Abstract
Keywords
1 Introduction
Line-field Confocal Optical Coherence Tomography (LC-OCT) is a recently introduced optical imaging technique combining the principles of time-domain OCT and reflectance confocal microscopy (RCM) with line illumination and line detection using broadband near infrared light. LC-OCT performs two dimensional (2D) and three-dimensional (3D) imaging with a quasi-isotropic resolution of ∼1 μm [
As in OCT and RCM, the contrast of LC-OCT images originates from the backscattering of light, due to refractive index inhomogeneities within the sample. The amount of detected backscattered light is determined by three main optical parameters specific to the imaged sample [
Beyond morphological information, LC-OCT images contain information on optical properties of the sample. Those optical properties are determined by the size, shape and density of tissue light scatterers (nucleus, mitochondria, cytoskeleton, extracellular fiber such as collagen) at cellular and sub-cellular levels. The extraction of optical properties would thus allow access to quantitative information complementary to the morphological information provided by the LC-OCT images. Optical properties could be used as a tool for tissue characterization and quantification of tissue structural changes, which could for instance occur during the development of a pathology.
Quantification of the attenuation coefficient μ using conventional OCT has been used for several biomedical applications, such as atherosclerosis plaque characterization [
In contrast, fewer work has been reported on the separate measurement of the optical parameters μa, μs and g using OCT. However, the interest in measuring the optical properties, and especially the scattering parameters μs and g, is that each of them provides different and complementary information on tissue structure. μs is determined by several factors, including the density, size and shape of the scattering particles, while g is defined by the size and shape of these particles [
A few methods based on curve-fitting allow the measurement of the optical properties μa, μs and g. Thrane et al. [
As a combination of RCM and OCT (in focus-tracking mode as will be described later), LC-OCT is particularly suitable for the application of the model developed by Jacques et al. [
2 Materials and methods
2.1 Scattering phantoms
In order to mimic optical properties of biological tissues such as skin [
The phantoms are composed of a PDMS matrix (Sylgard 184 silicone Elastomer Kit, Neyco, France) with a refractive index of 1.42 at the wavelength of 800 nm [
In order to select the appropriate scatterers to mimic optical properties of the skin, Mie theory (assuming spherical particles) was used to simulate μs and g values of the phantoms as a function of the refractive index, size and density of the particles embedded in PDMS. However, all the parameters necessary to predict the optical properties by Mie theory were not precisely known. For example, only the mean particle size was sometimes given by the manufacturer, without information on the size distribution. The refractive index of the nanoparticles was not provided either. For ZnO and SiO2 particles, we approximated the refractive index by optical index values extracted from the literature at the 800 nm wavelength [
The PDMS matrix was fabricated using a ratio of 10:1 by weight of PDMS pre-polymer and curing agent. All phantoms were prepared by first mixing the curing agent with a variable amount of scattering powder. The mixture was placed in an ultrasonic bath for 30 min to prevent particles aggregation, and then mixed with the PDMS pre-polymer. The obtained mixture was poured on a 40-mm diameter petri dish. The volume poured was chosen in order to obtain 1–2.5 mm thick phantoms, a thickness allowing their characterization by integrating spheres. Air bubbles were removed using a vacuum pump for 1 h, and the phantom mixture was finally cured for
We also designed two bilayered phantoms with distinct optical properties in each layer, as listed in
Figure 1.LC-OCT vertical image (i.e., cross-sectional view) of a bilayered phantom. The LC-OCT image is displayed in a logarithmic intensity scale (arbitrary unit).
Table Infomation Is Not Enable2.2 Integrating spheres and collimated transmission measurements
Mie theory allows to define target values for μs and g. However, as previously mentioned, the characterization of the optical properties by Mie theory is not very reliable due to uncertainties on the size distribution and the refractive indices of the particles used in our phantoms. Therefore, these target values are indicative values but cannot be used as reference values to compare with values obtained from LC-OCT images. Thus, the optical properties of our samples were characterized experimentally, using integrating spheres and collimated transmission devices.
Integrating spheres measurement is a common method to measure optical properties of samples [
We used a set-up with two integrating spheres (2″ Integrating Sphere IS200-4, Thorlabs, USA). The sample was placed between the two spheres. Light from a high-power broadband Xenon light source (HPX 2000, Ocean Insight, Dunedin, Florida) was guided to one of the two spheres using a 50/125 optical fiber and collimated into a 6-mm diameter beam. Diffuse reflected and transmitted light were collected using an optical fiber (plastic fiber, PMMA Toray, 50-cm long, 1-mm diameter, 0.22 NA) coupled to a spectrometer (AvaSpec2048, Avantes, Netherlands). Collimated transmission measurement was carried out with a monochromatic fiber laser diode at 785 nm (Micron Cheetah, Sacher LaserTechnik, Germany). The laser beam was collimated at the fiber output and its diameter was reduced using a diaphragm. The phantom was placed a few cm behind the diaphragm, perpendicular to the laser beam. A collection fiber (105 μm core diameter, 0.1 NA), connected to the spectrometer, was placed one meter behind the phantom in order to collect the ballistic light. Due to its small diameter, low numerical aperture and large distance to the sample, the fiber acts as a pinhole rejecting scattered photons.
