Download Fast Algorithms in Simulations of

Fast Algorithms in Simulations of
Light Scattering from Biological Cells
PI: Jiming Song
Abstract
Elastic light scattering spectroscopy has the potential to significantly improve medical diagnoses by
providing a valuable, non-invasive means of differentiating normal from abnormal cells. The goal is to
develop fast algorithms in electromagnetic simulations of light scattering from biological cells. Numerical
simulations are helpful in understanding measured data and for determining the physical characteristic of
cells. The findings of this project therefore may help medical researchers to more quickly and efficiently
identify diseased cells.
Mie theory has been used to approximate tissue scattering at the cellular level by assuming that cells are
homogeneous spheres. The finite-difference time-domain method has the disadvantage of increasing
dispersion error, in addition to involving higher computational complexity for larger cells. Recently, fast
algorithms with lower complexity have been developed in computational electromagnetics. These
algorithms work well for scattering from metal objects, but are not efficient for scattering from lossy
materials such as biological cells and semiconductors.
We propose to solve the problem by using an integral equation approach that models cellular shape more
accurately. We will first develop fast algorithms for light scattering from low-contrast homogeneous cells,
then from general inhomogeneous cells with arbitrary shapes. We will investigate the current fast
multipole method for lossy media, as well as other methods such as the adaptive integral method, precorrected FFT, and fast summation.
Several important applications that might be studied by developing the proposed approach include
scattering from non-spherical particles in the atmosphere, modeling of interconnects and components on
lossy silicon, and electromagnetic non-destructive evaluation.
1
Fast Algorithms in Simulations of
Light Scattering from Biological Cells
Identification of the Problem
A number of recent studies have focused on the optical properties of tissue in the near-infrared
region and diagnostic applications where scattering is dominant over absorption. The impetus for this
work has been the successful application of imaging techniques such as optical coherence tomography
(OCT) [1] of human tissue and confocal microscopy (CM) [2]. Elastic light scattering spectroscopy can
provide a valuable, non-invasive means to quantitatively probe tissue morphology. The scattering in
tissue arises from local changes in the index of refraction between cell components and other small tissue
structures. The bulk scattering properties are measured experimentally. In order to interpret and develop
optical diagnostic techniques, it is critical to understand the relationship between the bulk scattering
properties of tissue and the local variation in the index of refraction on the cellular level.
Widely used to model light propagation in tissue, the Monte Carlo method deals exclusively with
macroscopic tissue scattering properties. Most cells are on the order of a single micron. The electric size
is several wavelengths and is in the resonant region. Rayleigh approximation cannot be used because it
applies solely to very small objects. Mie theory has been used to approximate tissue scattering at the
cellular level by assuming cells are homogeneous spheres of a single size. However, experimental
evidence suggests that the Mie theory model of a biological cell may not be appropriate. McGrann et al
[3] found that the forward scattering of lymphocytes varied inversely with cell volume, which is not
expected from a Mie theory model. Some approaches have been developed for numerical simulations of
light scattering from biological cells.
Previous Work on Numerical Simulations
A finite-difference time-domain (FDTD) method has been used to calculate light scattering from
biological cells [4-6]. The FDTD method solves Maxwell’s equations numerically in the time domain.
However, there are two disadvantages to using FDTD to solve scattering from large biological cells
(comparing the wavelength of the light). First, the dispersion error from wave propagation in the
numerical grid is cumulative and becomes larger as simulation size increases. The second disadvantage of
FDTD is its high computational complexity. It needs discretizations in a three-dimensional domain, even
when the cell is homogeneous. In addition, it requires more grid points per wavelength for larger cells,
and has difficulty modeling curved objects.
Several fast and efficient algorithms have been recently developed in computational electromagnetics to
solve integral equations derived from Maxwell’s equations [7]. The scattering by arbitrarily shaped
objects can be obtained by finding the solution of an integral equation, where the unknown function is the
induced current distribution. In the traditional approach, the integral equation is discretized into a matrix
equation by the method of moments (MOM). The matrix equation is then solved by Gaussian elimination,
which requires N3 floating-point operations to solve N linear equations, or N2 operations per iteration if
the conjugate gradient (CG) method is used. The MOM matrix is a full matrix and needs N2 elements to
be stored. Hence, traditional methods can require significant amounts of computer memory and a
substantial number of floating point operations.
