Abstract

Microbubble-based ultrasound contrast agents are used in clinical settings to enhance backscattered ultrasound signals from blood during perfusion and blood flow measurements. The dynamics of microbubbles contained in ultrasound contrast agents are typically studied with a high-speed camera attached to a microscope. Such microbubbles, with resting diameters between 1 µm and 7 µm, are considered in optical focus if the bubble centers are in the focal plane of the objective lens. Nonetheless, when a three-dimensional object, a stack of infinitely thin two-dimensional layers, is imaged through a microscope, the image formed onto the charge coupled device element consists of contributions from all layers. If a bubble is larger than the depth of focus, the part of the bubble above the focal plane influences the image formation and therefore the bubble size measured. If a bubble is of a size in the order of the wavelengths of the light used, the system resolution and the segmentation method influence the bubble size measured. In this study, the projections of three dimensional microbubbles (hollow spheres) were computed with an ideal, weighted three-dimensional point spread function to find out under which circumstances the optical image formation leads to a significant deviation in measurement of the actual size. The artificial images were subjected to segmentation techniques for objectively comparing original microbubble sizes with measured microbubble sizes. Results showed that a systematic error was observed for objects in focus with radius ≤ 1.65µm. Also it was concluded that even though a three-dimensional object is in focus, there is discrepancy of up to 0.66% in size measurement. In addition, size measurement of an object for the same shift above and below focus could differ by up to 3.6%. Moreover, defocusing above 25% severely deviates size measurements while defocusing up to 90% could result in mean percentage error of up to 67.96.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. A. L. Klibanov, P. T. Rasche, M. S. Hughes, J. K. Wojdyla, K. P. Galen, J. H. Wible, and G. H. Brandenburger, “Detection of individual microbubbles of ultrasound contrast agents: imaging of free-floating and targeted bubbles,” Invest. Radiol. 39 (3), 187–195 (2004).
    [Crossref] [PubMed]
  2. C.-D. Ohl, T. Kurz, R. Geisler, O. Lindau, and W. Lauterborn, “Bubble dynamics, shock waves and sonoluminescence,” Philos. Trans. Roy. Soc. A 357269–294 (1999).
    [Crossref]
  3. M. Postema, A. Bouakaz, C. T. Chin, and N. de Jong, “Simulations and measurements of optical images of insonified ultrasound contrast microbubbles,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50 (5), 523–536 (2003).
    [Crossref]
  4. K. Okada, N. Kudo, K. Niwa, and K. Yamamoto, “A basic study on sonoporation with microbubbles exposed to pulsed ultrasound,” J. Med. Ultrason. 32 (1), 3–11 (2005).
    [Crossref]
  5. P. Prentice, A. Cuschieri, K. Dholakia, M. Prausnitz, and P. Campbell, “Membrane disruption by optically controlled microbubble cavitation,” Nature Phys., 1 (2), 107–110 (2005).
    [Crossref]
  6. H. Netten, L. J. van Vliet, F. R. Boddeke, P. de Jong, and I. T. Young, “A fast scanner for fluorescence microscopy using a 2-D CCD and time delayed integration,” Bioimaging 2 (4), 184–192 (1994).
    [Crossref]
  7. J. -B. Sibarita, “Deconvolution microscopy,” Adv. Biochem. Eng./Biotechnol. 95, 201–243 (2005).
    [Crossref]
  8. D. A. Agard, “Optical sectioning microscopy: Cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
    [Crossref] [PubMed]
  9. I. T. Young, “Quantitative microscopy,” IEEE Eng. Med. Biol. 15 (1), 59–66 (1996).
    [Crossref]
  10. M. Postema, Fundamentals of Medical Ultrasonics, (CRC Press, 2011).
  11. Q. Wu, F. A. Merchant, and K. R. Castleman, Microscope Image Processing (Elsevier, 2008).
  12. S. Kotopoulis and M. Postema, “Microfoam formation in a capillary,” Ultrasonics 50, 260–268 (2010).
    [Crossref]
  13. B. Matérn, “Precision of area estimation: a numerical study,” J. Microsc. 153, 269–284 (1989).
    [Crossref]

