial scales and high computational cost. clotFoam is an open-source software developed in OpenFOAM that employs a continuum model of platelet advection, diffusion, and aggregation in a dynamic fluid environment and a simplified coagulation model with proteins that advect, diffuse, and react within the fluid and with wall-bound species through reactive boundary conditions. Our framework provides the foundation on which one can build more complex models and perform reliable simulations in almost any computational domain.
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Affiliation(s)
- David Montgomery
- Department of Applied Mathematics and Statistics, Colorado School of Mines, 1500 Illinois St, Golden, CO 80401, United States of America
| | - Federico Municchi
- Department of Mechanical Engineering, Colorado School of Mines, 1500 Illinois St, Golden, CO 80401, United States of America
| | - Karin Leiderman
- Department of Mathematics, University of North Carolina at Chapel Hill, 216 Lenoir Dr, Chapel Hill, NC 27599, United States of America
- Computational Medicine Program, University of North Carolina at Chapel Hill, 216 Lenoir Dr, Chapel Hill, NC 27599, United States of America
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10
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Continuum modeling of thrombus formation and growth under different shear rates. J Biomech 2022; 132:110915. [PMID: 35032838 DOI: 10.1016/j.jbiomech.2021.110915] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2021] [Revised: 12/10/2021] [Accepted: 12/14/2021] [Indexed: 01/18/2023]
Abstract
Obstruction of blood flow due to thrombosis is a major cause of ischemic stroke, myocardial infarction, and in severe cases, mortality. In particular, in blood wetting medical devices, thrombosis is a common reason for failure. The prediction of thrombosis by understanding signaling pathways using computational models, lead to identify the risk of thrombus formation in blood-contacting devices and design improvements. In this study, a mathematical model of thrombus formation and growth is presented. A biochemical model of platelet activation and aggregation is developed to predict thrombus size and shape at the site of vascular injury. Computational fluid dynamics using the finite volume method is employed to compute the velocity and pressure fields which are influenced by the growing thrombi. The passive transport of platelets, agonists, the platelet activation kinetics, their adhesion to the growing thrombi and embolization of platelets are solved by a fully coupled set of convection-diffusion-reaction equations. The thrombogenic surface representing blood-contacting material or injured blood vessel was incorporated into the model as a surface flux boundary condition to initiate thrombus formation. The blood is considered as a Newtonian fluid, while the thrombus is treated as a porous medium. The results are compared with in vitro experiments of a microfluidic chamber at an initial inlet venous shear rate of 200s-1 using a pressure-inlet boundary condition. The thrombus development due to agonist concentrations and change in the shear rate as well as thromboembolism for this benchmark problem is successfully computed. Furthermore, to extend the current model to a physiologically relevant configuration, thrombus formation in a blood tube is simulated. Two different heterogeneous reaction rates for platelet aggregation are used to simulate thrombus growth under a constant inlet flow rate. The findings show that the thrombus shape can be substantially altered by the hemodynamic conditions, increase in the shear rate and due to the combined effects of shear induced platelet activation and the heterogeneous reaction rates. It is also concluded that the model is able to predict thrombus formation in different physiological and pathological hemodynamics.
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11
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Xu Y, Yu G, Nie R, Wu Z. Microfluidic systems toward blood hemostasis monitoring and thrombosis diagnosis: From design principles to micro/nano fabrication technologies. VIEW 2022. [DOI: 10.1002/viw.20200183] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022] Open
Affiliation(s)
- Yi Xu
- Soft Intelligence Lab State Key Laboratory of Digital Manufacturing Equipment and Technology School of Mechanical Science and Engineering Huazhong University of Science and Technology Wuhan China
| | - Guang Yu
- Experimental Medicine Center Tongji Hospital Tongji Medical College Huazhong University of Science and Technology Wuhan China
| | - Ruqiong Nie
- Department of Cardiology Sun Yat‐Sen Memorial Hospital Sun Yat‐Sen University Guangzhou China
| | - Zhigang Wu
- Soft Intelligence Lab State Key Laboratory of Digital Manufacturing Equipment and Technology School of Mechanical Science and Engineering Huazhong University of Science and Technology Wuhan China
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12
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Kucukal E, Man Y, Gurkan UA, Schmidt BE. Blood Flow Velocimetry in a Microchannel During Coagulation Using Particle Image Velocimetry and Wavelet-Based Optical Flow Velocimetry. J Biomech Eng 2021; 143:091004. [PMID: 33764427 PMCID: PMC8299809 DOI: 10.1115/1.4050647] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2020] [Revised: 03/05/2021] [Indexed: 01/05/2023]
Abstract
This article describes novel measurements of the velocity of whole blood flow in a microchannel during coagulation. The blood is imaged volumetrically using a simple optical setup involving a white light source and a microscope camera. The images are processed using particle image velocimetry (PIV) and wavelet-based optical flow velocimetry (wOFV), both of which use images of individual blood cells as flow tracers. Measurements of several clinically relevant parameters such as the clotting time, decay rate, and blockage ratio are computed. The high-resolution wOFV results yield highly detailed information regarding thrombus formation and corresponding flow evolution that is the first of its kind.
