TERAHERTZ MODELINGAND SIMULATION

28 NOV 07Jason Payne

Associate Research Biomedical EngineerRadio Frequency Radiation Branch

Robert J. ThomasPhysicist

Optical Radiation BranchAir Force Research Laboratory

PA 07-196

Distribution A: Approved for Public Release

AFRL-HE-BR-JA-2007-0005

ATTACHMENT 11

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Overview

• AFRL Modeling and Simulation Background

• Previous Work

• Model Development

• Results

• Future Considerations

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Introduction

• The Air Force Research Laboratory at Brooks City-Base has been a leader in the effort to determine the bioeffects and establish safety standards for radio frequency and laser energyfor over 20 years

• Modeling and Simulation (M&S) expertise above and below the THz region may be leveraged in order to predict potential Bioeffects in the THz region

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Modeling Procedures

RF-Approach THz Modeling

Laser-ApproachTHz Modeling

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Finite Difference Time Domain

• The Finite Difference Time Domain (FDTD) method is a direct time-domain numerical solution technique for Maxwell’s equations– Yee’s algorithm numerically solves for both

the Electric and Magnetic fields in a region of interest and over a finite period of time

– FDTD for electromagnetics was first introduced by Kane Yee in 1966

• Early application for FDTD techniques was scattering problems, e.g., radar cross sections

• As available computational resources increased, FDTD methods became feasible for many classes of problems, including RF dosimetry Yee Space Grid

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Maxwell’s Equations

tBE∂∂

−=×∇

tDJH∂∂

+=×∇

vD ρ=⋅∇

0=⋅∇ B

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Previous M&S Work

Modeling using FDTD (model of absorption of RF energy)

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FDTD Models for THz Energy

• 1D and 2D FDTD codes are used to calculate energy absorption in skin models due to THz energy

• Resolution of skin models is typically set to 1 micron

• Both homogeneous and multi-layer skin slab models are utilized within the FDTD simulations

• Resulting SAR values then serve as input to thermal modeling software

SAR vs Depth Profile

020406080

100120140160180

0 50 100 150 200 250 300

Depth (microns)N

orm

aliz

ed S

AR

(W

/Kg/

mW

/cm

^2) Epidermis/Dermis

ModelWater Model

SAR vs. Depth profiles for a uniform 1 THz beam incident upon a water model

and a two layer skin model

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FDTD Assumptions and Considerations

• Compare Modeling and Simulation results to empirical studies

• Improved skin models– Realistic skin slab models– Further study and

refinement of the thermal and electromagnetic properties of skin

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THRESHOLD MODELING RESULTS

• Thermal Damage Thresholds Modeled• Pulse Duration Ranges for Pure Thermal Effects

– Short Pulse (< ~10 microseconds) Work May Require Additional Mechanisms

• Study Provides Baseline for Injury Threshold Estimates in 0.2 – 2.0 THz Region

• Assist in Bridging Exposure Limits (Laser and RF)• Related Laser Research (Strong Absorption) Should

Mimic Trends in Damage Thresholds

“THz Frequency Bioeffects,” Draft for RFR Dosimetry Handbook

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Our Approach to Heat Transfer

z

rCylindrical Symmetry

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Complete Boundary Conditions

Convection + Radiative + Evaporative

Sink / Heat BathInsulator

r

z

Convection + Radiative + Evaporative

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Physical Properties

0.13.00.31.01.00.3

F(THz)λ(mm)

0.13.00.31.01.00.3

F(THz)λ(mm)

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Linear Absorption vs. SAR Source Terms

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Ambient Effects Considered

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Thresholds and ANSI (1-mm)

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Spot Size Dependence of Threshold

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Peak Temperature at Threshold

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Frequency-Dependence of Thresholds

λ(mm) F(THz)0.3 1.01.0 0.33.0 0.1

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Comparison to Expt. Data

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Standards, Thresholds, and Sensation

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Food for Further Thought (Study)

Chen, et. al. Histological and Modeling Study of Skin Thermal Injury to 2.0 μm Laser Irradiation in press Lasers Surg. Med. (2007).

2.0-um Thresholds vs Time

1

10

100

0.1 1.0 10.0

Time (s)Th

resh

old

(W/c

m2 )

2.0 um Damage Threshold200um Damage DepthExpt (Large Spot)- Chen et. al.

(and SPIE Photonics West 2007)

200 μm – depth damage at threshold endpoint

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THz Thermal Damage Implications

1-D, 1.2-THz

J

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The Whole Story?

