Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood - - PowerPoint PPT Presentation

▶
towards a parallel 3d simulation of platelet aggregation
SMART_READER_LITE
LIVE PREVIEW

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood - - PowerPoint PPT Presentation

Jun 11, 2023 370 likes •1.12k views

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation Oral Exam Elijah Newren January 7, 2004 Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation p. 1/22 B.6.2 Summarized Formulas .

slide-1
SLIDE 1

Towards a Parallel, 3D Simulation

  • f Platelet Aggregation and Blood

Coagulation

Oral Exam — Elijah Newren January 7, 2004

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 1/22

slide-2
SLIDE 2

B.6.2 Summarized Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 B.6.3 Why dividing by zero does not occur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

1 Introduction

Coupled, intricate systems exist to maintain the fluidity of the blood in the vascular system while allowing for the rapid formation of a solid clot to prevent excessive blood loss subsequent to vessel injury [10]. These systems can be invoked as part of the body’s normal defense mechanism against blood loss (a process referred to as hemostasis), but these same systems are also invoked during unwanted, pathological and perhaps life threatening clot formation known as thrombosis. Indeed, these systems can be seen as a delicate balancing act continually occurring to control clot formation and lysis in order to prevent hemorrhage without causing thrombosis [2]. Despite more than a century of research in blood biochemistry, platelet and vascular wall biology, and fluid dynamics, the complexity of blood clotting under flow has prevented quantitative and predictive modeling [13]. Yet quantitative modeling of blood function under flow could have numerous diagnostic and therapeutic uses. When the wall of a blood vessel is injured, a variety of embedded molecules become exposed. This initiates two interacting processes known as platelet aggregation and blood coagulation. Both

  • f these processes involve multiple subprocesses. Platelet aggregation starts when platelets sus-

pended in the blood, which normally circulate in an inactive state, adhere to damaged tissue and undergo an activation process. During the activation of a platelet, the platelet changes from its rigid discoidal shape to a more deformable spherical form with several long, thin pseudopodia; the platelet’s surface membrane becomes sticky to other activated platelets; and the platelet begins to 4

slide-3
SLIDE 3

Outline

  • Biological Problem
  • Model Components
  • Numerical and Communication Methods
  • Future Work

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 2/22

slide-4
SLIDE 4

Outline

  • Biological Problem
  • Model Components
  • Numerical and Communication Methods
  • Future Work

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 2/22

slide-5
SLIDE 5

A Blood Clot

A colorized scanning electron micrograph of a blood clot formed in vitro without fl

  • w

Platelets Fibrin Red blood cells

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 3/22

slide-6
SLIDE 6

Platelet Aggregation

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 4/22

slide-7
SLIDE 7

Platelet Aggregation

Simulation of Platelet Aggregation by H. Yu and A. Fogelson

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 4/22

slide-8
SLIDE 8

Blood Coagulation

Reactions: (a) schematic of injured site. SE—exposed subendothelium, E—endothelium; (b) TF-VIIa system on subendothelium; (c) plasma-phase reactions; (d) VIIIa:IXa and Va:Xa complexes on activated platelet surface; (e) TM:IIa complex on endothelial surface.

→

⊕ indicates enzymatically-promoted reaction. ⊣ indicates inhibition. indicates inactivation.

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 5/22

slide-9
SLIDE 9

Interactions

  • Platelets accelerate Coagulation

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 6/22

slide-10
SLIDE 10

Interactions

  • Platelets accelerate Coagulation
  • Coagulation accelerates Platelet Aggregation

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 6/22

slide-11
SLIDE 11

Interactions

  • Platelets accelerate Coagulation
  • Coagulation accelerates Platelet Aggregation
  • Inhibitory Effects

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 6/22

slide-12
SLIDE 12

Interactions

  • Platelets accelerate Coagulation
  • Coagulation accelerates Platelet Aggregation
  • Inhibitory Effects
  • Fibrinolysis

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 6/22

slide-13
SLIDE 13

Interactions

  • Platelets accelerate Coagulation
  • Coagulation accelerates Platelet Aggregation
  • Inhibitory Effects
  • Fibrinolysis
  • Advection & Diffusion

