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biharmonic equation
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Mathematical model and numerical method for studying platelet adhesion and aggregation during blood clotting
Mathematical model and numerical method for studying platelet adhesion and aggregation during blood clotting,10.1016/00219991(84)90086X,Journal of C
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Mathematical model and numerical method for studying platelet adhesion and aggregation during blood clotting
(
Citations: 67
)
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A. L. Fogelson
The repair of small blood vessels and the pathological growth of internal blood clots involve the formation of platelet aggregates adhering to portions of the vessel wall. Our microscopic model represents blood by a suspension of discrete massless platelets in a viscous incompressible fluid. Platelets are initially noncohesive; however, if stimulated by an abovethreshold concentration of the chemical ADP or by contact with the adhesive injured region of the vessel wall, they become cohesive and secrete more ADP into the fluid. Cohesion between platelets and adhesion of a platelet to the injured wall are modeled by creating elastic links. Repulsive forces prevent a platelet from coming too close to another platelet or to the wall. The forces affect the fluid motion in the neighborhood of an aggregate. The platelets and secreted ADP both move by fluid advection and diffusion. The equations of the model are studied numerically in two dimensions. The platelet forces are calculated implicitly by minimizing a nonlinear energy function. Our minimization scheme merges Gill and Murray's (Math. Programming 7 (1974), 311) modified Newton's method with elements of the Yale sparse matix package. The streamfunction formulation of the Stokes' equations for the fluid motion under the influence of platelet forces is solved using Bjorstad's biharmonic solver (''Numerical Solution of the Biharmonic Equation,'' Ph.D. Thesis, Stanford University, 1980). The ADP
transport equation
is solved with an alternatingdirection implicit scheme. A linkedlist
data structure
is introduced to keep track of changing platelet states and changing configurations of interplatelet links.
Journal:
Journal of Computational Physics  J COMPUT PHYS
, vol. 56, no. 1, pp. 111134, 1984
DOI:
10.1016/00219991(84)90086X
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Citation Context
(22)
...For example, models for the blood clotting systems [
18
], cellular energetics [58], stochastic annealing [19], electrical activity of neural masses [48, 57] and noisy oscillators in a diversity of physical systems [20]...
R. J. Biscay
,
et al.
High order local linearization methods: An approach for constructing A...
...Finally Eq. (
14
) is the equation of motion of the massive boundary, which carries the mass density M(s) and has its motion described by the function Y(s,t)...
...Note that the only force density in Eq. (
14
) is the penalty force density...
...The velocity of the massive boundary is also calculated in the same fashion; see Eq. (
14
)...
...(1)–(2), (5)–(7), and (12)–(
14
) using the numerical procedure described in section ‘‘Mathematical Formulation of the Penalty Immersed Boundary Method and Numerical Implementation’’...
Yongsam Kim
,
et al.
Blood Flow in a Compliant Vessel by the Immersed Boundary Method
...The IB met hod was created to study fluid dynamics of heart valves [26, 27, 28] and has been applied to many problems mostly in biofluids [9, 8,
11
, 12, 18, 20, 34]...
Sookkyung Lim
,
et al.
Dynamics of a Closed Rod with Twist and Bend in Fluid
...Examples include platelet aggregation in blood clotting [9,
11
], swimming of microorganisms [9,10], biofilm processes [8], mechanical properties of cells [1], cochlear dynamics [3], and insect flight [18,19]...
Elijah P. Newren
,
et al.
A Comparison of Implicit Solvers for the Immersed Boundary Equations
...Such aggregation process was first studied mathematically by Fogelson et al. [
34
,35]...
Wing Kam Liu
,
et al.
Immersed finite element method and its applications to biological syst...
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