## Can OCT be sensitive to nanoscale structural alterations in biological tissue? |

Optics Express, Vol. 21, Issue 7, pp. 9043-9059 (2013)

http://dx.doi.org/10.1364/OE.21.009043

Acrobat PDF (2241 KB)

### Abstract

Exploration of nanoscale tissue structures is crucial in understanding biological processes. Although novel optical microscopy methods have been developed to probe cellular features beyond the diffraction limit, nanometer-scale quantification remains still inaccessible for *in situ* tissue. Here we demonstrate that, without actually resolving specific geometrical feature, OCT can be sensitive to tissue structural properties at the nanometer length scale. The statistical mass-density distribution in tissue is quantified by its autocorrelation function modeled by the Whittle-Mateŕn functional family. By measuring the wavelength-dependent backscattering coefficient *μ _{b}(λ)* and the scattering coefficient

*μ*, we introduce a technique called inverse spectroscopic OCT (ISOCT) to quantify the mass-density correlation function. We find that the length scale of sensitivity of ISOCT ranges from ~30 to ~450 nm. Although these sub-diffractional length scales are below the spatial resolution of OCT and therefore

_{s}*not resolvable*, they are nonetheless

*detectable*. The sub-diffractional sensitivity is validated by 1) numerical simulations; 2) tissue phantom studies; and 3)

*ex vivo*colon tissue measurements cross-validated by scanning electron microscopy (SEM). Finally, the 3D imaging capability of ISOCT is demonstrated with

*ex vivo*rat buccal and human colon samples.

© 2013 OSA

## 1. Introduction

1. M. Cremer, K. Küpper, B. Wagler, L. Wizelman, J. von Hase, Y. Weiland, L. Kreja, J. Diebold, M. R. Speicher, and T. Cremer, “Inheritance of gene density-related higher order chromatin arrangements in normal and tumor cell nuclei,” J. Cell Biol. **162**(5), 809–820 (2003). [CrossRef] [PubMed]

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6. A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 Å spatial resolution light microscope: I. light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy **13**(3), 227–231 (1984). [CrossRef]

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*in situ*tissue. Most of these techniques require specific fluorophores that could potentially interfere with endogenous biological processes and only enable imaging of molecular species for which fluorescence dyes exist. Other

*in vivo*optical techniques based on the light reflectance [14

14. A. J. Radosevich, J. Yi, J. D. Rogers, and V. Backman, “Structural length-scale sensitivities of diffuse reflectance in continuous random media under the Born approximation,” Opt. Lett. **37**, 5220–5222 (2012). [CrossRef] [PubMed]

15. A. J. Radosevich, N. N. Mutyal, V. Turzhitsky, J. D. Rogers, J. Yi, A. Taflove, and V. Backman, “Measurement of the spatial backscattering impulse-response at short length scales with polarized enhanced backscattering,” Opt. Lett. **36**(24), 4737–4739 (2011). [CrossRef] [PubMed]

16. A. J. Gomes, S. Ruderman, M. DelaCruz, R. K. Wali, H. K. Roy, and V. Backman, “In vivo measurement of the shape of the tissue-refractive-index correlation function and its application to detection of colorectal field carcinogenesis,” J. Biomed. Opt. **17**(4), 047005 (2012). [CrossRef] [PubMed]

*in vivo*tissue [17

17. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science **254**(5035), 1178–1181 (1991). [CrossRef] [PubMed]

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19. B. Povazay, K. Bizheva, A. Unterhuber, B. Hermann, H. Sattmann, A. F. Fercher, W. Drexler, A. Apolonski, W. J. Wadsworth, J. C. Knight, P. S. Russell, M. Vetterlein, and E. Scherzer, “Submicrometer axial resolution optical coherence tomography,” Opt. Lett. **27**(20), 1800–1802 (2002). [CrossRef] [PubMed]

20. L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography,” Nat. Med. **17**(8), 1010–1014 (2011). [CrossRef] [PubMed]

21. J. Yi, Q. Wei, H. F. Zhang, and V. Backman, “Structured interference optical coherence tomography,” Opt. Lett. **37**(15), 3048–3050 (2012). [CrossRef] [PubMed]