In order to reduce the computational burden of the traditional approach, the three-dimensional (3D), fast
multipole method (FMM) was proposed by Coifman, Rokhlin, and Wandzura [8] and later developed by a
number of researchers to solve electromagnetic scattering problems [9-10]. The FMM speeds up the
evaluation of matrix-vector products in an iterative CG solution of the matrix equation. Furthermore, it
reduces the complexity of a matrix-vector product from N2 to N1.5. The idea of interpolation and
anterpolation [9] was later combined with the fast multipole method to create a multilevel fast multipole
2
algorithm (MLFMA). This results in an N log N algorithm for performing matrix-vector products for
surface scatterers, and a complexity N algorithm for volumetric scatterers. This is a vast improvement
over traditional methods, especially for large problems that previously required the resources of a
supercomputer but can now be solved on a workstation-size computer. Problems with as many as 10
million unknowns have been solved with the multilevel approach [11].
Current FMM and MLFMA methods work well for electromagnetic wave scattering from metal objects
(e.g. aircrafts and tanks) because the Green’s functions for propagation in free space are used and the
metallic targets are approximated as perfect electrical conductors. To apply the integral equation approach
in light scattering from biological cells, the Green’s functions for propagation in lossy media are used
taking into account the attenuation due to the absorption of lights by biological cells. Most approaches use
complex images [12] or angle-dependent reflection to approximate the Green’s functions in low loss
media. However, no results have been reported on applying fast algorithms to very lossy media such as
biological cells, radar absorbing materials, and semiconductors.
Current Work, Proposed Work, and Impact of Project
With the support of a start-up package from the Department of Electrical and Computer Engineering, the
PI and one of his graduate students have worked on developing formulations in electromagnetic
simulations of light scattering from biological cells. We have obtained some well-conditioned equations.
We need to study these equations, implement them for light scattering from biological cells, and then
develop and apply fast and efficient algorithms in numerical simulations.
We propose to solve light scattering from biological cells using an integral equation approach, which
more accurately models the physical shape of cells. The total electric field distributions inside the cells
are treated as unknowns. The equivalent electric currents are derived from the difference between the
cells and the background in the index of the refraction. The scattered fields can be calculated from the
electric currents using the Green’s functions related to the background materials. Therefore an integral
equation can be derived. The PI’s previous work was electromagnetic simulations of scattering from
metal targets like aircrafts and tanks, which used Green’s functions for propagation in free space. The
proposed work on scattering of light from biological cells will use the Green’s function for propagation in
the biological cells, which, in most cases, are lossy.
The development of fast algorithms will enable researchers to study several other important applications,
including light scattering from biological cells and non-spherical particles in the atmosphere,
electromagnetic scattering from penetrable objects, electromagnetic modeling of interconnects and
components on lossy silicon, electromagnetic non-destructive evaluation (NDE), and analysis of antennas.
Approaches and Research Plan
We propose the following approaches to solve the integral equation derived for light scattering from
biological cells.
Phase 1: Develop fast and efficient algorithms for scattering from low contrast cells. Most cells are
measured immersed in liquids like the blood plasma. The relative index of refraction is very close to 1.
The real part of the index is 1.0385 and the imaginary part (loss) is 10-5 [6]. We propose to develop fast
and efficient algorithms to take advantage of this low contrast. We will derive special equations using
higher order approximations and transfer the volume integral to the form such that fast and efficient
algorithms such FMM can be used.
Phase 2: Develop fast and efficient algorithms for scattering from homogeneous cells: If the
biological cells are homogeneous, the volume integral equation can be replaced by a surface integral
equation using equivalence principle. The resulting surface integral equation can be solved using FMM
and MLFMA, which is more efficient than solving the volume integral integration. Only the tangent
components of both electric and magnetic fields need to be modeled as unknowns, making the number of
3
unknowns proportional to the surface area. The number of unknowns in FDTD is proportional to the
volume. With this approach, we can quickly and efficiently solve homogeneous cells with arbitrary
shapes.
