BLI Profiles
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Research Interests
light/tissue interactions, Monte Carlo methods, transport and diffusion theory
Research Abstract
My research at BLI involves analyzing mathematical models of light/tissue interactions, particularly in the transport regime, and developing computational strategies for implementing them. The ongoing study of efficient Monte Carlo solutions of both direct and adjoint radiative transport equations figures prominently in this work. We have developed 1. efficient perturbation/differential Monte Carlo tools for solving many direct problems simultaneously, and estimating sensitivity coefficients, using only a single set of random walks; 2. a tool for computing and displaying rigorous (transport) tissue interrogation maps from which detailed interactions of light fields with tissue volumes can be both quantitatively and qualitatively assessed; 3. adaptive Monte Carlo algorithms whose estimates converge geometrically rather than at the much slower rate governed by the central limit theorem of probability.
Geometric Convergence for Monte
Carlo Methods Applied to Particle Transport Problems
Initially under the sponsorship of Los Alamos National Laboratory, CGU Mathematics Clinic teams and technical staff of the Claremont Research Institute of Applied Mathematical Sciences have since 1996-7 been exploring the possibility of obtaining geometric convergence in Monte Carlo algorithms by using either a method (sequential correlated sampling) suggested by Halton for matrix problems or by using newly developed biased and unbiased adaptive importance sampling algorithms. Success has been achieved with all these methods, but the exponential learning is partly offset by the computational complexity for these first generation adaptive algorithms. Since 2003 a second generation of adaptive algorithms has been developed that eliminates most of the computational shortcomings of the original methods. Very recently a third generation adaptation has been explored that would enable a preset accuracy to be achieved optimally by adjusting the spatial-directional phase space decomposition used to the dimensions required to attain maximal computational efficiency. Efforts continue at making these new techniques practical, with the current applications focused on problems in biomedical optics.
References:
- L. Li, 'Quasi-Monte Carlo Methods for Transport Equations", Ph.D. dissertation, The Claremont Graduate School, 1995.
- "Adaptive Methods for Accelerating Monte Carlo Convergence" Claremont Graduate University Mathematics Clinic interim report to Los Alamos National Laboratory, January, 1997.
- "Adaptive Methods for Accelerating Monte Carlo Convergence" Claremont Graduate University Mathematics Clinic final report to Los Alamos National Laboratory, June, 1997.
- "Adaptive Methods for Accelerating Monte Carlo Convergence" Claremont Graduate University Mathematics Clinic final report to Los Alamos National Laboratory, September, 1997..
- J. Spanier and L. Li,
"General Sequential Sampling Methods for
- L. Li and J. Spanier, "Approximation of Transport Equations by Matrix Equations and Sequential Sampling", Monte Carlo Methods and Applications, 3, (1997).
- J. Spanier, "Monte
Carlo Methods for Flux Expansion Solutions of Transport Problems",
Nu. Sci.
- Y. Lai and J. Spanier, "Adaptive importance sampling algorithms for transport problems", Monte Carlo and Quasi-Monte Carlo Methods 1998, Lecture Notes in Computational Science and Engineering, H. Niederreiter and J. Spanier, Eds. Springer-Verlag, New York, pp. 273-283, 1999.
- J. Spanier, "Geometrically convergent learning algorithms for global solutions of transport problems", Monte Carlo and Quasi-Monte Carlo Methods 1998, H. Niederreiter and J. Spanier, Eds. , Lecture Notes in Computational Science and Engineering, Springer-Verlag, New York, pp. 98-113, 1999.
- C. Hayakawa and J. Spanier, "Comparison of Monte Carlo Algorithms for Obtaining Geometric Convergence for Model Transport Problems", Monte Carlo and Quasi-Monte Carlo Methods 1998, H. Niederreiter and J. Spanier, Eds. , Lecture Notes in Computational Science and Engineering, Springer-Verlag, New York, pp. 214-226, 1999.
- R. Kong and J. Spanier, "Error Analysis of Sequential Monte Carlo Methods for Transport Problems", Monte Carlo and Quasi-Monte Carlo Methods 1998, H. Niederreiter and J. Spanier, Eds. , Lecture Notes in Computational Science and Engineering, Springer-Verlag, New York, pp. 252-272, 1999.
