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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 4, Iss. 11 — Nov. 1, 2013
  • pp: 2546–2554
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Application of quantitative second-harmonic generation microscopy to dynamic conditions

Mohammad M. Kabir, V. V. G. Krishna Inavalli, Tung-Yuen Lau, and Kimani C. Toussaint, Jr.  »View Author Affiliations


Biomedical Optics Express, Vol. 4, Issue 11, pp. 2546-2554 (2013)
http://dx.doi.org/10.1364/BOE.4.002546


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Abstract

We present a quantitative second-harmonic generation (SHG) imaging technique that quantifies the 2D spatial organization of collagen fiber samples under dynamic conditions, as an image is acquired. The technique is demonstrated for both a well-aligned tendon sample and a randomly aligned, sparsely distributed collagen scaffold sample. For a fixed signal-to-noise ratio, we confirm the applicability of this method for various window sizes (pixel areas) as well as with using a gridded overlay map that allows for correlations of fiber orientations within a given image. This work has direct impact to in vivo biological studies by incorporating simultaneous SHG image acquisition and analysis.

© 2013 Optical Society of America

1. Introduction

In an effort to adapt quantitative SHG imaging to eventual in vivo biological studies, this paper examines the experimental conditions that permit quantitative SHG imaging under dynamic conditions. We look at two extremes of test samples: stained tendon with well-aligned, highly organized collagen fibers and unstained, synthesized collagen scaffold. Using these samples, we apply quantitative SHG imaging to two dynamic situations. The first determines fiber-orientation information as the samples are spatially scanned in a plane. The second situation computes the same information for a collagen gel sample as it dries to form a 2D collagen scaffold assembly. To facilitate computation, a straightforward 2D gradient method (which is applied to the intensity of the images in real-space) is employed. Furthermore, we apply our approach to an example application to image and quantitatively analyze stromal collagen fibers belonging to individual cores in a standard breast tissue microarray (TMA) sample as they are progressively stage scanned, and where each core has been clinically classified as either benign or malignant. The paper is organized in the following way: section 2 describes the sample preparation, experimental setup, and quantitative measures used. Section 3 presents the results and discussion, while section 4 gives the conclusion.

2. Sample preparation and experimental setup

2.1 Sample preparation

Tendon, collagen scaffold, and tissue microarray samples were used in this study. Porcine tendon tissues were obtained from a local abattoir and embedded and preserved in OCT compound at −80° C. Next, the samples were brought to −20° C and 4-μm thick sections were cut using a cryostat (Leica CM3050S). They were then thawed and stained with a hematoxylene and eosin (H&E) stain. Finally, each tissue section was mounted with a permanent mounting media (Permount) onto a microscope coverslip (No 1.5).

The procedure for synthesizing the collagen scaffold follows closely to that described in the literature [25

25. C. B. Raub, V. Suresh, T. Krasieva, J. Lyubovitsky, J. D. Mih, A. J. Putnam, B. J. Tromberg, and S. C. George, “Noninvasive Assessment of Collagen Gel Microstructure and Mechanics Using Multiphoton Microscopy,” Biophys. J. 92(6), 2212–2222 (2007). [CrossRef] [PubMed]

]. High concentration type I collagen solution (BD Biosciences) was extracted from rat tail tendon. A solution of 50 μL of 10x PBS was added to 426 μL of ultra-pure H2O, followed by 0.5 μL of 1 N NaOH and 23.5 μL of collagen solution. The components were mixed in an eppendorf tube, sealed and refrigerated at 4° C for 24 hours. During experimentation, 10 μl volumes were transferred onto a coverslip for imaging.

A breast tissue microarray sample (US Biomax BR1003) was obtained from formalin-fixed, paraffin-embedded tissue. The sample comprised 1-mm diameter, 5-μm thick, cores of histologically variant classes of tissues (e.g., normal, dysplastic, and malignant). The samples were stained with H&E and mounted with xylene mounting medium onto a microscope coverslip (No 1.5).