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 6/22

slide-14
SLIDE 14

Problem Summary

  • Little is known

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 7/22

slide-15
SLIDE 15

Problem Summary

  • Little is known
  • Experimental difficulty

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 7/22

slide-16
SLIDE 16

Problem Summary

  • Little is known
  • Experimental difficulty
  • Other computational work

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 7/22

slide-17
SLIDE 17

Problem Summary

  • Little is known
  • Experimental difficulty
  • Other computational work
  • My goals

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 7/22

slide-18
SLIDE 18

Outline

  • Biological Problem
  • Model Components
  • Numerical and Communication Methods
  • Future Work

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 2/22

slide-19
SLIDE 19

Model Components

  • Fluid Solver

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 8/22

slide-20
SLIDE 20

Model Components

  • Fluid Solver
  • Method for representing the surface of platelets and vessel

walls and for tracking the connections between the various structures

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 8/22

slide-21
SLIDE 21

Model Components

  • Fluid Solver
  • Method for representing the surface of platelets and vessel

walls and for tracking the connections between the various structures

  • Fluid-structure interactions

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 8/22

slide-22
SLIDE 22

Model Components

  • Fluid Solver
  • Method for representing the surface of platelets and vessel

walls and for tracking the connections between the various structures

  • Fluid-structure interactions
  • Advection-diffusion-reaction equations throughout fl

uid

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 8/22

slide-23
SLIDE 23

Model Components

  • Fluid Solver
  • Method for representing the surface of platelets and vessel

walls and for tracking the connections between the various structures

  • Fluid-structure interactions
  • Advection-diffusion-reaction equations throughout fl

uid

  • Presence of platelets and walls

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 8/22

slide-24
SLIDE 24

Model Components

  • Fluid Solver
  • Method for representing the surface of platelets and vessel

walls and for tracking the connections between the various structures

  • Fluid-structure interactions
  • Advection-diffusion-reaction equations throughout fl

uid

  • Presence of platelets and walls
  • Reactions on surfaces

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 8/22

slide-25
SLIDE 25

Model Components

  • Fluid Solver
  • Method for representing the surface of platelets and vessel

walls and for tracking the connections between the various structures

  • Fluid-structure interactions
  • Advection-diffusion-reaction equations throughout fl

uid

  • Presence of platelets and walls
  • Reactions on surfaces
  • Coupling of diffusion and binding/unbinding of surface

chemicals

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 8/22

slide-26
SLIDE 26

Outline

  • Biological Problem
  • Model Components
  • Numerical and Communication Methods
  • Fluid Solver
  • Parallel Programming
  • Immersed Boundary Method
  • Future Work

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 2/22

slide-27
SLIDE 27

Navier Stokes Solver

ut + ∇p = −(u · ∇)u + ν∆u + f ∇ · u = 0

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 9/22

slide-28
SLIDE 28

Navier Stokes Solver

un+1 − un ∆t + ∇pn+ 1

2 = −[(u · ∇)u]n+ 1 2 + ν

2∆(un+1 + un) + f n+ 1

2

∇ · un+1 = 0

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 9/22

slide-29
SLIDE 29

Navier Stokes Solver

u∗,k − un ∆t + ∇pn+ 1

2,k = −[(u · ∇)u]n+ 1 2 + ν

2∆(u∗,k + un) + f n+ 1

2

un+1,k − un ∆t + ∇pn+ 1

2 ,k+1 = u∗,k − un

∆t + ∇pn+ 1

2,k

∇ · un+1,k = 0

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 9/22

slide-30
SLIDE 30

Outline

  • Biological Problem
  • Model Components
  • Numerical and Communication Methods
  • Fluid Solver
  • Parallel Programming
  • Immersed Boundary Method
  • Future Work

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 2/22

slide-31
SLIDE 31

Parallel Programming

  • Shared memory vs. distributed memory

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 10/22

slide-32
SLIDE 32

Parallel Programming

  • Shared memory vs. distributed memory
  • MPI

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 10/22

slide-33
SLIDE 33

Parallel Programming

  • Shared memory vs. distributed memory
  • MPI
  • Explicit send and receives

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 10/22

slide-34
SLIDE 34

Parallel Programming

  • Shared memory vs. distributed memory
  • MPI
  • Explicit send and receives
  • Easy to cause program to hang

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 10/22

slide-35
SLIDE 35

Parallel Programming

  • Shared memory vs. distributed memory
  • MPI
  • Explicit send and receives
  • Easy to cause program to hang
  • Communication performance crucial