2010 (1)

S. Kotopoulis and M. Postema, “Microfoam formation in a capillary,” Ultrasonics 50, 260–268 (2010).
[Crossref]

2005 (3)

K. Okada, N. Kudo, K. Niwa, and K. Yamamoto, “A basic study on sonoporation with microbubbles exposed to pulsed ultrasound,” J. Med. Ultrason. 32 (1), 3–11 (2005).
[Crossref]

P. Prentice, A. Cuschieri, K. Dholakia, M. Prausnitz, and P. Campbell, “Membrane disruption by optically controlled microbubble cavitation,” Nature Phys., 1 (2), 107–110 (2005).
[Crossref]

J. -B. Sibarita, “Deconvolution microscopy,” Adv. Biochem. Eng./Biotechnol. 95, 201–243 (2005).
[Crossref]

2004 (1)

A. L. Klibanov, P. T. Rasche, M. S. Hughes, J. K. Wojdyla, K. P. Galen, J. H. Wible, and G. H. Brandenburger, “Detection of individual microbubbles of ultrasound contrast agents: imaging of free-floating and targeted bubbles,” Invest. Radiol. 39 (3), 187–195 (2004).
[Crossref] [PubMed]

2003 (1)

M. Postema, A. Bouakaz, C. T. Chin, and N. de Jong, “Simulations and measurements of optical images of insonified ultrasound contrast microbubbles,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50 (5), 523–536 (2003).
[Crossref]

1999 (1)

C.-D. Ohl, T. Kurz, R. Geisler, O. Lindau, and W. Lauterborn, “Bubble dynamics, shock waves and sonoluminescence,” Philos. Trans. Roy. Soc. A 357269–294 (1999).
[Crossref]

1996 (1)

I. T. Young, “Quantitative microscopy,” IEEE Eng. Med. Biol. 15 (1), 59–66 (1996).
[Crossref]

1994 (1)

H. Netten, L. J. van Vliet, F. R. Boddeke, P. de Jong, and I. T. Young, “A fast scanner for fluorescence microscopy using a 2-D CCD and time delayed integration,” Bioimaging 2 (4), 184–192 (1994).
[Crossref]

1989 (1)

B. Matérn, “Precision of area estimation: a numerical study,” J. Microsc. 153, 269–284 (1989).
[Crossref]

1984 (1)

D. A. Agard, “Optical sectioning microscopy: Cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[Crossref] [PubMed]

Agard, D. A.

D. A. Agard, “Optical sectioning microscopy: Cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[Crossref] [PubMed]

Boddeke, F. R.

H. Netten, L. J. van Vliet, F. R. Boddeke, P. de Jong, and I. T. Young, “A fast scanner for fluorescence microscopy using a 2-D CCD and time delayed integration,” Bioimaging 2 (4), 184–192 (1994).
[Crossref]

Bouakaz, A.

M. Postema, A. Bouakaz, C. T. Chin, and N. de Jong, “Simulations and measurements of optical images of insonified ultrasound contrast microbubbles,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50 (5), 523–536 (2003).
[Crossref]

Brandenburger, G. H.

A. L. Klibanov, P. T. Rasche, M. S. Hughes, J. K. Wojdyla, K. P. Galen, J. H. Wible, and G. H. Brandenburger, “Detection of individual microbubbles of ultrasound contrast agents: imaging of free-floating and targeted bubbles,” Invest. Radiol. 39 (3), 187–195 (2004).
[Crossref] [PubMed]

Campbell, P.

P. Prentice, A. Cuschieri, K. Dholakia, M. Prausnitz, and P. Campbell, “Membrane disruption by optically controlled microbubble cavitation,” Nature Phys., 1 (2), 107–110 (2005).
[Crossref]

Castleman, K. R.

Q. Wu, F. A. Merchant, and K. R. Castleman, Microscope Image Processing (Elsevier, 2008).

Chin, C. T.

