Multiphysics Simulations in BioHeating and BioTechnology

John Dunec, Ph.D. COMSOL

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Agenda BioHeating and BioTechnology Introduction BioHeating Examples using COMSOL Low Frequency Joule Heating High Frequency Microwave Heating Chemical Heating Acoustic Heating Tissue Damage Simulation

Other Bio Examples Step-by-Step Demo: Low Frequency Cancer Therapy

Multiphysics: Multiple Interacting Phenomena

Could be simple: Heat convected by Flow

Could be complex: Local temperature sets

reaction rates Multiple exothermic

reactions Convected by flow in pipes

and porous media Viscosity strongly

temperature dependent

COMSOL Multiphysics Solves These!

Multiphysics Everything can link to everything. Flexible You can model just about anything.

Usable You can keep your sanity doing it.

Extensible If its not specifically thereadd it!

Trusted by 90,000+ Users Worldwide

Anywhere you can type a number you can type an equation

Or an interpolation function And it can depend on anything known in your problem

Example: Concentration-dependant viscosity:

( )221001.0 c+=

Low concentration, High velocity

High concentration, Low velocity

COMSOL Multiphysics 4.4 Product Suite

Examples: Low Frequency Joule Heating

100 sec

300 sec

Necrosis Boundary

IsoTherms Voltage Equipotential

Two Physics Involved

Select Two Individual Physics Electric Currents - and - Heat Transfer Or One Coupled Multiphysics Heat Transfer >

EM Heating > Joule Heating

Two Methods: RMS DC or True 1.2 KHz AC

Recall: RMS value of an AC signal is AC Magnitude divided by the square root of 2

31 volts AC at 1200 Hz Equivalent to 22 volts RMS DC

2AC

RMSDCVV =

Two Physics

Arte

ry

Insu

late

d

T=T b

lood

on

Surfa

ces

Electromagnetics

Heat Transfer

Link Electrical Power Loss to Heat Source

BioHeat Equation

Electrical Heat Source Coupling

( ) ( ) Electricalmetabolicbbbbp QQTTCTkdtdTC +++=

Time-varying electromagnetic field E* is Complex Conjugate of E

{ }*Re21 EJ

EJ

=

=

RMSAC

DC

Q

Q

Solve for EM and Heat

IsoTherms (600 sec) Voltage Isopotentials

Examples: High Frequency RF Heating

E-Field Temperature

Necrosis Boundary

Geometry

Geometry Liver Tissue

Insulated Catheter

CoAxial Cable inside

Catheter

Slit in Coax Shielding to emit waves

Metalize end to reflect waves

Use 2D Symmetry

Slit in CoAx. Shielding C

oAxi

al

Cath

eter

Metalize end of CoAx Dielectric

Two Physics Involved

Select Two Individual Physics Electromagnetic Waves - and - Heat Transfer Or One Coupled Multiphysics Heat Transfer >

EM Heating > Microwave Heating

Two Physics

CoAx

ial C

athe

ter:

PEC

Live

r Tis

sue

Slit

Scattering Boundary Scattering Boundary

Scattering Boundary

CoAx

Die

lect

ric

CoAxial Port

CoAx

ial C

athe

ter:

Insu

late

d Liver

Tissue with

Capillary Perfusion T = T

blood

T = Tblood

T = Tblood

Electromagnetics

Heat Transfer Co

Axia

l Cat

hete

r: In

sula

ted

Link Electrical Power Loss to Heat Source

BioHeat Equation

Electrical Heat Source Coupling

( ) ( ) Electricalmetabolicbbbbp QQTTCTkdtdTC +++=

Time-varying electromagnetic field E* is Complex Conjugate of E H* is Complex Conjugate of H

{ }*HBEJ += jQElectrical *Re21

Mesh for Waves

Frequency = 2.45[GHz] 10 DOF / wavelength 2nd Order Elements Max Elem Size = 3 mm

Make even finer in CoAx

dielectric

Set Frequency (2.45 GHz) and Solve

E-Field Temperature IsoTherms

Example: Hip Replacement

PMMA (Polymethyl methacrylate) is an acrylic cement mixed with powdered bone

Curing reaction is exothermic Potential Problems Thermal osteonecrosis if

temperature rise is too high

Polymer shrinking and void formation

Heat from Curing

Reaction After 700 sec

PMM

A Cement

Temperature After 700 sec

COMSOL Implementation Two (possibly 3) Physics Bioheat Transfer with Damage Integral Reaction ODE (or Diffusion Equa) (Structural Equation with Thermal Expansion)

Three Domains Live Bone Cement Metal

Reaction Dynamics

Cure polymerization reaction is

As a lumped-mass (no diffusion) reaction this is expressed as

Where is the normalized concentration of hardened form B

hardenedk

liquid BA

curedfully 1liquid all0

==

( ) ( )nmRTEeKt

= 1/0

Alpha at T=700 sec

Heat Transfer

Reaction heat proportional to reaction rate

This is a source term in the Bioheating equation

rreactionexothermic qQ =

( ) ( ) Reactionmetabolicbbbbp QQTTCTkTC +++==

0 since 0 u

u

Qreaction at t = 700 sec Temperature at t = 700 sec

Link Reaction Heat to Heat Transfer

Add Heat Source Term to Heat Transfer in Cement Domain

rreactionexothermic qQ =

Solve as Transient for 1600 seconds

Temperature of MidPoint vs Time

Example: Focused Ultrasound Heating

High-Intensity Focused Ultrasound (HIFU) uses sonic energy to heat damaged or diseased tissue (For Example: Uterine fibroids)