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 10/22

slide-36
SLIDE 36

Parallelizing the NS Solver

1 2 3 4 −1 1 2 3 4 −1

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 11/22

slide-37
SLIDE 37

Outline

  • Biological Problem
  • Model Components
  • Numerical and Communication Methods
  • Fluid Solver
  • Parallel Programming
  • Immersed Boundary Method
  • Future Work

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 2/22

slide-38
SLIDE 38

Immersed Boundary Method

Γ X(s,t)

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 12/22

slide-39
SLIDE 39

Immersed Boundary Equations

f(x, t) =

  • Γ

F(s, t)δ(x − X(s, t)) ds dX dt = u(X(s, t), t) =

  • Ω

u(x, t)δ(x − X(s, t)) dx F(s, t) = Some function of X(s, t) and its derivatives

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 13/22

slide-40
SLIDE 40

Immersed Boundary Equations

fij =

  • k

Fkδh(xij − Xk) dXk dt = Uk =

  • ij

uijδh(xij − Xk)h2 Fk =

  • i

T0(Xi − Xk − ℓ0) Xi − Xk Xi − Xk

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 13/22

slide-41
SLIDE 41

Data Structures

IBData Array of IBCells IBCell List of IBPs List of IBLs

  • SAMRAI

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 14/22

slide-42
SLIDE 42

Data Structures

IBData Array of IBCells IBCell List of IBPs List of IBLs

  • SAMRAI
  • IBP and IBL access

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 14/22

slide-43
SLIDE 43

Data Structures

IBData Array of IBCells IBCell List of IBPs List of IBLs

  • SAMRAI
  • IBP and IBL access
  • Non-uniqueness of IBLs

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 14/22

slide-44
SLIDE 44

Calculating Forces

Interpolating Velocites Updating the IB Spreading Forces Calculating Forces NS Solver

  • Obtaining non-local IBPs

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 15/22

slide-45
SLIDE 45

Calculating Forces

Interpolating Velocites Updating the IB Spreading Forces Calculating Forces NS Solver

  • Obtaining non-local IBPs
  • Smarter dummies

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 15/22

slide-46
SLIDE 46

Spreading Forces

Interpolating Velocites Updating the IB Spreading Forces Calculating Forces NS Solver

  • Delta function has four width stencil

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 16/22

slide-47
SLIDE 47

Spreading Forces

Interpolating Velocites Updating the IB Spreading Forces Calculating Forces NS Solver

  • Delta function has four width stencil
  • Need two ghost cells of IBPs with corresponding forces

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 16/22

slide-48
SLIDE 48

Interpolating Velocities

Interpolating Velocites Updating the IB Spreading Forces Calculating Forces NS Solver

  • Delta function has four width stencil

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 17/22

slide-49
SLIDE 49

Interpolating Velocities

Interpolating Velocites Updating the IB Spreading Forces Calculating Forces NS Solver

  • Delta function has four width stencil
  • Need two ghost cells of cell centered velocities

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 17/22

slide-50
SLIDE 50

Updating the IB Location

Interpolating Velocites Updating the IB Spreading Forces Calculating Forces NS Solver

  • CFL condition

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 18/22

slide-51
SLIDE 51

Updating the IB Location

Interpolating Velocites Updating the IB Spreading Forces Calculating Forces NS Solver

  • CFL condition
  • Connecting IBLs to IBPs

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 18/22

slide-52
SLIDE 52

Updating the IB Location

Interpolating Velocites Updating the IB Spreading Forces Calculating Forces NS Solver

  • CFL condition
  • Connecting IBLs to IBPs
  • “Long Distance” Communication (LDC)

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 18/22

slide-53
SLIDE 53

Updating the IB Location

Interpolating Velocites Updating the IB Spreading Forces Calculating Forces NS Solver

  • CFL condition
  • Connecting IBLs to IBPs
  • “Long Distance” Communication (LDC)
  • Deletion of extra IBLs and IBPs

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 18/22

slide-54
SLIDE 54

Optimizations

Interpolating Velocites Updating the IB Spreading Forces Calculating Forces NS Solver

  • Minimizing size of the dummy list

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 19/22

slide-55
SLIDE 55

Optimizations

Interpolating Velocites Updating the IB Spreading Forces Calculating Forces NS Solver

