Ph.D. New York University

Medical Imaging, Mathematical physics

Professor Isaacson works in two areas: mathematical physics and medical imaging.

His work in mathematical physics has centered on the development
of methods for approximating energy levels, particle masses, and critical
exponents in quantum mechanics, quantum field theory, and statistical mechanics.

His work in medical imaging has centered on the development of
algorithms and devices for measuring and displaying the electrical state
of the interior of a body from measurements made on the body's exterior.

The long term goal of this research is to improve the diagnosis
and treatment of heart disease and cancer.

Here is a Ventilation Perfusion Image made by the Act3 Impedance Imaging System

Publications:

"Singular Perturbations and Asymptotic Eigenvalue Degeneracy," Communications in Pure and Applied Math., Vol. XXIX, 531-551, 1976.

"The Critical Behavior of ?42 ?," Communication in Mathematical Physics, 53, 257-275, 1977.

"The Eigenvalues and Eigenfunctions of a Spherically Symmetric Anharmonic Oscillator," (with D. Marchesin) Communications in Pure and Applied Math., Vol. XXXI, 659-670, 1978.

"Numerical Methods for Studying Anharmonic Oscillator Approximations to the ?42 ?Quantum Field Theory," (with D. Marchesin and P. J. Paes- Leme) International Journal of Engineering, 18, 341-349, 1980.

"The Ground State Energy per Particle for Infinite Particle Quantum Systems," Communication in Mathematical Physics, 73, 99-104, 1980.

"Spectral Properties of Systems with many Degrees of Freedom," (with E. L. Isaacson, D. Marchesin, and P. J. Paes-Leme) in Seminar on Numerical Analysis and its Application to Continuum Physics, 47-53, 1980.

"Numerical Analysis of Coupled Oscillator Schrodinger Operators, I. Single and Double Well Anharmonic Oscillator," (with E. L. Isaacson, D. Marchesin, and P. J. Paes-Leme) Mathe. of Computation, 37, 273-292, 198l.

"The Continuum Limit of a Classical Three Component Heisenberg Model is Brownian Motion on the Surface of a Sphere," Journal of Mathematical Physics, 23 (1), 138-140, 1982.

"Numerical Analysis of Coupled Oscillator Schrodinger Operators, II. Two Coupled Anharmonic Oscillators," (with E. L. Isaacson, D. Marchesin, and P. J. Paes-Leme) SIAM J. of Numerical Analysis, 19, (1), 126-141, 1982.

"Critical Behavior of the Two-State Doubling Algorithm," (with E.L. Isaacson, D. Marchesin, and P. J. Paes-Leme) Journal of Mathematical Physics, 24 (1), 4l-45, 1983.

"Eigenvalues of 4, 8, and 16, Coupled Anharmonic Oscillators," (with E. L. Isaacson, D. Marchesin, and P. J. Paes-Leme), Physical Review D, Vol. 27, No. 12, 3036-3039, 1983.

"Large Coupling Behavior of the Energy Eigenvalues of Two Anharmonic Oscillators," Journal of Mathematical Physics, 24 (6), 1477-81, 1983.

"Numerical Analysis of Coupled Oscillator Schrodinger Operators, III. The Doubling Algorithm," (with E. L. Isaacson, D. Marchesin, and P. J. Paes-Leme), SIAM J. Sci. and Stat. Computing, Vol. 6, No. 1, 158-168, 1985.

"Critical Behavior of Doubling Approximations of the Phi(4 ):2 Lattice Field Theories" (with E. L. Isaacson, D. Marchesin, and P. J. Paes-Leme), Phys. Rev. D., vol. 31, No. 2, 438-440, 1985.

"Kurt O. Friedrichs" Contributions to Quantum Mechanics," Ch. VIII in Kurt Otto Friedrichs, Selecta, Vol. 2, edited by C. Morawetz, 602-605, Birkhauser, 1986.

"Distinguishability of Conductivities by Electric Current Computed Tomography," IEEE Trans. on Medical Imaging, Vol. MI-5, No. 2, 91-95, 1986.

"Current Topics in Impedance Imaging" (with D. G. Gisser and J. C. Newell). Clinical Physics and Physiological Measurement, Vol. 8, Supp. A, 39-46, 1987.

"Electromagnetically Induced Flow Potentials in Man," (with J. C. Goble) Proc. of IEEE Eng. in Medicine and Biology, 1987.

