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Kim OV. Platelet Receptor-Ligand Stochasticity Drives Fluidization of Blood Clots. Biophys J 2021; 120:187-188. [PMID: 33472025 DOI: 10.1016/j.bpj.2020.12.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2020] [Accepted: 12/08/2020] [Indexed: 10/22/2022] Open
Affiliation(s)
- Oleg V Kim
- Department of Cell and Developmental Biology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania.
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2
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Zheng X, Yazdani A, Li H, Humphrey JD, Karniadakis GE. A three-dimensional phase-field model for multiscale modeling of thrombus biomechanics in blood vessels. PLoS Comput Biol 2020; 16:e1007709. [PMID: 32343724 PMCID: PMC7224566 DOI: 10.1371/journal.pcbi.1007709] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2019] [Revised: 05/14/2020] [Accepted: 02/03/2020] [Indexed: 01/10/2023] Open
Abstract
Mechanical interactions between flowing and coagulated blood (thrombus) are crucial in dictating the deformation and remodeling of a thrombus after its formation in hemostasis. We propose a fully-Eulerian, three-dimensional, phase-field model of thrombus that is calibrated with existing in vitro experimental data. This phase-field model considers spatial variations in permeability and material properties within a single unified mathematical framework derived from an energy perspective, thereby allowing us to study effects of thrombus microstructure and properties on its deformation and possible release of emboli under different hemodynamic conditions. Moreover, we combine this proposed thrombus model with a particle-based model which simulates the initiation of the thrombus. The volume fraction of a thrombus obtained from the particle simulation is mapped to an input variable in the proposed phase-field thrombus model. The present work is thus the first computational study to integrate the initiation of a thrombus through platelet aggregation with its subsequent viscoelastic responses to various shear flows. This framework can be informed by clinical data and potentially be used to predict the risk of diverse thromboembolic events under physiological and pathological conditions.
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Affiliation(s)
- Xiaoning Zheng
- Division of Applied Mathematics, Brown University, Providence, Rhode Island, United States of America
| | - Alireza Yazdani
- Division of Applied Mathematics, Brown University, Providence, Rhode Island, United States of America
| | - He Li
- Division of Applied Mathematics, Brown University, Providence, Rhode Island, United States of America
| | - Jay D. Humphrey
- Department of Biomedical Engineering, Yale University, New Haven, Connecticut, United States of America
| | - George E. Karniadakis
- Division of Applied Mathematics, Brown University, Providence, Rhode Island, United States of America
- * E-mail:
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3
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Brass LF, Tomaiuolo M, Welsh J, Poventud-Fuentes I, Zhu L, Diamond SL, Stalker TJ. Hemostatic Thrombus Formation in Flowing Blood. Platelets 2019. [DOI: 10.1016/b978-0-12-813456-6.00020-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
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4
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Lu Y, Lee MY, Zhu S, Sinno T, Diamond SL. Multiscale simulation of thrombus growth and vessel occlusion triggered by collagen/tissue factor using a data-driven model of combinatorial platelet signalling. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2018; 34:523-546. [PMID: 27672182 PMCID: PMC5798174 DOI: 10.1093/imammb/dqw015] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/26/2016] [Accepted: 08/23/2016] [Indexed: 12/23/2022]
Abstract
During clotting under flow, platelets bind and activate on collagen and release autocrinic factors such as ADP and thromboxane, while tissue factor (TF) on the damaged wall leads to localized thrombin generation. Towards patient-specific simulation of thrombosis, a multiscale approach was developed to account for: platelet signalling [neural network (NN) trained by pairwise agonist scanning (PAS), PAS-NN], platelet positions (lattice kinetic Monte Carlo, LKMC), wall-generated thrombin and platelet-released ADP/thromboxane convection–diffusion (partial differential equation, PDE) and flow over a growing clot (lattice Boltzmann). LKMC included shear-driven platelet aggregate restructuring. The PDEs for thrombin, ADP and thromboxane were solved by finite element method using cell activation-driven adaptive triangular meshing. At all times, intracellular calcium was known for each platelet by PAS-NN in response to its unique exposure to local collagen, ADP, thromboxane and thrombin. When compared with microfluidic experiments of human blood clotting on collagen/TF driven by constant pressure drop, the model accurately predicted clot morphology and growth with time. In experiments and simulations at TF at 0.1 and 10 molecule-TF/\documentclass[12pt]{minimal}
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}{}$\mu$\end{document}m channel occurred relatively abruptly at 600 and 400 s, respectively (with no occlusion at zero TF). Prior to occlusion, intrathrombus concentrations reached 50 nM thrombin, ~ 1 \documentclass[12pt]{minimal}
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}{}$\mu$\end{document}M ADP, while the wall shear rate on the rough clot peaked at ~ 1000–2000 s\documentclass[12pt]{minimal}
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}{}$^{-1}$\end{document}. Additionally, clotting on TF/collagen was accurately simulated for modulators of platelet cyclooxygenase-1, P2Y\documentclass[12pt]{minimal}
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}{}$_{1}$\end{document} and IP-receptor. This multiscale approach facilitates patient-specific simulation of thrombosis under hemodynamic and pharmacological conditions.
