EE 5821 Module 2: Model

Module by: david thonglyvong

Summary: EE 5821 Module 2: Model

David Thonglyvong

#2835134

EE 5821: Biomedical Modeling and Analysis

Spring 2008

Module 2: Method and Model

Modeling to Exhibit Microwave Imaging Methods to Improve Early Signs of Breast Cancer Detection

METHOD AND MODEL

CONFOCAL MICROWAVE IMAGING (CMI)

This approach avoids complex image reconstruction algorithms by synthetically focusing reflections from the breast. As the illuminating signal is ultrawideband, this translates to simply time-shifting and summing signals. This imaging method also differs from tomographic microwave imaging in terms of the overall goal. This goal of this method is to identify the presence and general location of the significant scatterers in the breast, rather than to recover the complete dielectric properties of the breast [7].

Confocal microwave imaging focuses on backscattered signals to create images that indicate regions of significant scattering. When compared with normal tissues, the malignant tissues have larger microwave scattering cross-sections of comparable size at the frequencies of interest.

To validate experimental investigations performing CMI, theoretical analysis is done using the finite-difference time-domain (FDTD) method. The nature of the dielectric medium is incorporated in the constitutive FDTD equations using first order Debye dispersion relation [9], [10].

Geometry can be created that consists of a cylinder of dispersive dielectric nature with its axis in the z direction. In the z direction the scattered geometry is assumed to be uniform, and hence the field variations are zero. When this assumption is incorporated in the Maxwell’s curl equations, the variations of the magnetic and electric fields only exist with respect to the y and x spatial coordinate variables and with respect to the time parameter. The source excitation is a constant current source confined in the xz plane polarized in the negative z direction. So the x and y components of the electric current density do not exist. Thus the problem is treated as 2D with only electric field in the z direction and magnetic fields in the x and y directions present. The electric fields in a non magnetic medium are given by:

Hx(i,j,t+1)=Hx(i,j,t)−dtμ0dy(Ez(i,j,t)−Ez(i,j−1,t))Hx(i,j,t+1)=Hx(i,j,t)−dtμ0dy(Ez(i,j,t)−Ez(i,j−1,t)) size 12{H rSub { size 8{x} } \( i,j,t+1 \) =H rSub { size 8{x} } \( i,j,t \) - { { ital "dt"} over {μ rSub { size 8{0} } ital "dy"} } \( E rSub { size 8{z} } \( i,j,t \) - E rSub { size 8{z} } \( i,j - 1,t \) \) } {} (1)

Hy(i,j,t+1)=Hy(i,j,t)−dtμ0dx(Ez(i,j,t)−Ez(i,j−1,t))Hy(i,j,t+1)=Hy(i,j,t)−dtμ0dx(Ez(i,j,t)−Ez(i,j−1,t)) size 12{H rSub { size 8{y} } \( i,j,t+1 \) =H rSub { size 8{y} } \( i,j,t \) - { { ital "dt"} over {μ rSub { size 8{0} } ital "dx"} } \( E rSub { size 8{z} } \( i,j,t \) - E rSub { size 8{z} } \( i,j - 1,t \) \) } {} (2)

E z ( i , j , t + 1 ) = ε ∞ ε ∞ + χ 0 ( i , j ) E z ( i , j , t ) E z ( i , j , t + 1 ) = ε ∞ ε ∞ + χ 0 ( i , j ) E z ( i , j , t ) size 12{E rSub { size 8{z} } \( i,j,t+1 \) = { {ε rSub { size 8{ infinity } } } over {ε rSub { size 8{ infinity } } +χ rSub { size 8{0} } \( i,j \) } } E rSub { size 8{z} } \( i,j,t \) } {}

(3)

Where

χ0(i,j)=(εs−ε∞)(1−exp(−dt/t0))χ0(i,j)=(εs−ε∞)(1−exp(−dt/t0)) size 12{χ rSub { size 8{0} } \( i,j \) = \( ε rSub { size 8{s} } - ε rSub { size 8{ infinity } } \) \( 1 - "exp" \( - ital "dt"/t rSub { size 8{0} } \) \) } {} (4)

is the susceptibility function.

Δχm(i,j)=(εs−ε∞)(exp(−mdt/t0)(1−exp(−dt/t0))2Δχm(i,j)=(εs−ε∞)(exp(−mdt/t0)(1−exp(−dt/t0))2 size 12{Δχ rSub { size 8{m} } \( i,j \) = \( ε rSub { size 8{s} } - ε rSub { size 8{ infinity } } \) \( "exp" \( - ital "mdt"/t rSub { size 8{0} } \) \( 1 - "exp" \( - ital "dt"/t rSub { size 8{0} } \) \) rSup { size 8{2} } } {} (5)

Where εsεs size 12{ε rSub { size 8{s} } } {} is the static permittivity, ε∞ε∞ size 12{ε rSub { size 8{ infinity } } } {} is optical permittivity, and t0t0 size 12{t rSub { size 8{0} } } {} is the dielectric relaxation time.

To model a cancerous tumor in a breast we will be using a software tool called XFdtd, made by Remcom Inc. XFdtd is a full wave electromagnetic solver based on the Finite Difference Time Domain method. It is fully three-dimensional.  Applications include microwave, RF, antennas, scattering, biological EM including MRI and SAR, photonics, packaging, EMC, and electromagnetic behavior of specialized materials.  XFdtd offers many important and unique capabilities including Fast Meshing Algorithm, mesh preview before calculation, a wide variety of complex electric and magnetic materials including nonlinear and frequency-dependent, nonlinear device modeling including both diodes and capacitors, anisotropic materials, and many others.

