Simulation of Electromagnetic Heating of Cryopreserved SAMPLES
description
Transcript of Simulation of Electromagnetic Heating of Cryopreserved SAMPLES
Simulation of Simulation of Electromagnetic Electromagnetic
Heating of Heating of Cryopreserved Cryopreserved
SAMPLESSAMPLESC. C. LuC. C. Lu
Department of Electrical and Computer Department of Electrical and Computer EngineeringEngineering
University of KentuckyUniversity of Kentucky
Lexington, KY 40506Lexington, KY 40506
*
University of KentuckyUniversity of Kentucky 22
OUTLINEOUTLINE
INTRODUCTIONINTRODUCTION FORMULATION OF EM AND HEAT FORMULATION OF EM AND HEAT
TRANSFER ANALYSISTRANSFER ANALYSIS IMPLEMENTATIONIMPLEMENTATION SIMULATION RESULTSSIMULATION RESULTS SUMMARYSUMMARY
University of KentuckyUniversity of Kentucky 33
INTRODUCTION (1)INTRODUCTION (1)CRYOPRESERVATION STEPSCRYOPRESERVATION STEPS
SAMPLE PROCESS (CPA FILLING)SAMPLE PROCESS (CPA FILLING) COOL SAMPLE TO LOW TEMPERATURECOOL SAMPLE TO LOW TEMPERATURE PRESERVE SAMPLE IN LOW PRESERVE SAMPLE IN LOW
TEMPERATURE STATUSTEMPERATURE STATUS WORM THE SAMPLE TO ROOM WORM THE SAMPLE TO ROOM
TEMPERATURE (REWARMINGTEMPERATURE (REWARMING POSTPROCESSINGPOSTPROCESSING
University of KentuckyUniversity of Kentucky 44
INTRODUCTION (2)INTRODUCTION (2)SYSTEM CONFIGURATIONSYSTEM CONFIGURATION
Microwave Source
Cavity
Sample
Liquid Nitrogen
Temperature monitor
University of KentuckyUniversity of Kentucky 55
INTRODUCTION (2)INTRODUCTION (2)
Rewarming requirements for minimum Rewarming requirements for minimum tissue damagetissue damage Small temperature gradient: Small temperature gradient: uniformuniform High warming rate: High warming rate: rapidrapid
Using microwave for rewarmingUsing microwave for rewarming: : Volumetric heating: EM energy is Volumetric heating: EM energy is
delivered to every point in a sampledelivered to every point in a sample Rapid warming is realized by very high E-Rapid warming is realized by very high E-
field intensity in a resonant cavityfield intensity in a resonant cavity
University of KentuckyUniversity of Kentucky 66
INTRODUCTION (3)INTRODUCTION (3)
DifficultiesDifficulties Thermal runaway (hot spot absorbs more Thermal runaway (hot spot absorbs more
power and gets even hotter)power and gets even hotter) Conflicting controls: Conflicting controls: uniformityuniformity requires low requires low
frequency fields (deeper penetration), frequency fields (deeper penetration), rapidrapid heating requires high frequency fieldheating requires high frequency field
SolutionsSolutions Trade-off in selection of resonant frequencyTrade-off in selection of resonant frequency Control of field patternControl of field pattern Selection of right cryoprotectant agent (CPA)Selection of right cryoprotectant agent (CPA)
University of KentuckyUniversity of Kentucky 77
Methods to study microwave Methods to study microwave rewarming for rewarming for
cryopreservationcryopreservation Experimental studiesExperimental studies
Realistic modelingRealistic modeling Validation of theory and numerical codesValidation of theory and numerical codes
Numerical studiesNumerical studies Ideal configurationIdeal configuration High accuracyHigh accuracy Easy to search optimum warming conditionsEasy to search optimum warming conditions Results used as guidelines for system designResults used as guidelines for system design
University of KentuckyUniversity of Kentucky 88
