Fourier transform-second-harmonic generation imaging of biological tissues

doi:10.1364/OE.17.014534

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Fourier transform-second-harmonic generation imaging of biological tissues

Raghu A. Rao, Monal R. Mehta, and Kimani C. Toussaint »View Author Affiliations

Optics Express, Vol. 17, Issue 17, pp. 14534-14542 (2009)
http://dx.doi.org/10.1364/OE.17.014534

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Abstract

Fourier transform-second-harmonic generation imaging is employed to obtain quantitative metrics of collagen fibers in biological tissues. In particular, the preferred orientation and maximum spatial frequency of collagen fibers for selected regions of interest in porcine trachea, ear, and cornea are determined. These metrics remain consistent when applied to collagen fibers in the ear, which can be expected from observation. Collagen fibers in the trachea are more random with large standard deviations in orientation, and large variations in maximum spatial frequency. In addition, these metrics are used to investigate structural changes through a 3D stack of the cornea. This technique can be used as a quantitative marker to assess the structure of collagen fibers that may change due to damage from disease or physical injury.

1. Introduction

Collagens are a family of fibrous proteins found in all multicellular animals, and account for 25% of the total protein mass in mammals [1

B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, Molecular Biology of the Cell (Garland Science, 2008).

]. Collagen molecules organize into hierarchical fibrillar structures that form fiber bundles which display a high degree of spatial organization. These fibers can be found in the cornea, bone, cartilage, and skin [1

B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, Molecular Biology of the Cell (Garland Science, 2008).

–5

L. Klein and J. Chandrarajan, “Collagen degradation in rat skin but not in intestine during rapid growth - effect on collagen type-1 and type-3 from skin,” Proc. Natl. Acad. Sci. USA 74, 1436–1439 (1977). [CrossRef] [PubMed]

]. Connective tissue diseases such as osteogenesis imperfecta and Ehlers-Danlos Syndrome are known to alter the organization of collagen fibers [6

S. M. Weis, J. L. Emery, K. D. Becker, D. J. McBride, J. H. Omens, and A. D. McCulloch, “Myocardial mechanics and collagen structure in the osteogenesis imperfecta murine (oim),” Circ. Res. 87, 663–669 (2000). [PubMed]

, 7

J. R. Mao and J. Bristow, “The Ehlers-Danlos syndrome: on beyond collagens,” J. Clin. Invest. 107, 1063–1069 (2001). [CrossRef] [PubMed]

]. Therefore, monitoring the structure of fibrillar collagen is quintessential for understanding its function in tissues. Within the past decade, second-harmonic generation (SHG) microscopy has become an increasingly popular technique for achieving this [8

H. T. Chen, H. F. Wang, M. N. Slipchenko, Y. K. Jung, Y. Z. Shi, J. B. Zhu, K. K. Buhman, and J. X. Cheng, “A multimodal platform for nonlinear optical microscopy and microspectroscopy,” Opt. Express 17, 1282–1290 (2009). [CrossRef] [PubMed]

–17

S. V. Plotnikov, A. M. Kenny, S. J. Walsh, B. Zubrowski, C. Joseph, V. L. Scranton, G. A. Kuchel, D. Dauser, M. S. Xu, C. C. Pilbeam, D. J. Adams, R. P. Dougherty, P. J. Campagnola, and W. A. Mohler, “Measurement of muscle disease by quantitative second-harmonic generation imaging,” J. Biomed. Opt. 13, 11 (2008). [CrossRef]

SHG microscopy has been extensively used in medicine and biology to obtain images of highly-ordered structures such as collagen fibers, microtubulin, and skeletal muscle, with high resolution and contrast [8

–17

]. This form of nonlinear optical microscopy results from coherent second-order nonlinear scattering wherein a noncentrosymmetric structure emits light at half the wavelength of the incident (pump) optical field. Collagen fibers, being intrinsically noncentrosymmetric, emit SHG, and thus produce high-contrast images using this technique, without the need for staining. Notwithstanding the impressive advances in SHG imaging, most studies in the past have relied on the qualitative assessment of obtained images for analysis [12

C. H. Yu, S. P. Tai, C. T. Kung, I. J. Wang, H. C. Yu, H. J. Huang, W. J. Lee, Y. F. Chan, and C. K. Sun, “In vivo and ex vivo imaging of intra-tissue elastic fibers using third-harmonic-generation microscopy,” Opt. Express 15, 11167–11177 (2007). [CrossRef] [PubMed]

, 13

S. W. Teng, H. Y. Tan, J. L. Peng, H. H. Lin, K. H. Kim, W. Lo, Y. Sun, W. C. Lin, S. J. Lin, S. H. Jee, P. T. C. So, and C. Y. Dong, “Multiphoton autofluorescence and second-harmonic generation imaging of the ex vivo porcine eye,” Invest. Ophthalmol. Vis. Sci. 47, 1216–1224 (2006). [CrossRef] [PubMed]

, 18

N. Morishige, A. J. Wahlert, M. C. Kenney, D. J. Brown, K. Kawamoto, T. Chikama, T. Nishida, and J. V. Jester, “Second-harmonic imaging microscopy of normal human and keratoconus cornea,” Invest. Ophthalmol. Vis. Sci. 48, 1087–1094 (2007). [CrossRef] [PubMed]

]. Recently, researchers have made major strides in developing quantitative metrics for this imaging modality [9

W. L. Chen, T. H. Li, P. J. Su, C. K. Chou, P. T. Fwu, S. J. Lin, D. Kim, P. T. C. So, and C. Y. Dong, “Second harmonic generation chi tensor microscopy for tissue imaging,” Appl. Phys. Lett. 94, 3 (2009).