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Affiliation(s)
- E. Kucukal
- Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH 44106
| | - Y. Man
- Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH 44106
| | - Umut A. Gurkan
- Warren E. Rupp Associate Professor Department of Mechanical and Aerospace Engineering, Case Comprehensive Cancer Center, Case Western Reserve University, Cleveland, OH 44106; Department of Biomedical Engineering, Case Comprehensive Cancer Center, Case Western Reserve University, Cleveland, OH 44106
| | - B. E. Schmidt
- Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH 44106
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13
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Nechipurenko DY, Shibeko AM, Sveshnikova AN, Panteleev MA. In Silico Hemostasis Modeling and Prediction. Hamostaseologie 2020; 40:524-535. [PMID: 32916753 DOI: 10.1055/a-1213-2117] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
Computational physiology, i.e., reproduction of physiological (and, by extension, pathophysiological) processes in silico, could be considered one of the major goals in computational biology. One might use computers to simulate molecular interactions, enzyme kinetics, gene expression, or whole networks of biochemical reactions, but it is (patho)physiological meaning that is usually the meaningful goal of the research even when a single enzyme is its subject. Although exponential rise in the use of computational and mathematical models in the field of hemostasis and thrombosis began in the 1980s (first for blood coagulation, then for platelet adhesion, and finally for platelet signal transduction), the majority of their successful applications are still focused on simulating the elements of the hemostatic system rather than the total (patho)physiological response in situ. Here we discuss the state of the art, the state of the progress toward the efficient "virtual thrombus formation," and what one can already get from the existing models.
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Affiliation(s)
- Dmitry Y Nechipurenko
- Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia.,Center for Theoretical Problems of Physicochemical Pharmacology of the Russian Academy of Sciences, Moscow, Russia.,Dmitry Rogachev National Research Center of Pediatric Hematology, Oncology and Immunology, Moscow, Russia
| | - Aleksey M Shibeko
- Center for Theoretical Problems of Physicochemical Pharmacology of the Russian Academy of Sciences, Moscow, Russia.,Dmitry Rogachev National Research Center of Pediatric Hematology, Oncology and Immunology, Moscow, Russia
| | - Anastasia N Sveshnikova
- Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia.,Center for Theoretical Problems of Physicochemical Pharmacology of the Russian Academy of Sciences, Moscow, Russia.,Dmitry Rogachev National Research Center of Pediatric Hematology, Oncology and Immunology, Moscow, Russia
| | - Mikhail A Panteleev
- Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia.,Center for Theoretical Problems of Physicochemical Pharmacology of the Russian Academy of Sciences, Moscow, Russia.,Dmitry Rogachev National Research Center of Pediatric Hematology, Oncology and Immunology, Moscow, Russia
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14
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Modelling the linkage between influenza infection and cardiovascular events via thrombosis. Sci Rep 2020; 10:14264. [PMID: 32868834 PMCID: PMC7458909 DOI: 10.1038/s41598-020-70753-0] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2020] [Accepted: 07/27/2020] [Indexed: 12/31/2022] Open
Abstract
There is a heavy burden associated with influenza including all-cause hospitalization as well as severe cardiovascular and cardiorespiratory events. Influenza associated cardiac events have been linked to multiple biological pathways in a human host. To study the contribution of influenza virus infection to cardiovascular thrombotic events, we develop a dynamic model which incorporates some key elements of the host immune response, inflammatory response, and blood coagulation. We formulate these biological systems and integrate them into a cohesive modelling framework to show how blood clotting may be connected to influenza virus infection. With blood clot formation inside an artery resulting from influenza virus infection as the primary outcome of this integrated model, we demonstrate how blood clot severity may depend on circulating prothrombin levels. We also utilize our model to leverage clinical data to inform the threshold level of the inflammatory cytokine TNFα which initiates tissue factor induction and subsequent blood clotting. Our model provides a tool to explore how individual biological components contribute to blood clotting events in the presence of influenza infection, to identify individuals at risk of clotting based on their circulating prothrombin levels, and to guide the development of future vaccines to optimally interact with the immune system.