M. Postema, A. Bouakaz, C. T. Chin, and N. de Jong, “Simulations and measurements of optical images of insonified ultrasound contrast microbubbles,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50 (5), 523–536 (2003).
[Crossref]

Cuschieri, A.

P. Prentice, A. Cuschieri, K. Dholakia, M. Prausnitz, and P. Campbell, “Membrane disruption by optically controlled microbubble cavitation,” Nature Phys., 1 (2), 107–110 (2005).
[Crossref]

de Jong, N.

M. Postema, A. Bouakaz, C. T. Chin, and N. de Jong, “Simulations and measurements of optical images of insonified ultrasound contrast microbubbles,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50 (5), 523–536 (2003).
[Crossref]

de Jong, P.

H. Netten, L. J. van Vliet, F. R. Boddeke, P. de Jong, and I. T. Young, “A fast scanner for fluorescence microscopy using a 2-D CCD and time delayed integration,” Bioimaging 2 (4), 184–192 (1994).
[Crossref]

Dholakia, K.

P. Prentice, A. Cuschieri, K. Dholakia, M. Prausnitz, and P. Campbell, “Membrane disruption by optically controlled microbubble cavitation,” Nature Phys., 1 (2), 107–110 (2005).
[Crossref]

Galen, K. P.

A. L. Klibanov, P. T. Rasche, M. S. Hughes, J. K. Wojdyla, K. P. Galen, J. H. Wible, and G. H. Brandenburger, “Detection of individual microbubbles of ultrasound contrast agents: imaging of free-floating and targeted bubbles,” Invest. Radiol. 39 (3), 187–195 (2004).
[Crossref] [PubMed]

Geisler, R.

C.-D. Ohl, T. Kurz, R. Geisler, O. Lindau, and W. Lauterborn, “Bubble dynamics, shock waves and sonoluminescence,” Philos. Trans. Roy. Soc. A 357269–294 (1999).
[Crossref]

Hughes, M. S.

A. L. Klibanov, P. T. Rasche, M. S. Hughes, J. K. Wojdyla, K. P. Galen, J. H. Wible, and G. H. Brandenburger, “Detection of individual microbubbles of ultrasound contrast agents: imaging of free-floating and targeted bubbles,” Invest. Radiol. 39 (3), 187–195 (2004).
[Crossref] [PubMed]

Klibanov, A. L.

A. L. Klibanov, P. T. Rasche, M. S. Hughes, J. K. Wojdyla, K. P. Galen, J. H. Wible, and G. H. Brandenburger, “Detection of individual microbubbles of ultrasound contrast agents: imaging of free-floating and targeted bubbles,” Invest. Radiol. 39 (3), 187–195 (2004).
[Crossref] [PubMed]

Kotopoulis, S.

S. Kotopoulis and M. Postema, “Microfoam formation in a capillary,” Ultrasonics 50, 260–268 (2010).
[Crossref]

Kudo, N.

K. Okada, N. Kudo, K. Niwa, and K. Yamamoto, “A basic study on sonoporation with microbubbles exposed to pulsed ultrasound,” J. Med. Ultrason. 32 (1), 3–11 (2005).
[Crossref]

Kurz, T.

C.-D. Ohl, T. Kurz, R. Geisler, O. Lindau, and W. Lauterborn, “Bubble dynamics, shock waves and sonoluminescence,” Philos. Trans. Roy. Soc. A 357269–294 (1999).
[Crossref]

Lauterborn, W.

C.-D. Ohl, T. Kurz, R. Geisler, O. Lindau, and W. Lauterborn, “Bubble dynamics, shock waves and sonoluminescence,” Philos. Trans. Roy. Soc. A 357269–294 (1999).
[Crossref]

Lindau, O.

C.-D. Ohl, T. Kurz, R. Geisler, O. Lindau, and W. Lauterborn, “Bubble dynamics, shock waves and sonoluminescence,” Philos. Trans. Roy. Soc. A 357269–294 (1999).
[Crossref]

Matérn, B.