• Thermal Damage Thresholds Only• Estimates from Published Tissue Values• Short-Pulse (non-thermal) Mechanisms Not

Addressed

• Experimental Validation of Damage Thresholds Needed to Anchor Model (and Assumptions)

– Strongest Validation from Existing Experimental Data at Much Higher Frequencies

• Threshold Endpoint Assumptions need Refinement – See Chen et. al., 2.0 micron Histopathology Study, 2007 (In Press)

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Acknowledgements

• AFRL/HEDR (AFRL/RHDR)– Dr. Jill McQuade– Ms. Kalyn Yaws– Dr. Pat Roach

• AFRL/HEDO (AFRL/RHDO)– Mr. Paul Maseberg– Mr. C.D. Clark III

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Selected References

• Chen B, Thomsen S, Thomas RJ, Welch AJ, Modeling thermal damage in skin from 2000 nm laser irradiation. Journal of Biomedical Optics 11:064028; 2006.

• Clark CD, Thomas RJ, Maseberg PDS, Buffington GD, Irvin LJ, Stolarski J, Rockwell BA, Modeling of surface thermodynamics and damage thresholds in the IR and THz regime, in: Optical Interactions with Tissues and Cells XVIII, vol. 643505, 1–12, SPIE; 2007.

• Taflove A, Hagness SC, Computational Electrodynamics - The Finite-Difference Time-Domain Method, 2nd ed., Artech House, Norwood, MA; 2000.

• Pickwell E, Cole B, Fitzgerald AJ, Wallace V, Pepper M, Simulation of terahertz pulse propagation in biological systems. Applied Physics Letters 84:2190–2192; 2004.

• Pickwell E, Fitzgerald A, Cole B, Taday P, Pye R, Ha T, Pepper M, Wallace V, Simulating the response of terahertz radiation to basal cell carcinoma using ex vivo spectroscopy measurements. Journal of Biomedical Optics 10:064021; 2005.

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• BACKUP SLIDES

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Thermal Modeling

• Pennes Bioheat solvers are used to predict thermal effects and damage thresholds (2nd Degree Burn) within skin slab models

• Bioheat equation is modified to take SAR values as thermal input

Temperature rise in skin slab model due to a uniform 1 THz

beam with incident power density of 1 W / cm2

( ) ( )[ ] ( ) ( )[ ]artbb TtxTCWtxSARtxTktxtTC −−+∇⋅∇=∂∂ ,,,, ρρ

• Arrhenius Integral has been implemented within software to predict damage thresholds for a given exposure condition

( ) ( )∫ ⎟⎟⎠⎞

⎜⎜⎝

⎛ −=Ω

2

1,

expt

t

a dttzRT

ECz

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Thermal Modeling Cont.

Damage Threshold

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01

Exposure Time (s)

Pow

er D

ensi

ty (W

/ cm

^2) Epidermis/Dermis

Model

1 THz

Temperature Rise at Damage Threshold

25

30

35

40

1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01

Exposure Time (s)

Tem

pera

ture

Ris

e (C

) Epidermis/DermisModel

1 THz

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Warmth Detection and Pain Thresholds

Damage, Pain and Warmth Detection Thresholds at 1 THz

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

0.001 0.01 0.1 1 10Exposure Duration (s)

Pow

er D

ensi

ty (W

/cm

^2)

Damage Threshold43 Degrees, Pain46 Degrees, Pain300 GHz PEL1 THz PELWarmth Detection

• Heating of the skin to 43-46°C has been shown to cause discomfort

• Warmth detection on the skin may occur for a temperature rise of 0.07°C

• Permissible exposure limits adopted for the THz region may take into account such warmth, pain and damage thresholds

TERAHERTZ MODELING�AND SIMULATION�28 NOV 07Overview IntroductionModeling ProceduresFinite Difference Time DomainMaxwell’s EquationsPrevious M&S WorkFDTD Models for THz EnergyFDTD Assumptions and ConsiderationsTHRESHOLD MODELING �RESULTSOur Approach to Heat TransferComplete Boundary ConditionsPhysical Properties Linear Absorption vs. SAR Source TermsAmbient Effects ConsideredThresholds and ANSI (1-mm)Spot Size �Dependence of ThresholdPeak Temperature at ThresholdFrequency-Dependence of ThresholdsComparison to Expt. DataStandards, Thresholds, and SensationFood for Further Thought (Study)THz Thermal Damage ImplicationsThe Whole Story?AcknowledgementsSelected ReferencesThermal ModelingThermal Modeling Cont.Warmth Detection and �Pain Thresholds