Thickness dependence of optical second harmonic generation in collagen fibrils

Simultaneous backward and forward second harmonic generations from isolated type-I collagen matrix are observed. Optical interference behaviors of these nonlinear optical signals are studied with accurately determined fibril thickness by an atomic force microscope. The nonlinear emission directions are strongly dependent on the coherent interaction within and between collagen fibrils. A linear relationship is obtained to estimate collagen fibril thickness with nanometer precision noninvasively by evaluating the forward/backward second harmonic generation ratio. ©2007 Optical Society of America OCIS codes: (170.3880) Medical and biological imaging; (180.6900) Three-dimensional microscopy; (190.4720) Optical nonlinearities of condensed matter. References and links 1. Y. C. Guo, H. E. Savage, F. Liu, S. P. Schantz, P. P. Ho, and R. R. Alfano, "Subsurface tumor progression investigated by noninvasive optical second harmonic tomography," Proc. Natl. Acad. Sci. U. S. A. 96, 10854-10856 (1999). 2. P. Stoller, B. M. Kim, A. M. Rubenchik, K. M. Reiser, and L. B. Da Silva, "Polarization-dependent optical second-harmonic imaging of a rat-tail tendon," J. Biomed. Opt. 7, 205-214 (2002). 3. E. Brown, T. McKee, E. diTomaso, A. Pluen, B. Seed, Y. Boucher, and R. K. Jain, "Dynamic imaging of collagen and its modulation in tumors in vivo using second-harmonic generation," Nat. Med. 9, 796-800 (2003). 4. A. Zoumi, A. Yeh, and B. J. Tromberg, "Imaging cells and extracellular matrix in vivo by using secondharmonic generation and two-photon excited fluorescence," Proc. Natl. Acad. Sci. U. S. A. 99, 11014-11019 (2002). 5. 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). 6. 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). 7. S. W. Chu, I. H. Chen, T. M. Liu, C. K. Sun, S. P. Lee, B. L. Lin, P. C. Cheng, M. X. Kuo, D. J. Lin, and H. L. Liu, "Nonlinear bio-photonic crystal effects revealed with multimodal nonlinear microscopy," J. Microsc.Oxf. 208, 190-200 (2002). 8. M. Both, M. Vogel, O. Friedrich, F. von Wegner, T. Kunsting, R. H. A. Fink, and D. Uttenweiler, "Second harmonic imaging of intrinsic signals in muscle fibers in situ," J. Biomed. Opt. 9, 882-892 (2004). 9. G. Peleg, A. Lewis, M. Linial, and L. M. Loew, "Nonlinear optical measurement of membrane potential around single molecules at selected cellular sites," Proc. Natl. Acad. Sci. U. S. A. 96, 6700-6704 (1999). 10. W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, "Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation," Proc. Natl. Acad. Sci. 100, 7075-7080 (2003). 11. L. Moreaux, O. Sandre, S. Charpak, M. Blanchard-Desce, and J. Mertz, "Coherent scattering in multiharmonic light microscopy," Biophys. J. 80, 1568-1574 (2001). 12. J. Mertz and L. Moreaux, "Second-harmonic generation by focused excitation of inhomogeneously distributed scatterers," Opt. Commun. 196, 325-330 (2001). #85172 $15.00 USD Received 23 Jul 2007; revised 29 Aug 2007; accepted 29 Aug 2007; published 5 Sep 2007 (C) 2007 OSA 17 September 2007 / Vol. 15, No. 19 / OPTICS EXPRESS 12005 13. E. S. Tasheva, A. Koester, A. Q. Paulsen, A. S. Garrett, D. L. Boyle, H. J. Davidson, M. Song, N. Fox, and G. W. Conrad, "Mimecan/osteoglycin-deficient mice have collagen fibril abnormalities," Mol. Vis. 8, 407-415 (2002). 14. R. Fleischmajer, B. R. Olsen, R. Timpl, J. S. Perlish, and O. Lovelace, "Collagen fibril formation during embryogenesis," Proc. Natl. Acad. Sci. 80, 3354-3358 (1983). 15. S. W. Chu, S. Y. Chen, G. W. Chern, T. H. Tsai, Y. C. Chen, B. L. Lin, and C. K. Sun, "Studies of χ/χ tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy," Biophys. J. 86, 39143922 (2004). 16. S. W. Chu, S. P. Tai, C. L. Ho, C. H. Lin, and C. K. Sun, "High-resolution simultaneous three-photon fluorescence and third-harmonic-generation microscopy," Microsc. Res. Tech. 66, 193-197 (2005). 17. 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). 18. Y. R. Shen, The Principles of Nonlinear Optics (John Wiley & Sons, Hoboken, NJ, 2002). 19. E. Claridge, S. Cotton, P. Hall, and M. Moncrieff, "From colour to tissue histology: physics-based interpretation of images of pigmented skin lesions," Med. Image Anal. 7, 489-502 (2003). 20. T. Gutsmann, G. E. Fantner, M. Venturoni, A. Ekani-Nkodo, J. B. Thompson, J. H. Kindt, D. E. Morse, D. K. Fygenson, and P. K. Hansma, "Evidence that collagen fibrils in tendons are inhomogeneously structured in a tubelike manner," Biophys. J. 84, 2593-2598 (2003).