B. Matérn, “Precision of area estimation: a numerical study,” J. Microsc. 153, 269–284 (1989).
[Crossref]

Merchant, F. A.

Q. Wu, F. A. Merchant, and K. R. Castleman, Microscope Image Processing (Elsevier, 2008).

Netten, H.

H. Netten, L. J. van Vliet, F. R. Boddeke, P. de Jong, and I. T. Young, “A fast scanner for fluorescence microscopy using a 2-D CCD and time delayed integration,” Bioimaging 2 (4), 184–192 (1994).
[Crossref]

Niwa, K.

K. Okada, N. Kudo, K. Niwa, and K. Yamamoto, “A basic study on sonoporation with microbubbles exposed to pulsed ultrasound,” J. Med. Ultrason. 32 (1), 3–11 (2005).
[Crossref]

Ohl, C.-D.

C.-D. Ohl, T. Kurz, R. Geisler, O. Lindau, and W. Lauterborn, “Bubble dynamics, shock waves and sonoluminescence,” Philos. Trans. Roy. Soc. A 357269–294 (1999).
[Crossref]

Okada, K.

K. Okada, N. Kudo, K. Niwa, and K. Yamamoto, “A basic study on sonoporation with microbubbles exposed to pulsed ultrasound,” J. Med. Ultrason. 32 (1), 3–11 (2005).
[Crossref]

Postema, M.

S. Kotopoulis and M. Postema, “Microfoam formation in a capillary,” Ultrasonics 50, 260–268 (2010).
[Crossref]

M. Postema, A. Bouakaz, C. T. Chin, and N. de Jong, “Simulations and measurements of optical images of insonified ultrasound contrast microbubbles,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50 (5), 523–536 (2003).
[Crossref]

M. Postema, Fundamentals of Medical Ultrasonics, (CRC Press, 2011).

Prausnitz, M.

P. Prentice, A. Cuschieri, K. Dholakia, M. Prausnitz, and P. Campbell, “Membrane disruption by optically controlled microbubble cavitation,” Nature Phys., 1 (2), 107–110 (2005).
[Crossref]

Prentice, P.

P. Prentice, A. Cuschieri, K. Dholakia, M. Prausnitz, and P. Campbell, “Membrane disruption by optically controlled microbubble cavitation,” Nature Phys., 1 (2), 107–110 (2005).
[Crossref]

Rasche, P. T.

A. L. Klibanov, P. T. Rasche, M. S. Hughes, J. K. Wojdyla, K. P. Galen, J. H. Wible, and G. H. Brandenburger, “Detection of individual microbubbles of ultrasound contrast agents: imaging of free-floating and targeted bubbles,” Invest. Radiol. 39 (3), 187–195 (2004).
[Crossref] [PubMed]

Sibarita, J. -B.

J. -B. Sibarita, “Deconvolution microscopy,” Adv. Biochem. Eng./Biotechnol. 95, 201–243 (2005).
[Crossref]

van Vliet, L. J.

H. Netten, L. J. van Vliet, F. R. Boddeke, P. de Jong, and I. T. Young, “A fast scanner for fluorescence microscopy using a 2-D CCD and time delayed integration,” Bioimaging 2 (4), 184–192 (1994).
[Crossref]

Wible, J. H.

A. L. Klibanov, P. T. Rasche, M. S. Hughes, J. K. Wojdyla, K. P. Galen, J. H. Wible, and G. H. Brandenburger, “Detection of individual microbubbles of ultrasound contrast agents: imaging of free-floating and targeted bubbles,” Invest. Radiol. 39 (3), 187–195 (2004).
[Crossref] [PubMed]

Wojdyla, J. K.

A. L. Klibanov, P. T. Rasche, M. S. Hughes, J. K. Wojdyla, K. P. Galen, J. H. Wible, and G. H. Brandenburger, “Detection of individual microbubbles of ultrasound contrast agents: imaging of free-floating and targeted bubbles,” Invest. Radiol. 39 (3), 187–195 (2004).
[Crossref] [PubMed]

Wu, Q.