2.2 Experimental setup & image analysis

Figure 1(a)
Fig. 1 (a) Schematic of the experimental setup used and (b) an example SHG image of stained tendon sample with associated circular histogram (top right) and FFT spectrum (bottom right). See text for details.
shows the schematic of the experimental setup used for the purpose of this study. All experiments were carried out with a spectrally tunable, Ti:sapphire pulsed laser (Spectra-Physics Mai-Tai HP DeepSee), producing 100-fs duration pulses with 80-MHz repetition rate. The excitation wavelength used in this study is spectrally centered at 780 nm, and a combination of half-wave plate and polarizer are used to control the input power. A pair of galvanometer-based scanning mirrors (GVS012, Thorlabs) is used to scan the beam over a desired rectangular area. Scanning incorporates two triangular patterns of the same amplitude but with frequencies that are not harmonically related. This ensures fast and uniform illumination over the entire scanned area. Next, the scanned beam is reflected by a short pass, 670-nm dichroic beam splitter, and subsequently focused onto the sample using a 1.4 NA oil-immersion objective lens (Olympus U Plan S Apo 100x). The backward emitted SHG signal is collected by the same illumination objective followed by a laser-blocking filter (Semrock FF01-680/sp-25) and an SHG filter (Semrock FF01-390/18-25). The signal is captured using an EMCCD camera (Hamamatsu EM-CCD C9100-13) with a total pixel area of 512 x 512 with a constant EM gain of 100x for all images.

Figure 1(b) displays the interface used for the real-time quantitative SHG analysis. Continuous frames of 512 x 512 pixel images are captured by the EMCCD camera and displayed on the screen. A customized MATLAB code permits simultaneous data analysis with image capture. A 2D gradient method [26

26. G. Stockman and L. G. Shapiro, Computer Vision (Prentice Hall PTR, 2001).

, 27

27. R. Gonzalez and R. Woods, Digital Image Processing (3rd Edition) (Prentice Hall, 2007).

] is employed to determine the fiber orientation. First, a region of interest (ROI) is identified (outlined by the green rectangle). Next, the preferred fiber orientation at each pixel within the ROI is obtained by calculating the local intensity gradient and the result is subsequently depicted in the form of a circular histogram [Fig. 1(b), top right corner]. The associated circular variance, which varies from 0 to 1, renders a quantitative measurement of orientation isotropy, and information about it can be found elsewhere [28

28. N. I. Fisher, Statistical Analysis of Circular Data (Cambridge University Press, Cambridge, 1995).

, 29

29. A. S. S. R. Jammalamadaka, Topics in Circular Statistics (World Scientific, Singapore, 2001).

]. An FFT spectrum of the ROI is also displayed [Fig. 1(b), bottom right corner], which can be used to directly determine preferred fiber orientation [15

15. R. A. Rao, M. R. Mehta, and K. C. Toussaint Jr., “Fourier transform-second-harmonic generation imaging of biological tissues,” Opt. Express 17(17), 14534–14542 (2009). [CrossRef] [PubMed]

].

3. Results and discussion

In order to determine the capabilities of our approach under dynamic conditions, we first examine the application of quantitative SHG for two sample types for various imaging areas. Specifically, we estimate the acquisition time and processing time as a function of input power, sample type, scan area, fiber density, and desired signal-to-noise ratio (SNR). Figure 2
Fig. 2 SHG images of (a) tendon and (b) collagen scaffold fibers for various pixel areas and a fixed SNR of 7. The corresponding pixel areas are: (i) 120 x 120 (ii) 240 x 240 (iii) 360 x 360 and (iv) 512 x 512 pixels. The same scale applies to all images. (c) The acquisition time for each image area is plotted against the pixel area.
summarizes the results of this experiment, where (a) corresponds to images of tendon and (b) images of collagen scaffold for window sizes (green box) referring to (i) 120 x 120 (ii) 240 x 240 (iii) 360 x 360 and (iv) 512 x 512 pixels. As mentioned earlier, these two sample types are representative of two of the more extreme conditions: well-aligned, highly organized, dense (stained) collagen fibers, and randomly aligned, fairly disorganized, more sparse (unstained) collagen fibers. To make any comparison between the two image types feasible, an SNR of 7 is maintained for both samples by using an input power of ~3 mW and 40 mW for the tendon and scaffold samples, respectively. In terms of the fiber orientation analysis that is typical for quantitative SHG, it is clear from Figs. 2(a) and 2(b) that a change in the window size does not bring about any significant changes in the preferred orientation results (indicated at the bottom of each image). Indeed, we observe across all window sizes, the circular variance is lower for tendon than scaffold, consistent with the fact that the latter is a more randomly aligned sample. Figure 2(c) depicts the acquisition time per window size for each sample, ranging from ~400 ms to 6 sec. Note that although the EMCCD camera can capture a frame in ~32 ms, we use much longer image acquisition times to account for the low conversion efficiency of second-harmonic generation. In addition, we confirm that the acquisition time scales with window size for the first three pixel areas; however, for 512 x 512 pixels, more than 4x the base window size (120 x 120), the corresponding acquisition time is ~12x longer. This comes from the fact that the average power is distributed over a larger area, and thus, the corresponding laser dwell time per point needs to increase in order to generate SHG. Therefore, it is expected that for increased window sizes and fixed input power, the acquisition time will increase in order to maintain the same SNR between various window sizes. Finally, Table 1

