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In vivo flow mapping in complex vessel networks by single image correlation.

Sironi L, Bouzin M, Inverso D, D'Alfonso L, Pozzi P, Cotelli F, Guidotti LG, Iannacone M, Collini M, Chirico G - Sci Rep (2014)

Bottom Line: Fluorescent flowing objects produce diagonal lines in the raster-scanned image superimposed to static morphological details.The analytical expression of the CCF has been derived by applying scanning fluorescence correlation concepts to drifting optically resolved objects and the theoretical framework has been validated in systems of increasing complexity.The power of the technique is revealed by its application to the intricate murine hepatic microcirculatory system where blood flow speed has been mapped simultaneously in several capillaries from a single xy-image and followed in time at high spatial and temporal resolution.

View Article: PubMed Central - PubMed

Affiliation: Università degli Studi di Milano-Bicocca, Physics Department, Piazza della Scienza 3, I-20126, Milan, Italy.

ABSTRACT
We describe a novel method (FLICS, FLow Image Correlation Spectroscopy) to extract flow speeds in complex vessel networks from a single raster-scanned optical xy-image, acquired in vivo by confocal or two-photon excitation microscopy. Fluorescent flowing objects produce diagonal lines in the raster-scanned image superimposed to static morphological details. The flow velocity is obtained by computing the Cross Correlation Function (CCF) of the intensity fluctuations detected in pairs of columns of the image. The analytical expression of the CCF has been derived by applying scanning fluorescence correlation concepts to drifting optically resolved objects and the theoretical framework has been validated in systems of increasing complexity. The power of the technique is revealed by its application to the intricate murine hepatic microcirculatory system where blood flow speed has been mapped simultaneously in several capillaries from a single xy-image and followed in time at high spatial and temporal resolution.

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Validation measurements in Zebrafish embryos (3 days post fertilization d.p.f.).(a)–(d) Confocal xy-images acquired by detecting the fluorescence signal (shown in red) of DsRed-expressing RBCs (λexc = 561 nm, detection bandwidth = 575–650 nm), overlaid to (non-confocal) transmitted-light images. fline = 1000 Hz, δx = 0.04 μm, scale bar, 10 μm; γ = 90°, 50°, 0°, −50° in (a), (b), (c) and (d), respectively. γ and v are sketched in the reference Cartesian xy-plane. (e) Exemplifying experimental CCFs for increasing column distance, showing the expected decrease of the peak time for lower (J-I)δx values. (f) Normalized CCFs for γ ∈ [0°, 90°] and (J-I)δx = 6.6 μm, fitted to equation (3); errors are within the size of data points. (g), (h) Experimental CCF peak amplitude (in g) and peak time (in h) for γ ∈ [−90°, 90°] (mean ± standard deviation (s.d.), from n = 7 xy-images), fitted to equation (S.44) and equation (4) (derived in the approximation D = 0 in Supplementary Note 2). Best-fit parameters a = 6.3 ± 0.2 μm in (f) and /v/ = 424 ± 11 μm/s in (g). (i) Flow speed /v/ recovered from the CCFs fit (open circles, mean ± s.d., n = 4) and /v/0 recovered directly from the CCFs peak time (filled squares, weighted average ± s.d., n = 7). In the lower panel, /v///v/0 is shown for γ ∈ [−80°, 80°]. For γ = ± 90°, /v/0 has not been recovered since the CCF turns into a decay (see panel f).
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f2: Validation measurements in Zebrafish embryos (3 days post fertilization d.p.f.).(a)–(d) Confocal xy-images acquired by detecting the fluorescence signal (shown in red) of DsRed-expressing RBCs (λexc = 561 nm, detection bandwidth = 575–650 nm), overlaid to (non-confocal) transmitted-light images. fline = 1000 Hz, δx = 0.04 μm, scale bar, 10 μm; γ = 90°, 50°, 0°, −50° in (a), (b), (c) and (d), respectively. γ and v are sketched in the reference Cartesian xy-plane. (e) Exemplifying experimental CCFs for increasing column distance, showing the expected decrease of the peak time for lower (J-I)δx values. (f) Normalized CCFs for γ ∈ [0°, 90°] and (J-I)δx = 6.6 μm, fitted to equation (3); errors are within the size of data points. (g), (h) Experimental CCF peak amplitude (in g) and peak time (in h) for γ ∈ [−90°, 90°] (mean ± standard deviation (s.d.), from n = 7 xy-images), fitted to equation (S.44) and equation (4) (derived in the approximation D = 0 in Supplementary Note 2). Best-fit parameters a = 6.3 ± 0.2 μm in (f) and /v/ = 424 ± 11 μm/s in (g). (i) Flow speed /v/ recovered from the CCFs fit (open circles, mean ± s.d., n = 4) and /v/0 recovered directly from the CCFs peak time (filled squares, weighted average ± s.d., n = 7). In the lower panel, /v///v/0 is shown for γ ∈ [−80°, 80°]. For γ = ± 90°, /v/0 has not been recovered since the CCF turns into a decay (see panel f).