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15
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Mitrophanov AY, Merrill-Skoloff G, Grover SP, Govindarajan V, Kolanjiyil A, Hariprasad DS, Unnikrishnan G, Flaumenhaft R, Reifman J. Injury Length and Arteriole Constriction Shape Clot Growth and Blood-Flow Acceleration in a Mouse Model of Thrombosis. Arterioscler Thromb Vasc Biol 2020; 40:2114-2126. [PMID: 32640902 DOI: 10.1161/atvbaha.120.314786] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
OBJECTIVE Quantitative relationships between the extent of injury and thrombus formation in vivo are not well understood. Moreover, it has not been investigated how increased injury severity translates to blood-flow modulation. Here, we investigated interconnections between injury length, clot growth, and blood flow in a mouse model of laser-induced thrombosis. Approach and Results: Using intravital microscopy, we analyzed 59 clotting events collected from the cremaster arteriole of 14 adult mice. We regarded injury length as a measure of injury severity. The injury caused transient constriction upstream and downstream of the injury site resulting in a 50% reduction in arteriole diameter. The amount of platelet accumulation and fibrin formation did not depend on arteriole diameter or deformation but displayed an exponentially increasing dependence on injury length. The height of the platelet clot depended linearly on injury length and the arteriole diameter. Upstream arteriolar constriction correlated with delayed upstream velocity increase, which, in turn, determined downstream velocity. Before clot formation, flow velocity positively correlated with the arteriole diameter. After the onset of thrombus growth, flow velocity at the injury site negatively correlated with the arteriole diameter and with the size of the above-clot lumen. CONCLUSIONS Injury severity increased platelet accumulation and fibrin formation in a persistently steep fashion and, together with arteriole diameter, defined clot height. Arterial constriction and clot formation were characterized by a dynamic change in the blood flow, associated with increased flow velocity.
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Affiliation(s)
- Alexander Y Mitrophanov
- From the DoD Biotechnology High Performance Computing Software Applications Institute, Telemedicine and Advanced Technology Research Center, US Army Medical Research and Development Command, Ft. Detrick, MD (A.Y.M., V.G., A.K., D.S.H., G.U., J.R.).,The Henry M. Jackson Foundation for the Advancement of Military Medicine, Inc, Bethesda, MD (A.Y.M., V.G., A.K., D.S.H., G.U.)
| | - Glenn Merrill-Skoloff
- Division of Hemostasis and Thrombosis, Department of Medicine, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA (G.M.-S., S.P.G., R.F.)
| | - Steven P Grover
- Division of Hemostasis and Thrombosis, Department of Medicine, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA (G.M.-S., S.P.G., R.F.)
| | - Vijay Govindarajan
- From the DoD Biotechnology High Performance Computing Software Applications Institute, Telemedicine and Advanced Technology Research Center, US Army Medical Research and Development Command, Ft. Detrick, MD (A.Y.M., V.G., A.K., D.S.H., G.U., J.R.).,The Henry M. Jackson Foundation for the Advancement of Military Medicine, Inc, Bethesda, MD (A.Y.M., V.G., A.K., D.S.H., G.U.)
| | - Arun Kolanjiyil
- From the DoD Biotechnology High Performance Computing Software Applications Institute, Telemedicine and Advanced Technology Research Center, US Army Medical Research and Development Command, Ft. Detrick, MD (A.Y.M., V.G., A.K., D.S.H., G.U., J.R.).,The Henry M. Jackson Foundation for the Advancement of Military Medicine, Inc, Bethesda, MD (A.Y.M., V.G., A.K., D.S.H., G.U.)