Table 1. Image processing time for various image sizes.

table-icon
View This Table
presents the processing time required for each image size for each sample. The time is observed to scale with both the image size and the distribution of fibers on the image, as can be observed for tendon and scaffold images of the same size; hence, for the same pixel area, tendon sample requires a longer processing time compared to the sparsely distributed scaffold sample. It should be noted that the three parameters considered, namely, imaging window size, SNR, and acquisition time, are all interdependent. For our purposes, we have chosen the SNR to be the fixed parameter since we believe it to be the more pragmatic choice to a microscopist.

For the second dynamic situation, we attempt to carry out quantitative-SHG imaging of a collagen gel solution in real time, as it dries at room temperature (~23° C) over a period of 30 min. In this case, 10 μL of solution dries to form a 2D collagen fiber layer on a microscope coverslip. To visualize this process, the objective lens is focused on to the bottom of the coverslip. A video (Media 3) is captured and select frames are shown in Fig. 4
Fig. 4 SHG images of collagen scaffold fiber formation (Media 3) at different times in (i)10 (ii)11.4 (iii)11.6 (iv)12.2 minutes. The same scale applies to all images.
. Initially, blurred images are observed, consistent with the fact that collagen fibers occupy a 3D volume, causing SHG signals to be generated and scattered from various layers within that volume. As the fibers begin to settle down, the SNR increases [see Fig. 4 (ii)-(iv)]. In addition, we confirm that the preferred orientation and circular variance, our metrics of interest, can easily be computed during drying; note that the circular variance decreases with time as more defined fiber structures become visible. It is worth mentioning here, that collagen scaffolds are extremely important to many areas of tissue and bioengineering, especially for bone repair applications. An approach that noninvasively monitors the drying and assembly of such fibers in situ, while simultaneously quantifying fiber organization, would be attractive to these fields and could ultimately facilitate new strategies in fiber scaffold design.

Conclusion

In an effort to move quantitative-SHG imaging to eventual in vivo studies, we demonstrated its application to several dynamic situations and calculated the quantitative metrics. Primarily we have considered two extremes of collagen sample types: well-aligned, dense (stained) tendon samples and sparsely distributed, randomly aligned (unstained) collagen scaffolds. We first established the minimum acquisition time for a fixed input power and SNR of 7, and for various window sizes (pixel areas) ranging from 120 x 120 to 512 x 512 pixels (the maximum pixel area for our EMCCD camera). We found that the acquisition time scales with window size for small to moderate pixel areas, and increases nonlinearly for the maximum pixel area—a direct result of the increased laser dwell time necessary to generate an SHG signal. We then showed that quantitative metrics such as preferred fiber orientation and circular variance can be computed simultaneously for each sample as an SHG image is acquired. In one case, we computed the aforementioned metrics for each sample during lateral stage scanning. Here, we established that for a window size of 240 x 240 pixels, average input powers of 3 mW and 40 mW were required for the tendon and collagen scaffold samples, respectively, with a corresponding minimum acquisition time of 1.2 s per frame and a processing time from ~500 to 700 ms depending on the density of fiber distribution. For the second dynamic condition we again determined the desired quantitative metrics during a collagen gel drying process. We observed a progressively smaller degree of circular variance as the fibers dried and assembled on the coverslip. Our approach was also applied to a simulated clinical scenario by demonstrating quantitative SHG imaging on regularly, stage-scanned breast tissue cores in a tissue microarray sample. By analyzing localized fiber orientations for each imaged area, we showed that it was possible for our approach to discern between healthy and malignant tissues under this dynamic condition. We believe that our approach has potential application to real-time imaging of other noncentrosymmetric biological structures such as axons for neuroimaging studies [30