23. J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. **4**(1), 95–105 (1999). [CrossRef] [PubMed]

*can one extract such information at nanometer scale from OCT?*

24. R. Barer and S. Tkaczyk, “Refractive index of concentrated protein solutions,” Nature **173**(4409), 821–822 (1954). [CrossRef] [PubMed]

25. J. M. Schmitt and G. Kumar, “Turbulent nature of refractive-index variations in biological tissue,” Opt. Lett. **21**(16), 1310–1312 (1996). [CrossRef] [PubMed]

28. J. D. Rogers, İ. R. Capoğlu, and V. Backman, “Nonscalar elastic light scattering from continuous random media in the Born approximation,” Opt. Lett. **34**(12), 1891–1893 (2009). [CrossRef] [PubMed]

29. J. Yi and V. Backman, “Imaging a full set of optical scattering properties of biological tissue by inverse spectroscopic optical coherence tomography,” Opt. Lett. **37**(21), 4443–4445 (2012). [CrossRef] [PubMed]

*ex vivo*colon biopsy samples, and deduce the mass-density correlation functions from the epithelial and stoma compartments. At the same time, SEM images were taken, and the nano-scale image correlation functions were calculated for comparison. We found that ISOCT can indeed quantify the sub-micron structural variations from these two distinct tissue types.

## 2. Inverse spectroscopic optical coherence tomography (ISOCT)

*µ*and the reflection ratio

_{b}(λ)*α*(defined as the ratio of backscattering and scattering coefficients,

*α = μ*), to much more accurately deduce the R.I. correlation function [29

_{b}/ μ_{s}29. J. Yi and V. Backman, “Imaging a full set of optical scattering properties of biological tissue by inverse spectroscopic optical coherence tomography,” Opt. Lett. **37**(21), 4443–4445 (2012). [CrossRef] [PubMed]

### 2.1 Whittle-Mateŕn correlation function

*l*determines the physical length scale of the correlation function, beyond which the function drops off quickly, as shown in Fig. 2(a). This parameter can be conceptualized as the cut-off length scale of the correlation function. The precise physical meaning of

_{c}*l*depends on

_{c}*D*. For example, for

*D*< 3,

*l*defines the upper range for which

_{c}*C*(

_{n}*ρ*) is a power law with the fractal dimension

*D*: it defines the upper extent of the mass fractal range. For

*D*= 4,

*C*(

_{n}*ρ*) is an exponential function and

*l*is the correlation length, where

_{c}*C*(

_{n}*l*) =

_{c}*C*(0)

_{n}*e*

^{−1}. An extreme case is when

*l*approaches 0, and the correlation function is compressed into a delta function acting as a dipole scatterer for which the scattering is fairly isotropic. On the other hand, biological tissue usually satisfies

_{c}*kl*>> 1 [30

_{c}30. İ. R. Capoğlu, J. D. Rogers, A. Taflove, and V. Backman, “Accuracy of the Born approximation in calculating the scattering coefficient of biological continuous random media,” Opt. Lett. **34**(17), 2679–2681 (2009). [CrossRef] [PubMed]

*k*=

*2π/λ*is the wave number. The shape of the Whittle-Mateŕn function can be fully described by

*D*and

*l*is a scaling factor of the correlation function quantifying the variance of the R.I. fluctuation. A definition of an R.I. correlation function requires a normalization such that at the origin (

_{c}. N_{c}*ρ*= 0), the function should be equal to the variance of the R.I. fluctuation

*σ*. The Whittle-Mateŕn correlation function approaches infinity at the origin when

_{n}^{2}*D*≤ 3. When

*D*> 3, this function has finite value and

*N*can be analytically associated with

_{c}*σ*[28

_{n}^{2}28. J. D. Rogers, İ. R. Capoğlu, and V. Backman, “Nonscalar elastic light scattering from continuous random media in the Born approximation,” Opt. Lett. **34**(12), 1891–1893 (2009). [CrossRef] [PubMed]

*N*and

_{c}*σ*, one option is to perform a conditional normalization:where

_{n}^{2}*ρ*is the lower length scale of sensitivity. Since a system is no longer sensitive to structures smaller than

_{l}*ρ*, one may assume that the value of the correlation function remains flat when at

_{l}*ρ*.