Q. Wu, F. A. Merchant, and K. R. Castleman, Microscope Image Processing (Elsevier, 2008).

Yamamoto, K.

K. Okada, N. Kudo, K. Niwa, and K. Yamamoto, “A basic study on sonoporation with microbubbles exposed to pulsed ultrasound,” J. Med. Ultrason. 32 (1), 3–11 (2005).
[Crossref]

Young, I. T.

I. T. Young, “Quantitative microscopy,” IEEE Eng. Med. Biol. 15 (1), 59–66 (1996).
[Crossref]

H. Netten, L. J. van Vliet, F. R. Boddeke, P. de Jong, and I. T. Young, “A fast scanner for fluorescence microscopy using a 2-D CCD and time delayed integration,” Bioimaging 2 (4), 184–192 (1994).
[Crossref]

Adv. Biochem. Eng./Biotechnol. (1)

J. -B. Sibarita, “Deconvolution microscopy,” Adv. Biochem. Eng./Biotechnol. 95, 201–243 (2005).
[Crossref]

Annu. Rev. Biophys. Bioeng. (1)

D. A. Agard, “Optical sectioning microscopy: Cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[Crossref] [PubMed]

Bioimaging (1)

H. Netten, L. J. van Vliet, F. R. Boddeke, P. de Jong, and I. T. Young, “A fast scanner for fluorescence microscopy using a 2-D CCD and time delayed integration,” Bioimaging 2 (4), 184–192 (1994).
[Crossref]

IEEE Eng. Med. Biol. (1)

I. T. Young, “Quantitative microscopy,” IEEE Eng. Med. Biol. 15 (1), 59–66 (1996).
[Crossref]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

M. Postema, A. Bouakaz, C. T. Chin, and N. de Jong, “Simulations and measurements of optical images of insonified ultrasound contrast microbubbles,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50 (5), 523–536 (2003).
[Crossref]

Invest. Radiol. (1)

A. L. Klibanov, P. T. Rasche, M. S. Hughes, J. K. Wojdyla, K. P. Galen, J. H. Wible, and G. H. Brandenburger, “Detection of individual microbubbles of ultrasound contrast agents: imaging of free-floating and targeted bubbles,” Invest. Radiol. 39 (3), 187–195 (2004).
[Crossref] [PubMed]

J. Med. Ultrason. (1)

K. Okada, N. Kudo, K. Niwa, and K. Yamamoto, “A basic study on sonoporation with microbubbles exposed to pulsed ultrasound,” J. Med. Ultrason. 32 (1), 3–11 (2005).
[Crossref]

J. Microsc. (1)

B. Matérn, “Precision of area estimation: a numerical study,” J. Microsc. 153, 269–284 (1989).
[Crossref]

Nature Phys. (1)

P. Prentice, A. Cuschieri, K. Dholakia, M. Prausnitz, and P. Campbell, “Membrane disruption by optically controlled microbubble cavitation,” Nature Phys., 1 (2), 107–110 (2005).
[Crossref]

Philos. Trans. Roy. Soc. A (1)

C.-D. Ohl, T. Kurz, R. Geisler, O. Lindau, and W. Lauterborn, “Bubble dynamics, shock waves and sonoluminescence,” Philos. Trans. Roy. Soc. A 357269–294 (1999).
[Crossref]

Ultrasonics (1)

S. Kotopoulis and M. Postema, “Microfoam formation in a capillary,” Ultrasonics 50, 260–268 (2010).
[Crossref]

Other (2)

M. Postema, Fundamentals of Medical Ultrasonics, (CRC Press, 2011).

Q. Wu, F. A. Merchant, and K. R. Castleman, Microscope Image Processing (Elsevier, 2008).

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Figures (15)