30. D. A. Dombeck, K. A. Kasischke, H. D. Vishwasrao, M. Ingelsson, B. T. Hyman, and W. W. Webb, “Uniform polarity microtubule assemblies imaged in native brain tissue by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. U.S.A. 100(12), 7081–7086 (2003). [CrossRef] [PubMed]

], and collagen fibers during cervical remodeling for studies of premature birth [21

21. T. Y. Lau, H. K. Sangha, E. K. Chien, B. L. McFarlin, A. J. Wagoner Johnson, and K. C. Toussaint Jr., “Application of Fourier transform-second-harmonic generation imaging to the rat cervix,” J. Microsc. 251(1), 77–83 (2013). [CrossRef] [PubMed]

]. Additionally, our basic approach can also be applied to other nonlinear imaging methods [31

31. J. P. Ogilvie, D. Débarre, X. Solinas, J. L. Martin, E. Beaurepaire, and M. Joffre, “Use of coherent control for selective two-photon fluorescence microscopy in live organisms,” Opt. Express 14(2), 759–766 (2006). [CrossRef] [PubMed]

]. We are currently investigating extending our method to video rates using a combination of a detector with higher quantum efficiency and GPU-based parallel processing algorithm.

Acknowledgments

M.M.K. acknowledges support from the National Science Foundation CAREER award (DBI 09-54155).

References and links

1.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961). [CrossRef]

2.

S. Tokutake, Y. Imanishi, and M. Sisido, “Efficiency of Second Harmonic Generation from Amino Acids, Peptides, and Polypeptides Carrying Polarizable Aromatic Groups,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 170, 245–257 (1989).

3.

J. N. Gannaway and C. J. R. Sheppard, “Second-harmonic imaging in the scanning optical microscope,” Opt. Quantum Electron. 10(5), 435–439 (1978). [CrossRef]

4.

R. Hellwarth and P. Christensen, “Nonlinear optical microscopic examination of structure in polycrystalline ZnSe,” Opt. Commun. 12(3), 318–322 (1974). [CrossRef]

5.

I. Freund and M. Deutsch, “Second-harmonic microscopy of biological tissue,” Opt. Lett. 11(2), 94–96 (1986). [CrossRef] [PubMed]

6.

P. J. Campagnola and L. M. Loew, “Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms,” Nat. Biotechnol. 21(11), 1356–1360 (2003). [CrossRef] [PubMed]

7.

M. Strupler, A. M. Pena, M. Hernest, P. L. Tharaux, J. L. Martin, E. Beaurepaire, and M. C. Schanne-Klein, “Second harmonic imaging and scoring of collagen in fibrotic tissues,” Opt. Express 15(7), 4054–4065 (2007). [CrossRef] [PubMed]

8.

F. Tiaho, G. Recher, and D. Rouède, “Estimation of helical angles of myosin and collagen by second harmonic generation imaging microscopy,” Opt. Express 15(19), 12286–12295 (2007). [CrossRef] [PubMed]

9.

R. LaComb, O. Nadiarnykh, and P. J. Campagnola, “Quantitative Second Harmonic Generation Imaging of the Diseased State Osteogenesis Imperfecta: Experiment and Simulation,” Biophys. J. 94(11), 4504–4514 (2008). [CrossRef] [PubMed]

10.

X. Chen, O. Nadiarynkh, S. Plotnikov, and P. J. Campagnola, “Second harmonic generation microscopy for quantitative analysis of collagen fibrillar structure,” Nat. Protoc. 7(4), 654–669 (2012). [CrossRef] [PubMed]

11.

T. Hompland, A. Erikson, M. Lindgren, T. Lindmo, and C. de Lange Davies, “Second-harmonic generation in collagen as a potential cancer diagnostic parameter,” J. Biomed. Opt. 13(5), 054050 (2008). [CrossRef] [PubMed]

12.

P. G. Ellingsen, M. B. Lilledahl, L. M. S. Aas, C. L. Davies, and M. Kildemo, “Quantitative characterization of articular cartilage using Mueller matrix imaging and multiphoton microscopy,” J. Biomed. Opt. 16(11), 116002 (2011). [CrossRef] [PubMed]

13.