_{≤}ρ_{l}*et al*. established a linear relationship between the R.I. and local molecular mass-density [24

24. R. Barer and S. Tkaczyk, “Refractive index of concentrated protein solutions,” Nature **173**(4409), 821–822 (1954). [CrossRef] [PubMed]

*ε*is the local concentration of the solid material (e.g., macromolecules) and

*χ*is the R.I. increment.

*n*is the R.I. of water. It has been experimentally verified that this relationship holds in the physiological range, and the value of

_{0}*χ*is ~0.18cm

^{3}/g with very little variation among different substances and up to at least 50% concentrations [31]. This linear equation allows one to investigate the mass-density properties by quantifying the R.I. correlation function.

### 2.2 W-M correlation function and Henyey Greenstein phase function

### 2.3 Forward model for ISOCT

28. J. D. Rogers, İ. R. Capoğlu, and V. Backman, “Nonscalar elastic light scattering from continuous random media in the Born approximation,” Opt. Lett. **34**(12), 1891–1893 (2009). [CrossRef] [PubMed]

29. J. Yi and V. Backman, “Imaging a full set of optical scattering properties of biological tissue by inverse spectroscopic optical coherence tomography,” Opt. Lett. **37**(21), 4443–4445 (2012). [CrossRef] [PubMed]

*μ*is equal to 4π times the backscattering cross section per unit volume [29

_{b}**37**(21), 4443–4445 (2012). [CrossRef] [PubMed]

*kl*>> 1,

_{c}*μ*spectrum exhibits a power law with its exponent (often called the scattering power, SP) equal to 4

_{b}*-D*,When

*kl*<< 1, the medium shows Rayleigh scattering since

_{c}*l*is much smaller than the illumination wavelength, and

_{c}*μ*has the wavelength dependence of

_{b}*k*

^{4}(

*λ*

^{−4}). Figure 2(b) shows the spectrum of

*μ*at various

_{b}*D*values. Since the scattering at a particular wavelength depends on the length scale of the scatterers, we normalized the wavelength by

*l*so that

_{c}*μ*is a function of

_{b}*λ*/

*l*, i.e. (

_{c}*kl*)

_{c}^{−1}. For showing the power law dependence, Fig. 2(b) plotted in log-log scale with the x-axis labeling

*kl*in an ascending order. The y-axis labeled

_{c}*μ*normalized by

_{b}*k*and

*N*. We see that in the Rayleigh regime (

_{c}*kl*<< 1),

_{c}*μ*spectrum is independent of

_{b}*D*since they all behave as dipole scatterers; while when

*kl*>>1,

_{c}*μ*spectrum shows power law dependence (linear curve in log-log plot) with different

_{b}*D*values.

*kl*>>1 and

_{c}*D*> 2,Figure 2(c) shows α curves at various

*D*values. When

*kl*<< 1 in the Rayleigh regime, the scattering has the dipole scattering pattern whose backscattering ratio α is 1.5. When

_{c}*kl*>>1, the value of α decreases as

_{c}*D*becomes larger. The physical interpretation of a larger

*D*is that more large structures are present in the medium, resulting in more forward-directed scattering.

### 2.4 Inverse methods for ISOCT

*I*is the illumination intensity;

_{0}*r*is the reflectance of the reference arm;

*n*is the refractive index of tissue (~1.38); and

*z*is the penetration depth;

*L*is the coherence length of the light source. The maximum intensity is proportional to

*μ*and the decay rate along depth is proportional to

_{b}*μ*. By taking the natural log, the above equation becomes a linear function:As shown in step 1 in Fig. 3, the value of

_{s}*μ*can be estimated by least square (LS) fitting the A-line signal. The microscopic heterogeneity of

_{s}*μ*(

_{b}*z*) can be recovered with the fitted

*μ*:and thus the reflection ratio α(z). The exponential term compensates the illumination attenuation along the penetration depth.

_{s}*μ*spectrum. At each wave band selected by a scanning Gaussian window, the process in step 1 is iterated to obtain the

_{b}*μ*(z) spectrum. We empirically chose the window width to be

_{b}*k*= 0.18μm

_{w}^{−1}(~15nm at 710nm) granting ten independent points on the spectrum. By another LS fit on the spectrum, the exponent of the spectrum and thus

*D*(

*z*) is obtained according to Eq. (5).

