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Simulation of Electromagnetic Heating of Cryopreserved SAMPLES

Simulation of Electromagnetic Heating of Cryopreserved SAMPLES. C. C. Lu Department of Electrical and Computer Engineering University of Kentucky Lexington, KY 40506. OUTLINE. INTRODUCTION FORMULATION OF EM AND HEAT TRANSFER ANALYSIS IMPLEMENTATION SIMULATION RESULTS SUMMARY.

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Simulation of Electromagnetic Heating of Cryopreserved SAMPLES

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

  2. OUTLINE • INTRODUCTION • FORMULATION OF EM AND HEAT TRANSFER ANALYSIS • IMPLEMENTATION • SIMULATION RESULTS • SUMMARY University of Kentucky

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

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

  5. INTRODUCTION (2) • Rewarming requirements for minimum tissue damage • Small temperature gradient: uniform • High warming rate: rapid • Using microwave for rewarming: • 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 University of Kentucky

  6. INTRODUCTION (3) • Difficulties • 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 • Solutions • Trade-off in selection of resonant frequency • Control of field pattern • Selection of right cryoprotectant agent (CPA) University of Kentucky

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

  8. 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 Kentucky

  9. 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 Kentucky

  10. MAXWELL’S EQUATION SOLVER EM Source HEAT TRANSFER EQUATION SOLVER Heat Source SIMULATION DIAGRAM University of Kentucky

  11. PREVIOUS WORKS • Separate EM and heat transfer solution • FEM for heat transfer and approximate EM solution (D. Chen and Singh, 1992) • Heating pattern analysis using spheres (X. Bai and D. Pegg, 1992) • Combined analysis: • FDTD: Ma, et al (1995), • Torres and Jacko (1997) • X. Han (2004) University of Kentucky

  12. EM SOLUTION METHODS • FDTD, FEM, MOM can all be applied for the simulation • FDTD: Time consuming for resonant frequency search, and long iteration for CW source • FEM: Difficult for mesh generating, slow convergence • MOM: Efficient and accurate (sample size is normally electrically small). Easy for mesh generation. University of Kentucky

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

  14. THE INTEGRAL EQUATIONS (EM) University of Kentucky

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

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

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

  18. HEAT TRANSFER SOLUTION • The traditional control volume method Applies to rectlinear grids only! Ti+1 Ti University of Kentucky

  19. HEAT TRANSFER SOLUTION 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 Sampling point University of Kentucky

  20. CONTROL VOLUME METHOD(2D VIEW) 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 Sampling point University of Kentucky

  21. VALIDATION OF EM CODE FIELD IN A DIELECTRIC SPHERE Parameters: EXACT NUMERICAL Incident Direction University of Kentucky

  22. VALIDATION OF EM CODEFIELD IN A DIELECTRIC SPHERICAL SHELL + + + + Exact University of Kentucky

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

  24. z y x VALIDATION OF THERMAL CODETEMPERATURE IN A CUBIC SAMPLE Time(s) Numerical University of Kentucky + + + + Exact

  25. z y x VALIDATION OF THERMAL CODETEMPERATURE IN A CIRCULAR CYLINDER University of Kentucky

  26. z y x VALIDATION OF THERMAL CODETEMPERATURE IN A SPHERE University of Kentucky

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

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

  29. 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 Kentucky

  30. DIELECTRIC PERMITTIVITY MEASUREMENT Negative slop: Good for stablized heating University of Kentucky

  31. COMBINED SIMULATION • 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 Kentucky

  32. z y x COMBINED SIMULATION(SOURCE ON VS OFF) 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 Kentucky

  33. z y x COMBINED SIMULATIONFr-TRACK COMPARISON 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 Kentucky

  34. z y x COMBINED SIMULATIONFr vs TIME 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 Kentucky

  35. z y x COMBINED SIMULATIONINPUT POWER LEVEL 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 0.15 DIPOLE MOMENT 0.1 University of Kentucky

  36. SUMMARY • Mixed surface and volume mesh provide flexible modeling of cavities and samples. • Coupled EM and heat transfer solution simulates the realistic rewarming process. • Simulation results showed that • High power level results in large T-gradient • Resonant frequency tracking increases warming rate • CAP concentration level leads to different warming performance University of Kentucky

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