IPRPI & RPI Logos Inverse Problems Center

Joyce McLaughlin

David Isaacson

Antionette Maniatty

Assad Oberai

Steven Roecker

Birsen Yazici

Mourad Zeghal

Research Scientists


Center Participants

Assad Oberai
Assistant Professor Mechanical, Aerospace and Nuclear Engineering
Rensselaer Polytechnic Institute

Ph.D., Stanford University Mechanical Engineering
M.S., University of Colorado at Boulder Mechanical Engineering
B.S., Osmania University Mechanical Engineering

Career Highlights:
Assad Oberai received his PhD. in Mechanical Engineering from Stanford University in 1998. His doctoral work involved developing accurate and efficient finite element methods for solving time-harmonic, wave propagation problems in unbounded domains. As a post-doctoral researcher at Stanford University he developed multiscale formulations of large eddy simulation for modeling turbulent flows and numerical methods for predicting noise generated by such flows. In 2001, Assad joined Boston University as an Assistant Professor and in 2006 he moved to the Mechanical, Aerospace and Nuclear Engineering Department at RPI. Here, he continues to work on numerical methods for inverse problems and problems with multiple scales.

In 2004, Assad was awarded the DOD Breast Cancer Research Program Concept Award for work on quantifying the nonlinear, elastic properties of tissue. In 2004, he was also awarded the DOE Early Career PI award in applied mathematics for developing algorithms for solving multiscale problems. In 2005 he received the NSF CAREER award for work on Large Eddy Simulation of turbulent flows.

In 2006 and 2007, the papers "Coupling between elastic strain and interstitial fluid flow; ramifications for poroelasticity imaging" by R. Leiderman, P.E. Barbone, A.A. Oberai & J.C. Bamber, 2006 and "Elastic modules imaging; some exact solutions of the compressible elastography inverse problem" by P.E. Barbone and A.A. Oberai, 2007, were Institute of Physics Select Papers. In 2007 Assad received the ASME Special Achievement Award for Young Investigators in Applied Mechanics, 2007. In 2009 he received the Humboldt Foundation award for experienced researchers. In 2010, he obtained an Erasmus Mundus Master Course Lectureship at Universidad Policnica de Catalua, Barcelon, Spain.

Research Areas:

Assad's research involves developing numerical methods for solving inverse problems and problems with multiple spatial and temporal scales. His work on multiscale problems includes modeling turbulent flows, problems with shocks and coupling molecular and continuum descriptions in fluids.

In the field of inverse problems Assad is working on the promising new area of biomechanical imaging. Here the goal is to develop algorithms that quantify the spatial distribution of mechanical properties of tissue. This is accomplished by first deforming the tissue by some means (a gentle compression for example) and observing its deformation using ultrasound (or sometimes MRI). Once the displacement is known an inverse problem is solved wherein the given an appropriate mechanical model for the tissue (linear elastic, or hyperelastic or poroelastic) and the deformation, the spatial distribution of the mechanical properties is sought. Assad's work is focused on developing algorithms for solving these types of inverse problems. This approach can be used to measure the mechanical properties of tissue in-vivo and has found applications in the detection and diagnosis of different types of cancers and in the development of patient specific mechanical models for surgical planning.

Recent Publications:


Yixiao Zhang, Paul E. Barbone, Isaac Harari, and Assad A. Oberai “Uniqueness of the Interior Plane Strain Time-Harmonic Viscoelastic Inverse Problem", to appear in the Journal of the Mechanics and Physics of Solids, 2016.

Olalekan A. Babaniyi, Assad A. Oberai & Paul E. Barbone “Lateral Displacement Estimation in Elastography Using Sparse Relaxation of the Momentum Equation", to appear in Inverse Problems in Science and Egineering, 2016.

Li Dong, Philip Wijesinghe, James T. Dantuono, David D. Sampson, Peter R.T. Munro , Brendan F. Kennedy, and Assad A. Oberai, “Quantitative Optical Coherence Elastography as an Inverse Elasticity Problem", IEEE Journal of Selected Topics in Quantum Electronics, DOI: 10.1109/JSTQE.2015.2512597, 2016.

Tengxiao Liu Olalekan A. Babaniyi, Timothy J. Hall, Paul E. Barbone & Assad A. Oberai “Mechanical Heterogeneity of Invasive Breast Carcinomas" PlosOne, DOI: 10.1371/journal.pone.0130258, July 2015.


Elizabeth P. Canovic, D. Thomas Seidl, Samuel R. Polio, Assad A. Oberai, Paul E. Barbone, Dimitrije Stamenovic, and Michael L. Smith, “Biomechanical imaging of cell stiffness and prestress with subcellular resolution", Biomechanics and Modeling in Mechanobiology, 1-14,2013.

Elizabete R. Ferreira, Assad A. Oberai, Timothy J. Hall,“Progress in inferring desmoplastic stromal tissue microsturcture noninvasively with ultrasound nonlinear elasticity imaging", The Journal of the Acoustical Society of America, Volumn 135, Number 5, 4212-4214, 2013.