### 2.5 Experimental setting for ISOCT

**37**(21), 4443–4445 (2012). [CrossRef] [PubMed]

^{−1}and ± 0.22mm

^{−1}for

*µ*and

_{b}*μ*, respectively, and ± 0.2 for

_{s}*D*[29

**37**(21), 4443–4445 (2012). [CrossRef] [PubMed]

*D*measurement on biological tissue, a 1:5 diluted 0.08μm polystyrene-microsphere solution (Thermo Scientific, 10% solids by weight) was used to normalize the OCT spectrum due to its Rayleigh scattering spectrum of

*k*

^{4}.

## 3. Length scale of sensitivity of ISOCT

*D*. Then liquid phantoms composed of microspheres were measured by ISOCT to test the length scale of sensitivity. Lastly,

*ex vivo*colon biopsies were measured with SEM verification to test whether submicron discrepancies in different tissue compartments could be detected by ISOCT.

### 3.1 Numerical perturbation on W-M correlation function

*r*, we used a Gaussian smoothing window

_{min}*G*to filter out the fine structural details in the R.I. fluctuations, similar to an imaging process with a finite spatial resolution. The changes in D measurements were recorded and the minimum detectable change in

*D*defined the length scale of sensitivity in ISOCT.

*(see the detailed derivation in Appendix 2)*:in which

*ACF*(

*f*) stands for the autocorrelation function of an arbitrary function

*f*. We configured the original

*C*with

_{n}*D*= 2.8 and

*l*= 1μm, which are realistic values according to our previous measurements [29

_{c}**37**(21), 4443–4445 (2012). [CrossRef] [PubMed]

*G*was set to be

*r*[14

_{min}14. A. J. Radosevich, J. Yi, J. D. Rogers, and V. Backman, “Structural length-scale sensitivities of diffuse reflectance in continuous random media under the Born approximation,” Opt. Lett. **37**, 5220–5222 (2012). [CrossRef] [PubMed]

*For the upper length scale of sensitivity*

_{.}*r*, we retained fine structures by subtracting the above filtered R.I. fluctuation with the original. The equivalent correlation function is:where

_{max}*δ*is a delta function in the spatial domain. The spectrum of

*µ*from 650 to 800nm was then numerically generated from

_{b}*C*and

_{n}’,*D*was measured according to Eq. (4).

*C*at small length scales leveled off below

_{n}’*r*as in Fig. 4(a) when the finer structural detail was eliminated. In Fig. 4(b), the larger length scale correlation dropped to 0 much faster than the original. Examples of perturbed R.I. fluctuation was shown in [14

_{min}14. A. J. Radosevich, J. Yi, J. D. Rogers, and V. Backman, “Structural length-scale sensitivities of diffuse reflectance in continuous random media under the Born approximation,” Opt. Lett. **37**, 5220–5222 (2012). [CrossRef] [PubMed]

*D*values in terms of the original is shown in Figs. 4(c) and 4(d) with systematically increasing

*r*and

_{min}*r*. Within the given wavelength range, we found that a change in

_{max}*D*could only be detected at length scales larger than

*r*= 35nm and smaller than

_{min}*r*= 450nm, given a 5% sensitivity threshold. This shows that ISOCT is primarily sensitive to the shape of the R.I. (and therefore the mass-density correlation function) for length scales between

_{max}*r*= 35nm and

_{min}*r*= 450nm. The measured

_{max}*D*value increased with increasing

*r*since removing finer structures equivalently manifested as a larger length-scale medium. On the other hand, with the

_{min}*r*perturbation,

_{max}*D*measurements decreased since the medium appeared to possess more small structures.

*One should note that, although the length scale of sensitivity was from ~35 to ~450nm, the calculated l*

_{c}could extend to larger length scales to match the measured optical properties as if the correlation functional form maintains the same form when ρ>450nm.### 3.2 Phantom study

*D*. Aqueous phantoms were composed of a suspension of polystyrene microspheres in a series of diameters ranging from 30nm to 4.3μm as shown in Fig. 5(a). The volume fraction of the microspheres followed an inverse power law with respect to their microsphere diameters (power = −1.2), so that the correlation function was approximated to that of a W-M function with

*D*= 2.8 assuming infinite numbers of sphere diameters [33

33. C. J. R. Sheppard, “Fractal model of light scattering in biological tissue and cells,” Opt. Lett. **32**(2), 142–144 (2007). [CrossRef] [PubMed]

^{−1}.

