Simulation of Electromagnetic Heating of Cryopreserved SAMPLES C. C. Lu Department of Electrical and Computer Engineering University of Kentucky Lexington, KY 40506

University of Kentucky2 OUTLINE INTRODUCTION INTRODUCTION FORMULATION OF EM AND HEAT TRANSFER ANALYSIS FORMULATION OF EM AND HEAT TRANSFER ANALYSIS IMPLEMENTATION IMPLEMENTATION SIMULATION RESULTS SIMULATION RESULTS SUMMARY SUMMARY

University of Kentucky3 INTRODUCTION (1) CRYOPRESERVATION STEPS SAMPLE PROCESS (CPA FILLING) SAMPLE PROCESS (CPA FILLING) COOL SAMPLE TO LOW TEMPERATURE COOL SAMPLE TO LOW TEMPERATURE PRESERVE SAMPLE IN LOW TEMPERATURE STATUS PRESERVE SAMPLE IN LOW TEMPERATURE STATUS WORM THE SAMPLE TO ROOM TEMPERATURE (REWARMING WORM THE SAMPLE TO ROOM TEMPERATURE (REWARMING POSTPROCESSING POSTPROCESSING

University of Kentucky4 INTRODUCTION (2) SYSTEM CONFIGURATION Microwave Source Cavity Sample Liquid Nitrogen Temperature monitor

University of Kentucky5 INTRODUCTION (2) Rewarming requirements for minimum tissue damage Rewarming requirements for minimum tissue damage Small temperature gradient: uniform Small temperature gradient: uniform High warming rate: rapid High warming rate: rapid Using microwave for rewarming: Using microwave for rewarming: Volumetric heating: EM energy is delivered to every point in a sample Volumetric heating: EM energy is delivered to every point in a sample Rapid warming is realized by very high E-field intensity in a resonant cavity Rapid warming is realized by very high E-field intensity in a resonant cavity

University of Kentucky6 INTRODUCTION (3) Difficulties Difficulties Thermal runaway (hot spot absorbs more power and gets even hotter) Thermal runaway (hot spot absorbs more power and gets even hotter) Conflicting controls: uniformity requires low frequency fields (deeper penetration), rapid heating requires high frequency field Conflicting controls: uniformity requires low frequency fields (deeper penetration), rapid heating requires high frequency field Solutions Solutions Trade-off in selection of resonant frequency Trade-off in selection of resonant frequency Control of field pattern Control of field pattern Selection of right cryoprotectant agent (CPA) Selection of right cryoprotectant agent (CPA)

University of Kentucky7 Methods to study microwave rewarming for cryopreservation  Experimental studies Realistic modeling Realistic modeling Validation of theory and numerical codes Validation of theory and numerical codes  Numerical studies Ideal configuration Ideal configuration High accuracy High accuracy Easy to search optimum warming conditions Easy to search optimum warming conditions Results used as guidelines for system design Results used as guidelines for system design

University of Kentucky8 IMPORTANT FACTORS AFFACTING REWARMING PROCESS  Microwave frequency  Cavity shape  Complex permittivity of CPA and its temperature dependency  Size and Shape of sample under test

University of Kentucky9 OPTIMIZATION OF REWARMING PROCESS GIVEN: Maximum allowed temperature gradient SEARCH: Control parameters to realize maximum warming rate METHOD: Numerical solution of the EM equations and the heat transfer equation

University of Kentucky10 MAXWELL’S EQUATION SOLVER HEAT TRANSFER EQUATION SOLVER Heat Source EM Source SIMULATION DIAGRAM

University of Kentucky11 PREVIOUS WORKS Separate EM and heat transfer solution Separate EM and heat transfer solution FEM for heat transfer and approximate EM solution (D. Chen and Singh, 1992) FEM for heat transfer and approximate EM solution (D. Chen and Singh, 1992) Heating pattern analysis using spheres (X. Bai and D. Pegg, 1992) Heating pattern analysis using spheres (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 Kentucky12 EM SOLUTION METHODS FDTD, FEM, MOM can all be applied for the simulation FDTD, FEM, MOM can all be applied for the simulation FDTD: Time consuming for resonant frequency search, and long iteration for CW source FDTD: Time consuming for resonant frequency search, and long iteration for CW source FEM: Difficult for mesh generating, slow convergence FEM: Difficult for mesh generating, slow convergence MOM: Efficient and accurate (sample size is normally electrically small). Easy for mesh generation. MOM: Efficient and accurate (sample size is normally electrically small). Easy for mesh generation.