Introduction
In recent years, optical second-harmonic-generation (SHG) has begun to emerge as a viable imaging contrast mechanism in biomedical research field due to its noninvasiveness and intrinsic sectioning ability [1][2][3][4][5][6][7][8][9][10].The virtual-transition characteristic of SHG provides the optical "noninvasive" nature desirable for microscopy applications, especially for clinical imaging.Combined with a near-infrared excitation could not only strengthen the noninvasiveness by suppressing phototoxicity but also dramatically increase the penetration depth.Thereby, this imaging modality is well suited for in vivo tissue characterization.Similar to multiphoton induced fluorescence, the quadratic power dependence of SHG allows localized excitation and provides intrinsic optical sectioning capability.However, the coherent nature of SHG makes it a fundamentally different contrast mechanism from multiphoton fluorescence [11].The emitted SHG retains phase information of excitation, and thus coherent interaction among nonlinear scatterers plays an important role in determining the overall intensity as well as the radiation direction [12].
Type I collagen is the most abundant protein in mammals and is also an exceptionally strong SHG upconverter among tissue constituents.SHG microscopy has become a versatile tool to study the extracellular collagen matrix in vivo or ex vivo [3][4][5][6][7].It has been shown that collagen fibril diameter variation is a vital diagnostic symptom for certain diseases [13] and is a key parameter for fibrillogenesis studies [14].The fibril diameter in most previous applications was only resolvable by electron microscopy, which could possibly alter fibril thickness during the complex preparation procedures.Although optical microscopy provides a more noninvasive and straightforward examination, its axial resolution is typically insufficient to resolve the thickness of a single collagen fibril.
In this report, delicate SHG coherent effects inside a collagen fibril and between adjacent fibrils are studied.We demonstrate simultaneous backward SHG (BSHG) and forward SHG (FSHG) imaging on a type-I collagen matrix.The collagen matrix is then in situ mapped with an atomic force microscope (AFM) to accurately determine the thickness and the arrangement of constituent fibrils.Both FSHG and BSHG intensities are found to be strongly influenced by the thickness of collagen fibrils due to coherent interaction.We propose a novel method to estimate the collagen fibril thickness from the power ratio of FSHG / BSHG (F/B).

Experimental setup
The SHG microscope operating in forward collection mode (dia-detection) has been described previously [15].The pumping source was a home-built Cr:forsterite modelocked laser, which is centered at 1230 nm.For backward collection part (epi-detection), the focusing objective was used to collect the backward SHG emission into a built-in photomultiplier tube of the scanning system.The 615 nm SHG signal was extracted by a dichroic beamsplitter and an interference filter in both the epi-and dia-collection routes.There was no confocal pinhole in the scanning system to improve the backward collection efficiency.The epi-and dia-detection efficiencies were calibrated with multiphoton excited fluorescence, which exhibited an isotropic emission profile, from DNA-bounded Hoechst dye in hepatic cells [16].
The collagen matrices were collected and processed from fresh bovine skin and were attached to a cleaned cover glass surface, which had been positively charged by oxygen-ion plasma processing to attach collagen fibril tightly.For atomic force microscope observation, a commercial Bioscope AFM with a NanoScope IV software (Digital Instruments) was used with tapping mode in liquid phase.Scanning was performed at about 0.5-Hz in constant amplitude mode.

