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Bio-Electromagnetic Modeling: Challenges and Observations MILICA POPOVIĆ D E P A RT M E N T O F E L E C T R I C A L A N D C O M P U T E R E N G I N E E R I N G MCGILL UNIVERSITY M ONTRÉAL, CA NADA McGill University James McGill (1744 – 1813) 2 • McGill’s first structure, the Arts Building was completed in 1843 and still serves as the focal point of the downtown campus. Redpath Museum, commissioned in 1880 and opened in 1882, is the oldest building built specifically as a museum in North America. Its natural history collections boast material collected by the same individuals who founded the collections of the Royal Ontario Museum and the Smithsonian. Research Support 3 McGill University Natural Sciences and Engineering Research Council of Canada – NSERC Le Fonds Québécois de la recherche sur la nature et les technologies Research Group 4 Houssam Kanj, PhD (June 2008) Amir Hajiaboli, PhD (June 2009) Guangran Zhu (Kevin), PhD candidate Emily Porter, M. Eng program Zahra Al-Roubaie, M.Eng. (October 2008) Yi Zhang, M.Eng. (October 2007) Negar Tavassolian, M. Eng. (October 2006) Chun Yiu Chu, M. Eng. (October 2005) Lawrence Duong, M. Eng. (October 2005) Nicholas Yak, M. Eng. (October 2005) Qingsheng Han (Ted), M. Eng. (October 2004) Outline 5 Motivation Methods Challenges Results Detecting breast cancer with microwaves 6 • In the microwave frequency range, tumors have a higher water content than the surrounding fatty tissue. tumors are “visible” to microwaves • The losses of microwave propagation in the fatty tissue are low (< 4dB/cm). low-power microwave signal can penetrate through the fatty tissue without diminishing too quickly Tumor vs. breast tissue: electrical properties in the microwave range 7 • Older data Parameters at 6GHz Fat Tumor Relative permittivity εr Electric conductivity σ (S/m) 9 0.4 50 7 • Recent data: [Lazebnik et al, 2007, Physics in Medicine and Biology] : Contrast still exists, but is much lower. (~10%) Microwave-tissue interaction 8 Tumor causes microwave scatter Tumor absorbs microwave energy Techniques: Microwave tomography Radar-like pulse imaging (backscatter) Microwave-induced thermo-acoustic Acoustic source, detecting Doppler shift with microwaves Challenges in antenna design 9 Signal: pulse centered around 6 GHz Antenna transmits and receives all key Fourier components of the microwave-centered pulse broadband operation Simple to manufacture Cost-effective Small in size Antenna design I 10 • • • a = c = 5mm d = 35mm Rs varied between 50 & 800 /□ Antenna design II 11 • Compact: 34.25mm × 20mm × 1.3mm • Thin film resistive loading is used (standard values) • Repeatable • Accurate • Design was optimized for: • Return loss • Efficiency • Fidelity Antenna design III 12 • TWTLTLA = • • Traveling Wave Tapered & Loaded Transmission Line Antenna Merge the guiding structure with the radiating element to form a single transitional structure Use resistive loading to achieve traveling wave characteristics Antenna design - final 13 Uniplanar and very compact: 14mm × 17.5mm Low profile Microstrip Antipodal Tapered GND Ultra Broadband Easy transition to co-ax Antenna design - final 14 Computational challenges: example 15 Finite-difference time-domain (SEMCAD-X) simulations Realistic, MRI – based, detailed numerical models huge FDTD mesh computational cost Computational challenges: example 16 • • • To decrease the problem size: we use the regression tree analysis method (with the user-defined penalty factor) we cluster the voxels of similar property into bigger brick-like solids result: manageable computational problem with sufficient representation of anatomical complexity Computational challenges: example 17 Electrical permittivity distribution, 6 GHz Direct, manual mapping from MRI voxels Simplified model through regression tree algorithm Computational challenges: example 18 Electrical conductivity distribution [S/m], 6 GHz Direct, manual mapping from MRI voxels Simplified model through regression tree algorithm Computational challenges: example 19 The difference in the fields computed near the