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Affiliation(s)
- Yichen Lu
- Department of Chemical and Biomolecular Engineering, Institute for Medicine and Engineering, University of Pennsylvania, Philadelphia PA 19104, USA
| | - Mei Yan Lee
- Department of Chemical and Biomolecular Engineering, Institute for Medicine and Engineering, University of Pennsylvania, Philadelphia PA 19104, USA
| | - Shu Zhu
- Department of Chemical and Biomolecular Engineering, Institute for Medicine and Engineering, University of Pennsylvania, Philadelphia PA 19104, USA
| | - Talid Sinno
- Department of Chemical and Biomolecular Engineering, Institute for Medicine and Engineering, University of Pennsylvania, Philadelphia PA 19104, USA
| | - Scott L Diamond
- Department of Chemical and Biomolecular Engineering, Institute for Medicine and Engineering, University of Pennsylvania, Philadelphia PA 19104, USA
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5
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Chang HY, Yazdani A, Li X, Douglas KAA, Mantzoros CS, Karniadakis GE. Quantifying Platelet Margination in Diabetic Blood Flow. Biophys J 2018; 115:1371-1382. [PMID: 30224049 PMCID: PMC6170725 DOI: 10.1016/j.bpj.2018.08.031] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2018] [Revised: 07/23/2018] [Accepted: 08/24/2018] [Indexed: 12/23/2022] Open
Abstract
Patients with type 2 diabetes mellitus (T2DM) develop thrombotic abnormalities strongly associated with cardiovascular diseases. In addition to the changes of numerous coagulation factors such as elevated levels of thrombin and fibrinogen, the abnormal rheological effects of red blood cells (RBCs) and platelets flowing in blood are crucial in platelet adhesion and thrombus formation in T2DM. An important process contributing to the latter is the platelet margination. We employ the dissipative particle dynamics method to seamlessly model cells, plasma, and vessel walls. We perform a systematic study on RBC and platelet transport in cylindrical vessels by considering different cell shapes, sizes, and RBC deformabilities in healthy and T2DM blood, as well as variable flowrates and hematocrit. In particular, we use cellular-level RBC and platelet models with parameters derived from patient-specific data and present a sensitivity study. We find T2DM RBCs, which are less deformable compared to normal RBCs, lower the transport of platelets toward the vessel walls, whereas platelets with higher mean volume (often observed in T2DM) lead to enhanced margination. Furthermore, increasing the flowrate or hematocrit enhances platelet margination. We also investigated the effect of platelet shape and observed a nonmonotonic variation with the highest near-wall concentration corresponding to platelets with a moderate aspect ratio of 0.38. We examine the role of white blood cells (WBCs), whose count is increased notably in T2DM patients. We find that WBC rolling or WBC adhesion tends to decrease platelet margination due to hydrodynamic effects. To the best of our knowledge, such simulations of blood including all blood cells have not been performed before, and our quantitative findings can help separate the effects of hydrodynamic interactions from adhesive interactions and potentially shed light on the associated pathological processes in T2DM such as increased inflammatory response, platelet activation and adhesion, and ultimately thrombus formation.