, 14

R. M. Williams, W. R. Zipfel, and W. W. Webb, “Interpreting second-harmonic generation images of collagen I fibrils,” Biophys. J. 88, 1377–1386 (2005). [CrossRef]

–16

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

, 19

P. Matteini, F. Ratto, F. Rossi, R. Cicchi, C. Stringari, D. Kapsokalyvas, F. S. Pavone, and R. Pini, “Photothermally-induced disordered patterns of corneal collagen revealed by SHG imaging,” Opt. Express 17, 4868–4878 (2009). [CrossRef] [PubMed]

Although there are several recent approaches to quantitative SHG imaging, we briefly discuss a few. One approach uses forward-to-backward (F/B) ratio of the emitted SHG signal to reveal additional information about the environment of collagen fibers [14

R. M. Williams, W. R. Zipfel, and W. W. Webb, “Interpreting second-harmonic generation images of collagen I fibrils,” Biophys. J. 88, 1377–1386 (2005). [CrossRef]

]. It was found that solutions (NaCl) of high ionic strength reduced the F/B ratio for adult tendons, and was attributed to sub-diffraction structural changes in collagen fibers. In another study, the F/B ratio was used to differentiate between types of collagen [15

G. Cox, E. Kable, A. Jones, I. K. Fraser, F. Manconi, and M. D. Gorrell, “3-dimensional imaging of collagen using second harmonic generation,” J. Struct. Biol. 141, 53–62 (2003). [CrossRef] [PubMed]

]. Type I collagen which is highly crystalline produces strong a F/B SHG signal, while Type III and IV collagen which are less crystalline produces a weaker signal. Yet another metric is the relative components of the second-order nonlinear susceptibility tensor [16

]. These elements are extracted from the SHG images in order to determine the orientation angle of myosin and collagen harmonophores in gastrocnemius muscle and tendon. Recently, these elements were obtained at the pixel level to differentiate between different SHG generators within the human dermis and the collagen-muscle junction of a chicken wing [9

]. Another measure is the distribution of length of structures in a tissue [17

]. In particular the SHG signal emitted from the myosin filaments of sarcomeres, were quantified by length distribution to investigate the mice and human skeletal muscle tissue. It was thus possible to examine the disease stage, recovery, and aging of the muscle tissues. In addition to these approaches, Fourier analysis could be used to derive quantitative markers for assessment of biological structures [19

]. Very recently, along with other parameters, the geometric distribution of spatial frequencies in the 2D Fourier transform (FT) was used to quantify the disorganization of collagen fibers due to photo-thermal damage in porcine corneas. It was found that regularity in fiber organization leads to an elliptical FT distribution whereas randomness leads to a more circular distribution. Aside from this work, to our knowledge, Fourier analysis has yet to be fully utilized in SHG imaging as a means of deriving quantitative measures for biological structures. In this paper, we propose the use of Fourier transform-SHG (FT-SHG) microscopy to obtain information on collagen fiber orientation and maximum spatial frequency in an image. Such a tool could aid in identifying parameters that represent the organization of collagen fibers, which could lead to the development of quantitative biomarkers help discriminate between healthy and damaged tissues.

We use FT-SHG microscopy to identify two parameters: “preferred” orientation and maximum spatial frequency. Selected regions of interest are considered for analysis of SHG images of collagen fibers in porcine trachea, ear, and cornea. The FT-SHG method is applied to 2D images as well as a 3D image stack of the cornea.

2. Theory

The FT is an essential mathematical tool that has been used in a variety of fields to analyze the frequency content of acquired signals and is typically carried out in 1D [20

S. Haykin and B. Van Veen, Signals and Systems (Wiley, 2005).

]. The technique can be applied to images through the use of the 2D FT, whereby image contents are decomposed into a superposition of harmonic functions (of varying amplitudes and phases) along horizontal and vertical axes [21

H. G. Adelmann, “Butterworth equations for homomorphic filtering of images,” Comput. Biol. Med. 28, 169–181 (1998). [CrossRef] [PubMed]

–23

H. M. Shieh, C. H. Chung, and C. L. Byrne, “Resolution enhancement in computerized tomographic imaging,” Appl. Opt. 47, 4116–4120 (2008). [CrossRef] [PubMed]

]. The associated spatial frequencies are simply the modulations in intensity in the image per unit distance [24

B. E. A Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Interscience, 2007).

, 25

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

]. Lower frequencies are closer to the origin (point at which spatial frequency is zero), while higher frequencies are further away. The thickness and spacing of a 1D periodic structure can be determined via the spectrum in Fourier space. For an aperiodic structure, the Fourier transform is more complex, making it more challenging to extract information about features in real space. In reality, our images of biological systems are between these two extremes, and often data analysis is complicated by noise due to the scattering of the photons used to acquire the image. This limits the spatial resolution that could be obtained in optical microscopy to less than the theoretical value, and hence the fidelity with which the maximum spatial frequency can be determined in Fourier space [24