"Measurement of Flow Related Potentials in Man at 1.5 Tesla" (with J. C. Goble) Abstract Soc. of Magnetic Resonance in Medicine, Vol. 1, p. 24, 1987.

"Theory and Performance of an Adaptive Current Tomography System" (with J. C. Newell and D. Gisser) Clin. Physics and Physiol. Meas., 9 Suppl: A:34-41, 1988.

"Electric Current Computed Tomography and Eigenvalues I" (with D. G. Gisser and J. C. Newell). SIAM J. Appl. Math., 50, p 1623-1634, 1990.

"An Electric Current Tomograph" (with D. G. Gisser and J. C. Newell) IEEE Trans. on Biomed.. Eng., Vol. 35, No. 10, p. 828-833, 1988.

"Errors Due to Measuring Voltage on Current-Carrying Electrodes in Electric Current Computed Tomography" (with K. S. Cheng, J. C. Newell, and D. G. Gisser). IEEE trans. in Biomedical Eng., 37, 60-65, 1990.

"Electrode Models for Electric Current Computed Tomography", with K.
S. Cheng, J. C. Newell, and D. G. Gisser) IEEE Trans. in Biomedical Eng.,

Vol. 36, No. 9, p. 918-924, 1989.

"Comment on Calderon's Papers: "On an Inverse Boundary Value Problem" (with E. L. Isaacson) Mathematics of Computation, Vol. 52 #186, 553-559, 1989 .

"Rapid Assessment of Electrode Characteristics" (with J. C. Newell and D. G. Gisser). IEEE Trans. in Biomed. Eng., 37, 735-738, 1990.

"The Application of Electric Current Computed Tomography to Defect Imaging in Metals," (with M. R. Eggleston, R. J. Schwabe, and L. F. Coffin). Review of Quantitative NDE, Vol. 9A, p. 455-462, Plenum 1990.

"Effect of Measurement Precision and Finite Numbers of Electrodes on Linear Impedance Imaging Algorithms" (with M. Cheney) SIAM J. App. Math, vol. 51, No. 6, p. 1705-1731, 1991.

"Exact Solutions to a Linearized Inverse Boundary Value Problem," ( with M. Cheney and E. L. Isaacson) Inverse Problems, 6, p. 923-934, 1990.

"Current Problems in Impedance Imaging," (with M. Cheney) in Inverse Problems in P.D.E., p. 141-150, D. Colton et al, ed. SIAM, Phila.,1990.

A Linearized Inverse Boundary Value Problem for Maxwell's Equations," (with M. Cheney and E. Somersalo) accepted in J. Comp. and Applied Math., 42, p. 123-136, 1992..

"Existence and Uniqueness for an Electrode Model for ECCT," (with M. Cheney and E. Somersalo) SIAM J. App. Math., 52, p.1023-1040, 1992.

"NOSER: An Algorithm for Solving the Inverse Conductivity Problem," (with M. Cheney, J. Newell, S. Simske, and J. Goble), International J. Imaging Systems and Technology, 2, p. 66-75, 1990.

"Invariant Imbedding, Layer-Stripping, and Impedance Imaging," (with M. Cheney), Inverse Problems and Invariant Embedding, ed., J. Corones, et al., SIAM, 1991.

"Distinguishability in Impedance Imaging," (with M. Cheney), accepted in IEEE Trans. Biomed. Engr., 39, #8, p. 852-860, 1992.

"Fast Reconstruction Algorithm for Three Dimensional Electrical Impedance Tomography," with (J. C. Goble), IEEE Engr. in Medicine and Biology, vol. 12, No. 1, 1990.

"Mathematical Aspects of Impedance Imaging, with Emphasis on Linear Reconstruction Algorithms," (with M. Cheney), Digital Image Synthesis and Inverse Optics, vol. 1351, p. 2-8, 1990.

"Power Considerations in Impedance Imaging," (with M. Cheney, J. Newell, and D. Gisser), IEEE Engr. in Medicine and Biology, vol. 12, No. 1, 1990.

"Thoracic Impedance Images During Ventilation," (with M. Cheney, J. Newell, D. Gisser, and J. Goble, IEEE Engr. in Medicine and Biology,vol. 12, No. 1, 1990.

"An Overview of Inversion Algorithms for Impedance Imaging," (with M. Cheney), Inverse Scattering and Applications, Contemp. Math. 122, p. 29-39, AMS, 1991.

