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Pedro Goldman, PhD

KHS 246
Ryerson University
350 Victoria Street
Toronto, Ontario M5B 2K3
416-979-5000 x7418


Radiation Therapy of Tumours, Fast Inverse Dose Optimizations for Intensity Modulated Radiation Therapy (IMRT) and Tomotherapy, Alternative Methods for Efficient CT Image Reconstruction, Physics Education.


Currently, the main thrust of my research is focused on the radiation treatment of tumours. Intensity Modulated Radiation Therapy (IMRT) is becoming a new standard technique for radiotherapy. Given the availability of online imaging tools and the improved conformal dose distributions obtained through IMRT and its dynamic delivery features, it is possible, in principle, to deliver adaptive radiotherapy, i.e. the ability to readapt the treatment plan each time it is delivered based on fresh images of the tumour region. This is presently still not possible. One of the main reasons is the long time it takes to optimize a treatment plan - in other words, to obtain the optimal intensities of all the (thousands!) of beamlets (narrow energy beams) used to treat the tumour. A fast and reliable optimization algorithm is crucial then not only for designing good radiation treatment plans but also for the successful implementation of future interactive adaptive treatment techniques. Conventional optimization algorithms use numerical searches that usually require numerous iterations (i.e. long computation times) and may result in suboptimal plans due to trapping in local minima of the objective function being optimized. A direct solution of the inverse problem using conventional quadratic objective functions without imposing positive beam constraints would be computationally faster but until now it resulted in unrealistic negative beam intensities. My work introduced a new Fast Inverse Dose Optimization (FIDO) method for the direct solution of the inverse problem that avoids negative beamlet intensities and is several orders of magnitude faster than present optimization techniques. Our research currently is dedicated to the development of a full fledged three-dimensional.planning system including scattering effects, Dose-Volume constraints, as well as gantry angle optimization and biological effects.

A second line of research regarding the radiation treatment of tumours is the optimization of Intensity Modulated Arc Therapy (IMAT). We have produced a new method to calculate analytic pre-optimized intensities and are now investigating a very fast, full optimization of IMAT including all constraints mentioned above.

We are interested as well in the problem of inverse image reconstruction in Computed Tomography (CT). One perspective is the application of FIDO for a novel solution of this problem. The second is an imaging perspective involving the creation of novel alternatives to Fourier transforms in order to avoid the nasty artifacts that Fourier introduces in Medical Imaging.

I am as well very much interested in Physics Education. I believe that research into Physics Education should be supported and promoted in Canada. Teaching is one of the most important aspects in our roles as Physicists and its improvement should become an integral part of our work. I do believe as well that it is our duty to the community to become involved with physics/science teachers in elementary, intermediate and high schools.


S. P. Goldman, J. Z. Chen, E. Wong and J. J. Battista (2006), ‘Dose Rate Optimization for Intensity Modulated Arc Therapy', 48th Annual Meeting of the American Association of Physicists in Medicine

S. P. Goldman, J. Z. Chen and J. J. Battista (2005) ‘Feasibility of a fast inverse dose optimization algorithm for IMRT via matrix inversion without negative beamlet intensities', Med. Phys. 32 , 3007-30016

S.P. Goldman, F.R. Hallett, and W. Harris (2005) ‘Teaching Physics to a Non-Physics Audience – Three Personal Perspectives', Physics in Canada 61 , 107-112

S.P. Goldman and M. Cassar (2005) ‘Atoms in strong fields', in Handbook of Atomic, Molecular and Optical Physics [2 nd Edition] , edited by G.W.F. Drake

S. P. Goldman, J. Z. Chen and J. J. Battista (2004), ‘Fast Inverse Dose Optimization (FIDO) for IMRT via Matrix Inversion with no Negative Intensities', XIV th International Conference on the Use of Computers in Radiation Therapy, pages 112-115.

S.P. Goldman and G.W.F. Drake (2000) High accuracy for atomic calculations involving logarithmic sums, Phys. Rev. A 61 , 052513 (7 pages)

G.W.F. Drake and S.P. Goldman (1999) Bethe logarithms for Ps - , H - and heliumlike atoms, Can. J. Phys. 77 , 835-845

S.P. Goldman (1999) Atomic and molecular calculations made easy and very accurate, Phys. Scripta T83 , 61-68

S.P. Goldman (1998) Uncoupling correlated calculations in atomic physics - extreme accuracy and ease, Phys. Rev. A57 , R667-R680

J.A. Kempe and S.P. Goldman (1998) Accurate modified configuration interaction single-centered calculations for H 2 + , J. Chem. Phys. 108 , 7679-7683

S.P. Goldman (1997) Accurate modified configuration interaction calculations for many electron systems made easy, Phys. Rev. Lett. 78 , 2325-2329