- R. Kong and J. Spanier, "Sequential correlated sampling algorithms for transport problems", Monte Carlo and Quasi-Monte Carlo Methods 1998, H. Niederreiter and J. Spanier, Eds. , Lecture Notes in Computational Science and Engineering, Springer-Verlag, New York, pp. 238-251, 1999.
- Kong, R. and J. Spanier, “Residual Versus Error for Transport Problems”, in Monte Carlo and QuasiMonte Carlo Methods 2000, K.T. Fand, F.J. Hickernell and H. Niederreiter (eds.), Proceedings of a conference held at Hong Kong Baptist University, Hong Kong, S.A.R., China, November 27-December 1, 2000, Springer, pp. 306-317, 2002.
- Spanier, J. and R.
Kong, “A New Adaptive Method for Geometric Convergence”,
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Radiation Transport and Diffusion in Biomedical Applications
In collaborations with researchers at the Beckman Laser Institute
and Medical Clinic at the University of California at Irvine,
a research plan has been developed that should provide for improved
models and computational support for determining the effects of
the interactions of light (produced by lasers) and tissue. This
problem arises in particular, in laser diagnostic, surgical and
treatment procedures and is studied in both clinical and experimental
settings. The plan calls for the development of advanced
Monte Carlo methods incorporated into a new computational engine,
the Virtual Tissue System (VTS) that will be capable of modeling
real tissue systems more accurately and with greater speeds than
is currently possible with conventional
References:
- J. Spanier and E.H.
Maize, "Quasirandom Methods for Estimating Integrals Using
Relatively Small Samples,"
- Bruce J. Tromberg, R.C. Haskell, S.J. Madsen and L.O. Svaasand, "Characterization of tissue optical properties using photon density waves", Comments Mol. Cell. Biophys., 8, 6, (1995).
- Bruce J. Tromberg, O. Coquoz, J.B. Fishkin, T. Pham, E.R. Anderson, J. Butler, M. Cahn, J.D. Gross, V. Venugopalan, and D. Pham, "Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration", Phil. Trans. Royal Soc. London, 352, (1997).
- F. Bevilacqua, D. Piguet, P. Marquet, J.D. Gross, B.J. Tromberg and C. Depeursinge, "In vivo local optical determination of tissue optical properties", Proc. SPIE, 3194, (1998).
- Bruce J. Tromberg, L.O. Svaasand, M.K. Fehr, S.J. Madsen, P. Wyss, B. Sansone, and Y. Tadir, "A mathematical model for light dosimetry in photodynamic destruction of human endometrium", Phys. Med. Biol., 40, (1995).
- Hayakawa, C., J. Spanier,
F. Bevilacqua, A.K. Dunn, J.S. You, B.J. Tromberg and V. Venugopalan,
“Use of Perturbation
- Viator, J., B. Choi, M. Ambrose, J. Spanier and J.S. Nelson, “In Vivo Port-Wine Stain Depth Determination with a Photoacoustic Probe”, Applied Optics, 42, 3215-3224, (2003).
- Hayakawa, C. and J.
Spanier, “Perturbation Monte Carlo Methods for the Solution
of Inverse Problems”,
- Hayakawa, C., B.Y. Hill, J.S. You, F. Bevilacqua, J. Spanier and V. Venugopalan, “Use of the ?-P1approximation for recovery of optical absorption, scattering, and asymmetry coefficients in turbid media”, Applied Optics, 43, pp. 4677-4684, (2004).
- Tseng, S.H., C. Hayakawa, B.J. Tromberg, J. Spanier and A.J. Durkin, “Quantitative spectroscopyof superficial turbid media”, Optics. Let., 30, 3165-7, (2005).
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Theory and Applications of Fractional Calculus
This is a long-standing interest shared with collaborator Keith
Oldham (
References:
- K.B. Oldham and J. Spanier, "The Replacement of Fick's Laws by a Formulation Involving Semi-Differentiation," J. of Electroanalytical Chemistry and Interfacial Electrochemistry, 26, 331-341, (1970).
- K.B. Oldham and J.
Spanier, "The Fractional Calculus," Academic Press,
3 K.B. - K.B. Oldham and J. Spanier, "A General Solution of the Diffusion Equation for Semiinfinite Geometries", J. Math. Anal. Appl., 39, 655-669, (1972).
- K.B. Oldham and J. Spanier, "The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order", Dover Publications, Inc., 2006
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