"Detection and Imaging of Electric Conductivity and Permittivity at Low Frequency," (with L. F. Fuks, M. Cheney, D. G. Gisser and J. C. Newell) Trans. Biomed. Eng. 38, p. 1106-1110, 1991.

"Layer Stripping: A Direct Numerical Method for Impedance Imaging," (with M. Cheney, E. Somersalo, and E. L. Isaacson), Inverse Problems, 7, 899-926, 1991.

"An Inverse Boundary Value Problem for Maxwell's Equations," (with M. Cheney and E. Somersalo), Applied Computational Electromagnetics, 7, p. 74-77, 1991.

"A Layer Stripping Approach to Impedance Imaging," (with M. Cheney, E. Somersalo, and E. L. Isaacson) Applied Computational Electro-magnetics, 7, p. 79-86, 1991.

"A Layer-Stripping Reconstruction Algorithm for Impedance Imaging," (with M. Cheney, E. Somersalo, E. L. Isaacson, and E. Coffee) IEEE-EMBS, vol. 13, No. 1, 1991.

"A High-Speed High Precision Electrical Impedance Tomograph," (with G. Saulnier, R. Cook, D. Gisser, J. Goble, C. Hochgraf and J. Newell) IEEE-EMBS, vol. 13, No. 1, 1991.

"Electric Current Computed Tomography" (with M. Cheney, J. C. Newell, D. G. Gisser, and J. C. Goble), 7th Annual Review of Progress in Applied Computational Electromagnetics, p. 87-93, 1991.

"An Algorithm for Impedance Imaging," (with P. Edic), IEEE-EMBS 14, 1693, 1992.

"Comments on Reconstruction Algorithms," (with M. Cheney and J. C. Newell) Clinical Physics and Physiological Measurements, 13(A), p. 83-89, 1992.

"Electrical Impedance Tomography in Three Dimensions," (with M. Cheney and J. Goble) Journal of Computational Electromagnetics, p. 128-147, 1992.

"In-vivo Impedance Images Using Sinusoidal Current Patterns," (with J. C. Newell, M. Cheney, G. Saulnier, D. Gisser, J. Goble, R. Cook, P. Edic and C. Newton), Clinical Applications of Impedance Imaging, D. Holder Ed., Univ. Coll. London Press, p. 62-71, 1993.

"Electrical Impedance Imaging," (with Newell, Saulnier, Edic, Gisser, Cheney, and Cook) BMES Bulletin, 19-23, 1993.

"Layer-Stripping Reconstruction Algorithm for Impedance Imaging," (with M. Cheney, E. J. Somersalo, and E. L. Isaacson), Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 14, p.1694-1695, 1993.

"Impedance Images of the Chest," (with J. C. Newell, M. Cheney, G. J. Saulnier, D. G. Gisser, J. C. Goble, R. D. Cook, and P. M. Edic), Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 14, p. 1752-1753, 1993.

"Impedance Imaging Using Interior and Exterior Measurements," (with C. Caldwell and M. Cheney) in Physiological Imaging, Spectroscopy, and Early-Detection Diagnostic Methods, ed., R. L. Barbour and M. J. Carvlin, SPIE Proceedings series vol. 1887, 1993.

"Imaging the Interior of the Body with Electric Fields," (with M. Cheney) in Physiological Imaging, Spectroscopy, and Early-Detection Diagnostic Methods, ed., R. L. Barbour and M. J. Carvlin, SPIE Proceedings series vol. p. 1887, 1993.

"Accute Pulmonary Edema Assessed by Electrical Impedance Imaging," (with J. C. Newell, M. Cheney, G. J. Saulnier, and D. G. Gisser, Proc. IEEE/EMBS Vol. 15, p. 92, 1993, in press.

"Implementation of a Real-Time Electric Impedance Tomograph," (with P. M. Edic, G. J. Saulnier, M. Cheney, J. C. Newell, D. G. Gisser and R. D. Cook), Proc. IEEE/EMBS Vol. 15, p. 84, 1993.

"Real-Time Adaptive Current Tomography," (with J. C. Newell, P. M. Edic, G. J. Saulnier, M. Cheney, and D. G. Gisser), Electrical Impedance Tomography Workshop, Barcelona, September 1993.