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Affiliation(s)
- Hung-Yu Chang
- Division of Applied Mathematics, Brown University, Providence, Rhode Island
| | - Alireza Yazdani
- Division of Applied Mathematics, Brown University, Providence, Rhode Island
| | - Xuejin Li
- Division of Applied Mathematics, Brown University, Providence, Rhode Island
| | - Konstantinos A A Douglas
- S. Lepida Biomedical Laboratory, Athens, Greece; Division of Endocrinology, Diabetes and Metabolism, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, Massachusetts
| | - Christos S Mantzoros
- Division of Endocrinology, Diabetes and Metabolism, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, Massachusetts
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6
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Review of Mechanical Testing and Modelling of Thrombus Material for Vascular Implant and Device Design. Ann Biomed Eng 2017; 45:2494-2508. [DOI: 10.1007/s10439-017-1906-5] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2017] [Accepted: 08/16/2017] [Indexed: 10/19/2022]
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7
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A Short Review of Advances in the Modelling of Blood Rheology and Clot Formation. FLUIDS 2017. [DOI: 10.3390/fluids2030035] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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8
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Imai Y, Omori T, Shimogonya Y, Yamaguchi T, Ishikawa T. Numerical methods for simulating blood flow at macro, micro, and multi scales. J Biomech 2016; 49:2221-2228. [DOI: 10.1016/j.jbiomech.2015.11.047] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2015] [Accepted: 11/07/2015] [Indexed: 02/04/2023]
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9
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Kassab GS, An G, Sander EA, Miga MI, Guccione JM, Ji S, Vodovotz Y. Augmenting Surgery via Multi-scale Modeling and Translational Systems Biology in the Era of Precision Medicine: A Multidisciplinary Perspective. Ann Biomed Eng 2016; 44:2611-25. [PMID: 27015816 DOI: 10.1007/s10439-016-1596-4] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2015] [Accepted: 03/18/2016] [Indexed: 12/18/2022]
Abstract
In this era of tremendous technological capabilities and increased focus on improving clinical outcomes, decreasing costs, and increasing precision, there is a need for a more quantitative approach to the field of surgery. Multiscale computational modeling has the potential to bridge the gap to the emerging paradigms of Precision Medicine and Translational Systems Biology, in which quantitative metrics and data guide patient care through improved stratification, diagnosis, and therapy. Achievements by multiple groups have demonstrated the potential for (1) multiscale computational modeling, at a biological level, of diseases treated with surgery and the surgical procedure process at the level of the individual and the population; along with (2) patient-specific, computationally-enabled surgical planning, delivery, and guidance and robotically-augmented manipulation. In this perspective article, we discuss these concepts, and cite emerging examples from the fields of trauma, wound healing, and cardiac surgery.
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Affiliation(s)
- Ghassan S Kassab
- California Medical Innovations Institute, San Diego, CA, 92121, USA
| | - Gary An
- Department of Surgery, University of Chicago, Chicago, IL, 60637, USA
| | - Edward A Sander
- Department of Biomedical Engineering, University of Iowa, Iowa City, IA, 52242, USA
| | - Michael I Miga
- Department of Biomedical Engineering, Vanderbilt University, Nashville, TN, 37235, USA
| | - Julius M Guccione
- Department of Surgery, University of California, San Francisco, CA, 94143, USA
| | - Songbai Ji
- Thayer School of Engineering, Dartmouth College, Hanover, NH, 03755, USA.,Department of Surgery and of Orthopaedic Surgery, Geisel School of Medicine, Dartmouth College, Hanover, NH, 03755, USA
| | - Yoram Vodovotz
- Department of Surgery, University of Pittsburgh, W944 Starzl Biomedical Sciences Tower, 200 Lothrop St., Pittsburgh, PA, 15213, USA. .,Center for Inflammation and Regenerative Modeling, McGowan Institute for Regenerative Medicine, University of Pittsburgh, Pittsburgh, PA, 15219, USA.
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10
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Tierra G, Pavissich JP, Nerenberg R, Xu Z, Alber MS. Multicomponent model of deformation and detachment of a biofilm under fluid flow. J R Soc Interface 2016; 12:rsif.2015.0045. [PMID: 25808342 DOI: 10.1098/rsif.2015.0045] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
A novel biofilm model is described which systemically couples bacteria, extracellular polymeric substances (EPS) and solvent phases in biofilm. This enables the study of contributions of rheology of individual phases to deformation of biofilm in response to fluid flow as well as interactions between different phases. The model, which is based on first and second laws of thermodynamics, is derived using an energetic variational approach and phase-field method. Phase-field coupling is used to model structural changes of a biofilm. A newly developed unconditionally energy-stable numerical splitting scheme is implemented for computing the numerical solution of the model efficiently. Model simulations predict biofilm cohesive failure for the flow velocity between [Formula: see text] and [Formula: see text] m s(-1) which is consistent with experiments. Simulations predict biofilm deformation resulting in the formation of streamers for EPS exhibiting a viscous-dominated mechanical response and the viscosity of EPS being less than [Formula: see text]. Higher EPS viscosity provides biofilm with greater resistance to deformation and to removal by the flow. Moreover, simulations show that higher EPS elasticity yields the formation of streamers with complex geometries that are more prone to detachment. These model predictions are shown to be in qualitative agreement with experimental observations.