  • Minimizing size of the dummy list
  • Coalescing of communication steps

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 19/22

slide-56
SLIDE 56

Alternate Methods

  • Make IBPs and IBLs global among processors
  • Easier to implement
  • Requires an all-to-all broadcast message
  • Allows use of II method (or hybrid IB/II method)
  • Reduces four messages to two

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 20/22

slide-57
SLIDE 57

Alternate Methods

  • Make IBPs and IBLs global among processors
  • Make IBPs and IBLs “global per interface”
  • Allow use of II method (or hybrid IB/II method)
  • Requires a “reduced” all-to-all broadcast message
  • Still requires normal spreading and interpolation

communication

  • Still requires LDC for links between interfaces
  • Increases number of messages required from four to five

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 20/22

slide-58
SLIDE 58

Outline

  • Biological Problem
  • Model Components
  • Numerical and Communication Methods
  • Future Work

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 2/22

slide-59
SLIDE 59

Future Work

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 21/22

slide-60
SLIDE 60

Future Work

  • Debugging

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 21/22

slide-61
SLIDE 61

Future Work

  • Debugging
  • Immersed Interface Method

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 21/22

slide-62
SLIDE 62

Future Work

  • Debugging
  • Immersed Interface Method
  • Improving Stability of Implicit Solves

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 21/22

slide-63
SLIDE 63

Future Work

  • Debugging
  • Immersed Interface Method
  • Improving Stability of Implicit Solves
  • Forces Between Connecting Interfaces

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 21/22

slide-64
SLIDE 64

Future Work

  • Debugging
  • Immersed Interface Method
  • Improving Stability of Implicit Solves
  • Forces Between Connecting Interfaces
  • Modeling of Red Blood Cells

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 21/22

slide-65
SLIDE 65

Future Work

  • Debugging
  • Immersed Interface Method
  • Improving Stability of Implicit Solves
  • Forces Between Connecting Interfaces
  • Modeling of Red Blood Cells
  • Chemical Interactions

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 21/22

slide-66
SLIDE 66

Future Work

  • Debugging
  • Immersed Interface Method
  • Improving Stability of Implicit Solves
  • Forces Between Connecting Interfaces
  • Modeling of Red Blood Cells
  • Chemical Interactions
  • Adaptive Mesh Refinement

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 21/22

slide-67
SLIDE 67

Conclusion

THE END

Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 22/22

slide-68
SLIDE 68

LDC

P1 P2 C1 C2 C3 C4

Return Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 18/22

slide-69
SLIDE 69

LDC

2 4 1 3 2 4 1 3 1 3 2 4 1 3 2 4 1 3 2 4 1 3 4 2 1 2 3 4 1 3 2 4 1 3 2 4

A B C D E F G H I

Return Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 18/22

slide-70
SLIDE 70

LDC

1 3 4 2

D

Return Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 18/22

slide-71
SLIDE 71

LDC

1 3 4 2

D

1 if O2 does not update pt 1, then me needs to send him pt 3 (LDC1) 2 if me does not update pt 2 and O3 = O2 then me needs to receive pt 4 from O2 (LDC1) 3 if O3 does not update pt 2 and O4 = O3, then me needs to send pt 4 to O3. (LDC2)

Return Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 18/22

slide-72
SLIDE 72

Preliminary Data Structures

An IBData object contains

  • Array of IBCells

An IBPoint is composed of

  • Spatial coordinates (location)
  • Whether or not IBPoint is

tethered

  • Force & Velocity vectors

An IBCell contains

  • List of IBPoints
  • List of IBLinks

An IBLink is composed of

  • Resting Length
  • Tension
  • Whether a periodic boundary is

crossed

Return Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 14/22

slide-73
SLIDE 73

Final Data Structures

An IBData object contains

  • Array of IBCells
  • List of dummy IBPoints

An IBPoint is composed of

  • Unique identifier
  • Spatial coordinates (location)
  • Force & Velocity vectors
  • Whether or not IBPoint is

tethered

  • Owner & Local link count

An IBCell contains

  • List of IBPoints
  • List of IBLinks

An IBLink is composed of

  • Unique identifier
  • Resting Length
  • Tension
  • Whether a periodic boundary is

crossed

  • Pointers to two IBPoints

Return Towards a Parallel, 3D Simulation of Platelet Aggregation and Blood Coagulation – p. 19/22