| | - Daniel S Hariprasad
- From the DoD Biotechnology High Performance Computing Software Applications Institute, Telemedicine and Advanced Technology Research Center, US Army Medical Research and Development Command, Ft. Detrick, MD (A.Y.M., V.G., A.K., D.S.H., G.U., J.R.).,The Henry M. Jackson Foundation for the Advancement of Military Medicine, Inc, Bethesda, MD (A.Y.M., V.G., A.K., D.S.H., G.U.)
| | - Ginu Unnikrishnan
- From the DoD Biotechnology High Performance Computing Software Applications Institute, Telemedicine and Advanced Technology Research Center, US Army Medical Research and Development Command, Ft. Detrick, MD (A.Y.M., V.G., A.K., D.S.H., G.U., J.R.).,The Henry M. Jackson Foundation for the Advancement of Military Medicine, Inc, Bethesda, MD (A.Y.M., V.G., A.K., D.S.H., G.U.)
| | - Robert Flaumenhaft
- Division of Hemostasis and Thrombosis, Department of Medicine, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA (G.M.-S., S.P.G., R.F.)
| | - Jaques Reifman
- From the DoD Biotechnology High Performance Computing Software Applications Institute, Telemedicine and Advanced Technology Research Center, US Army Medical Research and Development Command, Ft. Detrick, MD (A.Y.M., V.G., A.K., D.S.H., G.U., J.R.)
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16
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Jigar Panchal H, Kent NJ, Knox AJS, Harris LF. Microfluidics in Haemostasis: A Review. Molecules 2020; 25:E833. [PMID: 32075008 PMCID: PMC7070452 DOI: 10.3390/molecules25040833] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2020] [Revised: 02/11/2020] [Accepted: 02/12/2020] [Indexed: 12/17/2022] Open
Abstract
Haemostatic disorders are both complex and costly in relation to both their treatment and subsequent management. As leading causes of mortality worldwide, there is an ever-increasing drive to improve the diagnosis and prevention of haemostatic disorders. The field of microfluidic and Lab on a Chip (LOC) technologies is rapidly advancing and the important role of miniaturised diagnostics is becoming more evident in the healthcare system, with particular importance in near patient testing (NPT) and point of care (POC) settings. Microfluidic technologies present innovative solutions to diagnostic and clinical challenges which have the knock-on effect of improving health care and quality of life. In this review, both advanced microfluidic devices (R&D) and commercially available devices for the diagnosis and monitoring of haemostasis-related disorders and antithrombotic therapies, respectively, are discussed. Innovative design specifications, fabrication techniques, and modes of detection in addition to the materials used in developing micro-channels are reviewed in the context of application to the field of haemostasis.
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Affiliation(s)
- Heta Jigar Panchal
- School of Biological and Health Sciences, Technological University Dublin (TU Dublin) - City Campus, Kevin Street, Dublin D08 NF82, Ireland; (H.J.P.); (A.J.S.K.)
| | - Nigel J Kent
- engCORE, Faculty of Engineering, Institute of Technology Carlow, Kilkenny Road, Carlow R93 V960, Ireland;
| | - Andrew J S Knox
- School of Biological and Health Sciences, Technological University Dublin (TU Dublin) - City Campus, Kevin Street, Dublin D08 NF82, Ireland; (H.J.P.); (A.J.S.K.)
| | - Leanne F Harris
- School of Biological and Health Sciences, Technological University Dublin (TU Dublin) - City Campus, Kevin Street, Dublin D08 NF82, Ireland; (H.J.P.); (A.J.S.K.)
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17
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Mena SE, Li Y, McCormick J, McCracken B, Colmenero C, Ward K, Burns MA. A droplet-based microfluidic viscometer for the measurement of blood coagulation. BIOMICROFLUIDICS 2020; 14:014109. [PMID: 31966348 PMCID: PMC6968952 DOI: 10.1063/1.5128255] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2019] [Accepted: 01/03/2020] [Indexed: 05/20/2023]
Abstract
A continuous microfluidic viscometer is used to measure blood coagulation. The viscometer operates by flowing oil and blood into a cross section where droplets are generated. At a set pressure, the length of the droplets is inversely proportional to the viscosity of the blood sample being delivered. Because blood viscosity increases during coagulation as the blood changes from a liquid to a solid gel, the device allows to monitor coagulation by simply measuring the drop length. Experiments with swine blood were carried out in its native state and with the addition of coagulation activators and inhibitors. The microfluidic viscometer detected an earlier initiation of the coagulation process with the activator and a later initiation with the inhibitor compared to their corresponding controls. The results from the viscometer were also compared with the clinical method of thromboelastography (TEG), which was performed concurrently for the same samples. The time to initiation of coagulation in the microfluidic viscometer was correlated with the reaction time in TEG. Additionally, the total time for the measurement of clot strengthening in TEG correlated with the time for the maximum viscosity observed in the microfluidic viscometer. The microfluidic viscometer measured changes in viscosity due to coagulation faster than TEG detected the clot formation. The present viscometer is a simple technology that can be used to further study the entire coagulation process.
