26.6.2012 Modeling of endothelial mechanical conditions during microbubble enhanced blood-brain...

26.6.2012

Modeling of endothelial mechanical conditions during microbubble enhanced blood-brain barrier disruption

W. Wiedemair 1, Ž. Tuković 2, D. Poulikakos 1, V. Kurtcuoglu 1

1 Laboratory of Thermodynamics in Emerging Technologies, ETH Zurich, Switzerland 2 Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Croatia

26.6.2012 Wiedemair – Blood-Brain Barrier Disruption

Biomedical modeling

2

A bit out of ‘classical’ engineering scope

Biomedical technology rapidly growing

Need for accurate modeling & analysis

Usually multiphysics problem

OpenFOAM single platform

Tailoring solver framework

South Dakota School of Mining and Engineering

U. Olgac et al., Am J Physiol Heart Circ Physiol (2009)

B. Siyahhan et al.


Outline

3

o Introduction & motivation

o Problem specification

oMultidomain model

oMethods

o Results

o Conclusion


Blood-Brain Barrier

4

o Body: Transfer of substances to tissue via circulation and ‘leaky junctions’

o Brain: Intracellular gap closely sealed ‘tight junctions’ & specialized cells

Blood Brain Barrier

Introduction

McGraw Hill

Pearson Education, Inc.

o Impermeable to almost all substanceso Protect cerebral compartmento Maintain homeostatic environmento Inhibit passage for systemically

administered drugs


Modified from Philips Healthcare

FUS induced BBB disruption

5

Many (bio-) chemical means to circumvent BBBo Affect entire brain (non-selective) o Exposition to high dosage o Substances generally unhealthy

Ultrasound & microbubbleso Forced μ-bubble oscillation induced micro-streamingo Impact on capillary level Exact mechanisms unknowno Local and transient (reversible)o MRI guidance

Introduction

Sealing membrane

Water

Transducer

Stereotactic frame

B. Werner, Unversity Children‘s Hospital Zurich


Blood-brain barrier inhibits drug uptake

Transient, local increase of permeability

FUS driven cavitation of µ-bubbles

FUS induced BBBD

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o Successfully and reproducibly appliedo Animal studies [1]

o Human pre-clinical tests o Thin line between BBBD and vessel destruction Risk assessmento Difficult to access experimentally Modeling

www.nutralegacy.com

Introduction

L. Strobel et al.

[1] K. Hynynen, Adv. Drug Delivery. Rev. 60, pp. 1209-17 (2008)


Ingredients

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o Encapsulated microbubbles (2-6 µm )o Blood is composite fluid (parachute RBCs)o Compliant microvesselo Focused ultrasound (OoM: 1 MHz)

K. Tsukuda et al., Phys. Microvasc. Res. (2001)

Introduction

S. Chopra, PhD thesis, Berlin, 2005


Mesho Axial symmetry wedge mesh

Methods

8

Methods

Framework o Accommodate multiple domains o Different physics / constitutive lawso Domain couplingo Flexible & extensible


Solid:

Uniform, isotropic, elastico Multimaterial rheologyo Updated Lagrangian formulation [1]

Vessel:o Thickness: 0.3 – 0.7 μm o Young’s modulus: 1- 10 MpaRBCs:o Motile & deformable

Fluid:

Incompressible, laminar, Newtono Viscosity: 1.5 mPa s o Density: 1030 kg/m3

o Separate plasma and cells o ALE formulation

Modeling

9

Methods

[1] Ž . Tuković , H. Jasak, Trans Famena 31 55-70 (2007)


Solution procedure

10

Methods

Combine several OF features:

o ODE solverso Topological modifiers Layer addition-removal

o Fluid-Structure Interaction (FSI)o Multiregion rheologyo Automatic mesh motion subset motion

o Self-contained – one platform !!!

Topo Change

Converged

Deform. limit

Solve mRPE

δa

δpi , δτi

δui

vi

Mesh update

Layer add/remove

t = t + δt

(Subset- )Mesh motion

Fluid solver

Solid solver

k =

k +

1


o Modified RPE for thin lipid shell & confined environment

Bubble as spherical actuatoro Solving at run-time adaptive time stepping

o Fifth order Runge-Kutta o Good in case of adaptive time stepping

ODE solver:

11

Methods

3 2 22 0 0 0 0

0 02 2 4 3

4 443 41 1 1 ( )

2 3sL

L L UST T

a a a a aaaL aLaa a P P P t

R R a a a a a

Ferrara K W et al., Annu Rev Biomed Eng (2007)


o Partitioned approacho Modularityo Code re-use (efficient solvers)o Stability

o Strong couplingo Unfavorable ratio and rather thin wallo Multiple outer iterations

o Kinematic and dynamic equilibrium at interfaceo Dirichlet-Neumann formulationo Patch-to-patch interpolationo Adaptive under-relaxation or IQN–ILS [1]

Fluid-Structure Interaction

12

Methods

[1] Degroote J et al. Comput Struct (2009)

P L A S M A

R B CV E S S E L

FSI


o Automatic mesh motion [1] [1]

o Tetrahedral cell-and-face decompositiono Laplacian equation for vertex motion - variable diffusivity

o Topological Modifiers: Automatic layer addition removalo Subset motion solverSolution based dynamic mesh adaptation & topology adaptation

Dynamic mesh

13

R

t

Methods

[1] H. Jasak , Ž . Tuković , Trans Famena 30 1–20 (2007)

26.6.2012 Wiedemair – Blood-Brain Barrier Disruption 14

Flow properties with RBC

o P & v mainly undisturbed

o RBC inertia effects upon bubble motion reversal

o Shear layer along vessel wall

Wiedemair W et al., Phys Med Biol, 57, 1019-1045 (2012)

Results


Flow propertiesResults


Flow and shearResults


Normal and tangential loadingo Transmural pressure

o Wall shear stress

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Interface parameters with RBCResults

,tm i I eP z P R z P

v

I

L

r R

dWSS

dn


o Ptm & WSS above physiological range

o Marked peaks in spatial gradients

o Peaks in vicinity of RBCs


Results

Differential interface parameters


o How much impact from RBCs o Vessel size and rigidity:o Ultrasound frequency, amplitude, patterno Bubble size & shell properties

Goal: Derive parametric model

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Parameter variationsResults



Advantages / Limitations

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Prediction of microscopic mechanical quantities based on external and internal parameters

Tissue & RBC properties known by order of magnitude

Simplifications: spherical bubble, smooth vessel structure

Variable parameters / geometries

Access to various potentially relevant quantities

Extensible framework

Discussion


… and beyond

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Free surface tracking

o Non-spherical oscillation

Validate mRPE modeling

o Large amplitude oscillations

Discussion

F U S


Conclusion

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o Tailored, coupled multi-domain model

o Extraction of dynamic parameters for fluid & interface

o RBCs show marked impact on micro-flow and wall conditions

o Twofold purpose: Assess microscale conditions & safety

www.nutralegacy.com

Conclusion

Pic with ‘positive‘

BBBD


Acknowledgements

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ETH Zurich• Bercan Siyahhan• Bernhard Grieser• Michael Wild

WIKKI Ltd. London• Prof. Hrvoje Jasak• Dr. Henrik Rusche

IT’IS Research Zurich• Adamos Kyriakou• Dr. Esra Neufeld• Prof. Niels Kuster

University Children’s Hospital Zurich• Beat Werner• Zsofia Kovacs

Financial support through the Swiss National Science Foundation, NCCR Co-Me

Acknowledgments

www.mergeleftmarketing.com

• Dr. Heng Xiao• Yvonne Reinhardt• Maike Schubert

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