Olalekan A. Babaniyi, Paul E. Barbone, Assad A. Oberai, “Using equilibrium equation constraints to obtain precise lateral displacement estimates in ultrasound imaging", The Journal of the Acoustical Society of America, Volumn 134, Number 5 (November 2013).


Ferreira, E.R., Oberai, A.A., and Barbone, P.E., "Uniqueness of the elastography inverse problem for incompressible nonlinear planar hyperelasticity," Inverse Problems, Volume 28, Number 6, 065008 (2012).

Goenezen, S., Dord, J-F., Sink, Z., Barbone, P.E., Jiang, J., Hall, T.J., and Oberai, A.A., "Linear and Nonlinear Elasticity Imaging: An Application to Breast Cancer Diagnosis," IEEE Transactions on Medical Imaging, 2012 Aug;31(8):1628-37. doi: 10.1109/TMI.2012.2201497. Epub 2012 May 30.

McLaughlin, J.R., Oberai, A. and Yoon, J-R., "Formulas for detecting a spherical stiff inclusion from interior data: A sensitivity analysis for the Helmholtz equation," Inverse Problems, Volume 28, Number 8, 2012, special July 2012 issue on coupled physics.

Rivas, C.A., Barbone, P.E. and Oberai, A.A., "An augmented Lagrangian stabilized B-splines FEM formulation for the solution of an inverse elasticity problem," submitted to Computer Method in Applied Mechanics and Engineering.

Zhang, Y., Oberai, A.A., Barbone, P.E., and Harari, I., "Solution of the time-harmonic viscoelastic inverse problem with interior data in two dimensions," International Journal for Numerical Methods in Engineering, 92(13), 1100-1116, 2012.


 Goenezen, S., Barbone, P.E., and Oberai, A.A. “ Solution of the nonlinear elasticity imaging inverse problem: the incompressible case,” Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issues 13-16, Pages 1406-1420, March 2011.

Hall, T.J.,  Barbone, P.E.,  Oberai, A.A., Jiang, J., Dord, J.F., Goenezen, S. and Fisher, T.G., “ Recent results in nonlinear strain and modulus imaging.", Current Medical Imaging Reviews, Volume 7, Number 4, Nov. 2011, Pages 313-327.


Leiderman, R.,  Oberai, A.A., and Barbone, P.E.  “Theory of reconstructing the spatial distribution of the filtration coefficient in vascularized soft tissues: exact and approximate inverse solutions”. Comptes Rendus Mecanique, Vol. 338, Issues 7-8, Pages 412-423, July 2010.

Crescenti, R.A.,  Bamber, J.C.,  Oberai, A.A.,  Barbone, P.E.,  Richter, J.P.,  Rivas, C., Bush, N.L.,  and Webb, S. “Quantitative ultrasonic elastography for gel dosimetry., Ultrasound in Medicine & Biology”, 36 (2), 268-275, 2010.


Albocher , U., Oberai, A., Barbone, P.E. and Harari, I. "Adjoint-weighted equation for inverse problems of incompressible plane-stress elasticity", Computer Methods in Applied Mechanics and Engineering, volume 198 (30-32), 2412-2420, 2009.

Bamber, J.C.,  Oberai, A., Barbone, P.E., Richter, J.P, Rivas, C., Bush, N.L., Webb, S., Crescenti, R.A.“Quantitative ultrasonic elastography for gel dosimetry", Ultrasound in Medicine and Biology, Vol. 36, No. 2, pp.268-275, 2009.

Barbone, P.E., Rivas, C.E., Harari, I, Albocher, U., Oberai, A., Zhang, Y. "Adjoint-weighted variational formulation for the direct solution of inverse problems of general elasticity with full interior data”, Interntional Journal for Numerical Methods in Engineering, 81(13), 1713-1736, 2009.

Oberai, A., Feijoo, G.R., and Barbone, P.E. "Lanczos-iterated time reversal",  Journal of the Acoustical Society of America -Express Letters, 2(125), 70-76, 2009.

Oberai, A., Gokhale, N.H., Goenezen, S., Barbone, P.E., Hall, T.J., Sommer, A.M., Jiang, J."Linear and nonlinear elasticity imaging of tissue in-vivo: Demonstration of feasibility", Physics in Medicine and Biology, 54(5), 1191-1207, 2009.

Proper, A., Zhang, W., Bartolucci, S., Oberai, A., Koratkar, N. "In-Situ detection of impact damage in composites using carbon nanotube sensor networks”,  Nanoscience and Nanotechnology Letters, vol 1(1), 3-7, 2009. 

Richards, M.S., Barbone, P.E. and Oberai, A."Quantitative three-dimensional elasticity imaging from quasi-static deformation: a phantom study”, Physics in Medicine and Biology, 54(3), 2009.

Wang, Z. and Oberai, A. "Spectral analysis of the dissipation of the residual based variational multiscale method”, Computer Methods in Applied Mechanics and Engineering, Vol 199 (13-16), pp. 810-818, 2009.


Gokhale, N.H., Barbone, P.E. and Oberai, A.A., "Solution of the nonlinear elasticity imaging inverse problem: the compressible case," Inverse Problems, 24(4), 2008.


