A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes: Application to Stem Cell Injection After a Myocardial Infarction: Discontinuous Galerkin methods

F.J. Vermolen; L.Y.D. Crapts; J.K. Ryan

doi:10.1016/B978-0-12-811718-7.00006-X

A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes: Application to Stem Cell Injection After a Myocardial Infarction: Discontinuous Galerkin methods

F.J. Vermolen^*, L.Y.D. Crapts, J.K. Ryan

^*Corresponding author for this work

Numerical Analysis

Research output: Chapter in Book/Conference proceedings/Edited volume › Chapter › Scientific › peer-review

Abstract

We present a mathematical formalism for the simulation of angiogenesis treatment in the heart after a myocardial infarction. The formalism treats the injection of stem cells at the surface of the heart, which then, release growth factor TG-β. This growth factor attracts the endothelial cells that migrate toward the stem cells as a result of chemotaxis. The description of the formation of a vascular network is characterized by taking into account the vessel tips as well as their sprouts. The method is based on a Keller-Segel formalism for chemotaxis for the vessel tips, combined with a "snail trail" mechanism to simulate the migration of the sprouts. This chapter presents a discontinuous Galerkin method on quadrilateral meshes to solve the system of partial differential equations in two spatial dimensions.

Original language	English
Title of host publication	Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes
Editors	Miguel Cerrolaza, Sandra Shefelbine, Diego Garzón-Alvarado
Publisher	Elsevier
Pages	95-115
Number of pages	21
ISBN (Electronic)	9780128117194
ISBN (Print)	9780128117187
DOIs	https://doi.org/10.1016/B978-0-12-811718-7.00006-X
Publication status	Published - 2018

Bibliographical note

Chapter 6

Keywords

Chemotaxis
Discontinuous Galerkin method
Fibrosis
Myocardial infarction
Snail trail model
Stem cells

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10.1016/B978-0-12-811718-7.00006-X

Cite this

Vermolen, F. J., Crapts, L. Y. D., & Ryan, J. K. (2018). A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes: Application to Stem Cell Injection After a Myocardial Infarction: Discontinuous Galerkin methods. In M. Cerrolaza, S. Shefelbine, & D. Garzón-Alvarado (Eds.), Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes (pp. 95-115). Elsevier. https://doi.org/10.1016/B978-0-12-811718-7.00006-X

Vermolen, F.J. ; Crapts, L.Y.D. ; Ryan, J.K. / A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes : Application to Stem Cell Injection After a Myocardial Infarction: Discontinuous Galerkin methods. Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes. editor / Miguel Cerrolaza ; Sandra Shefelbine ; Diego Garzón-Alvarado. Elsevier, 2018. pp. 95-115

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abstract = "We present a mathematical formalism for the simulation of angiogenesis treatment in the heart after a myocardial infarction. The formalism treats the injection of stem cells at the surface of the heart, which then, release growth factor TG-β. This growth factor attracts the endothelial cells that migrate toward the stem cells as a result of chemotaxis. The description of the formation of a vascular network is characterized by taking into account the vessel tips as well as their sprouts. The method is based on a Keller-Segel formalism for chemotaxis for the vessel tips, combined with a {"}snail trail{"} mechanism to simulate the migration of the sprouts. This chapter presents a discontinuous Galerkin method on quadrilateral meshes to solve the system of partial differential equations in two spatial dimensions.",

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Vermolen, FJ, Crapts, LYD & Ryan, JK 2018, A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes: Application to Stem Cell Injection After a Myocardial Infarction: Discontinuous Galerkin methods. in M Cerrolaza, S Shefelbine & D Garzón-Alvarado (eds), Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes. Elsevier, pp. 95-115. https://doi.org/10.1016/B978-0-12-811718-7.00006-X

A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes: Application to Stem Cell Injection After a Myocardial Infarction: Discontinuous Galerkin methods. / Vermolen, F.J.; Crapts, L.Y.D.; Ryan, J.K.
Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes. ed. / Miguel Cerrolaza; Sandra Shefelbine; Diego Garzón-Alvarado. Elsevier, 2018. p. 95-115.

Research output: Chapter in Book/Conference proceedings/Edited volume › Chapter › Scientific › peer-review

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T1 - A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes

T2 - Application to Stem Cell Injection After a Myocardial Infarction: Discontinuous Galerkin methods

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AB - We present a mathematical formalism for the simulation of angiogenesis treatment in the heart after a myocardial infarction. The formalism treats the injection of stem cells at the surface of the heart, which then, release growth factor TG-β. This growth factor attracts the endothelial cells that migrate toward the stem cells as a result of chemotaxis. The description of the formation of a vascular network is characterized by taking into account the vessel tips as well as their sprouts. The method is based on a Keller-Segel formalism for chemotaxis for the vessel tips, combined with a "snail trail" mechanism to simulate the migration of the sprouts. This chapter presents a discontinuous Galerkin method on quadrilateral meshes to solve the system of partial differential equations in two spatial dimensions.

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BT - Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes

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Vermolen FJ, Crapts LYD, Ryan JK. A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes: Application to Stem Cell Injection After a Myocardial Infarction: Discontinuous Galerkin methods. In Cerrolaza M, Shefelbine S, Garzón-Alvarado D, editors, Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes. Elsevier. 2018. p. 95-115 doi: 10.1016/B978-0-12-811718-7.00006-X

A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes: Application to Stem Cell Injection After a Myocardial Infarction: Discontinuous Galerkin methods

Abstract

Bibliographical note

Keywords

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