B. E. A Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Interscience, 2007).

–26

J. B. Pawley, Handbook of Biological Confocal Microscopy (Springer, 2006). [CrossRef]

]. This maximum spatial frequency informs us about the minimum observable size (or feature) in real space. In our approach, we extract a maximum spatial frequency, F_high , above the noise floor. We first determine F_high by extracting a line spectrum from a 2D FT along the direction of interest. Then, a smoothing spline is applied to the profile using the curve fitting toolbox in Matlab. Finally, in order to mitigate the unwanted contributions of (photon) noise to our spectrum, we use a threshold of 10% above the noise floor, which is chosen from the FT of an area that clearly produces no SHG signal (black areas in images). Using this method, the threshold is determined for each specimen. The frequency at which the amplitude just reaches above the threshold is selected as F_high . This approach is common for noise removal in Fourier analysis [19

, 27

D. Pandian, C. Ciulla, E. Haacke, J. Jiang, and M. Ayaz, “Complex threshold method for identifying pixels that contain predominantly noise in magnetic resonance images,” J. Magn. Reson. Imag. 28, 727–735, (2008). [CrossRef]

The second parameter that we extract from the Fourier space is preferred orientation. Improved accuracy in Fourier space is often used to determine the orientation of an image in real space [28

J. C. Russ, The Image Processing Handbook (CRC Press, 2007).

]. When structures in an image have a preferred orientation, the high amplitudes on average align along a direction perpendicular to the preferred orientation in the 2D FT. Although there are other methods to obtain the orientation of structures, we employ a simple procedure that does not invoke the use of complex algorithms nor polarization modulation techniques [29

B. Josso, D. R. Burton, and M. J. Lalor, “Texture orientation and anisotropy calculation by Fourier transform and principal component analysis,” Mech. Syst. Signal Proc. 19, 1152–1161 (2005). [CrossRef]

–31

P. Stoller, K. M. Reiser, P. M. Celliers, and A. M. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys. J. 82, 3330–3342 (2002). [CrossRef] [PubMed]

]. In our approach, a binary image is created by isolating dominant spatial frequencies (highest amplitudes) using a desired amplitude threshold. The isolated frequencies are assigned an amplitude of 1, and all other frequencies are given an amplitude of zero. Finally, a best-fit line is applied to this binary image, which is along a direction that is perpendicular to the preferred orientation. The standard deviation in orientation is the standard error in fitting a line.

3. Experiment

3.1 Sample preparation

Porcine tissue samples of hyaline and elastic cartilage from the trachea and ear, respectively, and cornea were harvested from a local abattoir just after euthanasia, and stored in 10% formalin. The samples were then processed for 24 hrs using a standard xylene/ethanol gradient series. The samples were then embedded in paraffin wax, and 5-µm thick sections were cut with a microtome and mounted onto glass slides using a permanent mounting media.

3.2 Experimental setup

The schematic of the experimental setup for the SHG microscope is shown in Fig. 1. An epiconfiguration two-photon fluorescence microscope is modified into a trans-configuration SHG microscope. The beam is obtained from a tunable Ti:Sapphire laser (Spectra-Physics Tsunami) that produces 100 femtosecond-duration pulses at 80 MHz repetition rate. The pulses are linearly polarized and spectrally centered at 800 nm for the experiments reported here. The beam is spatially filtered and collimated before sending it to the galvanometer based xy scanner (Cambridge Technology) which is driven in a raster-scan pattern. After passing through a combination of relay lenses (scan and tube lens), the beam is reflected by a short-pass 680-nm dichroic beam splitter (Semrock FF670-SDi01-25X36) and subsequently focused onto the sample using an oil-immersion objective (Leica 63X HCXPLAPO). The transmitted signal from the sample is collected by a second objective (Leica 20X HCPLAPOCS). Spectral detection of the SHG signal is achieved by using a laser blocking filter (Semrock FF01-680/SP-25) followed by a 390/20 nm bandpass filter (Semrock FF01-390/18-25), and the SHG intensity is recorded with a photo-multiplier tube (Hamamatsu). Image stacks are acquired from various depths (z) into the sample at a rate of ~ one frame per second. The scan area for the trachea and ear is 163×163 µm, and 238×238 µm for the cornea. An average power of 37 mW is used on the cartilage samples, and 25 mW on the cornea. These power settings are chosen for optimum image contrast.

4. Results and Discussion

4.1 SHG Microscopy of Trachea, Ear, and Cornea

Figure 2 shows SHG images of unstained slices of adult porcine trachea (2a), ear (2b), and cornea (2c). It is observed from Fig. 2a that the matrix in trachea is that of collagen fibers with elliptical gaps. This is the expected structure of hyaline cartilage [32

K. Schenke-Layland, “Non-invasive multiphoton imaging of extracellular matrix structures,” J. Biophotonics 1, 451–462 (2008). [CrossRef]

]. The image of the ear shows rope-like regularly oriented collagen fibers as shown in Fig. 2b. However, the cornea contains patches of collagen fibers with varying density and orientation. SHG imaging of human cornea has previously been reported [18

, 19

] and shows similar features to those observed in Fig. 2c. The optical sectioning capability of SHG microscopy is observed in the movie in Fig. 2d, where a 3D rendering of fibers in ear is shown.

Fig. 1. Experimental setup of the SHG microscope. Details are provided in text.

Fig. 2. SHG intensity images of porcine tissue specimens from the (a) trachea and (b) ear cartilage, and (c) cornea for an incident wavelength of 780 nm and a second-harmonic wavelength of 390 nm; d) 3D reconstructed view of porcine ear cartilage (Media 1).