Fig. 1
Fig. 1 Simulation of ideal PSF in: 1D (left), 2D (middle) and 3D using parameters λ = 500nm, N A = 1.25 and n = 1.3.
Fig. 2
Fig. 2 Simulation of 3D objects with radius 0.5µm, 1µm, 2µm, 3µm, 4µm, and 5µm: from top left to bottom right.
Fig. 3
Fig. 3 Weighting function profile: Above the focus (1.747mm ≤ z ≤ 1.756mm) (left) and near the focus (right) for Δz = 133nm.
Fig. 4
Fig. 4 Simulation of Ideal 1D PSF (top left), 1D weighing function with 16 layers (top middle), 1D weighted PSFs (top right), and 16 2D weighted PSFs corresponding to the 16 layers.
Fig. 5
Fig. 5 Slices of white ring objects (first row) and black ring objects (second row) with radius and slice depth of: 0.5µm and 0.5 ∗ Δz ; 1µm and 1 ∗ Δz ; and 2µm and 2 ∗ Δz respectively from left to right. Note that multiples of Δz were used for each object to visualize same (16) number of slices with out overlapping. However, for the actual size measurement Δz = 133nm.
Fig. 6
Fig. 6 Simulation of shift of focus (green region) for objects of radius r = 0.5µm. First column is above focus, third column is below focus while the middle column is the 3D object. Going from the second row to the last, the shift is 25%, 50%, 75%, and 90% respectively.
Fig. 7
Fig. 7 Simulation of shift of focus (green region) for objects of radius r = 2µm. First column is above focus, third column is below focus while the middle column is the 3D object. Going from the second row to the last, the shift is 25%, 50%, 75%, and 90% respectively.
Fig. 8
Fig. 8 16 2D slice images of 3D object taken with 0.5 ∗ Δz for radius of r = 0.5µm.
Fig. 9
Fig. 9 Simulation of convolution between 16 weighted PSFs and object slices. Convolution result is normalized.
Fig. 10
Fig. 10 Effects of PSF on slices during convolution: White ring object slice at the focus (left), 2D PSF at the focus (middle), and Convolved slice (right). Second row shows intensity cross-sections of the respective images in the first row.
Fig. 11
Fig. 11 Effects of PSF on slices during convolution: Black ring object slice at the focus (left), 2D PSF at the focus (middle), and Convolved slice (right). Second row shows intensity cross-sections of the respective images in the first row
Fig. 12
Fig. 12 Segmentation of 16 stacked white ring object slices: the first two images are stacked weighed object slices and segmented object while the last two are the respective intensity cross-sections respectively.
Fig. 13
Fig. 13 Segmentation of 16 stacked black ring object slices: the first two images are stacked weighed object slices and segmented object while the last two are the respective intensity cross-sections respectively.
Fig. 14
Fig. 14 CCD images of 11 triacontakaidigons on a calibration grid (first row) segmented with a θ = 1/2(u′ + v′) threshold, where u′ is median intensity and v′ is median background value (bottom row) [3].
Fig. 15
Fig. 15 Measured object diameter versus true object diameter at different shift values above focus: White ring object (first column) and Black ring object (second column); Object size measured percentage error at different shift values above focus: White ring objects (third column) and black ring objects (fourth column). Shift of focus is 25%, 50%, 75% and 90%, from top to bottom respectively.

Tables (2)

Tables Icon

Table 1 Specified and measured diameters of Triacontakaidigons.

Tables Icon

Table 2 Comparison of black vs white ring object mean percentage errors for objects measured above and below focus.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

i ( x , y , z ) = o ( x , y , z ) h ( x x , y y , z z ) d x d y d z ,
i ( x , y ) = z ( w ( z ) o ( x , y , z ) h ( x x , y y ) d x d y ) ,
h ( r ) = [ 2 J 1 ( a r ) a r ] 2 ,
a = 2 π n s i n ( θ ) λ = 2 π N A λ ,
Δ z = λ 4 n [ 1 1 ( N A n ) 2 ] ,
w ( z ) | s i n ( π R 2 2 λ z ) | ,
ξ ( x , y ) = { 1 , o ( x , y ) T , 0 , o ( x , y ) > T .
o ( x , y , z ) = { 1 , ( x 2 + y 2 + z 2 ) r 2 , ( x 2 + y 2 + z 2 ) ( r R t ) 2 0 , Otherwise

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