M. B. Lilledahl, D. M. Pierce, T. Ricken, G. A. Holzapfel, and C. L. Davies, “Structural analysis of articular cartilage using multiphoton microscopy: Input for biomechanical modeling,” IEEE Trans. Med. Imaging 30(9), 1635–1648 (2011). [CrossRef] [PubMed]

14.

M. B. Lilledahl, O. A. Haugen, C. de Lange Davies, and L. O. Svaasand, “Characterization of vulnerable plaques by multiphoton microscopy,” J. Biomed. Opt. 12(4), 044005 (2007). [CrossRef] [PubMed]

15.

R. A. Rao, M. R. Mehta, and K. C. Toussaint Jr., “Fourier transform-second-harmonic generation imaging of biological tissues,” Opt. Express 17(17), 14534–14542 (2009). [CrossRef] [PubMed]

16.

R. A. R. Rao, M. R. Mehta, S. Leithem, and K. C. Toussaint Jr., “Quantitative analysis of forward and backward second-harmonic images of collagen fibers using Fourier transform second-harmonic-generation microscopy,” Opt. Lett. 34(24), 3779–3781 (2009). [CrossRef] [PubMed]

17.

M. Sivaguru, S. Durgam, R. Ambekar, D. Luedtke, G. Fried, A. Stewart, and K. C. Toussaint Jr., “Quantitative analysis of collagen fiber organization in injured tendons using Fourier transform-second harmonic generation imaging,” Opt. Express 18(24), 24983–24993 (2010). [CrossRef] [PubMed]

18.

R. Ambekar, M. Chittenden, I. Jasiuk, and K. C. Toussaint Jr., “Quantitative second-harmonic generation microscopy for imaging porcine cortical bone: Comparison to SEM and its potential to investigate age-related changes,” Bone 50(3), 643–650 (2012). [CrossRef] [PubMed]

19.

R. Ambekar, T. Y. Lau, M. Walsh, R. Bhargava, and K. C. Toussaint Jr., “Quantifying collagen structure in breast biopsies using second-harmonic generation imaging,” Biomed. Opt. Express 3(9), 2021–2035 (2012). [CrossRef] [PubMed]

20.

T. Y. Lau, R. Ambekar, and K. C. Toussaint, “Quantification of collagen fiber organization using three-dimensional Fourier transform-second-harmonic generation imaging,” Opt. Express 20(19), 21821–21832 (2012). [CrossRef] [PubMed]

21.

T. Y. Lau, H. K. Sangha, E. K. Chien, B. L. McFarlin, A. J. Wagoner Johnson, and K. C. Toussaint Jr., “Application of Fourier transform-second-harmonic generation imaging to the rat cervix,” J. Microsc. 251(1), 77–83 (2013). [CrossRef] [PubMed]

22.

S. H. Huang, C. D. Hsiao, D. S. Lin, C. Y. Chow, C. J. Chang, and I. Liau, “Imaging of zebrafish in Vivo with second-harmonic generation reveals shortened sarcomeres associated with myopathy induced by statin,” PLoS ONE 6(9), e24764 (2011). [CrossRef] [PubMed]

23.

B. E. Cohen, “Biological imaging: Beyond fluorescence,” Nature 467(7314), 407–408 (2010). [CrossRef] [PubMed]

24.

P. Pantazis, J. Maloney, D. Wu, and S. E. Fraser, “Second harmonic generating (SHG) nanoprobes for in vivo imaging,” Proc. Natl. Acad. Sci. U.S.A. 107(33), 14535–14540 (2010). [CrossRef] [PubMed]

25.

C. B. Raub, V. Suresh, T. Krasieva, J. Lyubovitsky, J. D. Mih, A. J. Putnam, B. J. Tromberg, and S. C. George, “Noninvasive Assessment of Collagen Gel Microstructure and Mechanics Using Multiphoton Microscopy,” Biophys. J. 92(6), 2212–2222 (2007). [CrossRef] [PubMed]

26.

G. Stockman and L. G. Shapiro, Computer Vision (Prentice Hall PTR, 2001).

27.

R. Gonzalez and R. Woods, Digital Image Processing (3rd Edition) (Prentice Hall, 2007).

28.

N. I. Fisher, Statistical Analysis of Circular Data (Cambridge University Press, Cambridge, 1995).

29.