Figure 2. FDTD Yee Cell.

Figure 3. Geometric structure formed by associating numerous Yee Cells.

A model representation of an area of a breast under CMI is designed. The size is set in to 22.5x15 cm for the frequency range of 3000 MHz. The material parameters for the tissue equivalent medium will be corn syrup and is given in Table 1. Corn syrup was used as a medium due to its low contrast when compared to that of the skin [11]. The plastic shell is defined to have an insignificant relative permittivity less than 5 and a loss tangent less than 0.05. The plastic shell thickness is defined as 2mm for a frequency of 3000 MHz. The tissue equivalent liquid shall have a minimum depth of 15 cm.

The area is to be exposed to the fields of appropriately sized transmit and receive dipoles (see Table 2) which are spaced 10 mm from the interface. The data collection and measurements are to be determined for the location directly above the feed of the dipole for a 1 W input power.

For the XFdtd simulation a 1mm cubical grid was chosen for all simulation. The plastic shell was defined as a dielectric with a relative permittivity of 3.7 and no electrical conductivity. The phantom and shell were sized to optimize calculation time and results to the best of our possibility. The dipole antenna was defined as two cylinders of the specified radius with a single FDTD cell space between them for the feed. A “tumor” model of 6 cm in diameter was inserted into the middle of the block area (see Table 3).

Table 1. Medium parameters [11].

Table 2: Dipole antenna dimensions

Table 3. “Tumor” model [11].

RESULTS AND CONCLUSION

The solid view of the XFdtd 6.0 geometry is shown in Figure 4 while Figure 5 shows the actual mesh used in the calculation. The applied excitation was a voltage source with a sinusoidal input. All calculations were run for 16 full-amplitude cycles of the sine wave. Further procedures were done in order to collect and analyze the scattered signals. The results which depict dielectric properties obtained from the scattered waveforms are displayed in Figures 6, 7, and 8.

Figure 4. Solid view of breast area geometry.

Figure 5. View of mesh area used in calculations.

Figure 6. View of dielectric response at 300 MHz.

Figure 7. View of dielectric response at 1500 MHz.

Figure 8. View of dielectric response at 3000 MHz.

The results from the software succeeds in showing how the Confocal Microwave Imaging method can be used to illustrate the detection of the differences in dielectric properties of normal breast tissues and cancerous breast tissues. Further advancement in technology and numerical methods will hopefully allow microwave imaging methods to surpass the traditional method of mammography.

REFERENCES

[1]W. T. Joines, Y. Zhang, C. LLi, and R. L. Jirtel, “The measured electrical properties of normal andmalignant human tissues from 50 to 900 mhz,” Med. Phys., vol. 21, pp. 547-550, Apr. 1994.

[2] A. J. Surowiec, S. S. Stuchly, J. R. Barr, and A. Swarup, “Dielectric properties of breast carcinoma and the surrounding tissues,” IEEE Trans. Biomed. Eng., vol. 35, no. 4, pp. 257-263, Apr. 1988.

[3] A. Swarup, S. S. Stuchly, and A. J. Surowiec, “Eielectric properties of mouse MCA1 fibrosarcoma at different stages of development,” Bioelectromagnetics, vol. 12, no. 1, pp. 1-8, 1991.

[4]S. S. Chaudhary, R. K. Mishra, A. Swarup, and J. M. Thomas, “Dielectric properties of normal and malignant human breast tissues at radiowave and microwave frequencies,” Indian J.f Biochem. Biophys., vol. 21, pp. 76-79, Feb. 1984.

[5]C. Gabriel, R. W. Lau, and S. Gabriel, “The dielectric properties of biological tissues: II. Measured in the frequency range 10 Hz to 20 GHz,” Phys. Med. Biol., vol. 41, pp. 2251-2269, Nov. 1996.

[6] E. C. Fear, S. C. Hagness, P. M. Meaney, M. Okoniewski, and M. A. Stuchly, “Enhancing breast tumor detection with near-field imaging,” IEEE Microwave Magazine, vol. 3, no.1, pp.48-56, Mar. 2002.

[7]S. C. Hagness, A. Taflove, and J. E. Bridges, “Two-dimensional FDTD analysis of a pulsed microwave confocal system for breast cancer detection: Fixed focus and antenna-array sensors,” IEEE. Trans. Biomed. Eng., vol. 45, pp. 1470-1479, Dec. 1998.

[8]----, “Three-dimensional FDTD analysis of a pulsed microwave confocal system for breast cancer detection: Design of an antenna array element,” IEEE. Trans. Antennas Propagat., vol. 47, pp. 783-791, May 1999.

[9]Kosmas, P., C. M. Rappaport, and E. Bishop, “Modeling with the FDTD method for microwave breast cancer detection,” IEEE Transactions on Microwave Theory and Techniques, vol. 52, pp. 1890–1897, 2004.

[10] Luebbers, R., F. P. Hunsberger, K. S. Kunz, R. B. Standler, and M. Schneider, “A frequency dependent finite-difference time domain formulation for dispersive materials,” IEEE Transactions on Electromagnetic Compatibility, vol. 32, pp. 222–227, 1990.

[11] B. Bindu, A. Lonappan, V. Thomas, C. K. Aanandan, and K. T. Mathew, “Active Microwave Imaging for Breast Cancer Detection,” Progress In Electromagnetics Research, PIER, vol. 58, pp. 149-169, 2006.

[12] http://remcom.com Images courtesy of Remcom XFdtd Tool.

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Last edited by david thonglyvong on May 15, 2008 5:33 pm GMT-5.