University of Kentucky13 PRESENT WORK Combined EM and heat transfer solution. Combined EM and heat transfer solution. Hexahedron grid and Roof-top basis function for EM solution Hexahedron grid and Roof-top basis function for EM solution Hexahedron grid and control volume for heat transfer solution Hexahedron grid and control volume for heat transfer solution Temperature varying electrical and thermal parameters for samples. Temperature varying electrical and thermal parameters for samples.

University of Kentucky14 THE INTEGRAL EQUATIONS (EM)

University of Kentucky15 MODEL REPRESENTATION Hexahedron cells (quadrangle faces) Hexahedron cells (quadrangle faces) Well connected mesh Well connected mesh Using rectilinear hexahedrons, it is possible to accurately model any arbitrarily shaped solid dielectrics.

University of Kentucky16 IE DISCRETIZATION Matrix elements for near-neighbor basis and testing functions In mixed-potential format: Short dipole as excitation source

University of Kentucky17 HEAT TRANSFER SOLUTION Heat transfer equation Heat transfer equation Heat source (EM field) Heat source (EM field) Discretization: Controlled volume method (time explicit approach) Discretization: Controlled volume method (time explicit approach)

University of Kentucky18 HEAT TRANSFER SOLUTION The traditional control volume method The traditional control volume method TiTi T i+1 Applies to rectlinear grids only!

University of Kentucky19 HEAT 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 Kentucky20 CONTROL VOLUME METHOD (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 Kentucky21 VALIDATION OF EM CODE FIELD IN A DIELECTRIC SPHERE Parameters: EXACTNUMERICAL Incident Direction

University of Kentucky22 VALIDATION OF EM CODE FIELD IN A DIELECTRIC SPHERICAL SHELL Exact

University of Kentucky23 VALIDATION OF THERMAL CODE: TEMPERATURE IN A CUBIC SAMPLE Numerical Exact y x z Cube Size: 6cm x 6cm x 6cm Sample points on x-y Plane

University of Kentucky24 VALIDATION OF THERMAL CODE TEMPERATURE IN A CUBIC SAMPLE Numerical Exact yx z Time(s)

University of Kentucky25 VALIDATION OF THERMAL CODE TEMPERATURE IN A CIRCULAR CYLINDER yx z

University of Kentucky26 VALIDATION OF THERMAL CODE TEMPERATURE IN A SPHERE yx z

University of Kentucky27 DIELECTRIC MODEL MEASUREMENT FOR FIXED FREQURNCY AND VARYING TEMPERATURES MEASUREMENT FOR FIXED FREQURNCY AND VARYING TEMPERATURES INTERPOLATION USING MEASUREMENT INTERPOLATION USING MEASUREMENT INTERPOLATION IS DONE FOR TWO PHASES (BEFORE AND AFTER PHASE CHANGES) INTERPOLATION IS DONE FOR TWO PHASES (BEFORE AND AFTER PHASE CHANGES)

University of Kentucky28 MEASUREMENT OF DIELECTRIC CONSTANTS Thermal Meter Computer Microwave Network Analyser Resonant Cavity Liquid Nitrogen

University of Kentucky29 MEASUREMENT OF DIELECTRIC CONSTANTS 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 Kentucky30 DIELECTRIC PERMITTIVITY MEASUREMENT Negative slop: Good for stablized heating

University of Kentucky31 COMBINED SIMULATION 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 Kentucky32 COMBINED SIMULATION (SOURCE ON VS OFF) yx z 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 Kentucky33 COMBINED SIMULATION Fr-TRACK COMPARISON yx z 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 Kentucky34 COMBINED SIMULATION Fr vs TIME yx z Cavity size: 0.457mx0.3225mx m 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 Kentucky35 COMBINED SIMULATION INPUT POWER LEVEL yx z 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 Kentucky36 SUMMARY Mixed surface and volume mesh provide flexible modeling of cavities and samples. Mixed surface and volume mesh provide flexible modeling of cavities and samples. Coupled EM and heat transfer solution simulates the realistic rewarming process. Coupled EM and heat transfer solution simulates the realistic rewarming process. Simulation results showed that Simulation results showed that High power level results in large T-gradient High power level results in large T-gradient Resonant frequency tracking increases warming rate Resonant frequency tracking increases warming rate CAP concentration level leads to different warming performance CAP concentration level leads to different warming performance