A. S. S. R. Jammalamadaka, Topics in Circular Statistics (World Scientific, Singapore, 2001).

30.

D. A. Dombeck, K. A. Kasischke, H. D. Vishwasrao, M. Ingelsson, B. T. Hyman, and W. W. Webb, “Uniform polarity microtubule assemblies imaged in native brain tissue by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. U.S.A. 100(12), 7081–7086 (2003). [CrossRef] [PubMed]

31.

J. P. Ogilvie, D. Débarre, X. Solinas, J. L. Martin, E. Beaurepaire, and M. Joffre, “Use of coherent control for selective two-photon fluorescence microscopy in live organisms,” Opt. Express 14(2), 759–766 (2006). [CrossRef] [PubMed]

OCIS Codes
(100.2960) Image processing : Image analysis
(180.4315) Microscopy : Nonlinear microscopy

ToC Category:
Microscopy

History
Original Manuscript: July 2, 2013
Revised Manuscript: August 22, 2013
Manuscript Accepted: October 14, 2013
Published: October 21, 2013

Virtual Issues
Novel Techniques in Microscopy (2013) Biomedical Optics Express

Citation
Mohammad M. Kabir, V. V. G. Krishna Inavalli, Tung-Yuen Lau, and Kimani C. Toussaint, "Application of quantitative second-harmonic generation microscopy to dynamic conditions," Biomed. Opt. Express 4, 2546-2554 (2013)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-4-11-2546