4.2 Preferred orientation

To estimate the preferred orientation, selected regions of the collagen fibers in porcine ear and trachea are considered as shown in Figs. 3a and 3b. Their respective 2D FT after being converted to binary images are shown in Fig. 3c. For the ear, the estimated preferred orientations for the three regions are 71.3°, 69.0°, and 69.4°, respectively. This is consistent across the regions of interest to within ~5°. The standard deviation (SD) is an indicator of the number of fibers that deviate from the preferred orientation. Thus, the standard deviation is higher for randomly oriented features. It is observed that the fibers are more random in region 3 (SD=4°) compared to those in region 2 (SD=1.6°).

For the trachea, the preferred orientation in regions 4 and 5 are 45.5° and 51.8°, respectively, while the orientation in region 6 is completely different with a value of 108°. The standard deviations are larger for trachea (on average) compared to those obtained for the ear, indicating that the collagen fibers are more randomly organized in the trachea.

Fig. 3. SHG image of porcine (a) ear and (b) trachea cartilage with selected regions of interest (colored and labeled boxes), and (c) estimated preferred orientation for each corresponding region as observed in Fourier space.

4.3 Maximum spatial frequency of biological tissues

Maximum spatial frequencies are obtained by dividing the SHG images of porcine ear and trachea cartilage into horizontal rectangular regions of interest (for representation, we only show one) as shown in Figs. 4a and 4b, respectively. Since the preferred orientation of the ear is relatively consistent at 70° as shown in Fig. 3c, we rotate the image of the ear by 20° so that the fibers are oriented preferentially along the vertical axis. This allows us to access the spatial frequencies along the direction of maximum variation which, in this case, is along the horizontal direction. With regards to the trachea, since the orientation varies from at least 45° to 108°, we are free to apply the same window of observation used on the ear, but without the need for any rotation of the image.

Histograms of the values of F_high from all regions of interest of the ear and trachea are shown in Fig. 4c and 4d, respectively. Overall, the image of the ear (Fig. 4a), as observed in real space (space domain), shows consistency in its structure. This is confirmed by the narrow distribution of the values of F_high as shown in the histogram (Fig. 4c), where the values for F_high remain between 0.51 and 0.79 µm^-1. In contrast, changes in the structure of the trachea (Fig. 4b) are clearly observed in the space domain across various regions, which are confirmed by the wider distribution in the values of F_high as shown in the Fig. 4d. Here, F_high varies from 0.34 and 1.47 µm^-1. This indicates that the size of the smallest feature in the trachea changes more in comparison to the ear. The error in all values of F_high is 0.006 µm-1, which corresponds to the separation between data points in the discrete Fourier domain.

Fig. 4. SHG image of porcine a) ear and b) trachea cartilage. The region of interest for estimating F_high is a rectangular box of height 2.87 µm. A histogram of the values of F_high from all the regions of interest for the c) ear and d) trachea.

4.4 Image stack of the Cornea

Figure 5 shows the regions of interest 1–3 for a slice in the image stack of the cornea. Region 1 has a relatively large standard deviation (6.1°) due to the random orientation of its fibers. It also has lower F_high (0.69 µm^-1) indicating that the smallest feature size is ~1.45 µm. However, regions 2 and 3 have regularly oriented fibers and thus have low standard deviations (~1.5°). In these regions, the values of F_high are relatively large (~1.02 µm^-1), corresponding to smallest feature size in each region of ~0.98 µm. Thus, regions 2 and 3 have comparatively thinner and closer spaced features than those in region 1.

Until now, we have determined the preferred orientation and highest spatial frequency in a plane for 2D images. Next, we extend the technique to 3D by using an image stack of the porcine cornea (3-µm thick specimen). The variations in the calculated preferred orientation and F_high versus depth, for the three regions in the image stack are shown in the Fig. 6. A movie of the variations in the two quantitative parameters, preferred orientation and F _high versus depth for three regions of interest in the 3D image stack is shown in the Fig. 6a. The arrows represent the preferred orientation of the regions, and the color of the border for each region of interest corresponds to a value of F_high as indicated by the color bar.

For region 1, the preferred orientation appears to oscillate about 120°. The standard deviation in orientation remains relatively large (4.9° to 7.8°). This indicates that the fibers in region 1 are more randomly oriented throughout the stack. The values of F_high are relatively small. The average value of F_high throughout the depth is 0.77 µm^-1, which corresponds to a minimum feature size of 1.3 µm.

In the case of region 2, the preferred orientation decreases from 37° to 27° over a depth of 0.49 µm. It then remains constant over a depth of 1.47 µm and then increases gradually to 37° at the end of the stack. F_high ranges from 0.73 to 1.50 µm^-1. It increases initially and then stays roughly the same (1.27 µm-1) before it decreases to 0.80 µm-1 at the end of the stack. As can be seen from Fig. 5, region 2 has more regularly oriented structures, and thus the standard deviations in orientation are smaller compared to those obtained for region 1.

For region 3, we observe that the preferred orientation remains consistent at ~125° throughout the stack. However, F_high initially decreases from 0.77 to 0.44 µm^-1 over a depth of 0.33µm and then gradually increases until the end of the stack. This indicates that fibers become more closely packed yet maintain the same orientation. For example, the minimum feature size decreases from 2.27 µm (at a depth of 0.33 µm) to 0.79 µm (at a depth of 2.77 µm), while the orientation stays at ~122° without deviating by more than 5°. Moreover, the standard deviation in orientation decreases at the end of the stack indicating that fibers become more regular.