All measurements were corrected for dark noise and normalized with respect to blank measurements without sample. The optical properties were computed using the Inverse Adding-Doubling (IAD) algorithm developed by Prahl [
In practice, the collimated transmission measurement could not be performed on some of the highly concentrated phantoms (3, 5, 7 and 9) since the ballistic intensity was too weak. However, phantoms 3, 5, 7 and 9 are made of the same scattering particles as phantoms 1, 4, 6 and 8 respectively. Since g is ruled by particle size and shape [
For bilayered phantoms, the top and bottom layers were analyzed separately since integrating spheres and collimated transmission do not allow to separate the scattering properties of two stacked layers. As previously mentioned, since the 100 μm-thick top layer was very fragile, the scattering properties of the top layer were measured on a thicker phantom fabricated with the same batch mixture as the thin top layer.
2.3 LC-OCT measurements
2.3.1 LC-OCT device
The LC-OCT device used in this work is described in [
2.3.2 Theoretical model for measuring μs and g
Within the single-scattering regime and in focus-tracking mode, the reflectance R(z) measured along an A-scan acquired by OCT or LC-OCT image (i.e., the depth-dependent fraction of incident light backscattered and collected by the device) can be described by an exponential decay with depth [
G(NA,g) describes the average optical path length traveled by the photons collected by the OCT system, taking into account the numerical aperture NA and the scattering anisotropy factor g of the imaged sample. This term takes into account the fact that photons emitted at the edge of the beam travel a longer optical path than photons emitted on the optical axis. For NA = 0.5 (numerical aperture of the LC-OCT device), G is close to 1 [
a(g) is called the scattering efficiency factor. It reflects the contribution of forward scattered photons, i.e., serpentile photons. Serpentile photons can contribute to the backscattered intensity because of their trajectory similar to that of ballistic photons. Then, if they follow a serpentile trajectory on the return path, photons can contribute to the collected intensity. Thus, serpentile photons slow down the extinction of the incident intensity by scattering in the sample. This effect has been formalized in the form of a function a(g):
b(g,NA) is qualified as collection efficiency and represents the fraction of light scattered from probed volume and collected by the microscope objective of the LC-OCT device. b(g,NA) is ruled by the phase function of the sample, described by the Henyey–Greenstein function in this model [
In this modeling of R(z), ρ and μeff can be considered as experimental observables and can be extracted from an LC-OCT image as described in the following section.
2.3.3 Processing of LC-OCT images for extracting μs and g on monolayered phantoms
The principle of our method consists in measuring μeff and ρ parameters from an LC-OCT image, and to convert these parameters into the optical properties μs and g using the previously described model proposed by Jacques et al. To do so, a 3D LC-OCT image is acquired for each phantom. The 3D image results from the acquisition of a stack of 2D LC-OCT horizontal images (i.e., en-face sections). Each image of the stack is obtained by demodulating the interferometric lines acquired successively in the horizontal plane during the lateral scan, using a phase-shifting algorithm [
ρ and μeff are extracted by applying a least square linear regression on log R(z) (
Figure 2.(a) 3D LC-OCT image (horizontal or en face view and vertical or cross-sectional view) of a phantom made of PDMS and TiO2 particles, in logarithmic intensity scale and (b) averaged intensity profile I(z) in the 3D LCOCT image as a function of depth, in logarithmic scale. A linear regression (red line) is applied on the intensity profile to obtain the measurement of the pair of observables μeff and ρ.
Finally, the resulting parameters ρ and μeff extracted from the 3D LC-OCT image are mapped to the optical properties μs and g using the model by Jacques et al. previously described. Several ways can be considered to recover μs and g from μeff and ρ using equations
Figure 3.Ratio of μeff/ρ as a function of g, calculated for λ = 800 nm, NA = 0.5 and Δz = 1.2 μm.