Barbone, P.E., Oberai, A.A., and Harari, I., "Adjoint-weighted variational formulation for direct solution of inverse heat conduction problem", Inverse Problems, Vol. 23, pp. 2325-2342, 2007.

Oberai, A.A., Barbone, P.E. & I. Harari, "The adjoint weighted equation for steady advection in a compressible fluid," International Journal for Numerical Methods in Fluids, Vol. 54(6-8), pp. 683-693, 2007.

Barbone, P.E. & A.A. Oberai, "Elastic modulus imaging: some exact Solutions of the compressible elastography inverse problem," Physics in Medicine and Biology, Vol. 52(6), pp. 1577-1593, 2007.


Leiderman, R., Barbone, P.E., Oberai, A.A. & J.C. Bamber, "Coupling between elastic strain and interstitial fluid flow: ramifications for poroelasticity imaging," Physics in Medicine and Biology. Vol. 51(24), pp. 6291-6313, 2006.

Oberai, A.A. & J. Wanderer, "A Dynamic Multiscale Viscosity Method for the Spectral Approximation of Conservation Laws," Computer Methods in Applied Mechanics and Engineering, Vol. 195(13-16), pp. 1778-1792, 2006.


Naka, Y., Oberai, A.A. & B. Shinn-Cunningham, "Acoustic eigenvalues of rectangular rooms with arbitrary wall impedances using the interval Newton/generalized bisection method," Journal of Acoustical Society of America, Vol. 118(6), pp. 3662-3671, 2005.

Oberai, A.A. & J. Wanderer, "Variational Formulation of the Germano Identity for the Navier-Stokes Equations," Journal of Turbulence, Vol. 6, 2005.

Oberai, A.A. & J. Wanderer, "A Dynamic Approach for Evaluating Parameters in a Numerical Method," International Journal for Numerical Methods in Engineering, Vol. 62, pp. 50-71, 2005.


Gokhale, N., Richards, M., Oberai, A., Barbone, P., and M. Doyley, "Simultaneous Elastic Image Registration and Elastic Modulus Reconstruction," Proceedings of the IEEE International Symposium on Biomedical Imaging, April 15-18, 2004, Arlington, VA, USA.

Oberai, A.A., Gokhale, N.H., Doyley, M.M. and J.C.Bamber, "Evaluation of the Adjoint Equation Based Algorithm for Elasticity Imaging," Physics in Medicine and Biology, Vol. 49, pp. 2955-2974, 2004.

Holmen, J., Hughes, T.J.R., Oberai, A.A. and G.N. Wells, "Sensitivity of the Scale Partition for Variational Multiscale LES of Channel Flow," Physics of Fluids, Vol. 16(3), pp. 824-827, 2004.

Feijoo, G.R., Oberai, A.A. and P.M. Pinsky, "An Application of Shape Optimization in the Solution of Inverse Acoustic Scattering Problems," Inverse Problems, Vol. 20, pp. 199-228, 2004.


Wagner, M.M., Pinsky, P.M., Oberai, A.A. and M. Malhotra, "A Krylov subspace projection method for simultaneous solution of Helmholtz problems at multiple frequencies," Computer Methods in Applied Mechanics and Engineering, Vol. 192(41-42), pp. 4609-4640, 2003.

Oberai, A.A., Gokhale, N.H. and G.R. Feijoo, "Solution of Inverse Problems in Elasticity Imaging Using the Adjoint Method," Inverse Problems, Vol. 19, pp. 297-313, 2003.

Hughes, T.J.R. and A.A. Oberai, "Calculation of Shear Stresses in Fourier-Galerkin Formulation of Turbulent Channel Flows: Projection, the Dirichlet Filter and Conservation," Journal of Computational Physics, Vol. 188(1), pp. 281--295, 2003.

Feijoo, G.R., Malhotra, M., Oberai, A.A. and P.M. Pinsky, "Shape sensitivity calculations for exterior acoustics problems," Engineering Computations, Vol.18(3/4), pp. 376--391.


Oberai, A.A., Roknaldin, F. and T.J.R. Hughes, "Trailing-edge noise from a finite chord airfoil," AIAA Journal, Vol 40(11), pp. 2206-2216, 2002.


Important Talks:

Oberai, A., Inverse Problems in Mechanics, Unified Framework Workshop , CenSSIS, Boston, MA, Nov. 2008.

Oberai, A., Inverse Problems in Mechanics, Department of Theoretical and Applied Mechanics, Cornell University, Sept. 2008.

Oberai, A., Studies of Inverse Problems in Biomechanics, Mechanics and Materials Colloquium, University of Colorado, May 2008.

Oberai, A., Constructing images of linear and nonlinear elastic and poroelastic tissue parameters, SIAM Conference on the Life Sciences, August 2008, Montreal, CA.

Contact Information:
Assad Oberai
Department of Mechanical, Aerospace and Nuclear Engineering
Jonsson Engineering Center rm: 5048
Rensselaer Polytechnic Institute
110 Eighth Street
Troy, N.Y. 12180
(518) 276-3386

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