Fig. 5. Regions of interest for estimating the highest spatial frequencies in the cornea. The image shown is cropped to 238×163 µm.

Fig. 6. (a) A movie showing the variations of the two quantitative markers, preferred orientation and F _high versus depth (Media 2). (b–d) Plot of the estimated preferred orientation, and F_high as a function of depth in an SHG image stack of the cornea for regions 1–3 from Fig. 6. Note that our axial resolution is on the order of the wavelength (~700 nm), while we mechanically step through the depth of our sample in 163-nm increments using a precision motor control of the objective focus. Oversampling helps mitigate the effect of Poisson noise by improving the visibility due to more photons per pixel, and improve the precision to which we can locate image features [26

J. B. Pawley, Handbook of Biological Confocal Microscopy (Springer, 2006). [CrossRef]

]. Thus, our sensitivity to changes in the features is improved.

We note that the size of the box chosen for estimating the preferred orientation and spatial frequency is not arbitrary. It should be chosen in such a way that it is not so small that it probes too few fibers leading to possible errors in the calculation of preferred orientation, such as those arising from a reduced number of pixels used in the FT.

5. Conclusion

We demonstrated the use of Fourier transform-second-harmonic generation (FT-SHG) imaging of collagen fibers as a means of performing quantitative analysis of obtained images. FT-SHG was applied to selected spatial regions in SHG images of collagen fibers in porcine trachea, ear, and cornea. Two quantitative markers, preferred orientation and maximum spatial frequency, F_high , were proposed for differentiating structural information between various spatial regions of interest in the specimens. The ear showed consistent maximum spatial frequency and orientation both in its real-space image as well as with respect to the obtained parameters. However, there were observable changes in the orientation and minimum feature size of fibers in the trachea which were quantified using our proposed parameters. Finally, the analysis was applied a 3D image stack of the cornea. It was observed that the standard deviation of the orientation was sensitive to the variation in fiber orientation and that F_high was sensitive to the minimum feature size. Regions that had variations in F_high while orientation remained relatively constant, suggested that this parameter is useful as an independent marker for characterizing changes in fiber structure. We emphasize that FT-SHG is a simple, yet powerful, tool for extracting information from images that is not obvious in real space.

Future work with FT-SHG includes quantification of the structural changes in collagen fibers due to damage from disease or injury. This could lead to developing standards essential for diagnostic applications. Here, FT-SHG is applied on the trachea, ear, and cornea, however, it can also be applied to others tissues containing fibrillar collagen such as artery walls, and include other noncentrosymmetric structures such as myosin.

Acknowledgements

This work was supported by the University of Illinois at Urbana-Champaign (UIUC) research start-up funds. M. R. M. acknowledges support from the National Science Foundation (DBI 0839113). We are grateful for the useful discussions we have had with Brynmor Davis and Kaspar Ko. We thank Duohai Pan and Jon Ekman for use of the microscope facilities, training and assistance at the Beckman Institute, UIUC. We appreciate the help of Larry Schook and Laurie Rund for providing the samples, and Donna Epps for sample preparation.

References and links

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13.	S. W. Teng, H. Y. Tan, J. L. Peng, H. H. Lin, K. H. Kim, W. Lo, Y. Sun, W. C. Lin, S. J. Lin, S. H. Jee, P. T. C. So, and C. Y. Dong, “Multiphoton autofluorescence and second-harmonic generation imaging of the ex vivo porcine eye,” Invest. Ophthalmol. Vis. Sci. 47, 1216–1224 (2006). [CrossRef] [PubMed]
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15.	G. Cox, E. Kable, A. Jones, I. K. Fraser, F. Manconi, and M. D. Gorrell, “3-dimensional imaging of collagen using second harmonic generation,” J. Struct. Biol. 141, 53–62 (2003). [CrossRef] [PubMed]
16.	F. Tiaho, G. Recher, and D. Rouede, “Estimation of helical angles of myosin and collagen by second harmonic generation imaging microscopy,” Opt. Express 15, 12286–12295 (2007). [CrossRef] [PubMed]
17.	S. V. Plotnikov, A. M. Kenny, S. J. Walsh, B. Zubrowski, C. Joseph, V. L. Scranton, G. A. Kuchel, D. Dauser, M. S. Xu, C. C. Pilbeam, D. J. Adams, R. P. Dougherty, P. J. Campagnola, and W. A. Mohler, “Measurement of muscle disease by quantitative second-harmonic generation imaging,” J. Biomed. Opt. 13, 11 (2008). [CrossRef]
18.	N. Morishige, A. J. Wahlert, M. C. Kenney, D. J. Brown, K. Kawamoto, T. Chikama, T. Nishida, and J. V. Jester, “Second-harmonic imaging microscopy of normal human and keratoconus cornea,” Invest. Ophthalmol. Vis. Sci. 48, 1087–1094 (2007). [CrossRef] [PubMed]
19.	P. Matteini, F. Ratto, F. Rossi, R. Cicchi, C. Stringari, D. Kapsokalyvas, F. S. Pavone, and R. Pini, “Photothermally-induced disordered patterns of corneal collagen revealed by SHG imaging,” Opt. Express 17, 4868–4878 (2009). [CrossRef] [PubMed]
20.	S. Haykin and B. Van Veen, Signals and Systems (Wiley, 2005).
21.	H. G. Adelmann, “Butterworth equations for homomorphic filtering of images,” Comput. Biol. Med. 28, 169–181 (1998). [CrossRef] [PubMed]
22.	H. Schomberg and J. Timmer, “The gridding method for image-reconstruction by fourier transformation,” IEEE Trans. Med. Imaging 14, 596–607 (1995). [CrossRef] [PubMed]
23.	H. M. Shieh, C. H. Chung, and C. L. Byrne, “Resolution enhancement in computerized tomographic imaging,” Appl. Opt. 47, 4116–4120 (2008). [CrossRef] [PubMed]
24.	B. E. A Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Interscience, 2007).
25.	J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
26.	J. B. Pawley, Handbook of Biological Confocal Microscopy (Springer, 2006). [CrossRef]
27.	D. Pandian, C. Ciulla, E. Haacke, J. Jiang, and M. Ayaz, “Complex threshold method for identifying pixels that contain predominantly noise in magnetic resonance images,” J. Magn. Reson. Imag. 28, 727–735, (2008). [CrossRef]
28.	J. C. Russ, The Image Processing Handbook (CRC Press, 2007).
29.	B. Josso, D. R. Burton, and M. J. Lalor, “Texture orientation and anisotropy calculation by Fourier transform and principal component analysis,” Mech. Syst. Signal Proc. 19, 1152–1161 (2005). [CrossRef]
30.	B. M. Palmer and R. Bizios, “Quantitative characterization of vascular endothelial cell morphology and orientation using Fourier transform analysis,” J. Biomech. Eng.-Trans. ASME 119, 159–165 (1997). [CrossRef]
31.	P. Stoller, K. M. Reiser, P. M. Celliers, and A. M. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys. J. 82, 3330–3342 (2002). [CrossRef] [PubMed]
32.	K. Schenke-Layland, “Non-invasive multiphoton imaging of extracellular matrix structures,” J. Biophotonics 1, 451–462 (2008). [CrossRef]