*D*value was averaged over 100 A-scans and taken from the surface of each phantom. For comparison, we also used Mie theory to calculate the

*µ*spectrum and further

_{b}*D*values for each phantom.

*D*maps were created in HSV (Hue-Saturation-Value) color space.

*D*encoded Hue and the image intensity encoded Saturation and Value. Ten frames of B-scan images were averaged to overcome the Brownian motion. Moreover, each wavelength-dependent B-scan image was smoothed by a moving window 32µm x 30µm in z (depth) and x (transverse), and then tomographic

*D*maps were calculated.

*D*value of 1.57 ± 0.04 and 1.51 ± 0.05 respectively, i.e. no observable change within the experimental uncertainty of 0.2. However, phantom No. 1-3 exhibited a measured

*D*-value of 1.78 ± 0.06, which was a detectable perturbation relative to phantoms No. 1-1 and 1-2 above the experimental uncertainty. Successive phantoms continued the trend of increasing

*D*-value perturbations. Figure 5(b) plots the measured

*D*changes for difference phantoms. The x-axis labels the largest particle size excluded in each phantom. As noted above, the change in D first became appreciable, i.e., above the experimental uncertainty, for phantom No.1-3. The difference became more significant with larger particles excluded. Without the small particles, the R.I. correlation function was flattened only at small length scales, verifying our above numerical simulation.

*D*value of 2.78 ± 0.08 and 2.42 ± 0.06, which was detectable given the experimental uncertainty of 0.2. When spheres larger than about 2.1µm were added, the

*D*value perturbation reached a plateau which indicates that those large spheres did not further alter the SP due to the small volume fraction, as in Fig. 5(c). We should note that the second group of experiments differs from the numerical simulation for estimating the upper length scale of sensitivity [Fig. 4(d)], in which we only eliminated larger length scale while retaining the fine structures. For a sphere, the R.I. correlation function is close to a triangular function that covers length scale from 0 up to the diameter of the sphere [32

32. L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. **93**, 70–83 (1941). [CrossRef]

*D*value in Fig. 5(c) instead of an increase as in Fig. 4(d). Nonetheless, the data in Fig. 5(c) still illustrates that

*D*can only be sensitive up to a certain upper length scale, above which the value of the correlation function is small and the scattering contribution is negligible.

*D*can be visualized from phantom No. 1-3 and become more dominant in phantom No. 1-4. Although we observed variation within the D maps, the overall difference was distinguishable [Fig. 6(b)]. Similarly for the second series of phantom study, the decrease of

*D*values could be observed by the tomographic

*D*maps while gray scale OCT images failed to discriminate different phantoms [Figs. 6(c) and 6(d)].

### 3.3 Experimental verification on biological tissue ex vivo

*ex vivo*human colon sample and compared with the high-resolution SEM images. The structure of colon mucosa consists of a folded epithelial cell layer (crypts) surrounded by the lamina propria (extracellular matrix surrounding crypts), as shown in Fig. 7(a). An SEM image shows distinct bundle structures of collagen in lamina propria (LP), while in the epithelial (Epi) layer, the structures appear more random and fine-grained. We calculated the image autocorrelation function on two tissue components, and Epi has a steeper decline in the correlation function in the sub-micron region than LP [Fig. 7(b)]. Meanwhile, thanks to the capability of localizing the OCT spectrum,

*D*and

*l*can be quantified along the penetration depth [Fig. 7(c)]. The correlation functional forms, which were measured by ISOCT, show a similar result as SEM image analysis, i.e., the Epi has a sharper correlation function than LP [Fig. 7(d)]. Both

_{c}*D*values in Epi and LP are mostly between 2 and 3 indicating that they are in a mass fractal regime, and it can be seen in Fig. 7(d) that the R.I. correlation function exhibits a power law at sub-micron length scales [30

30. İ. R. Capoğlu, J. D. Rogers, A. Taflove, and V. Backman, “Accuracy of the Born approximation in calculating the scattering coefficient of biological continuous random media,” Opt. Lett. **34**(17), 2679–2681 (2009). [CrossRef] [PubMed]

*ex vivo*intact sample, e.g., fixation changed the R.I. of the tissue composition. Yet, its validity for providing a qualitative structural comparison between the two tissue components remains.