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Affiliation(s)
- Giordano Tierra
- Mathematical Institute, Faculty of Mathematics and Physics, Charles University, 186 75 Prague 8, Czech Republic Department of Applied and Computational Mathematics and Statistics University of Notre Dame, Notre Dame, IN 46556, USA
| | - Juan P Pavissich
- Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, USA Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago, Chile
| | - Robert Nerenberg
- Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, USA
| | - Zhiliang Xu
- Department of Applied and Computational Mathematics and Statistics University of Notre Dame, Notre Dame, IN 46556, USA
| | - Mark S Alber
- Department of Applied and Computational Mathematics and Statistics University of Notre Dame, Notre Dame, IN 46556, USA
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11
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Continuous Modeling of Arterial Platelet Thrombus Formation Using a Spatial Adsorption Equation. PLoS One 2015; 10:e0141068. [PMID: 26517377 PMCID: PMC4627739 DOI: 10.1371/journal.pone.0141068] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2015] [Accepted: 10/05/2015] [Indexed: 02/03/2023] Open
Abstract
In this study, we considered a continuous model of platelet thrombus growth in an arteriole. A special model describing the adhesion of platelets in terms of their concentration was derived. The applications of the derived model are not restricted to only describing arterial platelet thrombus formation; the model can also be applied to other similar adhesion processes. The model reproduces an auto-wave solution in the one-dimensional case; in the two-dimensional case, in which the surrounding flow is taken into account, the typical torch-like thrombus is reproduced. The thrombus shape and the growth velocity are determined by the model parameters. We demonstrate that the model captures the main properties of the thrombus growth behavior and provides us a better understanding of which mechanisms are important in the mechanical nature of the arterial thrombus growth.
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12
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van Kempen THS, Bogaerds ACB, Peters GWM, van de Vosse FN. A constitutive model for a maturing fibrin network. Biophys J 2015; 107:504-513. [PMID: 25028892 DOI: 10.1016/j.bpj.2014.05.035] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2014] [Revised: 05/22/2014] [Accepted: 05/30/2014] [Indexed: 11/18/2022] Open
Abstract
Blood clot formation is crucial to maintain normal physiological conditions but at the same time involved in many diseases. The mechanical properties of the blood clot are important for its functioning but complicated due to the many processes involved. The main structural component of the blood clot is fibrin, a fibrous network that forms within the blood clot, thereby increasing its mechanical rigidity. A constitutive model for the maturing fibrin network is developed that captures the evolving mechanical properties. The model describes the fibrin network as a network of fibers that become thicker in time. Model parameters are related to the structural properties of the network, being the fiber length, bending stiffness, and mass-length ratio. Results are compared with rheometry experiments in which the network maturation is followed in time for various loading frequencies and fibrinogen concentrations. Three parameters are used to capture the mechanical behavior including the mass-length ratio. This parameter agrees with values determined using turbidimetry experiments and is subsequently used to derive the number of protofibrils and fiber radius. The strength of the model is that it describes the mechanical properties of the maturing fibrin network based on it structural quantities. At the same time the model is relatively simple, which makes it suitable for advanced numerical simulations of blood clot formation during flow in blood vessels.
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Affiliation(s)
- Thomas H S van Kempen
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, the Netherlands.
| | | | - Gerrit W M Peters
- Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, the Netherlands
| | - Frans N van de Vosse
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, the Netherlands
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13
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Wu Z, Xu Z, Kim O, Alber M. Three-dimensional multi-scale model of deformable platelets adhesion to vessel wall in blood flow. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2014; 372:rsta.2013.0380. [PMID: 24982253 PMCID: PMC4084525 DOI: 10.1098/rsta.2013.0380] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
When a blood vessel ruptures or gets inflamed, the human body responds by rapidly forming a clot to restrict the loss of blood. Platelets aggregation at the injury site of the blood vessel occurring via platelet-platelet adhesion, tethering and rolling on the injured endothelium is a critical initial step in blood clot formation. A novel three-dimensional multi-scale model is introduced and used in this paper to simulate receptor-mediated adhesion of deformable platelets at the site of vascular injury under different shear rates of blood flow. The novelty of the model is based on a new approach of coupling submodels at three biological scales crucial for the early clot formation: novel hybrid cell membrane submodel to represent physiological elastic properties of a platelet, stochastic receptor-ligand binding submodel to describe cell adhesion kinetics and lattice Boltzmann submodel for simulating blood flow. The model implementation on the GPU cluster significantly improved simulation performance. Predictive model simulations revealed that platelet deformation, interactions between platelets in the vicinity of the vessel wall as well as the number of functional GPIbα platelet receptors played significant roles in platelet adhesion to the injury site. Variation of the number of functional GPIbα platelet receptors as well as changes of platelet stiffness can represent effects of specific drugs reducing or enhancing platelet activity. Therefore, predictive simulations can improve the search for new drug targets and help to make treatment of thrombosis patient-specific.
