Biomechanical Imaging 

“Biomechanical imaging” refers to in vivo, or in some cases in situ, imaging
and measurement of mechanical property distributions in tissues. Doing so
requires the measurement of material (tissue) displacement via imaging,
the mathematical modeling of relevant tissue mechanics and deformation,
and subsequent inference of mechanical properties
through the solution of an appropriate inverse problem.
The papers below describe some work relevant to each of these aspects.

Recent tutorial talk:
Some math & mechanics of biomechanical imaging: current status and open questions,
2008 BIRS Workshop on Inverse Problems: Recent Progress and New Challenges.

Relevant papers on biomechanical imaging 

“Adjointweighted equation for inverse problems of incompressible planestress elasticity,”
Uri Albocher, Assad A. Oberai, Paul E. Barbone, Isaac Harari. submitted to Computer Methods in Appl.\ Mech.\
and Eng, in review, submitted Oct 2008.

“A review of the mathematical and computational foundations of biomechanical imaging,” Paul
E. Barbone and Assad A. A. Oberai. invited chapter in Computational Methods in Biomechanics,
Ed. Suvranu De, Springer, (in review) 2008.
 “Quantitative ultrasonic elastography for gel dosimetry,” Remo A Crescenti; Jeffrey C Bamber; Assad
A Oberai; Paul E Barbone; Joseph P Richter; Carlos Rivas; Nigel L Bush; Steve Webb, Ultrasound in
Medicine and Biology, submitted Oct. 2008.
 “Linear and Nonlinear elasticity imaging of soft tissue invivo: Demonstration of feasibility,” Assad
A. Oberai, Nachiket H. Gokhale Sevan Goenezen, Paul E. Barbone, Timothy J. Hall, Amy
M. Sommer, Jingfeng Jiang. Phys. Med. Biol., submitted August 2008.
 A stabilized Bsplines FEM formulation for the solution of an inverse elasticity problem arising in
medical imaging,” Carlos E. Rivas, Paul E. Barbone, and Assad A. Oberai. Proceedings of IMECE
ASME International Mechanical Engineering Congress and Exposition October 31 November 6, 2008,
Boston, MA, IMECE200866700, in press.
 “Adjointweighted variational formulation for the direct solution of plane stress inverse elasticity
problems,” Paul E. Barbone, Carlos E. Rivas, Isaac Harari, Uri Albocher, Assad A. Oberai, Sevan
Goenzen, to appear in Journal of Physics: Conference Series, 2008.
 “Divergence of finite element formulations for inverse problems treated as optimization problems,”
Carlos Rivas, Paul E. Barbone, Assad A. Oberai, to appear in Journal of Physics: Conference
Series, 2008.
 “Quantitative three dimensional elasticity imaging from quasistatic deformation: a phantom study”
Michael S. Richards, Paul E. Barbone, and Assad A. Oberai, Phys. Med. Biol., in second review,
Sept. 2008.
 “Solution of the nonlinear elasticity imaging inverse problem: the compressible case,”
Nachiket H. Gokhale, Assad A. Oberai, Paul E. Barbone, Inverse Problems, 24(4), August
2008.
 “The spatiotemporal strain response of oedematous and nonoedematous tissue to sustained
compression in vivo,” Gearóid P. Berry, Jeffrey C. Bamber, Peter S. Mortimer, Nigel L. Bush, Naomi R.
Miller, Paul E. Barbone. Ultrasound in Medicine and Biology, Volume 34, Issue 4, April 2008,
Pages 617629.
 “Adjoint weighted variational formulation for direct computational solution of an inverse heat
conduction problem,” Paul E. Barbone, Assad A. Oberai, and Isaac Harari, Inverse Problems, 23,
pp. 2325–2342, 2007.
 “The adjoint weighted equation for steady advection in a compressible fluid,” A. Oberai,
P. E. Barbone, and I. Harari, Int. J. Num. Meth. in Fluids, 54:683–693, 2007.
 “Elastic modulus imaging: some exact solutions of the compressible elastography inverse problem,”
Paul E Barbone and Assad A Oberai, Physics in Medicine and Biology, 52, pp. 1577–1593, 2007.
Included in Highlights of 2007.
 “Imaging the Elastic Nonlinearity of Tissues,” Hall, T.; Oberai, A. A.; Barbone, P. E.; Sommer, A. M.;
Gokhale, N. H.; Goenezen, S.; Jiang, J.; IEEE Ultrasonics Symposium, 2007. 2831 Oct. 2007
pp:452455.
 “Ultrasonic Elastography and Plane Strain Inverse Algorithms for Polymer Gel Dosimetry,” Crescenti,
R. A.; Bamber, J. C.; Oberai, A. A.; Barbone, P. E.; Richter, J. P.; Bush, N. L.; Webb, S.; IEEE
Ultrasonics Symposium, 2007. 2831 Oct. 2007 pp:2025  2027.
 “Coupling between elastic strain and interstitial fluid flow: Ramifications for poroelastic imaging,” R
Leiderman, PE Barbone, AA Oberai, JC Bamber. Physics in Medicine and Biology, 51 (24),
pp. 62916313, 2006.
Included in Highlights of 2006.
 “Towards an acoustic modelbased poroelastic imaging method: II. Experimental investigation,”
Gearóid P. Berry, Jeffrey C. Bamber, Naomi R. Miller, Paul E. Barbone, Nigel L. Bush,
Cecil G. Armstrong Ultrasound in Medicine and Biology, 32(12), pp. 18691885,
2006.
 “Towards an acoustic modelbased poroelastic imaging method: I. Theoretical foundation. GP Berry,”
JC Bamber, CG Armstrong, NR Miller, PE Barbone. Ultrasound in Medicine and Biology, 32(4),
pp. 547–567, 2006.
 “Elastic modulus imaging: on the uniqueness and nonuniqueness of the elastography inverse problem in
two dimensions,” Paul E. Barbone, Nachiket H. Gokhale, Inverse Problems, 20 (1): 283296 Feb
2004.
 “Simultaneous Elastic Image Registration and Elastic Modulus Reconstruction,” Nachiket Gokhale,
Mike Richards, Assad Oberai, Paul Barbone, and Marvin Doyley, Proceedings ISBI 2004: From Nano to
Macro, IEEE 2nd International Symposium on Biomedical Imaging, 1517 April 2004, Arlington VA.
IEEE Press, 2004, pp. 543–546.
 “Quantitative Elasticity Imaging: What can and cannot be inferred from strain images,” Paul E.
Barbone and Jeffrey C. Bamber, Physics in Medicine and Biology, 47(12), 2147–2164, June
2002.
 “Progress in Freehand Elastography of the Breast,” Jeffrey C. Bamber, Paul E. Barbone, Nigel
L. Bush, David O. Cosgrove, Marvin M. Doyley, Frank G. Fuechsel, Paul M. Meaney, Naomi
R. Miller, Tsuyoshi Shiina, and Francois Tranquart. IEICE Trans. Inf. & Syst., Vol. E85–D, No. 1,
pp. 5–14, January 2002.