IMPORTANT FACTORS IMPORTANT FACTORS AFFACTING REWARMING AFFACTING REWARMING
PROCESSPROCESS Microwave frequencyMicrowave frequency Cavity shapeCavity shape Complex permittivity of CPA and its Complex permittivity of CPA and its
temperature dependencytemperature dependency Size and Shape of sample under testSize and Shape of sample under test
University of KentuckyUniversity of Kentucky 99
OPTIMIZATION OF REWARMING OPTIMIZATION OF REWARMING PROCESSPROCESS
GIVENGIVEN: Maximum allowed temperature : Maximum allowed temperature gradientgradient
SEARCHSEARCH: Control parameters to realize : Control parameters to realize maximum warming ratemaximum warming rate
METHODMETHOD: Numerical solution of the EM : Numerical solution of the EM equations and the heat transfer equationequations and the heat transfer equation
University of KentuckyUniversity of Kentucky 1010
MAXWELL’S EQUATION SOLVER
HEAT TRANSFER EQUATION SOLVER
Heat Source
EM Source
, ,
, ,k C
( )T r
,E H
SIMULATION DIAGRAM
University of KentuckyUniversity of Kentucky 1111
PREVIOUS WORKSPREVIOUS WORKS
Separate EM and heat transfer solutionSeparate EM and heat transfer solution FEM for heat transfer and approximate FEM for heat transfer and approximate
EM solution (D. Chen and Singh, 1992)EM solution (D. Chen and Singh, 1992) Heating pattern analysis using spheres Heating pattern analysis using spheres
(X. Bai and D. Pegg, 1992)(X. Bai and D. Pegg, 1992) Combined analysis:Combined analysis:
FDTD: Ma, et al (1995), FDTD: Ma, et al (1995), Torres and Jacko (1997)Torres and Jacko (1997) X. Han (2004)X. Han (2004)
University of KentuckyUniversity of Kentucky 1212
EM SOLUTION METHODS EM SOLUTION METHODS
FDTD, FEM, MOM can all be FDTD, FEM, MOM can all be applied for the simulationapplied for the simulation FDTDFDTD: Time consuming for resonant : Time consuming for resonant
frequency search, and long iteration frequency search, and long iteration for CW sourcefor CW source
FEMFEM: Difficult for mesh generating, : Difficult for mesh generating, slow convergenceslow convergence
MOMMOM: Efficient and accurate (sample : Efficient and accurate (sample size is normally electrically small). size is normally electrically small). Easy for mesh generation.Easy for mesh generation.
University of KentuckyUniversity of Kentucky 1313
PRESENT WORK PRESENT WORK
Combined EM and heat transfer Combined EM and heat transfer solution.solution.
Hexahedron grid and Roof-top Hexahedron grid and Roof-top basis function for EM solutionbasis function for EM solution
Hexahedron grid and control Hexahedron grid and control volume for heat transfer solutionvolume for heat transfer solution
Temperature varying electrical and Temperature varying electrical and thermal parameters for samples.thermal parameters for samples.
University of KentuckyUniversity of Kentucky 1414
THE INTEGRAL EQUATIONS THE INTEGRAL EQUATIONS (EM)(EM)
G r r Ik
r r
r r, '
exp | ' |
| ' |a f k p FH IK
1
42
sca ( ) ( , ') ( ) ' ( , ') ( ) 'V S
V S
E r i G r r J r dV i G r r J r dS
( ) ( ) ( ), Samplesca incE r E r E r r
( ) ( )V bJ r i E r
tan tan( ) ( ) ( ) , Wallsca incE r E r E r r
University of KentuckyUniversity of Kentucky 1515
MODEL REPRESENTATIONMODEL REPRESENTATION Hexahedron cells (quadrangle faces)Hexahedron cells (quadrangle faces) Well connected meshWell connected mesh
Using rectilinear hexahedrons, it is possible to accurately model any arbitrarily shaped solid dielectrics.