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Affiliation(s)
- Ziheng Wu
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA
| | - Zhiliang Xu
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA
| | - Oleg Kim
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA
| | - Mark Alber
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA Department of Medicine, Indiana University School of Medicine, Indianapolis, IN 46202, USA
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14
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Marsden AL, Bazilevs Y, Long CC, Behr M. Recent advances in computational methodology for simulation of mechanical circulatory assist devices. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2014; 6:169-88. [PMID: 24449607 PMCID: PMC3947342 DOI: 10.1002/wsbm.1260] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2013] [Revised: 11/06/2013] [Accepted: 12/16/2013] [Indexed: 11/07/2022]
Abstract
Ventricular assist devices (VADs) provide mechanical circulatory support to offload the work of one or both ventricles during heart failure. They are used in the clinical setting as destination therapy, as bridge to transplant, or more recently as bridge to recovery to allow for myocardial remodeling. Recent developments in computational simulation allow for detailed assessment of VAD hemodynamics for device design and optimization for both children and adults. Here, we provide a focused review of the recent literature on finite element methods and optimization for VAD simulations. As VAD designs typically fall into two categories, pulsatile and continuous flow devices, we separately address computational challenges of both types of designs, and the interaction with the circulatory system with three representative case studies. In particular, we focus on recent advancements in finite element methodology that have increased the fidelity of VAD simulations. We outline key challenges, which extend to the incorporation of biological response such as thrombosis and hemolysis, as well as shape optimization methods and challenges in computational methodology.
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Affiliation(s)
- Alison L Marsden
- Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA, USA
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15
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Systems biology of platelet-vessel wall interactions. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2014; 844:85-98. [PMID: 25480638 DOI: 10.1007/978-1-4939-2095-2_5] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Platelets are small, anucleated cells that participate in primary hemostasis by forming a hemostatic plug at the site of a blood vessel's breach, preventing blood loss. However, hemostatic events can lead to excessive thrombosis, resulting in life-threatening strokes, emboli, or infarction. Development of multi-scale models coupling processes at several scales and running predictive model simulations on powerful computer clusters can help interdisciplinary groups of researchers to suggest and test new patient-specific treatment strategies.
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16
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Bodnár T, Fasano A, Sequeira A. Mathematical Models for Blood Coagulation. FLUID-STRUCTURE INTERACTION AND BIOMEDICAL APPLICATIONS 2014. [DOI: 10.1007/978-3-0348-0822-4_7] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
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17
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Frangi AF, Hose DR, Hunter PJ, Ayache N, Brooks D. Special issue on medical imaging and image computing in computational physiology. IEEE TRANSACTIONS ON MEDICAL IMAGING 2013; 32:1-7. [PMID: 23409282 DOI: 10.1109/tmi.2012.2234320] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
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18
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Zhang YT, Alber MS, Newman SA. Mathematical modeling of vertebrate limb development. Math Biosci 2012; 243:1-17. [PMID: 23219575 DOI: 10.1016/j.mbs.2012.11.003] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2012] [Revised: 11/09/2012] [Accepted: 11/15/2012] [Indexed: 01/15/2023]
Abstract
In this paper, we review the major mathematical and computational models of vertebrate limb development and their roles in accounting for different aspects of this process. The main aspects of limb development that have been modeled include outgrowth and shaping of the limb bud, establishment of molecular gradients within the bud, and formation of the skeleton. These processes occur interdependently during development, although (as described in this review), there are various interpretations of the biological relationships among them. A wide range of mathematical and computational methods have been used to study these processes, including ordinary and partial differential equation systems, cellular automata and discrete, stochastic models, finite difference methods, finite element methods, the immersed boundary method, and various combinations of the above. Multiscale mathematical modeling and associated computational simulation have become integrated into the study of limb morphogenesis and pattern formation to an extent with few parallels in the field of developmental biology. These methods have contributed to the design and analysis of experiments employing microsurgical and genetic manipulations, evaluation of hypotheses for limb bud outgrowth, interpretation of the effects of natural mutations, and the formulation of scenarios for the origination and evolution of the limb skeleton.
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Affiliation(s)
- Yong-Tao Zhang
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA.
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