2.3.4 Measurements on bilayered phantoms
For bilayered phantoms, two distinct areas of linear decay can be observed on the averaged intensity profile plotted in
Figure 4.Averaged intensity profile R(z) in the 3D LC-OCT image of a bilayered phantom as a function of depth (in logarithmic scale). For each layer, a linear regression (red line) is applied on the intensity profile to obtain the measurement of the pair of observables (ρtop, μtop) and (ρbottom, μbottom). The value of ρbottom is retrieved from the intercept with the interface between the two layers (z = 110 μm) corrected from attenuation in the top layer.
The resulting parameters ρtop, μefftop and ρbottom, μeffbottom are then mapped to the optical properties μs and g in each layer using the model by Jacques et al. as described in the previous section.
2.3.5 Calibration
As introduced in the previous section, the mean intensity I(z) (in gray levels) in an LC-OCT image can be converted into dimensionless units of reflectance R(z) using a calibration constant f such that R(z) = fI(z). To determine f, one of the phantoms was used as a calibration phantom. On the one hand, μs and g of the calibration phantom were obtained from integrating spheres and collimated transmission measurements. Using the model of Jacques et al. [
2.4 Evaluation of uncertainties
For each phantom, integrating spheres and collimated transmission measurements were performed three times. Mean values of μs and g obtained with integrating spheres and collimated transmission were calculated from these three measurements.
Since LC-OCT measurements are based on a calibration performed with a calibration phantom whose optical properties are obtained by integrating spheres and collimated transmission measurements, the uncertainties of the integrating spheres and collimated transmission method have a significant impact on the accuracy of LC-OCT measurements of μs and g. Values of μs and g were computed from mean values of μs and g obtained from three 3D LC-OCT image, and uncertainties on LC-OCT measurements were estimated as follows: first, the uncertainty on the calibration factor f was estimated from uncertainties obtained on μs and g values of the calibration phantom measured using integrating spheres and collimated transmission measurements. From the resulting uncertainty on f, the uncertainty on ρ, due to calibration, was obtained for each fabricated phantom. Additional uncertainties on ρ and μeff were experimentally observed due both to least square linear regression on the intensity depth profile extracted from the 3D image and to slight variations of ρ and μeff from one image to another of the same phantom. Finally, uncertainties on μs and g were evaluated for each fabricated phantom by propagating total uncertainties on ρ and μeff through the model of Jacques [
3 Results and discussion
3.1 Monolayered phantoms
Comparisons of μs and g values of monolayered phantoms obtained from LC-OCT mean intensity depth profiles and integrating spheres and collimated transmission measurements are given in
Figure 5.Comparison of μs values obtained by LC-OCT and combined integrating spheres and collimated transmission measurements on monolayered phantoms. Mean values and error bars were determined as explained in detail in Section 2.4.
Figure 6.Comparison of g values obtained by LC-OCT and combined integrating spheres and collimated transmission measurements on monolayered phantoms. Mean values and error bars were determined as explained in detail in Section 2.4.
First of all, one can observe that the optical scattering properties obtained correspond to the range of properties targeted, with μs values between 1 and 25 mm−1 and g values between 0.68 and 0.94. The obtained results confirm that μa ≪ μs for all phantoms. For phantoms made of the same particles (in terms of refractive index and size), one can notice that the value of μs increases with the particle concentration, in agreement with Mie theory. The measured values of μs do not correspond exactly to the theoretical values, but the order of magnitude is similar. As stated earlier, the theoretical values are indicative due to uncertainties in the size and refractive index of the scattering particles. Moreover, it should be noted that during the fabrication process, particle losses may have occurred when pouring the particle/hardener mixture into the prepolymer, which may also contribute to some deviations in μs. Concerning the g parameter, we can note that here again the values of g for the phantoms 1, 4 and 8 have the same order of magnitude compared to Mie theory. However, the value of g obtained for phantom 6, composed of 400 nm SiO2 particles, is largely higher (0.94) than the target value (0.7) and is equivalent to the value of g obtained for phantom 8, composed of SiO2 particles of larger size (1 μm). A possible explanation could be the aggregation of 400 nm particles into larger particles, of the order of 1 μm.
When looking at the comparison of μs and g values between the two measurement methods, results show that, for phantoms 1–6 and 8, LC-OCT is capable of providing measurements of optical properties consistent with those obtained by integrating spheres and collimated transmission measurements, with overlapping error bars (nearly overlapping for the μs measurement for phantom 2). For phantoms 7 and 9, one observes a good agreement of g values between the two methods. On the other hand, we observe a significant discrepancy between the value of μs measured by integrating spheres and collimated transmission and that measured by LC-OCT. To date, we have no definitive explanation for this discrepancy, but a potential explanation could be the presence of aggregates in phantoms. As shown by high-resolution bright field microscopy images (acquired with a 1.35 NA objective) given in
Figure 7.High-resolution microscopic images of phantom 9 acquired with a 1.35 NA objective. (a) Image acquired in a homogeneous region without aggregates and (b) image acquired in a region with particle aggregates.