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References

  1. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett.7(4), 118–119 (1961). [CrossRef]
  2. S. Tokutake, Y. Imanishi, and M. Sisido, “Efficiency of Second Harmonic Generation from Amino Acids, Peptides, and Polypeptides Carrying Polarizable Aromatic Groups,” Mol. Cryst. Liq. Cryst. (Phila. Pa.)170, 245–257 (1989).
  3. J. N. Gannaway and C. J. R. Sheppard, “Second-harmonic imaging in the scanning optical microscope,” Opt. Quantum Electron.10(5), 435–439 (1978). [CrossRef]
  4. R. Hellwarth and P. Christensen, “Nonlinear optical microscopic examination of structure in polycrystalline ZnSe,” Opt. Commun.12(3), 318–322 (1974). [CrossRef]
  5. I. Freund and M. Deutsch, “Second-harmonic microscopy of biological tissue,” Opt. Lett.11(2), 94–96 (1986). [CrossRef] [PubMed]
  6. P. J. Campagnola and L. M. Loew, “Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms,” Nat. Biotechnol.21(11), 1356–1360 (2003). [CrossRef] [PubMed]
  7. M. Strupler, A. M. Pena, M. Hernest, P. L. Tharaux, J. L. Martin, E. Beaurepaire, and M. C. Schanne-Klein, “Second harmonic imaging and scoring of collagen in fibrotic tissues,” Opt. Express15(7), 4054–4065 (2007). [CrossRef] [PubMed]
  8. F. Tiaho, G. Recher, and D. Rouède, “Estimation of helical angles of myosin and collagen by second harmonic generation imaging microscopy,” Opt. Express15(19), 12286–12295 (2007). [CrossRef] [PubMed]
  9. R. LaComb, O. Nadiarnykh, and P. J. Campagnola, “Quantitative Second Harmonic Generation Imaging of the Diseased State Osteogenesis Imperfecta: Experiment and Simulation,” Biophys. J.94(11), 4504–4514 (2008). [CrossRef] [PubMed]
  10. X. Chen, O. Nadiarynkh, S. Plotnikov, and P. J. Campagnola, “Second harmonic generation microscopy for quantitative analysis of collagen fibrillar structure,” Nat. Protoc.7(4), 654–669 (2012). [CrossRef] [PubMed]
  11. T. Hompland, A. Erikson, M. Lindgren, T. Lindmo, and C. de Lange Davies, “Second-harmonic generation in collagen as a potential cancer diagnostic parameter,” J. Biomed. Opt.13(5), 054050 (2008). [CrossRef] [PubMed]
  12. P. G. Ellingsen, M. B. Lilledahl, L. M. S. Aas, C. L. Davies, and M. Kildemo, “Quantitative characterization of articular cartilage using Mueller matrix imaging and multiphoton microscopy,” J. Biomed. Opt.16(11), 116002 (2011). [CrossRef] [PubMed]
  13. M. B. Lilledahl, D. M. Pierce, T. Ricken, G. A. Holzapfel, and C. L. Davies, “Structural analysis of articular cartilage using multiphoton microscopy: Input for biomechanical modeling,” IEEE Trans. Med. Imaging30(9), 1635–1648 (2011). [CrossRef] [PubMed]
  14. M. B. Lilledahl, O. A. Haugen, C. de Lange Davies, and L. O. Svaasand, “Characterization of vulnerable plaques by multiphoton microscopy,” J. Biomed. Opt.12(4), 044005 (2007). [CrossRef] [PubMed]
  15. R. A. Rao, M. R. Mehta, and K. C. Toussaint., “Fourier transform-second-harmonic generation imaging of biological tissues,” Opt. Express17(17), 14534–14542 (2009). [CrossRef] [PubMed]
  16. R. A. R. Rao, M. R. Mehta, S. Leithem, and K. C. Toussaint., “Quantitative analysis of forward and backward second-harmonic images of collagen fibers using Fourier transform second-harmonic-generation microscopy,” Opt. Lett.34(24), 3779–3781 (2009). [CrossRef] [PubMed]
  17. M. Sivaguru, S. Durgam, R. Ambekar, D. Luedtke, G. Fried, A. Stewart, and K. C. Toussaint., “Quantitative analysis of collagen fiber organization in injured tendons using Fourier transform-second harmonic generation imaging,” Opt. Express18(24), 24983–24993 (2010). [CrossRef] [PubMed]
  18. R. Ambekar, M. Chittenden, I. Jasiuk, and K. C. Toussaint., “Quantitative second-harmonic generation microscopy for imaging porcine cortical bone: Comparison to SEM and its potential to investigate age-related changes,” Bone50(3), 643–650 (2012). [CrossRef] [PubMed]
  19. R. Ambekar, T. Y. Lau, M. Walsh, R. Bhargava, and K. C. Toussaint., “Quantifying collagen structure in breast biopsies using second-harmonic generation imaging,” Biomed. Opt. Express3(9), 2021–2035 (2012). [CrossRef] [PubMed]
  20. T. Y. Lau, R. Ambekar, and K. C. Toussaint, “Quantification of collagen fiber organization using three-dimensional Fourier transform-second-harmonic generation imaging,” Opt. Express20(19), 21821–21832 (2012). [CrossRef] [PubMed]
  21. T. Y. Lau, H. K. Sangha, E. K. Chien, B. L. McFarlin, A. J. Wagoner Johnson, and K. C. Toussaint., “Application of Fourier transform-second-harmonic generation imaging to the rat cervix,” J. Microsc.251(1), 77–83 (2013). [CrossRef] [PubMed]
  22. S. H. Huang, C. D. Hsiao, D. S. Lin, C. Y. Chow, C. J. Chang, and I. Liau, “Imaging of zebrafish in Vivo with second-harmonic generation reveals shortened sarcomeres associated with myopathy induced by statin,” PLoS ONE6(9), e24764 (2011). [CrossRef] [PubMed]
  23. B. E. Cohen, “Biological imaging: Beyond fluorescence,” Nature467(7314), 407–408 (2010). [CrossRef] [PubMed]
  24. P. Pantazis, J. Maloney, D. Wu, and S. E. Fraser, “Second harmonic generating (SHG) nanoprobes for in vivo imaging,” Proc. Natl. Acad. Sci. U.S.A.107(33), 14535–14540 (2010). [CrossRef] [PubMed]
  25. C. B. Raub, V. Suresh, T. Krasieva, J. Lyubovitsky, J. D. Mih, A. J. Putnam, B. J. Tromberg, and S. C. George, “Noninvasive Assessment of Collagen Gel Microstructure and Mechanics Using Multiphoton Microscopy,” Biophys. J.92(6), 2212–2222 (2007). [CrossRef] [PubMed]
  26. G. Stockman and L. G. Shapiro, Computer Vision (Prentice Hall PTR, 2001).
  27. R. Gonzalez and R. Woods, Digital Image Processing (3rd Edition) (Prentice Hall, 2007).
  28. N. I. Fisher, Statistical Analysis of Circular Data (Cambridge University Press, Cambridge, 1995).
  29. A. S. S. R. Jammalamadaka, Topics in Circular Statistics (World Scientific, Singapore, 2001).
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