Results and discussion
Figure 1(A) -1(C) give the AFM, BSHG, and FSHG images, respectively, from the same selfassembled collagen fibril matrix.The similarity of these images is obvious, indicating their common contrast origin: collagen fibrils.It is well known that SHG from collagen is strongly dependent on laser polarization relative to fibril orientation [2,17].A fibril is selected for further thickness-intensity analysis.Here the laser polarization is chosen to highlight the selected fibril.The FSHG signal variation among fibrils seems to be larger than that of BSHG.With a near infrared excitation, the coherent buildup length in biological tissues is on the order of 10-μm for FSHG, and is only a few tens of nanometers (λ/2π) for BSHG [18].For a collagen fibril with thickness of a few hundred nanometers, FSHG sums up coherently along the excitation propagation path.So FSHG intensity depends quadratically on fibril thickness, or equivalently, on number of scatterers.On the other hand, when the fibril is thicker than the coherent buildup length of BSHG, the nonlinear emission field amplitude will oscillate with interaction distance due to destructive interference among scatterers.Thus, it is reasonable to find a higher signal variation with the FSHG signal.The BSHG and FSHG power variations along the selected fibril are shown in Fig. 2(A).The power variations originate from local collagen structure and arrangement, which were in situ mapped with nanometer resolution by the AFM.With careful alignment, the AFM image matches very well to the optical harmonic signals.A fibril is selected for further quantitative analysis.When there is no fibril crossing, coherent interaction within the collagen fibril determines the emitted SHG power and direction.For instance, in area I, both BSHG and FSHG gradually increase due to the fibril thickness increasing from ~ 130-nm (left) to 155-nm (right).This indicates that the SHG emission power is extremely sensitive to collagen fibril diameter.The fibril thickness becomes 185 ~ 195-nm around area II.And it can be observed that the FSHG power steadily grows up (neglecting the intersection points) with thickness while the BSHG power in area II remains similar to the maximum in area I.This is the result of coherent summation in the forward direction and destructive interference in the backward as the specimen size exceeds the coherent buildup length of BSHG.As shown in Fig. 2(B) and Fig. 3, the thicker the fibril is, the larger the F/B ratio.This dependence provides a noninvasive tool for collagen fibril thickness estimation with a precision down to 10-nm, which is much smaller than the axial resolution of our SHG microscope.
There are three fibrils crossing the target fibril in the selected area and the crossed points have been marked as III -V.At point III and IV, there are thin fibrils (thickness 60 ~ 70-nm) underlying the selected fibril (~ 190-nm) and the increase of BSHG as well as the decrease of FSHG are observed at both points.It should be noticed that the SHG intensity from these thin fibrils is significantly weaker than that of thicker fibrils, indicating again the possibility of using SHG for fibril diameter estimation.The decrease of FSHG and the increase of BSHG can be understood in terms of diffuse reflection from the underlying fibrils.The remarkably strong backscattering efficiency of collagen fibrils has been reported [19].These thin fibrils, though exhibit diminishing SHG power, can still backscatter the FSHG generated by the thick fibril above.This provides an explanation for the ~ 15% power variation of both imaging modalities.For point V, however, with another thicker fibril crossing the selected fibril, the FSHG is enhanced with reduced BSHG.Analyzing the AFM data, it can be found the selected fibril now has a thickness ~ 180-nm around point V while the crossing fibril is ~ 170-nm in thickness.At the intersection area, the selected fibril goes beneath the crossing fibril, resulting in a total thickness of ~ 280-nm.This flattening behavior of the fibril compression at intersection is in agreement with a recent AFM study, which proposed a mechanically tubelike structure with a hard shell and a soft core in collagen fibrils [20].Note that the thickness at point V is approaching λ SHG /2 and thus coherent effect will strongly affect the overall emission profile.The laser polarization is selected that both fibrils intersecting at point V exhibit high SHG conversion efficiencies [2].At point V, FSHG becomes stronger due to the coherent summation from the two intersecting fibrils while the BSHG from the two fibrils suffers from destructive interference, resulting in a reduced backward emission power.