The measurements of μs and g have fairly high uncertainties, represented by the error bars in
In summary, despite the issues encountered with phantoms 7 and 9, results obtained show that our measurement method is well suited to samples with medium to high scattering anisotropy (0.7 < g < 0.9) and scattering coefficients μs up to 12 mm−1, which already allows for application to biological tissues.
3.2 Bilayered phantoms
The results obtained on the bilayered phantoms are shown in
Figure 8.Comparison of μs and g values (mean ± standard deviation) obtained by LC-OCT and combined integrating spheres and collimated transmission measurements on two different bilayered phantoms.
Concerning μs values, one can also observe a good agreement for all layers. Overall, the difference between the two measurement methods on μs remains of the same order as the difference obtained on the monolayered phantoms. One can notice that the value of μs in the bottom layer of the bilayer phantom 2 is slightly lower than the value of μs obtained with the monolayer phantom 5 alone, a difference that can possibly be explained by a more important contribution of multiple scattering than with the monolayer phantom 5 since the linear regression on the bottom layer is applied deeper (from 100 to 200 μm). The model of Jacques et al. takes into account the multiple scattering in certain extent and when scattering is directed forward. In order to better account for multiple scattering in its entirety, multiple scattering models such as the EHF model proposed by Thrane et al. [
Nevertheless, our results obtained on bilayered phantoms demonstrate the potential of LC-OCT to provide layer-based measurements of distinct μs and g values from a single 3D image, unlike the integrating spheres and collimated transmission method which requires the two layers to be analyzed separately. Compared to the current state of the art, the application of our method on bilayered phantoms with different values of μs and g in each layer is innovative since previously reported multilayered phantoms have identical g values in all layers. However, our fabrication process would need to be improved for obtaining a more homogeneous thin top layer. Indeed, as for monolayered phantoms, aggregate deposition in the bottom of the thin layers has sometimes been observed. One solution could be to cut a thin layer from a thicker sample that would be more homogeneous.
4 Conclusion and perspectives
We have developed a method for measuring the scattering coefficient μs and the scattering anisotropy factor g of a sample from a single 3D image of that sample acquired by LC-OCT. Our approach is based on the extraction of two observables ρ and μeff from the LC-OCT image, by applying a linear fit to the mean intensity depth-profile within the 3D image (in logarithmic scale). Using a calibration with a phantom of known optical properties and a model previously introduced in the literature [
Compared to integrating spheres and collimated transmission measurements that require manipulating the sample (place it between the spheres, then move it on the collimated transmission bench) and involves constraints on the sample physical characteristics (minimum size corresponding to the beam diameter, minimum thickness to be placed between the two spheres without risk of damaging the sample, maximum thickness for the collimated transmission to be possible), LC-OCT does not require specific sample handling and constraints, which simplifies the measurement procedure and would facilitate in vivo measurements of μs and g. Moreover, LC-OCT allows measurements on multilayered samples with distinct optical properties in each layer, using a single 3D image, unlike integrating spheres and collimated transmission which require analyzing the different layers separately. In this paper, we demonstrate the applicability of our method to bilayered samples, with the ultimate aim of applying the approach to the two main layers of the skin, the epidermis and the dermis. However, our method is not limited to two layers, but could be applied to multilayered samples (>2) following the same approach as for bilayered samples, as described in Section 2.3.4.
Our layer-based approach is interesting since few papers have reported measurement by OCT of 1 distinct μs and g values on multilayered samples [
The model of Jacques et al. takes into account multiple scattering when scattering is strongly directed forward, but it does not extensively account for multiple scattering as the extended Huygens–Fresnel (EHF) model does [
Since LC-OCT provides morphological images, a future prospect could be to perform spatially resolved measurements of μs and g in a horizontal plane, in addition to the layer-based measurements obtained on the bilayered phantoms. Such spatially-resolved measurements could be obtained by dividing the 3D LC-OCT image into macro-voxels, in which values of μs and g could be extracted using the mean intensity depth profile in each macro-voxel. A macroscopic spatial distribution of μs and g could then be obtained. Further investigation is required to apply our method to biological tissues. LC-OCT is an imaging modality designed for biological tissue imaging, and in particular for skin imaging in vivo. Applied to biological tissue, the presented method could provide LC-OCT with the ability to quantify the scattering properties of tissue imaged in vivo, complementary to the qualitative information provided by the high-resolution of images. Potentially, the method could be used in vivo to characterize biological tissues and monitor structural changes that occur during the development of a pathology.
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