"Problems in Impedance Imaging," (with M. Cheney and J. C. Newell), in Inverse Problems in Mathematical Physics, ed., L. Paivarinta and E. Somersalo), Lecture Notes in Physics No. 422, Springer, New York, 1993

"Layer-Stripping Reconstruction Algorithms in Impedance Imaging," (with M. Cheney and E. Somersalo), in Inverse Problems in Mathematica Physics, ed., L. Paivarinta and E. Somersalo, Lecture Notes in Physics No. 422, Springer, New York, 1993.

"Solutions to Ill-Posed Problems in Functional Imaging," SPIE short course notes SC1, p. 1-60, SPIE, 1993.

"Exact Solutions to a linearized Electrical Impedance Imaging Problem," (with D. Ng), submitted SIAM 1995.

"ACT 3: A High Speed High Precision Electrical Impedance Tomograph," (with R. D. Cook, G. J. Saulnier, D. G. Gisser, J. C. Goble, and J. C. Newell). IEEE Trans. Biomed. Eng. 41 (8), pp.713-722, 1994.

"A Real-Time Electrical Impedance Tomograph," (with P. M. Edic, G. J. Saulnier, and J. C. Newell). IEEE Trans. Biomed. Eng. 42 (9), pp. 849-859, 1995.

"Issues in Electrical Impedance Imaging," IEEE Comp. Sci. and Eng. (24), pp. 53-62, 1995.

"Inverse Problems for a Perturbed Dissipative Half-Space," (with M. Cheney), 11, p. 865-888, Inverse Problems, 1995.

"Regional Ventillation and Perfusion Assessed by Electrical Impedance Imaging," (with J. C. Newell, and R. S. Blue). Proc. IEEE (in press) 1996.

"Effect of Electrode Size on Impedance Images of 3-D Objects," (with J. C. Newell, G. J. Saulnier, M. Cheney, and D. G. Gisser). IEEE-EMBS Proc. (in press) 1996.

"A 3-D Impedance Imaging Algorithms for Multiple Layers of Electrodes," (R. Blue and J. C. Newell) IEEE-EMBS (In press) 1996.

"Incorporating Noncircular Boundary Shape in Electrical Impedance Tomography," (with H. Jain and J. C. Newell), IEEE-EMBS Proc. (in press) 1996.

Jain, H., D. Isaacson, P. M. Edic and J. C. Newell. Electrical impedance tomography of complex conductivity distributions with noncircular boundary. IEEE Trans Biomed. Eng 44(11): 1051-1060, 1997

“Forward Electromagnetic Scattering Models for Sea Ice”, with M.Cheney,K.Golden, and others , Geoscience and Remote Sensing, Vol 36 No5 Part 2 ,1998.

“Inverse Electromagnetic Scattering Models for Sea Ice”, with M.Cheney,K.Golden, and others , Geoscience and Remote Sensing, Vol 36 No5 Part 2 ,1998.

Edic, P.M., D. Isaacson, G.J. Saulnier, H. Jain and J. C. Newell. An iterative Newton-Raphson method to solve the inverse admittivity problem. IEEE Trans. Biomed. Eng. 45(7):899-908, 1998.

" Electrical Impedance Tomography", with M.Cheney,and J.C.Newell, Siam Review. 41(1):85-101, 1999.

“Recovery of surface parameters from stepped-frequency radar returns”, with M,Cheney, V. Lytle, and S. Ackley , Math and Computers in Simulation 50 ,527-539, 1999.

“A reconstruction algorithm for Electrical Impedance Tomography Data Collected on Rectangular Electrode Arrays,” with J.Mueller,and J. Newell, IEEE Trans. on BME Vol.46,No 11, (1379-1386),Nov.1999

“An implementation of the reconstruction algorithm of A.Nachman for the 2-D inverse conductivity problem”, with S.Siltanen, and J.Mueller, accepted – to appear in Inverse Problems , 2000.

“Reconstruction of the conductivity changes due to ventilation and perfusion from EIT data collected on a rectangular electrode array”, with J.Mueller,and J.Newell, accepted – to appear in Physiological Measurement , 2000.

“Real Time Three Dimensional Electrical Impedance Imaging”, with R.S.Blue, and J.C.Newell, accepted – to appear in Physiological Measurement 2000.

"Optimal Acoustic Measurements", with M. Cheney, and M. Lassas, to appear in SIAM J. Appl. Math 2000.

RPI Math Faculty List