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Affiliation(s)
- Sarah E. Mena
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Yunzi Li
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Joseph McCormick
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
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18
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Danes N, Leiderman K. A density-dependent FEM-FCT algorithm with application to modeling platelet aggregation. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2019; 35:e3212. [PMID: 31117155 PMCID: PMC6718345 DOI: 10.1002/cnm.3212] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2018] [Revised: 03/05/2019] [Accepted: 05/02/2019] [Indexed: 05/17/2023]
Abstract
Upon injury to a blood vessel, flowing platelets will aggregate at the injury site, forming a plug to prevent blood loss. Through a complex system of biochemical reactions, a stabilizing mesh forms around the platelet aggregate forming a blood clot that further seals the injury. Computational models of clot formation have been developed to a study intravascular thrombosis, where a vessel injury does not cause blood leakage outside the blood vessel but blocks blood flow. To model scenarios in which blood leaks from a main vessel out into the extravascular space, new computational tools need to be developed to handle the complex geometries that represent the injury. We have previously modeled intravascular clot formation under flow using a continuum approach wherein the transport of platelet densities into some spatial location is limited by the platelet fraction that already reside in that location, i.e., the densities satisfy a maximum packing constraint through the use of a hindered transport coefficient. To extend this notion to extravascular injury geometries, we have modified a finite element method flux-corrected transport (FEM-FCT) scheme by prelimiting antidiffusive nodal fluxes. We show that our modified scheme, under a variety of test problems, including mesh refinement, structured vs unstructured meshes, and for a range of reaction rates, produces numerical results that satisfy a maximum platelet-density packing constraint.
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19
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Lee H, Na W, Lee BK, Lim CS, Shin S. Recent advances in microfluidic platelet function assays: Moving microfluidics into clinical applications. Clin Hemorheol Microcirc 2019; 71:249-266. [PMID: 30584134 DOI: 10.3233/ch-189416] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
The analysis of platelet aggregation and thrombosis kinetics has significantly advanced with progress in microfluidic technology. However, the results of platelet aggregation tests do not fully reflect the observed clinical outcomes. To address the present unmet clinical needs, the basic but essential biology of platelets should be reconsidered in relation to the characteristics of microfluidic systems employed for platelet tests. To this end, the present article provides an overview of commercially available point of care devices and focuses on recent microfluidic studies, describing their measurement principles. We critically discuss the characteristics of the microfluidics systems used to evaluate the complex processes underlying platelet aggregation, and that are specifically designed to mimic the pathophysiological environment of blood vessels, including hemodynamic factors as well as blood vessel injury. To this end, we summarize unsolved issues related to the application of platelet function tests based on microfluidics. Overall, we confirm that platelet function tests based on microfluidics provide a versatile platform that encompasses a variety of basic research, as well as clinical diagnostic applications.
