Abstract

We present a novel multi-resolution variational framework for vascular optical coherence elastography (OCE). This method exploits prior information about arterial wall biomechanics to produce robust estimates of tissue velocity and strain, reducing the sensitivity of conventional tracking methods to both noise- and strain-induced signal decorrelation. The velocity and strain estimation performance of this new estimator is demonstrated in simulated OCT image sequences and in benchtop OCT scanning of a vascular tissue sample.

© 2004 Optical Society of America

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References

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  1. G.C. Cheng, H.M. Loree, R.D. Kamm, M.C. Fishbein, R.T. Lee, �??Distribution of circumferential stress in ruptured and stable atherosclerotic lesions. A structural analysis with histopathological correlation,�?? Circulation 87(4), 1179-1187 (1993).
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    [CrossRef]
  6. C.L. de Korte, A.F.W. van der Steen, E.I. Cespedes, G. Pasterkamp, S.G. Carlier, F. Mastik, A.H. Schoneveld, P.W. Serruys, N. Bom, �??Characterization of plaque components and vulnerability with intravascular ultrasound elastography,�?? Phys. Med. Biol. 45, 1465-1475 (2000).
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    [CrossRef]
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    [CrossRef]
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  14. J. P. Lewis, Fast Template Matching, Vision Interface, 120-123 (1995).
  15. D. Huang, E.A. Swanson, C.P. Lin, et al., �??Optical coherence tomography,�?? Science 254, 1178-1181 (1991).
    [CrossRef]
  16. G.J. Tearney, M.E. Brezinski, B.E. Bouma, et al., �??In vivo endoscopic optical biopsy with optical coherence tomography,�?? Science 276, 2037-2039 (1997).
    [CrossRef]
  17. B.E. Bouma, G.J. Tearney, �??Power-efficient nonreciprocal interferometer and linear-scanning fiber-optic catheter for optical coherence tomography,�?? Opt Lett. 24, 531-533 (1999).
    [CrossRef]

Arterioscler. Thromb. Vasc. Biol. (1)

R.T. Lee, F.J. Schoen, H.M. Loree, M.W. Lark, P. Libby, �??Circumferential stress and matrix metalloproteinase 1 in human coronary atherosclerosis. Implications for plaque rupture,�?? Arterioscler. Thromb. Vasc. Biol. 16, 1070-1073 (1996).
[CrossRef] [PubMed]

Circulation (2)

G.C. Cheng, H.M. Loree, R.D. Kamm, M.C. Fishbein, R.T. Lee, �??Distribution of circumferential stress in ruptured and stable atherosclerotic lesions. A structural analysis with histopathological correlation,�?? Circulation 87(4), 1179-1187 (1993).
[CrossRef] [PubMed]

J.A. Schaar, C.L. de Korte, F. Mastik, C. Strijder, G. Pasterkamp, E. Boersma, P.W. Serruys, A.F.W. van der Steen, �??Characterizing vulnerable plaque features with intravascular elastography,�?? Circulation 108, 1-6 (2003).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J.M. Schmitt, �??Optical Coherence Tomography (OCT): a review,�?? IEEE J. Sel. Top. Quantum Electron. 5(4), 1205-1215 (1998).
[CrossRef]

J Am Coll Cardiol. (1)

I.K. Jang, B.E. Bouma, D.H. Kang, et al., �??Visualization of coronary atherosclerotic plaques in patients using optical coherence tomography: comparison with intravascular ultrasound,�?? J Am Coll Cardiol. 39, 604609 (2002).
[CrossRef]

J. Biol. Chem. (1)

R.T. Lee, C. Yamamoto, Y. Feng, S. Potter-Perigo, W.H. Briggs, K.T. Landschulz, T.G. Turi, J.F. Thompson, P. Libby, T.N. Wight, �??Mechanical strain induces specific changes in the synthesis and organization of proteoglycans by vascular smooth muscle cells,�?? J. Biol. Chem. 276, 13847-51 (2001).
[PubMed]

J. Biomed. Opt. (1)

D.D. Duncan, S.J. Kirkpatrick, �??Processing algorithms for tracking speckle shifts in optical elastography of biological tissues,�?? J. Biomed. Opt. 6(4), 418-426 (2001).
[CrossRef] [PubMed]