University of KentuckyUniversity of Kentucky 1616
IE DISCRETIZATIONIE DISCRETIZATION
( ) ( , ') ( ') 'i j
ij i jV VA t r G r r f r dr dr
Matrix elements for near-neighbor basis and testing functions
Testing function
Basis function
/ 1 , Sample
1, Wall
j
i
bi
t
f
r
r
2( ) ( , ') ' ( , ') ' '
i j jij b i j jV V V
b
A i t r g r r f dr g r r f dr drk
In mixed-potential format:
Short dipole as excitation source
University of KentuckyUniversity of Kentucky 1717
HEAT TRANSFER SOLUTIONHEAT TRANSFER SOLUTION
Heat transfer equationHeat transfer equation
Heat source (EM field)Heat source (EM field)
Discretization: Controlled volume method Discretization: Controlled volume method (time explicit approach)(time explicit approach)
( )T
C k T q rt
2 31( ) ( ) , (W/m )
2q r E r
1
O ( )i
n ni i
i i
V
T TV C k T dS q r V
t
University of KentuckyUniversity of Kentucky 1818
HEAT TRANSFER SOLUTIONHEAT TRANSFER SOLUTION
The traditional control volume methodThe traditional control volume method
11/ 2
i
i ii y z
xV
T Tk T dS k
Ti Ti+1
x
Applies to rectlinear grids only!
University of KentuckyUniversity of Kentucky 1919
HEAT TRANSFER SOLUTIONHEAT TRANSFER SOLUTION
Sampling point
Part of a Control Volume
A hexahedron volume cell (arbitrarily shaped 6-sided volume unit)—easy to model objects with curved boundaries.
Temperatures are sampled at the vertices of the hexahedron
A control volume is set for each sampling point
Boundary condition: dT/dn=(Tf-T)h
University of KentuckyUniversity of Kentucky 2020
CONTROL VOLUME METHODCONTROL VOLUME METHOD(2D VIEW)(2D VIEW)
Sampling point
Control Volume (enclosed by dash lines): flow through the RED dashed boundary is calculated for each sample point
Boundary condition is used to evaluate the head flow on boundary elements
University of KentuckyUniversity of Kentucky 2121
VALIDATION OF EM CODE VALIDATION OF EM CODE FIELD IN A DIELECTRIC SPHEREFIELD IN A DIELECTRIC SPHERE
0.15m, 3.3 1 , 300MHzrR i f Parameters:
EXACT NUMERICAL
Incident Direction
University of KentuckyUniversity of Kentucky 2222
VALIDATION OF EM CODEVALIDATION OF EM CODEFIELD IN A DIELECTRIC SPHERICAL FIELD IN A DIELECTRIC SPHERICAL
SHELLSHELL
0.04m, 0.01m, 64.56 0.5 , 300MHzrR t i f
+ + + + Exact
University of KentuckyUniversity of Kentucky 2323
VALIDATION OF THERMAL VALIDATION OF THERMAL CODE:CODE: TEMPERATURE IN A CUBIC TEMPERATURE IN A CUBIC
SAMPLESAMPLE
Numerical
+ + + + Exact
y
x
z
Cube Size:6cm x 6cm x 6cm
Sample points on x-y Plane
University of KentuckyUniversity of Kentucky 2424
VALIDATION OF THERMAL VALIDATION OF THERMAL CODECODE
TEMPERATURE IN A CUBIC SAMPLETEMPERATURE IN A CUBIC SAMPLE
Numerical
+ + + + Exact
yxz
Time(s)
University of KentuckyUniversity of Kentucky 2525
VALIDATION OF THERMAL VALIDATION OF THERMAL CODECODE
TEMPERATURE IN A CIRCULAR CYLINDERTEMPERATURE IN A CIRCULAR CYLINDER
yxz
University of KentuckyUniversity of Kentucky 2626
VALIDATION OF THERMAL VALIDATION OF THERMAL CODECODE
TEMPERATURE IN A SPHERETEMPERATURE IN A SPHERE
yxz
University of KentuckyUniversity of Kentucky 2727
DIELECTRIC MODELDIELECTRIC MODEL
MEASUREMENT FOR FIXED FREQURNCY MEASUREMENT FOR FIXED FREQURNCY AND VARYING TEMPERATURESAND VARYING TEMPERATURES
INTERPOLATION USING MEASUREMENTINTERPOLATION USING MEASUREMENT
INTERPOLATION IS DONE FOR TWO INTERPOLATION IS DONE FOR TWO PHASES (BEFORE AND AFTER PHASE PHASES (BEFORE AND AFTER PHASE CHANGES)CHANGES)
University of KentuckyUniversity of Kentucky 2828
MEASUREMENT OF DIELECTRIC MEASUREMENT OF DIELECTRIC CONSTANTSCONSTANTS
2
110
r
rr kfff
22
0
1
2
11
r
kQQ
Q
fk
fkr
1
1 2
1
2
1
1
2
31
Qfk
k
k
Thermal Meter
ComputerMicrowave Network Analyser
Resonant Cavity
Liquid Nitrogen
University of KentuckyUniversity of Kentucky 2929
MEASUREMENT OF DIELECTRIC MEASUREMENT OF DIELECTRIC CONSTANTSCONSTANTS 2
110
r
rr kfff
22
0
1
2
11
r
kQQ
Q
fk
fkr
1
1 2
1
2
1
1
2
31
Qfk
k
k
Step 1: Measurement of df and dQ for a set of known samples
Step 2: Calculate coefficients: k1 and k2
Step 3: For a sample with unknown permittivity, measure df and dQ
Step 4: Calculate permittivity
Repeat steps 3 and 4 for a new sample (or the same sample at a different temperature (this process is done automatically—controlled by a program).