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

ToC Category:
Microscopy

History
Original Manuscript: June 16, 2009
Revised Manuscript: July 30, 2009
Manuscript Accepted: July 31, 2009
Published: August 3, 2009

Virtual Issues
Vol. 4, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Raghu A. Rao, Monal R. Mehta, and Kimani C. Toussaint, "Fourier transform-second-harmonic generation imaging of biological tissues," Opt. Express 17, 14534-14542 (2009)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-17-17-14534

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References

B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, Molecular Biology of the Cell (Garland Science, 2008).
D. R. Keene, L. Y. Sakai, R. E. Burgeson, "Human bone contains type-III collagen, type-VI collagen, and fibrillin - type-III collagen is present on specific fibers that may mediate attachment of tendons, ligaments, and periosteum to calcified bone cortex," J. Histochem. Cytochem. 39, 59-69 (1991). [CrossRef] [PubMed]
Y. Komai and T. Ushiki, "The 3-dimensional organization of collagen fibrils in the human cornea and sclera," Invest. Ophthalmol. Vis. Sci. 32, 2244-2258 (1991). [PubMed]
R. C. Billinghurst, L. Dahlberg, M. Ionescu, A. Reiner, R. Bourne, C. Rorabeck, P. Mitchell, J. Hambor, O. Diekmann, H. Tschesche, J. Chen, H. VanWart, and A. R. Poole, "Enhanced cleavage of type II collagen by collagenases in osteoarthritic articular cartilage," J. Clin. Invest. 99, 1534-1545 (1997). [CrossRef] [PubMed]
L. Klein and J. Chandrarajan, "Collagen degradation in rat skin but not in intestine during rapid growth - effect on collagen type-1 and type-3 from skin," Proc. Natl. Acad. Sci. USA 74, 1436-1439 (1977). [CrossRef] [PubMed]
S. M. Weis, J. L. Emery, K. D. Becker, D. J. McBride, J. H. Omens, and A. D. McCulloch, "Myocardial mechanics and collagen structure in the osteogenesis imperfecta murine (oim)," Circ. Res. 87, 663-669 (2000). [PubMed]
J. R. Mao and J. Bristow, "The Ehlers-Danlos syndrome: on beyond collagens," J. Clin. Invest. 107, 1063-1069 (2001). [CrossRef] [PubMed]
H. T. Chen, H. F. Wang, M. N. Slipchenko, Y. K. Jung, Y. Z. Shi, J. B. Zhu, K. K. Buhman, and J. X. Cheng, "A multimodal platform for nonlinear optical microscopy and microspectroscopy," Opt. Express 17, 1282-1290 (2009). [CrossRef] [PubMed]
W. L. Chen, T. H. Li, P. J. Su, C. K. Chou, P. T. Fwu, S. J. Lin, D. Kim, P. T. C. So, and C. Y. Dong, "Second harmonic generation chi tensor microscopy for tissue imaging," Appl. Phys. Lett. 94, 3 (2009).
P. J. Campagnola and L. M. Loew, "Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms," Nat. Biotechnol. 21, 1356-1360 (2003). [CrossRef] [PubMed]
M. Han, G. Giese, and J. F. Bille, "Second harmonic generation imaging of collagen fibrils in cornea and sclera," Opt. Express 13, 5791-5797 (2005). [CrossRef] [PubMed]
C. H. Yu, S. P. Tai, C. T. Kung, I. J. Wang, H. C. Yu, H. J. Huang, W. J. Lee, Y. F. Chan, and C. K. Sun, "In vivo and ex vivo imaging of intra-tissue elastic fibers using third-harmonic-generation microscopy," Opt. Express 15, 11167-11177 (2007). [CrossRef] [PubMed]
S. W. Teng, H. Y. Tan, J. L. Peng, H. H. Lin, K. H. Kim, W. Lo, Y. Sun, W. C. Lin, S. J. Lin, S. H. Jee, P. T. C. So, and C. Y. Dong, "Multiphoton autofluorescence and second-harmonic generation imaging of the ex vivo porcine eye," Invest. Ophthalmol. Vis. Sci. 47, 1216-1224 (2006). [CrossRef] [PubMed]
R. M. Williams, W. R. Zipfel, and W. W. Webb, "Interpreting second-harmonic generation images of collagen I fibrils," Biophys. J. 88, 1377-1386 (2005). [CrossRef]