Phase 3: Develop fast and efficient algorithms scattering from inhomogeneous cells: The volume
integral equation is discretized to linear equations using the method of moments. The matrix is a full
matrix, which is too expensive to store and solve it using a direct solver. We will solve the matrix
equations using iterative solvers without generating the whole matrix. We will investigate the current fast
multipole method (FMM) for the Green’s functions in background media. Other fast and efficient
methods such as adaptive integral method (AIM), pre-corrected FFT, and fast summation will be
evaluated. In the long term, we will develop new fast and efficient algorithms.
Comparison with Other Approaches and Novelty of Proposed Approach
We are proposing a new approach to solving integral equations for scattering from biological cells. Most
cells are on the order of a micron. Their electric size is several wavelengths and in the resonant region.
Rayleigh approximation cannot be used because it applies exclusively to very small objects. Most tools
have used a Mie theory model, which is limited to modeling cells as homogeneous spheres. Finitedifference time-domain (FDTD) has been used in few groups for light scattering from biological cells, but
it has disadvantages of geometry modeling, dispersion error, and high complexity for larger cells. We also
propose to develop fast and efficient algorithms to accelerate the solutions of the integral equations.
Bibliography:
[1] J. Izatt, M. Hee, D. Huang, A. Swanson, C. Lin, J. Schuman, C. Puliafito, and J. Fujimoto, “Micron-resolution
biomedical imaging with optical coherence tomography,” Opt. Photonics News, vol. 4, pp. 14-19, 1993.
[2] M. Rajadhyaksha, M. Grossman, D. Esterwitz, R. Webb, and R. Anderson, “In vivo confocal scanning laser
microscope of human skin: melanin provides strong contrast,” J. Invest. Dermatol., vol. 104, pp.946-952, 1995.
[3] L. McGann, M. Walterson, and L. Hogg, “Light scattering and cell volumes in osmotically stressed and frozen
thawed cells,” Cytometry, vol. 9, pp. 33-38, 1998.
[4] A. Dunn, C. Smithpeter, A.J. Welch, and R. Richards-Kortum, “Finite-difference time-domain simulation of
light scattering from single cells,” J. Biomed. Optics, vol. 2, no. 3, pp.262-266, July 1997.
[5] R. Drezek, A. Dunn, and R. Richards-Kortum, “A pulsed finite-difference time-domain (FDTD) method for
calculating light scattering from biological cells over broad wavelength ranges,” Optics Express, vol. 6, no.7,
pp.147-157, March 2000.
[6] J.Q. Lu, P. Yang, X.-H. Hu, “Accurate Simulation of Light Scattering by a Red Blood Cell using the FDTD
Method”, CLEO 2002, paper CThO65, 2002.
[7] Fast and Efficient Algorithms in Computational Electromagnetics, edited by Chew, Jin, Michielssen, and Song,
Artech House, 2001.
[8] R. Coifman, V. Rokhlin, and S. Wandzura, “The fast multipole method for the wave equation: A pedestrian
prescription,” IEEE Anta. Propag. Mag., vol. 35, pp.7-12, June 1993.
[9] J. M. Song, C.-C. Lu, and W. C. Chew, “MLFMA for electromagnetic scattering by large complex objects,”
IEEE Trans. Ant. Propag., vol. 45, no. 10, pp.1488-1493, October 1997.
[10] J. M. Song, C. C. Lu, W. C. Chew, and S. W. Lee, “Fast Illinois solver code (FISC),” IEEE Ant. Propag. Mag.,
(invited), vol. 40, no. 3, pp.27-34, June 1998.
[11] S. Velamparambil, W.C. Chew, and J.M. Song, “10 million unknowns, is it that large,” IEEE Antennas and
Propagation Magazine, vol.45, no.2, pp.43-58, April 2003.
[12] F. Ling, J.M. Song, and J.M. Jin, “Multilevel fast multipole algorithm for analysis of large-scale microstrip
structures,’’ Microwave and Guided Wave Letters, vol. 9, no. 12, pp. 508-510, December, 1999.