University of KentuckyUniversity of Kentucky 3030
DIELECTRIC PERMITTIVITY DIELECTRIC PERMITTIVITY MEASUREMENTMEASUREMENT
Negative slop: Good for stablized heating
University of KentuckyUniversity of Kentucky 3131
COMBINED SIMULATIONCOMBINED SIMULATIONSTART
OUTPUT “T” PATTERN
SOLUTION OF WAVE EQUATION: “E” FIELD
SOLUTION OF HEAT TRANSFER EQUATION: “T”
CONVERT “E” TO HEAT SOURCE UPDATE ELECTRICAL AND
THERMAL PARAMETERS
DESIRED “T” PATTERN? NO
YES
1. Try for 5 near-by frequencies:
f0-2*df,
f0-df
f0
f0+df
f0+2*df
2. Interpolate to get new f0
3. Solve for E(f0)
University of KentuckyUniversity of Kentucky 3232
COMBINED SIMULATIONCOMBINED SIMULATION(SOURCE ON VS OFF)(SOURCE ON VS OFF)
yxz
Cavity size: 0.457mx0.3225mx0.5271m
Temperature sampled at corner of a cube with size 6cmx6cmx6cm
Dipole at (-0.13,0,0)
Air temperature is 20 (degs)
24 EM updates
Each update performs 6 solutions (5 trial and 1 actual)
1min per EM solution
144 min total solution time
University of KentuckyUniversity of Kentucky 3333
COMBINED SIMULATIONCOMBINED SIMULATIONFr-TRACK COMPARISONFr-TRACK COMPARISON
yxz
Cavity size: 0.457mx0.3225mx0.5271m
Temperature sampled at corner of a cube with size 6cmx6cmx6cm
EM source is a dipole at (-0.1,0,0)
Air temperature is 20 (degs)
University of KentuckyUniversity of Kentucky 3434
COMBINED SIMULATIONCOMBINED SIMULATIONFr vs TIMEFr vs TIME
yxz
Cavity size: 0.457mx0.3225mx0.5271m
Temperature sampled at corner of a cube with size 6cmx6cmx6cm
EM source is a dipole at (-0.1,0,0)
Air temperature is 20 (degs)
Initial frequency of dipole is 428 MHz
University of KentuckyUniversity of Kentucky 3535
COMBINED SIMULATIONCOMBINED SIMULATIONINPUT POWER LEVELINPUT POWER LEVEL
yxz
Cavity size: 0.457mx0.3225mx0.5271m
Temperature sampled at corner of a cube with size 6cmx6cmx6cm
EM source is a dipole at (-0.1,0,0)
Air temperature is 20 (degs)
DIPOLE MOMENT 0.1
DIPOLE MOMENT 0.15
University of KentuckyUniversity of Kentucky 3636
SUMMARYSUMMARY Mixed surface and volume mesh provide Mixed surface and volume mesh provide
flexible modeling of cavities and samples.flexible modeling of cavities and samples. Coupled EM and heat transfer solution Coupled EM and heat transfer solution
simulates the realistic rewarming process.simulates the realistic rewarming process. Simulation results showed thatSimulation results showed that
High power level results in large T-gradientHigh power level results in large T-gradient Resonant frequency tracking increases warming rateResonant frequency tracking increases warming rate CAP concentration level leads to different warming CAP concentration level leads to different warming
performanceperformance