Temperature Rise after 1 sec Sound Intensity (dB)

Geometry

Spherical Focusing Transducer Tissue immersed in Water 2D Axisymmetric Tissue

Water

PML

PML

Perfectly Matched Layer

Water

1st of Two Physics: Pressure Acoustics

Pressure Acoustics Setup PMLs Absorb Waves

Axial Symmetry

Set pressure on

Transducer Boundary

Tissue

Water

PML

PML

Perfectly Matched Layer

2nd of Two Physics: BioHeat Transfer

BioHeat Setup Solve only in Tissue (Here

without perfusion)

Outer Boundaries Water Temperature

Axial Symmetry Infinite Elements Heat Source from Sound

Tissue

Not Included in Heat Calc.

Inf Elem Infinite Element Dom

ain

Twater

Twater

Tw

ater

Link Sound Losses to Heat Source Gain

Pressure Acoustics: Include attenuation Set absorption, alpha

Bioheat Equation Add a heat source Use sound intensity and

absorption coef, alpha

]/[

23mWatt

IQsound =

Mesh to Support 10 GHz Sound Waves Wavelength = 1.483 mm 10 DOF / wavelength 2nd & 4th Order Elements Max Elem Size = 1.483 / 5

Make even finer at focus

135,000 elements

Solve (Frequency & Time Domain)

Temperature Rise after 1 sec Sound Intensity (dB)

Response to Acoustic Transducer Pressure: 1 MPa

Details 1 sec

Temperature Rise Along Vertical symmetry axis

Temperature Contours Near Acoustic Focus

Calculating Damage Based on Temperature Included in Biological Tissue (with Heat Transfer Module)

100 sec

Isotherms and Necrosis Boundary after 600 sec

Isotherms and Necrosis Boundary After 100 & 300 sec

300 sec

600 sec

Damage Equations 2 Approaches

Time Above Temperature: T > 50C for at least 50 sec

dtCTTimeAbovet

)50(500

>= dtAet

RTE

=

0

Energy Based (Ref Below) Energy Absorption

0 ,11)(

==

bloodAteTissueDeadPercent

secondsTimeAbove 5050

(Ref) Isaac Chang and Uyen Nguyen, Thermal modeling of lesion growth with radiofrequency ablation devices, BioMedical Engineering OnLine, 2004, 3:27, August 6, 2004. http://www.biomedical-engineering-online.com/content/3/1/27

100 sec

Example: Fluid Structure Interaction

Heart Mitral Valve Flow moves structure Mesh informs flow

Simulation of Blood Flow through the Mitral Valve of the Heart: A Fluid Structure Interaction Model. D.M. Espino, M. A. Watkins, D. Shepherd, D. L. Hukins & K G. Buchan COMSOL 2006 Conference

Stent Expansion

Plastic deformation upon catheter balloon inflation

Very Nonlinear Elasto-plastic Large deformation

Possible Extensions Contact analysis with blood

vessel walls Export deformed geometry Convection-diffusion of

antirejection coating

Plastic Strain

Geometry

Dog-boning / Foreshortening vs Pressure

Von Mises Stress Deflection

Antirejection Coating Convection-Diffusion

Diffusion in tissue Convection in blood

Measure flux to calculate

lifespan of coating

Worked Example: Joule Heating Here with 22 volt RMS DC

100 sec

300 sec

Necrosis Boundary

IsoTherms Voltage Equipotential

Arte

ry

Cath

eter

IsoPotential

Video Demo

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100 sec

IsoTherms Voltage Equipotential

Tissue Necrosis Boundary

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COMSOL Multiphysics 4.4 Product Suite

Multiphysics Simulations in BioHeating and BioTechnologyAgenda BioHeating and BioTechnologyMultiphysics: Multiple Interacting PhenomenaCOMSOL Multiphysics Solves These!Anywhere you can type a number you can type an equationCOMSOL Multiphysics 4.4 Product SuiteExamples: Low Frequency Joule HeatingTwo Physics InvolvedTwo Methods: RMS DC or True 1.2 KHz ACTwo PhysicsLink Electrical Power Loss to Heat SourceSolve for EM and HeatExamples: High Frequency RF HeatingGeometryTwo Physics InvolvedTwo PhysicsLink Electrical Power Loss to Heat SourceMesh for WavesSet Frequency (2.45 GHz) and SolveExample: Hip ReplacementCOMSOL ImplementationReaction DynamicsHeat TransferLink Reaction Heat to Heat TransferSolve as Transient for 1600 secondsExample: Focused Ultrasound HeatingGeometry1st of Two Physics: Pressure Acoustics2nd of Two Physics: BioHeat TransferLink Sound Losses to Heat Source GainMesh to Support 10 GHz Sound WavesSolve (Frequency & Time Domain)Details 1 secCalculating Damage Based on TemperatureDamage Equations 2 ApproachesExample: Fluid Structure InteractionStent ExpansionDog-boning / Foreshortening vs PressureAntirejection Coating Convection-DiffusionWorked Example: Joule Heating Here with 22 volt RMS DCVideo DemoTry COMSOL MultiphysicsContact UsQ&A SessionCOMSOL Multiphysics 4.4 Product Suite