4
Research Personnel
The PI and his graduate students will conduct the proposed research. The PI has extensive research
experience in the areas of fast algorithms in computational electromagnetics, as well as forward and
inverse scattering. One of few experts in fast and efficient algorithms in computational electromagnetics,
he spent several years at the Center for Computational Electromagnetics at the University of Illinois at
Urbana-Champaign. There he developed an industrial-strength code—the Fast Illinois Solver Code
(FISC)—which has been distributed to over 400 government and industrial users.
PI’s Long Term Research Plan
Drawing on his success in developing fast algorithms in computational electromagnetics and modeling,
the PI’s long-term research plan is to develop fast and efficient algorithms for electromagnetic modeling
and simulations of light scattering from biological cells. Similar approaches will be applied in other areas,
such as light scattering by non-spherical particles in climatology, electromagnetic nondestructive
evaluation (NDE), and electromagnetic modeling and simulations of interconnects and RF (radio
frequency) components over lossy silicon.
Past SPRIG Funding
None.
Subsequent Funding or Opportunities
The development and interpretation of optical diagnostic techniques is contingent on understanding the
relationship between the bulk scattering properties of tissues and the local variation in the index of
refraction on the cellular level. Fast and efficient simulations of light scattering from biological cells are
needed to achieve this understanding. If this project is funded with a Special Research Initiation Grant,
the PI will use his preliminary results to solicit additional research funds from NIH, NSF, etc. Future
work will be collaborative. Likely partners include Xin-Hua Hu, a physics professor at East Carolina
University, Greenville, North Carolina. Professor Hu is an expert in the area of measuring light scattering
from biological cells. When the PI presented an invited talk on the East Carolina campus, he discussed
collaborations with Professor Hu. The PI will also seek research collaborations on electrical properties of
cells with faculty in the Department of Biomedical Science at Iowa State’s College of Veterinary
Medicine. This approach also can be used in other areas, such as light scattering by non-spherical
particles in climatology and electromagnetic nondestructive evaluation (NDE). The PI and a colleague
from CNDE (Center for NDE) are writing proposal to DARPA to investigate fast and efficient
electromagnetic simulation for NDE applications.
5
Budget Details
Equipment
Hourly Labor/Undergrad RA
Supplies
Graduate Assistantship Support
Services
Travel Essential to Research
$
15,000
1,000
Amount Requested from Special Research Initiation Grants: $16,000
Graduate Assistantship Support: 11-month research assistantship for one graduate student.
Travel Essential to Research: one or two trips to visit the group in East Carolina University to discuss
measuring light scattering from biological cells, to evaluate research results, and to work on writing
papers and proposals.
6
Jiming Song
Department of Electrical and Computer Engineering
Iowa State University
Tel: (515) 294-8396
2215 Coover Hall
[email protected]
Ames, Iowa 50011-3060
www.eng.iastate.edu/~jisong
Jiming Song received the B.S. and M.S. degrees, both in physics, from Nanjing University, China, in
1983 and 1988, respectively. He earned his Ph.D. degree in electrical engineering from Michigan State
University in 1993.
From 1993 to 2000, Dr. Song worked as a postdoctoral research associate, research scientist, senior
research scientist, and visiting assistant professor at the University of Illinois at Urbana-Champaign. From
1996 to 2000, he also worked as a part-time research scientist at SAIC-DEMACO. Dr. Song was the
principal author of the Fast Illinois Solver Code (FISC), which has been distributed to more than 400
government and industrial users. From 2000 to 2002, he was a principal staff engineer/scientist at Digital
DNA Research Lab. of Semiconductor Products Sector of Motorola in Tempe, Arizona, and was working
on modeling and simulations of interconnects and RF components. He is currently an assistant professor
at Iowa State University. His research has dealt with modeling and simulations of interconnects on lossy
silicon and RF components, wave scattering using fast algorithms, wave interaction with inhomogeneous
media, and transient electromagnetic field.
Dr. Song has co-edited one book and co-authored six book chapters, 31 journal papers, and 85 conference
papers. He was the recipient of the Outstanding Academic Award from Michigan State University in 1992.