J. Eng. Mathematics (1)

M.R. Kaazempur-Mofrad, H.F. Younis , S. Patel, A.G. Isasi, R.C. Chan, D.P. Hinton, R.T. Lee, R.D. Kamm, �??Cyclic Strain in Human Carotid Bifurcation and its Potential Correlation to Atherogenesis: Idealized and Anatomically-Realistic Models,�?? J. Eng. Mathematics 47(3-4), 299-314 (2003).
[CrossRef]

Opt Lett. (1)

B.E. Bouma, G.J. Tearney, �??Power-efficient nonreciprocal interferometer and linear-scanning fiber-optic catheter for optical coherence tomography,�?? Opt Lett. 24, 531-533 (1999).
[CrossRef]

Opt. Express (2)

Phys. Med. Biol. (1)

C.L. de Korte, A.F.W. van der Steen, E.I. Cespedes, G. Pasterkamp, S.G. Carlier, F. Mastik, A.H. Schoneveld, P.W. Serruys, N. Bom, �??Characterization of plaque components and vulnerability with intravascular ultrasound elastography,�?? Phys. Med. Biol. 45, 1465-1475 (2000).
[CrossRef] [PubMed]

Science (2)

D. Huang, E.A. Swanson, C.P. Lin, et al., �??Optical coherence tomography,�?? Science 254, 1178-1181 (1991).
[CrossRef]

G.J. Tearney, M.E. Brezinski, B.E. Bouma, et al., �??In vivo endoscopic optical biopsy with optical coherence tomography,�?? Science 276, 2037-2039 (1997).
[CrossRef]

Ultrason. Imag. (1)

J. Ophir, E.I. Cspedes, H. Ponnekanti, Y. Yazdi, and X. Li, �??Elastography: A quantitative method for imaging the elasticity in biological tissues,�?? Ultrason. Imag. 13(2), 111-134 (1991).
[CrossRef]

Ultrasound in Med. & Biol. (1)

M.M. Doyley, F. Mastik, C.L. de Korte, S.G. Carlier, E.I. Cespedes, P.W. Serruys, N. Bom, A.F.W. van der Steen, �??Advancing intravascular ultrasonic palpation toward clinical applications,�?? Ultrasound in Med. & Biol. 27(11), 1471-1480 (2001).
[CrossRef]

Other (1)

J. P. Lewis, Fast Template Matching, Vision Interface, 120-123 (1995).

Supplementary Material (3)

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Figures (14)

Fig. 1.
Fig. 1.

Block diagram illustrating multi-resolution velocity field estimation

Fig. 2.
Fig. 2.

(a) Finite element geometry. (b) Finite element mesh.

Fig. 3.
Fig. 3.

(a) A comparison of a simulated PSF with fringe measurements from our OCT system, (b) OCT image simulation of an inclusion within a tissue block after demodulation.

Fig. 4.
Fig. 4.

Benchtop OCT imaging system for XY scanning of mechanically-loaded specimens.

Fig. 5.
Fig. 5.

Movie clips showing simulated axial compression (vertical loading in the downward direction) of a 500μm inclusion with (a) more compliant (464KB Quicktime movie) and (b) stiffer material properties than the surrounding tissue block (464KB Quicktime movie).

Fig. 6.
Fig. 6.

Axial velocity fields for a compliant inclusion. (a) True axial velocities from finite element modeling. (b) Axial velocity estimates from conventional motion tracking. c) Axial velocity estimates from multi-resolution variational method. Axial compression was applied in the downward direction.

Fig. 7.
Fig. 7.

Axial velocity fields for a stiff inclusion. (a) True axial velocities from finite element modeling. (b) Axial velocity estimates from conventional motion tracking. c) Axial velocity estimates from multi-resolution variational method. Axial compression was applied in the downward direction.

Fig. 8.
Fig. 8.

Axial strain fields for a compliant inclusion. (a) True axial strains from finite element modeling. (b) Axial strain estimates from conventional motion tracking. c) Axial strain estimates from multi-resolution variational method. Axial compression was applied in the downward direction.

Fig. 9.
Fig. 9.

