Multiphysics Simulations in BioHeating and BioTechnology
John Dunec, Ph.D. COMSOL © Copyright 2014 COMSOL. COMSOL, COMSOL Multiphysics, Capture the Concept, COMSOL Desktop, and LiveLink are either registered trademarks or trademarks of COMSOL AB. Excel, Microsoft, and Windows are either registered trademarks or trademarks of Microsoft Corporation in the United States and/or other countries. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see www.comsol.com/trademarks
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 there…add 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: Low concentration, High velocity
µ = 0.001× (1 + 2c
2
)
High concentration, Low velocity
COMSOL Multiphysics® 4.4 Product Suite
Examples: Low Frequency Joule Heating
100 sec
300 sec Necrosis Boundary
Voltage Equipotential
IsoTherms
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
VDC
• 31 volts AC at 1200 Hz • Equivalent to 22 volts RMS DC
RMS
VAC = 2
Heat Transfer
Two Physics
T=Tblood on Surfaces
Artery
Insulated
Electromagnetics
Link Electrical Power Loss to Heat Source BioHeat Equation
dT ρCp = ∇ ⋅ (k∇T ) + ρ bCbωb (Tb − T ) + Qmetabolic + QElectrical dt Electrical Heat Source Coupling
QDC = J ⋅ E QAC −RMS
{
1 = Re J ⋅ E* 2
}
Time-varying electromagnetic field E* is Complex Conjugate of E
Solve for EM and Heat
IsoTherms (600 sec)
Voltage Isopotentials
Examples: High Frequency RF Heating
Geometry
Necrosis Boundary E-Field
Temperature
Geometry • Insulated Catheter • CoAxial Cable inside Catheter
Slit in CoAx. Shielding
• Slit in Coax Shielding to emit waves • Metalize end to reflect waves • Use 2D Symmetry Metalize end of CoAx Dielectric
CoAxial Catheter
• Liver Tissue
Two Physics Involved Select Two Individual Physics • Electromagnetic Waves - and • Heat Transfer Or One Coupled Multiphysics • Heat Transfer > EM Heating > Microwave Heating
Electromagnetics
CoAxial Catheter: PEC
CoAxial Catheter: Insulated
Liver Tissue with Capillary Perfusion
T = Tblood
CoAxial Catheter: Insulated
Heat Transfer
Slit
T = Tblood
Scattering Boundary
CoAx Dielectric
Two Physics
Scattering Boundary
Liver Tissue
CoAxial Port
Scattering Boundary T = Tblood
Link Electrical Power Loss to Heat Source BioHeat Equation
dT ρCp = ∇ ⋅ (k∇T ) + ρ bCbωb (Tb − T ) + Qmetabolic + QElectrical dt Electrical Heat Source Coupling
QElectrical
{
1 = Re J ⋅ E* + jω B ⋅ H * 2
Time-varying electromagnetic field E* is Complex Conjugate of E H* is Complex Conjugate of H
}
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 Cement
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
Heat from Curing Reaction After 700 sec
• Polymer shrinking and void formation 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
Aliquid → Bhardened k
• As a lumped-mass (no diffusion) reaction this is expressed as
∂α n = K 0 e (− E / RT ) α m (1 − α ) ∂t • Where α is the normalized concentration of “hardened form” B
α = 0 all liquid α = 1 fully cured Alpha at T=700 sec
Heat Transfer • Reaction heat proportional to reaction rate
Qexothermic reaction = ρ qr α • This is a source term in the Bioheating equation
ρC p u ⋅ ∇T = ∇ ⋅ (k∇T ) + ρ bCbωb (Tb − T ) + Qmetabolic + QReaction
0 since u = 0
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
Qexothermic reaction = ρ qr α
Solve as Transient for 1600 seconds
Temperature of MidPoint vs Time
Example: Focused Ultrasound Heating Sound Intensity (dB)
Temperature Rise after 1 sec
• High-Intensity Focused Ultrasound (HIFU) uses sonic energy to heat damaged or diseased tissue (For Example: Uterine fibroids)
Geometry Perfectly Matched Layer
• Spherical Focusing Transducer • Tissue immersed in Water • 2D Axisymmetric
PML
Tissue
Water
PML Water
1st of Two Physics: Pressure Acoustics PML
•
PML’s Absorb Waves
Perfectly Matched Layer
Pressure Acoustics Setup Tissue
• Axial Symmetry • Set pressure on Transducer Boundary
Water
PML
2nd of Two Physics: BioHeat Transfer BioHeat Setup
Twater
Inf Elem
• Axial Symmetry • Infinite Elements • Heat Source from Sound
Twater
Not Included in Heat Calc.
Twater
• Outer Boundaries Water Temperature
Tissue
Infinite Element Domain
• Solve only in Tissue (Here without perfusion)
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
Qsound = 2α I [Watt / m 3 ]
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) Sound Intensity (dB)
Temperature Rise after 1 sec
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 600 sec
300 sec Isotherms and Necrosis Boundary After 100 & 300 sec
Isotherms and Necrosis Boundary after 600 sec
Damage Equations – 2 Approaches Time Above Temperature: •
T > 50C for at least 50 sec t
TimeAbove 50 = ∫ (T > 50C )dt 0
TimeAbove 50 ≥ 50 seconds
100 sec
Energy Based (Ref Below) • Energy Absorption t
Ω = ∫ Ae 0
− ∆E RT
dt
Percent ( Dead Tissue) = 1 − e − Ω At Ω = 1, ωblood → 0
(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.biomedicalengineering-online.com/content/3/1/27
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
Geometry
Possible Extensions • Contact analysis with blood vessel walls • Export deformed geometry • Convection-diffusion of antirejection coating Plastic Strain
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
Artery
Catheter
– Here with 22 volt RMS DC
100 sec
IsoPotential
300 sec Necrosis Boundary
Voltage Equipotential
IsoTherms
Video Demo • Please wait while the content is loading…
100 sec Tissue Necrosis Boundary Voltage Equipotential
IsoTherms
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COMSOL Multiphysics® 4.4 Product Suite