The relation between collagen fibril thickness and F/B ratio is summarized in Fig. 3.As the AFM-determined fibril thickness increases, F/B ratio steadily increases.Although the closed-loop controlled AFM provides thickness measurement with a nanometer precision, the thickness of areas I -VI in the figure was obtained by averaging several points nearby, which provided the major source of error.The typical data range of thickness in each area is about ±5 -±7.5 nm.Albeit that it has been shown theoretically that FSHG should be proportional to the square of the number of nonlinear scatterers [11], our observed F/B ratio fits well with a linear relationship with collagen fibril thickness.An empirical relation is deduced: collagen fibril thickness ≈ 2.81 × (F/B) + 49.8 (nm).To the best of our knowledge, this is the first experimental demonstration that provides fibril thickness estimation from far-field observation.Compared to other near-field optical scanning technique or AFM, the precision of our optical method may not be superior, but it provides a much faster scanning rate when determining a fibril thickness.The fibril thickness may also be determined by an electron microscope, which is much more costly and requires a complicated pre-processing on the fragile collagen specimens.
According to a recent calculation [12], as the active cluster size increases over 1/k 2ω , SHG will be essentially forward directed due to coherent interaction among individual scatters.The solid line in Fig. 3 illustrates the F/B ratio assuming that every collagen molecule within a fibril is an active nonlinear scatterer.So when the fibril thickness exceeds the coherent buildup length of BSHG, F/B increases dramatically.However, in our observation, the ratio remains to be close to unity with fibril thickness varying from 120-nm to 190-nm, suggesting that SHG is radiated from only a small part inside the collagen fibrils.Even when the accumulated collagen thickness approaches 280 nm (point V in Fig. 1), it seems that only < 110 nm active cluster size is contributing to SHG emission.A similar observation has been reported recently [17] with a shell emission geometry proposed.Our calculated active thickness is in good consistency with the proposed shell thickness, confirming that SHG is radiated from only a small part in the fibril rather than throughout the bulk.It should be remarked that if two thin fibrils are parallel-aligned with a gap smaller than optical resolution, it will be viewed as a "fat" fibril in SHG image.But both the FSHG and BSHG power should be the scalar sum of the nonlinear emission from the two fibrils with the F/B ratio remains unchanged.As in region VI, it can be found from the AFM image that the selected fibril split into two thinner fibrils with ~ 120-nm thickness and ~ 400-nm center spacing, which can hardly be resolved by the optical system.As a result, only one "fat" fibril is observed in SHG images, and the SHG power here is about twice to that of a single 120-nm fibril (~ the minimum in area I).Note that the real fibril thickness is revealed through the unvaried F/B ratio.

Conclusion
In summary, our result provides the first quantitative comparison between FSHG, BSHG, and accurately determined collagen fibril thickness.We demonstrate that with a single collagen

Fig. 1 .
Fig. 1. (A) AFM, (B) BSHG, and (C) FSHG images of a collagen fibril matrix on a cover glass.The selected fibril is marked with a rectangle.Several arrows in the AFM image indicate the points of discussion.Laser polarization is shown as double-sided arrows in (B) and (C).Scale bar: 3-μm.

Fig. 2 .
Fig. 2. (A).The integrated line graph of the rectangular area for BSHG (solid rectangles) and FSHG (hollow circles), showing the SHG power variation along the selected fibril.(B) F/B variation along the same fibril.The arrows show the location correspondence to the AFM image.

Fig. 3 .
Fig. 3. Solid circles are measured F/B ratio relative to collagen fibril thickness.If the collagen molecules all act as active SHG scatterers, the calculated F/B ratio is plotted as the solid line.Dashed line is F/B calculation based on active cluster sizes, indicating that only a fraction of the collagen molecules inside a fibril produce SHG effectively.Inset: an empirical linear relation on F/B ratio over collagen thickness is obtained.