G. Cox, E. Kable, A. Jones, I. K. Fraser, F. Manconi, and M. D. Gorrell, "3-dimensional imaging of collagen using second harmonic generation," J. Struct. Biol. 141, 53-62 (2003). [CrossRef] [PubMed]
F. Tiaho, G. Recher, and D. Rouede, "Estimation of helical angles of myosin and collagen by second harmonic generation imaging microscopy," Opt. Express 15, 12286-12295 (2007). [CrossRef] [PubMed]
S. V. Plotnikov, A. M. Kenny, S. J. Walsh, B. Zubrowski, C. Joseph, V. L. Scranton, G. A. Kuchel, D. Dauser, M. S. Xu, C. C. Pilbeam, D. J. Adams, R. P. Dougherty, P. J. Campagnola, and W. A. Mohler, "Measurement of muscle disease by quantitative second-harmonic generation imaging," J. Biomed. Opt. 13, 11 (2008). [CrossRef]
N. Morishige, A. J. Wahlert, M. C. Kenney, D. J. Brown, K. Kawamoto, T. Chikama, T. Nishida, and J. V. Jester, "Second-harmonic imaging microscopy of normal human and keratoconus cornea," Invest. Ophthalmol. Vis. Sci. 48, 1087-1094 (2007). [CrossRef] [PubMed]
P. Matteini, F. Ratto, F. Rossi, R. Cicchi, C. Stringari, D. Kapsokalyvas, F. S. Pavone, and R. Pini, "Photothermally-induced disordered patterns of corneal collagen revealed by SHG imaging," Opt. Express 17, 4868-4878 (2009). [CrossRef] [PubMed]
S. Haykin and B. Van Veen, Signals and Systems (Wiley, 2005).
H. G. Adelmann, "Butterworth equations for homomorphic filtering of images," Comput. Biol. Med. 28, 169-181 (1998). [CrossRef] [PubMed]
H. Schomberg and J. Timmer, "The gridding method for image-reconstruction by fourier transformation," IEEE Trans. Med. Imaging 14, 596-607 (1995). [CrossRef] [PubMed]
H. M. Shieh, C. H. Chung, and C. L. Byrne, "Resolution enhancement in computerized tomographic imaging," Appl. Opt. 47, 4116-4120 (2008). [CrossRef] [PubMed]
B. E. A Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Interscience, 2007).
J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
J. B. Pawley, Handbook of Biological Confocal Microscopy (Springer, 2006). [CrossRef]
D. Pandian, C. Ciulla, E. Haacke, J. Jiang, and M. Ayaz, "Complex threshold method for identifying pixels that contain predominantly noise in magnetic resonance images," J. Magn. Reson. Imag. 28, 727-735, (2008). [CrossRef]
J. C. Russ, The Image Processing Handbook (CRC Press, 2007).
B. Josso, D. R. Burton, and M. J. Lalor, "Texture orientation and anisotropy calculation by Fourier transform and principal component analysis," Mech. Syst. Signal Proc. 19, 1152-1161 (2005). [CrossRef]
B. M. Palmer and R. Bizios, "Quantitative characterization of vascular endothelial cell morphology and orientation using Fourier transform analysis," J. Biomech. Eng.-Trans. ASME 119, 159-165 (1997). [CrossRef]
P. Stoller, K. M. Reiser, P. M. Celliers, and A. M. Rubenchik, "Polarization-modulated second harmonic generation in collagen," Biophys. J. 82, 3330-3342 (2002). [CrossRef] [PubMed]
K. Schenke-Layland, "Non-invasive multiphoton imaging of extracellular matrix structures," J. Biophotonics 1, 451-462 (2008). [CrossRef]

Appl. Opt.

H. M. Shieh, C. H. Chung, and C. L. Byrne, "Resolution enhancement in computerized tomographic imaging," Appl. Opt. 47, 4116-4120 (2008). [CrossRef] [PubMed]

Appl. Phys. Lett.

W. L. Chen, T. H. Li, P. J. Su, C. K. Chou, P. T. Fwu, S. J. Lin, D. Kim, P. T. C. So, and C. Y. Dong, "Second harmonic generation chi tensor microscopy for tissue imaging," Appl. Phys. Lett. 94, 3 (2009).

Biophys. J.

R. M. Williams, W. R. Zipfel, and W. W. Webb, "Interpreting second-harmonic generation images of collagen I fibrils," Biophys. J. 88, 1377-1386 (2005). [CrossRef]
P. Stoller, K. M. Reiser, P. M. Celliers, and A. M. Rubenchik, "Polarization-modulated second harmonic generation in collagen," Biophys. J. 82, 3330-3342 (2002). [CrossRef] [PubMed]

Circ. Res.