## 4. Three dimensional (3D) ISOCT imaging of biological tissue

*D*on an

*ex vivo*rat buccal sample. There are three dominant layers: keratinized epithelium (KE), stratified epithelium (SE) and sub-mucosa (SM) [Fig. 8(a)]. The intensity discontinuity at layer conjunctions allows us to segment them at their boundaries so that the

*D*from each layer can be measured separately. Specifically, we smoothed the A-line signal by 15µm moving window and calculated the derivative. The first positive peak of the derivative marked the surface of the sample, the second dominant positive peak marked the surface of SM. We then smoothed the surface curves to remove noises. We numerically flattened the sample surface by shifting the A-lines, and averaged the image across transverse direction. By taking a derivative, the averaged thickness of KE was obtained by the distance between the first positive and the first negative peaks (boundary of KE and SE). We then marked the surface of SE by shifting the sample surface by the averaged thickness of KE. The wavelength-dependent attenuation from KE and SE was compensated before the

*D*calculation in SM as in Eq. (10) [34

34. C. Xu, J. M. Schmitt, S. G. Carlier, and R. Virmani, “Characterization of atherosclerosis plaques by measuring both backscattering and attenuation coefficients in optical coherence tomography,” J. Biomed. Opt. **13**(3), 034003 (2008). [CrossRef] [PubMed]

*D*map was plotted in HSV space, where

*D*encoded Hue and the image intensity encoded Saturation and Value [Fig. 8(b)]. The

*D*value histograms at each layer are shown in [Figs. 8(c)-8(e)]. The averaged

*D*± standard deviation from KE, SE and SM were calculated as 2.12 ± 0.59, 2.73 ± 0.49 and 4.82 ± 1.6, respectively. A similar increase of

*D*in SM can be observed in sub-mucosa which also contains a large portion of extracellular matrix such as the lamina propria in the above colon sample.

*ex vivo*human colon biopsies. The 3D pseudocolored

*D*map and the gray scale morphology were volume-rendered and overlaid concurrently. The cross sectional B-scan

*D*map is shown in the movie (Media 1).

## 5. Discussion and conclusions

*k*

^{4}spectral dependence. It is well known that when the size of the scatterers decreases and reaches the Rayleigh regime, the scattering cross-section is proportional to

*k*

^{4}[35]. When the tissue structure contains more Rayleigh scatterers, the SP is closer to 4, which yields a smaller

*D*, if quantified by ISOCT. When the size of the particles increases, the spectrum becomes flatter, leading to a larger

*D*. Thus, the way that ISOCT analyzes the spectrum, i.e., by quantifying the SP, is conceptually quantifying a relative scattering weight of the sub-diffractional structures. Higher

*D*values indicate a relatively low power ratio of the sub-diffractional scatterers. The introduction of the W-M correlation function further elucidates the physical reality and grants us a quantification method.

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*etc.*) in the discrete model lead to a change of the R.I. correlation function from the sphere diameter and below. We should note that the particle size can be bigger than 450nm, but it is still the sub-micron length scales that prominently determine

*D*measurement [Fig. 4(c) and 4(d)].

*D*from biological tissue. The accuracy for

*in vivo*applications relies on two central assumptions of a continuous R.I. fluctuation model: the Born approximation and a continuous medium. In ISOCT, the spectrum is extracted from a coherence volume (~10

^{3}μm

^{3}), within which the Born approximation is largely satisfied. However, in a highly scattering medium where multiple scattering dominates, the Born approximation no longer holds and measurements can be inaccurate. Previously, we have found that in the superficial layer, the backscattering coefficient has much higher tolerance to the stronger scattering medium (

*μ*up to 10mm

_{b}^{−1}) while the scattering coefficient

*μ*started to break the Born approximation above ~12mm

_{s}^{−1}[29

**37**(21), 4443–4445 (2012). [CrossRef] [PubMed]

26. M. Moscoso, J. B. Keller, and G. Papanicolaou, “Depolarization and blurring of optical images by biological tissue,” J. Opt. Soc. Am. A **18**(4), 948–960 (2001). [CrossRef] [PubMed]

27. C. J. R. Sheppard, “Fractal model of light scattering in biological tissue and cells,” Opt. Lett. **32**(2), 142–144 (2007). [CrossRef] [PubMed]