Mentions: The effects produced on the CCF overall shape and on the lag time (τmax) of its maximum by the most relevant parameters, such as the blood flow speed /v/, the column distance J–I, the scan frequency fline and the angle γ, have been investigated on simulated CCFs (Supplementary Fig. 2). The effect of an increasing flow speed is to shift the peak time τmax toward shorter lag times. The peak of the CCF is in fact directly related to the time it takes, on average, for flowing objects to travel the distance between the columns selected for the CCF derivation. For the same reason, an opposite shift of the peak time τmax toward longer lag times is found when the column distance is increased. The functional dependence of the peak time on the column distance and on the flow speed, as well as on the other image acquisition parameters, is reported in Supplementary Note 2. The scan frequency does not remarkably affect the CCF shape and peak time, but it determines the time axis scaling (τ ≈ nτline), defining therefore the time resolution in the CCFs sampling. The scan frequencies available on commercial microscopes also determine the range of blood flow speeds that can be measured: the condition vscan = fline (Nxδx) > /v/ leads, for scan frequencies ~10–8000 Hz and for an x-size of the field of view (Nxδx) ~ 150 μm, to a broad range /v/≲ 1.2 cm/s of measurable blood speeds. The dependence of the CCF on the angle between the scan path and the flow direction finally highlights the sensitivity of FLICS for blood flow speed measurements for any relative orientation of the scan and flow directions, as will be extensively investigated in the calibration measurements on Zebrafish embryos (Fig. 2). This proofs to be a great advantage for the characterization of intricate capillary networks.


In vivo flow mapping in complex vessel networks by single image correlation.

Sironi L, Bouzin M, Inverso D, D'Alfonso L, Pozzi P, Cotelli F, Guidotti LG, Iannacone M, Collini M, Chirico G - Sci Rep (2014)

