An integrated muscle mechanicfluid dynamic model of lamprey swimming - PowerPoint PPT Presentation

Title: An integrated muscle mechanicfluid dynamic model of lamprey swimming


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An integrated muscle mechanic-fluid dynamic model
of lamprey swimming

• Chia-Yu Hsu
• CCS, Mathematics, Tulane University
• Nov.8, 2009

SEAMS Workshop (Cha-Cha Days)
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Collaborators
Avis H. Cohen and Eric Tytell University of
MarylandPhilip Holmes Princeton UniversityLex
Smits Princeton University Tyler McMillen Cal
State FullertonThelma Williams University of
LondonBoyce Griffith - NYU Lisa Fauci Tulane
University
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Coupled System
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Goal

• To couple these systems of neuronal networks,
  mechanical muscular and the hydro-dynamics to
  generate the lamprey swimming pattern.

Movie courtesy from Lex Smits, Megan Leftwich,
Melissa Green
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Central Pattern Generator
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Methods for CPG
Avis Cohen and Eric Tytell, UMD
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Ultrastructure of vertebrate skeletal muscle
Action potential bursts - Calcium release from
SR Calcium binds to the muscle filaments ,
causing conformational changes in thick filaments
which form cross bridges force is generated .
Calcium then resequestered by SR, and muscle
relaxes.
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Ultrastructure of vertebrate skeletal muscle
Action potential bursts - Calcium release from
SR Calcium binds to the muscle filaments ,
causing conformational changes in thick filaments
which form cross bridges force is generated .
Calcium then resequestered by SR, and muscle
relaxes.
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Ultrastructure of vertebrate skeletal muscle
Action potential bursts - Calcium release from
SR Calcium binds to the muscle filaments ,
causing conformational changes in thick filaments
which form cross bridges force is generated .
Calcium then resequestered by SR, and muscle
relaxes.
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Ultrastructure of vertebrate skeletal muscle
Action potential bursts - Calcium release from
SR Calcium binds to the muscle filaments ,
causing conformational changes in thick filaments
which form cross bridges force is generated .
Calcium then resequestered by SR, and muscle
relaxes.
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Simplified Muscle Model
Passive elastic forces by Hookes Law
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Muscular activation on isshown in red.

• 280 muscle segments on each side of body
• The muscles in the head do not contract.
• Force generated depends on the activation wave,
  length of each muscle segment, speed of
  lengthening or shortening of muscle

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From Motoneuron to Muscle via Calcium Dynamics
The Hill muscle model produces forces according
to
This model is a modified version of that fitted
to single myotome data it incorporates nonlinear
length and velocity dependence.
Williams, Bowtell Curtin, J. Exp. Biol. 201,
869-875, 1998
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Mathematical Model
Flow is governed by the incompressible Navier
Stokes equations (Fluid coupled with elastic
structure)
Fk is a delta function layer of force exerted
by the Kth segment of the body on the fluid.
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Immersed Boundary Framework
Transmit f(X(t), t) to grid
f (X(t), t)
X (t?t) X (t) U(X(t),t) ?t
Solve Navier -Stokes on grid
Grid-based
U(X (t), t)
Interpolate grid velocity
C.Peskin, Acta Numerica, 2002, 479-517
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Numerical Solution/IBAMR

• Immersed boundary adapted mesh refinement method

Three levels of mesh refinement grids
B.Griffith, et all, J.Comput. Phys. 22310-49,
2007
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Free swimming
Movie courtesy from Cohen and Tytell
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Simulation of steady swimming
Fq1Hz, L4pi cm Re6100, St0.53, Mech/Act0.82
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Swimming with different activation frequencies
Fq2 Re1200 St1.23
Fq0.5 Re3800 St0.71
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Swimming in different viscosities
Water
25 pct
Movies courtesy from Eric Tytell
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Simulations-Swimming in different viscosities
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Simulation-Turning

• Asymmetric muscle contraction ratio

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3D lamprey model and simulation

• Circular links
• Lateral links
• Sinusoidal wave propagation

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Conclusion and Future work

• Phase lag shown on the tapered lamprey
• swimming model
• Integrative 3D model with muscular calcium
  dynamics
• Characterize wake structure as function of model
  parameters

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Acknowledgements

• Dr. Boyce Griffith
• (IBAMR support)
• Dr. Hideki Fujioka
• (Parallel computation support )
• Center for Computational Science, Mathematics,
  Tulane University
• Louisiana Optical Network Initiative (LONI)
• Grant support by NSF DMS-0652775 and
• NIH(CRCNS)RO1NS05427102.

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Thank You!
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Coupled System-See You in APS