*etc*. as in the buccal tissue presented in Fig. 8(a). There are distinct inter-layer boundaries where Fresnel reflections also contribute to the backscattered signal. We can treat each layer as a homogeneous medium within which the R.I. fluctuations are continuous and apply the algorithm. However, the deeper tissue is illuminated with wavelength-dependent attenuated incidence, which can be compensated for given the measurement of

*µ*. Once the penetration depth is over several times the mean free path length (MFP)

_{s}(λ)*l*(

_{s}*l*= 1/ µ

_{s}_{s}), the multiple scattering has a significant effect [39

39. R. K. Wang, “Signal degradation by multiple scattering in optical coherence tomography of dense tissue: a Monte Carlo study towards optical clearing of biotissues,” Phys. Med. Biol. **47**(13), 2281–2299 (2002). [CrossRef] [PubMed]

*D*measurement may be inaccurate.

*ex vivo*human colon biopsies provided experimental verification of this nanoscale sensitivity.

## Appendix:

*D*=3.

*k*is the momentum transfer whose value is equal to

_{s}*k*is the wave number and θ is the scattering azimuthal angle.

*D*,

*l*and

_{c}*N*follow the same definition in W-M correlation function. When

_{c}*D*= 3 and after plugging in the absolute value of

*k*, the above equation becomesIt is noted that the power spectral density is a function of θ, which describes the scattering power towards scattering angle. Essentially, the phase function

_{s}*p*(

*θ*) has the same shape as formulated above with the normalization so that the integration of the phase function is unity:The function is normalized in such way that

*G*(

*r*)in which the super script

*l*denotes the lower length scale. According to Wiener–Khinchin theorem, the Fourier transform of the correlation function is equal to power density spectrum.where

*FT*denotes Fourier transform and

*ACF*denotes autocorrelation function. Thus,

*h*stands for the upper length scale. A similar formulism in Eq. (18) is applied for

_{nΔh}:Where δ is the delta function in the spatial domain with the origin at zero. Thus,

## Acknowledgments

## References and links

1. | M. Cremer, K. Küpper, B. Wagler, L. Wizelman, J. von Hase, Y. Weiland, L. Kreja, J. Diebold, M. R. Speicher, and T. Cremer, “Inheritance of gene density-related higher order chromatin arrangements in normal and tumor cell nuclei,” J. Cell Biol. |

2. | C. Lanctôt, T. Cheutin, M. Cremer, G. Cavalli, and T. Cremer, “Dynamic genome architecture in the nuclear space: regulation of gene expression in three dimensions,” Nat. Rev. Genet. |

3. | O. Nadiarnykh, R. B. LaComb, M. A. Brewer, and P. J. Campagnola, “Alterations of the extracellular matrix in ovarian cancer studied by second harmonic generation imaging microscopy,” BMC Cancer |

4. | S. M. Pupa, S. Ménard, S. Forti, and E. Tagliabue, “New insights into the role of extracellular matrix during tumor onset and progression,” J. Cell. Physiol. |

5. | N. Théret, O. Musso, B. Turlin, D. Lotrian, P. Bioulac-Sage, J. P. Campion, K. Boudjéma, and B. Clément, “Increased extracellular matrix remodeling is associated with tumor progression in human hepatocellular carcinomas,” Hepatology |

6. | A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 Å spatial resolution light microscope: I. light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy |

7. | E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science |

8. | S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. |

9. | M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods |

10. | M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. |

11. | I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci. U.S.A. |

12. | Z. Wang, L. Millet, M. Mir, H. Ding, S. Unarunotai, J. Rogers, M. U. Gillette, and G. Popescu, “Spatial light interference microscopy (SLIM),” Opt. Express |

13. | C. Joo, T. Akkin, B. Cense, B. H. Park, and J. F. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. |

14. | A. J. Radosevich, J. Yi, J. D. Rogers, and V. Backman, “Structural length-scale sensitivities of diffuse reflectance in continuous random media under the Born approximation,” Opt. Lett. |

15. | A. J. Radosevich, N. N. Mutyal, V. Turzhitsky, J. D. Rogers, J. Yi, A. Taflove, and V. Backman, “Measurement of the spatial backscattering impulse-response at short length scales with polarized enhanced backscattering,” Opt. Lett. |