Dr. Song is a senior member of IEEE.
WORK EXPERIENCE:
IOWA STATE UNIVERSITY, Ames, IA
Assistant Professor (Aug. 2002 until present)
SEMICONDUCTOR PRODUCTS SECTOR of MOTOROLA, INC., Tempe, AZ
Principal Staff Engineer/Scientist (Aug. 2000 to Aug. 2002)
UNIVERSITY OF ILLINOIS, Urbana-Champaign, IL
Senior Research Scientist (Feb. 2000 to Aug. 2000).
Visiting Assistant Professor (Feb. 1998 to Aug. 2000).
Research Scientist (Oct. 1995 to Feb. 2000).
Postdoctoral Research Associate (Oct. 1993 to Sept. 1995).
SAIC-DEMACO, Champaign, IL
Research Scientist (May 1996 to July 2000, part time)
MICHIGAN STATE UNIVERSITY, East Lansing, MI
Postdoctoral Research Associate (May 1993 to Sept. 1993).
Graduate Research Associate (Sept. 1990 to May 1993).
NANJING UNIVERSITY, Nanjing, China
Graduate Research Associate (Sept. 1985 to July 1988).
BEIJING BROADCASTING COLLEGE, Beijing, China
Instructor (Sept. 1983 to July 1985).
7
EDUCATION:
Ph.D. in Electrical Engineering (Sept. 1989 to May 1993), Michigan State University, East Lansing, MI.
MS in Physics (Sept. 1985 to July 1988), Nanjing University, Nanjing, China.
BS in Physics (Sept. 1979 to July 1983), Nanjing University, Nanjing, China.
ACADEMIC HONORS:
Outstanding Academic Award, The College of Engineering, Michigan State University, 1992.
K. C. Wong Fellowship, K. C. Wong Education Foundation Ltd., Hong Kong, 1989-1992.
JOURNALS & PROPOSALS REVIEWED:
Electronics Letters, IEEE-AP, IEEE AP Magazine, IEEE CAD/ICAS, IEEE-CSE, IEEE-EC, IEEE-GRS, IEEEMTT, JEWA, J. of Physics, MOTL, Radio Science, JOSA.
CHAIRMAN AND ASSOCIATE EDITORSHIP:
Session chairman for IEEE-APS Conference, Applied Computational Electromagnetics Conferences.
KEY PUBLICATIONS IN RELATED TOPICS:
J.M. Song, C.-C. Lu, and W.C. Chew, “MLFMA for electromagnetic scattering by large complex objects,” IEEE
Transactions on Antennas and Propagation , vol. 45, no. 10, pp. 1488-1493, October 1997.
J. M. Song, C. C. Lu, W. C. Chew, and S. W. Lee, “Fast Illinois solver code (FISC),” IEEE Antennas and
Propagation Magazine, (invited), vol. 40, no. 3, pp. 27-34, June 1998.
J.M. Song and W.C. Chew, “Large Scale Computing with the Fast Illinois Solver Code-Requirements Scaling
Properties,” IEEE Computational Science and Engineering, vol. 5, no. 3, pp.19-23, July-Sept. 1998.
J.L. Ma, W.C. Chew, C.C. Lu, and J.M. Song, “Image reconstruction from TE scattering data using strong
permittivity theory,” IEEE Transactions on Antennas and Propagation, vol. 48, no. 6, pp.860-867, June 2000.
Fast and Efficient Algorithms in Computational Electromagnetics, edited by Chew, Jin, Michielssen, and Song,
Artech House, 2001.
S. Velamparambil, W.C. Chew, and J.M. Song, “10 million unknowns, is it that large,” IEEE Antennas and
Propagation Magazine, vol.45, no.2, pp.43-58, April 2003.
CURRENT AND PENDING RESEARCH SUPPORT
Start-up package from the Department of Electrical and Computer Engineering, Iowa State University.
$150,000, from August 2002 to May 2005.
Pending Proposal to Air Force Research Lab. through SAIC
“Multi-Sensor Phenomenology Modeling,” $227,000, from January 2004 to December 2006.
8