Axial strain fields for a stiff inclusion. (a) True axial strains from finite element modeling. (b) Axial strain estimates from conventional motion tracking. c) Axial strain estimates from multi-resolution variational method. Axial compression was applied in the downward direction.

Fig. 10.
Fig. 10.

Lesion detectability as a function of noise-induced decorrelation for (a) the compliant inclusion (correlation coefficients are 0.95, 0.79, 0.54 from left to right respectively) and (b) the stiff inclusion (correlation coefficients are 0.95, 0.81, 0.55 from left to right respectively).

Fig. 11.
Fig. 11.

Estimation errors in the stiff inclusion: (a) Root-mean-square velocity estimation error as a function of noise-induced decorrelation. (b) Root-mean-square strain estimation error as a function of noise-induced decorrelation.

Fig. 12.
Fig. 12.

OCT imaging of an aortic specimen undergoing lateral (right-to-left) motion (568KB Quicktime movie). Regions of the image outside the aorta have been masked out.

Fig. 13.
Fig. 13.

Estimated lateral velocity fields for an aortic specimen undergoing lateral stretching (right-to-left in the imaging plane) a) from the conventional method, and b) from the variational method.

Fig. 14.
Fig. 14.

Estimated lateral strain fields for an aortic specimen undergoing lateral stretching (right-to-left in the imaging plane) a) from the conventional method, and b) from the variational method.

Equations (21)

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I ( x , y ) = exp ( 2 μ s ¯ y ) [ σ b ( x , y ) * h ( x , y ) ]
h ( x , y ) = Γ ( y ) p ( x )
Γ ( y ) = Re [ E s ( y′ ) E s ( y′ + y ) ] = exp ( ( πy ln 2 Δλ λ 0 2 ) 2 ) cos ( 2 πy / λ 0 )
p ( x ) = exp [ 1 2 ( πDx λ 0 f ) 2 ]
I R ( x , y ) = exp ( 2 μ ¯ s y ) [ σ b δ ( x x 0 , x y 0 ) * h ( x , y ) ]
= exp ( 2 μ ¯ s y ) [ σ b δ ( x x 0 , y y 0 ) ]
I S ( x , y ) = exp ( 2 μ s ¯ y ) [ σ b δ ( x x 0 u , x y 0 v ) * h ( x , y ) ]
= exp ( 2 μ s ¯ y ) [ σ b h ( x x 0 u , y y 0 v ) ]
[ u ̂ v ̂ ] = arg max [ u v ] ρ x , y ( u , v )
ρ x , y ( u , v ) =
M / 2 M / 2 N / 2 N / 2 [ I R ( x′ x , y′ y ) μ R ] [ I S ( x′ x u , y′ y v ) μ S ] dx dy′ [ M / 2 M / 2 N / 2 N / 2 [ I R ( x′ x , y′ y ) μ R ] 2 dx dy′ M / 2 M / 2 N / 2 N / 2 [ I S ( x′ x u , y′ y v ) μ S ] dx dy′ ] 1 / 2
E ( V ( x , y ) ) = a E D ( V ( x , y ) ) + b E S ( V ( x , y ) ) + c E I ( V ( x , y ) )
E D ( V ( x , y ) ) = ρ x , y ( V ( x , y ) ) dxdy
E S ( V ( x , y ) ) = 2 V ( x , y ) 2 dxdy
E I ( V ( x , y ) ) = ·V ( x , y ) 2 dxdy
V ̂ ( x , y ) = arg min V ( x , y ) = [ u ( x , y ) v ( x , y ) ] { a E D ( V ( x , y ) ) + b E S ( V ( x , y ) ) + c E I ( V ( x , y ) ) }
σ b ( x , y , t + 1 ) = σ b ( x u ( x , y ) , y v ( x , y ) , t )
I n ( x , y , t ) = I ( x , y , t ) + nI ( x , y , t )
F = [ 1 + u x u y v x 1 + v y ]
E = [ ε xx ε xy ε xy ε yy ] = 1 2 ( F T + F 2 I )
RMS velocity = 1 N k = 1 N ( v k v k , real v k , real ) 2 RMS strain = 1 N k = 1 N ( ε k ε k , real ε k , real ) 2

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