antennas for the finer and the brick-approximated model was very, very small! Microwave-induced thermo-acoustic 20 2-D model of the central MRI-derived horizontal slice Microwave-induced thermo-acoustics 21 Faraday’s Law Simple force Equation H 1 E t Ampere’s Law u 1 p t o Continuity of Mass E 1 ( H J E ) t p K ( u SAR ap) t c 2-D Quantities : duality Ex p Hy Hz uz u y 1/ K a Jx SAR Microwave-induced thermo-acoustics 22 Challenge: multi-physics modeling The time constants of the microwave, thermal and acoustic processes are very different Acoustic properties of tissue (literature) – not very recent If we want to build a phantom model for experimental verification, challenge is to find materials that can mimic the tissues both in the electrical and in the acoustic sense, simultaneously Small break, one of my favorite quotes: 23 I keep six honest serving-men (They taught me all I knew); Their names are What and Why and When And How and Where and Who. Rudyard Kipling The Elephant's Child (1902) Indian-born British author (1865 - 1936) Human Eye and the Retina 24 http://thefutureofthings.com/articles/57/shedding-light-on-blindness.html Retina 25 Does the morphology of the photoreceptor outer-segment affect its optical filtering properties? Does the geometry of a photoreceptor help discriminate between different wavelengths? From: Neurobiology: Bright blue times, Russell G. Foster. Nature February 2005 Retinal rods and cones 26 Magnified image of the rods and cones of the human eye. © Omikron. Reproduced by permission of Photo Researchers, Inc. www.faqs.org/health/Sick-V1/Color-Blindness.html Rods and cones: tri-chromatic color vision 27 Spectral sensitivities of the three cone types and the rod. The tri-chromatic color vision theory was first introduced by Young in 1802. Retinal rods 28 Photoreceptor biochemistry: Hyperpolarization by rhodopsin decomposition Retinal rods and cones: outer-segment 29 Alan Fein and Ete Z. Szuts , Photoreceptor: Their Role in Vision, Cambridge Univ. Press 1982 Cone: outer-segment FDTD model (I) 30 L=6.75µm outer-segment length The disks’ radius decreases along the central axis of the photoreceptor τ1=τ2=15 nm D1=4.1µm D2= variable Cone: outer-segment FDTD model (II) 31 εr-cytoplasm=1.85 εr-membrane=2.01 εr-intercellular=1.79 membrane = 37.38 S/m Challenges: • Reliable electrical property values • Our plans: to include dispersion in future work Cone FDTD model: computational challenge 32 Cell size Δx=5 nm Δy=Δz= 30nm Time step Δt=1.46×10-2 fs Boundary condition 10 layers Uniaxial perfectly matched layer Total FDTD space 1500×200×200= 60 Mcells FDTD computation accelerated with a GPU which is optimized for parallelizing and memory bandwidth. Cone FDTD model: light excitation 33 E y Ae ( t-t0 ) 2 2σ 2 sin ( 2πf(t t 0 )) Type Gaussian modulated Polarization Y-polarized Modulation frequency f=622THz Time delay t0=400Δt Amplitude A=0.2V/m Mean variation σ=100 Δt |Ey| in the outer-segment t=21.9fs, 43.8fs, 87.6fs, 131.1fs. 34 D2=4.1μm |Ey| in the outer-segment t=21.9fs, 43.8fs, 87.6fs, 131.1fs. 35 D2=1.2μm Energy spectrum vs. the free-space wavelength 36 The results are normalized to the maximum value of energy spectrum at D2=4.1μm. Bulk (averaged permittivity) cone model 37 Bulk (averaged permittivity) cone model 38 Cone illumination for varying angle of incidence 39 Φ=π/45 Poynting power distribution across SF Cone illumination for varying angle of indicence 40 Φ=π/12 Poynting power distribution across SF Cone illumination for varying angle of incidence 41 Φ=π/10 Poynting power distribution across SF What is the total power available to the photo - pigment molecules? 42 Laminar (folded membrane layers) vs bulk (averaged,) structure Thank you! 43 Questions? Comments? [email protected] Energy Spectrum Calculation V(x, t) D/ 2 E (x, y, z 0, t)dy y D/ 2 Induced voltage at each time step after 43.8fs along outer-segment V(x, f) F{V ( x, t )} Induced voltage versus frequency S(x) 1081THz S (v) F {S ( x)} 211THz Signal energy over 211-1081THz 2 | V ( x , f ) | df Energy spectrum versus spatial frequency University of Adelaide, Adelaide, Australia 44