S. M. Weis, J. L. Emery, K. D. Becker, D. J. McBride, J. H. Omens, and A. D. McCulloch, "Myocardial mechanics and collagen structure in the osteogenesis imperfecta murine (oim)," Circ. Res. 87, 663-669 (2000). [PubMed]

Comput. Biol. Med.

H. G. Adelmann, "Butterworth equations for homomorphic filtering of images," Comput. Biol. Med. 28, 169-181 (1998). [CrossRef] [PubMed]

IEEE Trans. Med. Imaging

H. Schomberg and J. Timmer, "The gridding method for image-reconstruction by fourier transformation," IEEE Trans. Med. Imaging 14, 596-607 (1995). [CrossRef] [PubMed]

Invest. Ophthalmol. Vis. Sci.

S. W. Teng, H. Y. Tan, J. L. Peng, H. H. Lin, K. H. Kim, W. Lo, Y. Sun, W. C. Lin, S. J. Lin, S. H. Jee, P. T. C. So, and C. Y. Dong, "Multiphoton autofluorescence and second-harmonic generation imaging of the ex vivo porcine eye," Invest. Ophthalmol. Vis. Sci. 47, 1216-1224 (2006). [CrossRef] [PubMed]
N. Morishige, A. J. Wahlert, M. C. Kenney, D. J. Brown, K. Kawamoto, T. Chikama, T. Nishida, and J. V. Jester, "Second-harmonic imaging microscopy of normal human and keratoconus cornea," Invest. Ophthalmol. Vis. Sci. 48, 1087-1094 (2007). [CrossRef] [PubMed]
Y. Komai and T. Ushiki, "The 3-dimensional organization of collagen fibrils in the human cornea and sclera," Invest. Ophthalmol. Vis. Sci. 32, 2244-2258 (1991). [PubMed]

J. Biomech. Eng.-Trans. ASME

B. M. Palmer and R. Bizios, "Quantitative characterization of vascular endothelial cell morphology and orientation using Fourier transform analysis," J. Biomech. Eng.-Trans. ASME 119, 159-165 (1997). [CrossRef]

J. Biomed. Opt.

S. V. Plotnikov, A. M. Kenny, S. J. Walsh, B. Zubrowski, C. Joseph, V. L. Scranton, G. A. Kuchel, D. Dauser, M. S. Xu, C. C. Pilbeam, D. J. Adams, R. P. Dougherty, P. J. Campagnola, and W. A. Mohler, "Measurement of muscle disease by quantitative second-harmonic generation imaging," J. Biomed. Opt. 13, 11 (2008). [CrossRef]

J. Biophotonics

K. Schenke-Layland, "Non-invasive multiphoton imaging of extracellular matrix structures," J. Biophotonics 1, 451-462 (2008). [CrossRef]

J. Clin. Invest.

J. R. Mao and J. Bristow, "The Ehlers-Danlos syndrome: on beyond collagens," J. Clin. Invest. 107, 1063-1069 (2001). [CrossRef] [PubMed]
R. C. Billinghurst, L. Dahlberg, M. Ionescu, A. Reiner, R. Bourne, C. Rorabeck, P. Mitchell, J. Hambor, O. Diekmann, H. Tschesche, J. Chen, H. VanWart, and A. R. Poole, "Enhanced cleavage of type II collagen by collagenases in osteoarthritic articular cartilage," J. Clin. Invest. 99, 1534-1545 (1997). [CrossRef] [PubMed]

J. Histochem. Cytochem.

D. R. Keene, L. Y. Sakai, R. E. Burgeson, "Human bone contains type-III collagen, type-VI collagen, and fibrillin - type-III collagen is present on specific fibers that may mediate attachment of tendons, ligaments, and periosteum to calcified bone cortex," J. Histochem. Cytochem. 39, 59-69 (1991). [CrossRef] [PubMed]

J. Magn. Reson. Imag.

D. Pandian, C. Ciulla, E. Haacke, J. Jiang, and M. Ayaz, "Complex threshold method for identifying pixels that contain predominantly noise in magnetic resonance images," J. Magn. Reson. Imag. 28, 727-735, (2008). [CrossRef]

J. Struct. Biol.

G. Cox, E. Kable, A. Jones, I. K. Fraser, F. Manconi, and M. D. Gorrell, "3-dimensional imaging of collagen using second harmonic generation," J. Struct. Biol. 141, 53-62 (2003). [CrossRef] [PubMed]

Mech. Syst. Signal Proc.

B. Josso, D. R. Burton, and M. J. Lalor, "Texture orientation and anisotropy calculation by Fourier transform and principal component analysis," Mech. Syst. Signal Proc. 19, 1152-1161 (2005). [CrossRef]

Nat. Biotechnol.

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

Opt. Express

Proc. Natl. Acad. Sci. USA

L. Klein and J. Chandrarajan, "Collagen degradation in rat skin but not in intestine during rapid growth - effect on collagen type-1 and type-3 from skin," Proc. Natl. Acad. Sci. USA 74, 1436-1439 (1977). [CrossRef] [PubMed]

Other

B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, Molecular Biology of the Cell (Garland Science, 2008).
S. Haykin and B. Van Veen, Signals and Systems (Wiley, 2005).
J. C. Russ, The Image Processing Handbook (CRC Press, 2007).
B. E. A Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Interscience, 2007).
J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
J. B. Pawley, Handbook of Biological Confocal Microscopy (Springer, 2006). [CrossRef]

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