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Affiliation(s)
- Hoyoon Lee
- Department of Mechanical Engineering, Korea University, Seoul, Korea
| | - Wonwhi Na
- Engineering Research Center for Biofluid Biopsy, Korea University, Seoul, Korea
| | - Byoung-Kwon Lee
- Department of Internal Medicine, Gangnam Severance Hospital, Yonsei University Medical College, Seoul, Korea
| | - Chae-Seung Lim
- Department of Laboratory Medicine, Guro Hospital, Korea University, Seoul, Korea
| | - Sehyun Shin
- Department of Mechanical Engineering, Korea University, Seoul, Korea.,Engineering Research Center for Biofluid Biopsy, Korea University, Seoul, Korea
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20
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Microfluidic and computational study of structural properties and resistance to flow of blood clots under arterial shear. Biomech Model Mechanobiol 2019; 18:1461-1474. [PMID: 31055691 PMCID: PMC6748893 DOI: 10.1007/s10237-019-01154-0] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2018] [Accepted: 04/20/2019] [Indexed: 01/01/2023]
Abstract
The ability of a blood clot to modulate blood flow is determined by the clot’s resistance, which depends on its structural features. For a flow with arterial shear, we investigated the characteristic patterns relating to clot shape, size, and composition on the one hand, and its viscous resistance, intraclot axial flow velocity, and shear distributions on the other. We used microfluidic technology to measure the kinetics of platelet, thrombin, and fibrin accumulation at a thrombogenic surface coated with collagen and tissue factor (TF), the key clot-formation trigger. We subsequently utilized the obtained data to perform additional calibration and validation of a detailed computational fluid dynamics model of spatial clot growth under flow. We then ran model simulations to gain insights into the resistance of clots formed under our experimental conditions. We found that increased thrombogenic surface length and TF surface density enhanced the bulk thrombin and fibrin generation in a nonadditive, synergistic way. The height of the platelet deposition domain—and, therefore, clot occlusivity—was rather robust to thrombogenic surface length and TF density variations, but consistently increased with time. Clot viscous resistance was non-uniform and tended to be higher in the fibrin-rich, inner “core” region of the clot. Interestingly, despite intraclot structure and viscous resistance variations, intraclot flow velocity variations were minor compared to the abrupt decrease in flow velocity around the platelet deposition region. Our results shed new light on the connection between the structure of clots under arterial shear and spatiotemporal variations in their resistance to flow.
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21
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Link KG, Stobb MT, Di Paola J, Neeves KB, Fogelson AL, Sindi SS, Leiderman K. A local and global sensitivity analysis of a mathematical model of coagulation and platelet deposition under flow. PLoS One 2018; 13:e0200917. [PMID: 30048479 PMCID: PMC6062055 DOI: 10.1371/journal.pone.0200917] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2018] [Accepted: 07/04/2018] [Indexed: 11/23/2022] Open
Abstract
The hemostatic response involves blood coagulation and platelet aggregation to stop blood loss from an injured blood vessel. The complexity of these processes make it difficult to intuit the overall hemostatic response without quantitative methods. Mathematical models aim to address this challenge but are often accompanied by numerous parameters choices and thus need to be analyzed for sensitivity to such choices. Here we use local and global sensitivity analyses to study a model of coagulation and platelet deposition under flow. To relate with clinical assays, we measured the sensitivity of three specific thrombin metrics: lag time, maximum relative rate of generation, and final concentration after 20 minutes. In addition, we varied parameters of three different classes: plasma protein levels, kinetic rate constants, and platelet characteristics. In terms of an overall ranking of the model’s sensitivities, we found that the local and global methods provided similar information. Our local analysis, in agreement with previous findings, shows that varying parameters within 50-150% of baseline values, in a one-at-a-time (OAT) fashion, always leads to significant thrombin generation in 20 minutes. Our global analysis gave a different and novel result highlighting groups of parameters, still varying within the normal 50-150%, that produced little or no thrombin in 20 minutes. Variations in either plasma levels or platelet characteristics, using either OAT or simultaneous variations, always led to strong thrombin production and overall, relatively low output variance. Simultaneous variation in kinetics rate constants or in a subset of all three parameter classes led to the highest overall output variance, incorporating instances with little to no thrombin production. The global analysis revealed multiple parameter interactions in the lag time and final concentration leading to relatively high variance; high variance was also observed in the thrombin generation rate, but parameters attributed to that variance acted independently and additively.
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Affiliation(s)
- Kathryn G. Link
- Department of Bioengineering, University of Utah, Salt Lake City, UT, United States of America
| | - Michael T. Stobb
- Department of Applied Mathematics, University of California Merced, Merced, CA, United States of America
| | - Jorge Di Paola
- Department of Pediatrics, University of Colorado School of Medicine, Aurora, CO, United States of America
| | - Keith B. Neeves
- Department of Pediatrics, University of Colorado School of Medicine, Aurora, CO, United States of America
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, CO, United States of America
| | - Aaron L. Fogelson
- Department of Mathematics, University of Utah, Salt Lake City, UT, United States of America
- Department of Bioengineering, University of Utah, Salt Lake City, UT, United States of America
| | - Suzanne S. Sindi
- Department of Applied Mathematics, University of California Merced, Merced, CA, United States of America
| | - Karin Leiderman
- Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO, United States of America
- * E-mail:
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