Validation measurements in Zebrafish embryos (3 days post fertilization d.p.f.).(a)–(d) Confocal xy-images acquired by detecting the fluorescence signal (shown in red) of DsRed-expressing RBCs (λexc = 561 nm, detection bandwidth = 575–650 nm), overlaid to (non-confocal) transmitted-light images. fline = 1000 Hz, δx = 0.04 μm, scale bar, 10 μm; γ = 90°, 50°, 0°, −50° in (a), (b), (c) and (d), respectively. γ and v are sketched in the reference Cartesian xy-plane. (e) Exemplifying experimental CCFs for increasing column distance, showing the expected decrease of the peak time for lower (J-I)δx values. (f) Normalized CCFs for γ ∈ [0°, 90°] and (J-I)δx = 6.6 μm, fitted to equation (3); errors are within the size of data points. (g), (h) Experimental CCF peak amplitude (in g) and peak time (in h) for γ ∈ [−90°, 90°] (mean ± standard deviation (s.d.), from n = 7 xy-images), fitted to equation (S.44) and equation (4) (derived in the approximation D = 0 in Supplementary Note 2). Best-fit parameters a = 6.3 ± 0.2 μm in (f) and /v/ = 424 ± 11 μm/s in (g). (i) Flow speed /v/ recovered from the CCFs fit (open circles, mean ± s.d., n = 4) and /v/0 recovered directly from the CCFs peak time (filled squares, weighted average ± s.d., n = 7). In the lower panel, /v///v/0 is shown for γ ∈ [−80°, 80°]. For γ = ± 90°, /v/0 has not been recovered since the CCF turns into a decay (see panel f).
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f2: Validation measurements in Zebrafish embryos (3 days post fertilization d.p.f.).(a)–(d) Confocal xy-images acquired by detecting the fluorescence signal (shown in red) of DsRed-expressing RBCs (λexc = 561 nm, detection bandwidth = 575–650 nm), overlaid to (non-confocal) transmitted-light images. fline = 1000 Hz, δx = 0.04 μm, scale bar, 10 μm; γ = 90°, 50°, 0°, −50° in (a), (b), (c) and (d), respectively. γ and v are sketched in the reference Cartesian xy-plane. (e) Exemplifying experimental CCFs for increasing column distance, showing the expected decrease of the peak time for lower (J-I)δx values. (f) Normalized CCFs for γ ∈ [0°, 90°] and (J-I)δx = 6.6 μm, fitted to equation (3); errors are within the size of data points. (g), (h) Experimental CCF peak amplitude (in g) and peak time (in h) for γ ∈ [−90°, 90°] (mean ± standard deviation (s.d.), from n = 7 xy-images), fitted to equation (S.44) and equation (4) (derived in the approximation D = 0 in Supplementary Note 2). Best-fit parameters a = 6.3 ± 0.2 μm in (f) and /v/ = 424 ± 11 μm/s in (g). (i) Flow speed /v/ recovered from the CCFs fit (open circles, mean ± s.d., n = 4) and /v/0 recovered directly from the CCFs peak time (filled squares, weighted average ± s.d., n = 7). In the lower panel, /v///v/0 is shown for γ ∈ [−80°, 80°]. For γ = ± 90°, /v/0 has not been recovered since the CCF turns into a decay (see panel f).
Mentions: The effects produced on the CCF overall shape and on the lag time (τmax) of its maximum by the most relevant parameters, such as the blood flow speed /v/, the column distance J–I, the scan frequency fline and the angle γ, have been investigated on simulated CCFs (Supplementary Fig. 2). The effect of an increasing flow speed is to shift the peak time τmax toward shorter lag times. The peak of the CCF is in fact directly related to the time it takes, on average, for flowing objects to travel the distance between the columns selected for the CCF derivation. For the same reason, an opposite shift of the peak time τmax toward longer lag times is found when the column distance is increased. The functional dependence of the peak time on the column distance and on the flow speed, as well as on the other image acquisition parameters, is reported in Supplementary Note 2. The scan frequency does not remarkably affect the CCF shape and peak time, but it determines the time axis scaling (τ ≈ nτline), defining therefore the time resolution in the CCFs sampling. The scan frequencies available on commercial microscopes also determine the range of blood flow speeds that can be measured: the condition vscan = fline (Nxδx) > /v/ leads, for scan frequencies ~10–8000 Hz and for an x-size of the field of view (Nxδx) ~ 150 μm, to a broad range /v/≲ 1.2 cm/s of measurable blood speeds. The dependence of the CCF on the angle between the scan path and the flow direction finally highlights the sensitivity of FLICS for blood flow speed measurements for any relative orientation of the scan and flow directions, as will be extensively investigated in the calibration measurements on Zebrafish embryos (Fig. 2). This proofs to be a great advantage for the characterization of intricate capillary networks.

Bottom Line: Fluorescent flowing objects produce diagonal lines in the raster-scanned image superimposed to static morphological details.The analytical expression of the CCF has been derived by applying scanning fluorescence correlation concepts to drifting optically resolved objects and the theoretical framework has been validated in systems of increasing complexity.The power of the technique is revealed by its application to the intricate murine hepatic microcirculatory system where blood flow speed has been mapped simultaneously in several capillaries from a single xy-image and followed in time at high spatial and temporal resolution.

View Article: PubMed Central - PubMed

Affiliation: Università degli Studi di Milano-Bicocca, Physics Department, Piazza della Scienza 3, I-20126, Milan, Italy.

ABSTRACT
We describe a novel method (FLICS, FLow Image Correlation Spectroscopy) to extract flow speeds in complex vessel networks from a single raster-scanned optical xy-image, acquired in vivo by confocal or two-photon excitation microscopy. Fluorescent flowing objects produce diagonal lines in the raster-scanned image superimposed to static morphological details. The flow velocity is obtained by computing the Cross Correlation Function (CCF) of the intensity fluctuations detected in pairs of columns of the image. The analytical expression of the CCF has been derived by applying scanning fluorescence correlation concepts to drifting optically resolved objects and the theoretical framework has been validated in systems of increasing complexity. The power of the technique is revealed by its application to the intricate murine hepatic microcirculatory system where blood flow speed has been mapped simultaneously in several capillaries from a single xy-image and followed in time at high spatial and temporal resolution.

Show MeSH
Related in: MedlinePlus