16. | A. J. Gomes, S. Ruderman, M. DelaCruz, R. K. Wali, H. K. Roy, and V. Backman, “In vivo measurement of the shape of the tissue-refractive-index correlation function and its application to detection of colorectal field carcinogenesis,” J. Biomed. Opt. |

17. | D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science |

18. | A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys. |

19. | B. Povazay, K. Bizheva, A. Unterhuber, B. Hermann, H. Sattmann, A. F. Fercher, W. Drexler, A. Apolonski, W. J. Wadsworth, J. C. Knight, P. S. Russell, M. Vetterlein, and E. Scherzer, “Submicrometer axial resolution optical coherence tomography,” Opt. Lett. |

20. | L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography,” Nat. Med. |

21. | J. Yi, Q. Wei, H. F. Zhang, and V. Backman, “Structured interference optical coherence tomography,” Opt. Lett. |

22. | A. Fercher, “Inverse Scattering, Dispersion, and Speckle in Optical Coherence Tomography,” Optical Coherence Tomography 119–146 (2008). |

23. | J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. |

24. | R. Barer and S. Tkaczyk, “Refractive index of concentrated protein solutions,” Nature |

25. | J. M. Schmitt and G. Kumar, “Turbulent nature of refractive-index variations in biological tissue,” Opt. Lett. |

26. | M. Moscoso, J. B. Keller, and G. Papanicolaou, “Depolarization and blurring of optical images by biological tissue,” J. Opt. Soc. Am. A |

27. | C. J. R. Sheppard, “Fractal model of light scattering in biological tissue and cells,” Opt. Lett. |

28. | J. D. Rogers, İ. R. Capoğlu, and V. Backman, “Nonscalar elastic light scattering from continuous random media in the Born approximation,” Opt. Lett. |

29. | J. Yi and V. Backman, “Imaging a full set of optical scattering properties of biological tissue by inverse spectroscopic optical coherence tomography,” Opt. Lett. |

30. | İ. R. Capoğlu, J. D. Rogers, A. Taflove, and V. Backman, “Accuracy of the Born approximation in calculating the scattering coefficient of biological continuous random media,” Opt. Lett. |

31. | H. G. Davies, M. H. F. Wilkins, J. Chayen, and L. F. La Cour, “The use of the interference microscope to determine dry mass in living cells and as a quantitative cytochemical method,” Quarterly J.Microscopical Sciences (New York) |

32. | L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. |

33. | C. J. R. Sheppard, “Fractal model of light scattering in biological tissue and cells,” Opt. Lett. |

34. | C. Xu, J. M. Schmitt, S. G. Carlier, and R. Virmani, “Characterization of atherosclerosis plaques by measuring both backscattering and attenuation coefficients in optical coherence tomography,” J. Biomed. Opt. |

35. | H. C. van de Hulst, |

36. | J. Yi, J. Gong, and X. Li, “Analyzing absorption and scattering spectra of micro-scale structures with spectroscopic optical coherence tomography,” Opt. Express |

37. | F. E. Robles and A. Wax, “Measuring morphological features using light-scattering spectroscopy and Fourier-domain low-coherence interferometry,” Opt. Lett. |

38. | C. Matzler, “Autocorrelation functions of granular media with free arrangement of spheres, spherical shells or ellipsoids,” J. Appl. Phys. |

39. | R. K. Wang, “Signal degradation by multiple scattering in optical coherence tomography of dense tissue: a Monte Carlo study towards optical clearing of biotissues,” Phys. Med. Biol. |

**OCIS Codes**

(170.3660) Medical optics and biotechnology : Light propagation in tissues

(170.4500) Medical optics and biotechnology : Optical coherence tomography

(290.0290) Scattering : Scattering

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: January 3, 2013

Revised Manuscript: March 7, 2013

Manuscript Accepted: March 11, 2013

Published: April 4, 2013

**Virtual Issues**

Vol. 8, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

Ji Yi, Andrew J. Radosevich, Jeremy D. Rogers, Sam C.P. Norris, İlker R. Çapoğlu, Allen Taflove, and Vadim Backman, "Can OCT be sensitive to nanoscale structural alterations in biological tissue?," Opt. Express **21**, 9043-9059 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-9043

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