Light distribution in fat cell layers at physiological temperatures

Abstract

Adipose tissue (AT) optical properties for physiological temperatures and in vivo conditions are still insufficiently studied. The AT is composed mainly of packed cells close to spherical shape. It is a possible reason that AT demonstrates a very complicated spatial structure of reflected or transmitted light. It was shown with a cellular tissue phantom, is split into a fan of narrow tracks, originating from the insertion point and representing filament-like light distribution. The development of suitable approaches for describing light propagation in a AT is urgently needed. A mathematical model of the propagation of light through the layers of fat cells is proposed. It has been shown that the sharp local focusing of optical radiation (light localized near the shadow surface of the cells) and its cleavage by coupling whispering gallery modes depends on the optical thickness of the cell layer. The optical coherence tomography numerical simulation and experimental studies results demonstrate the importance of sharp local focusing in AT for understanding its optical properties for physiological conditions and at AT heating.

Figure 1

In vivo microscopic images of fat tissue of a rat at back reflectance from a few millimeters of an intact abdominal fat layer using a CMOS camera: a white light source (a); green LED 517 nm (b); He–Ne laser 632.8 nm (c); the light breeze on the shallow seawater on a sunny day (d) (see Supporting Information); see the similarity of caustics formation due to focusing of shining light by a lens let array of these complex systems with shape variation in a semiregular manner, due to which phase is different from the out-of-water wavefront.

Figure 2

The adipocyte as an optical model: an optical model of adipocyte. CCM is the cell cytoplasmic membrane; CP is the cytoplasm; LD is the lipid droplet; adip is the adipocyte.

Figure 3

Simulations of Gaussian light beam propagation (waist of the beam is of 10 μm) through 2D fat tissue model (3-layer cell model at immersion in ISF with n = 1.36): two cell layer tissue model (a)-(c) and six-cell layer tissue model (d); symmetric [(a), (b) and (d)], and nonsymmetric light beam incidence (c); incidence to cell center in the upper layer (a) and (d); incidence between two adjusted cells (b); six-cell layer tissue model (e) and (f) with the incidence to cell center in the upper layer at immersion in ISF with n = 1.38 and 1.40, respectively.

Figure 4

Numerical simulation of OCT-images of AT layers: the reflection coefficient $R(100\mu m,{\mathbf{r}}_{\perp })$ at the 100 μm-depth (a), and the transverse structure of the reflected from this layer light beam (b) for AT fragment with 8 cell-layers along z-direction; examples of the A-scans for AT(c); the OCT light beam position on the upper surface of AT corresponds to the cell center (dash line) or between two cells (solid line) for AT fragment with 8 cell-layers along the z-direction.

Figure 5

Results of numerical simulation of OCT-images of AT layers: (a) example of the B-scan for AT fragment with 8 cell-layers along the z-direction; (b) the C-scan (in terms of $W$ values) of the 100 μm-depth layer for AT fragment with 8 cell-layers along the z-direction.

Figure 6

Ex vivo OCT images of human (a–c) and porcine (d–f) fat tissue slices for different temperatures: 23 °C (a); 30 °C (b); 38 °C (c); 25 °C (d); 30 °C (e); 38 °C (f). (a1)–(f1) typical 3D images; (a2)–(f2) typical B-scans.

Figure 7

Results of statistical analysis for intensity of all light spots at the bottom of OCT image of the AT samples (see Fig. 7, the bottom surface of the sample image); the evolution with the temperature of these light spots intensity distributions for human (a) and porcine (b) fat tissue slices is shown. To recalculate the optical thickness into a geometric one, we took the average refractive index of AT equal to 1.44. (c) Distribution of difference in intensity at 38 °C and room temperature t of light spots at the bottom of OCT image of the AT samples, where t = 23 °C for human AT, and 25°C for porcine AT (a, b, the bottom surface of the sample image). (d) Light spot intensity ratio I(38)/I(t) distribution on the number of the averaging window of 20 μm in width counted from 0 to 2000 μm of the longitudinal coordinate of (a, b), where t = 23 °C for human AT, and 25 °C for porcine AT (see Fig. 7, the bottom surface of the sample image), and S-8b and S-8c. (e) The results of the $D_b$ calculation for AT model shown in Fig. S-4b and for experimental data presented in (a).

Figure 8

In vivo transmission images of rat abdominal AT sites (cell layer thickness is of 120 ± 15 μm) in the initial state at room temperature (25 °C) (a) and after heating up to 30 °C (b) and 38 °C (c). These images were obtained using the CS235MU monochrome CMOS camera KiraluxTM, the number of pixels in the matrix of 1280 × 1024; 10 bits/pixel (Thorlabs Inc., Newton, New Jersey) with custom software ThorCam 5.6 (Thorlabs Inc., Newton, New Jersey), microscopic objective (lens 10 ×), and white light (a1, b1, c1), green LED with the wavelength of 517 nm(a2, b2, c2), light of He–Ne laser (632.8 nm) (a3, b3, c3). The corresponding 2D distributions of image brigtness were built using ImageJ. In vivo back reflectance images of rat abdominal AT (cell layer thickness is of 100 ± 15 μm) in the initial state (a4) and after hot saline solution (50 °C) application (b4); the initial state (a5) and after compression with a fiber tip (b5); image of another rat abdominal AT in the initial state (a6) and after applying the immersion optical clearing agent PEG-300 (b6) (the corresponding video are presented in Supporting Information). These images were obtained using the Basler A602f. monochrome CMOS camera (the number of pixels in the matrix of 656 × 491; 8 bits/pixel) with custom software made with National Instruments LabVIEW 8.5, microscopic objective (lens 10 × ), and green LED with the wavelength of 517 nm.

Figure 8

In vivo transmission images of rat abdominal AT sites (cell layer thickness is of 120 ± 15 μm) in the initial state at room temperature (25 °C) (a) and after heating up to 30 °C (b) and 38 °C (c). These images were obtained using the CS235MU monochrome CMOS camera KiraluxTM, the number of pixels in the matrix of 1280 × 1024; 10 bits/pixel (Thorlabs Inc., Newton, New Jersey) with custom software ThorCam 5.6 (Thorlabs Inc., Newton, New Jersey), microscopic objective (lens 10 ×), and white light (a1, b1, c1), green LED with the wavelength of 517 nm(a2, b2, c2), light of He–Ne laser (632.8 nm) (a3, b3, c3). The corresponding 2D distributions of image brigtness were built using ImageJ. In vivo back reflectance images of rat abdominal AT (cell layer thickness is of 100 ± 15 μm) in the initial state (a4) and after hot saline solution (50 °C) application (b4); the initial state (a5) and after compression with a fiber tip (b5); image of another rat abdominal AT in the initial state (a6) and after applying the immersion optical clearing agent PEG-300 (b6) (the corresponding video are presented in Supporting Information). These images were obtained using the Basler A602f. monochrome CMOS camera (the number of pixels in the matrix of 656 × 491; 8 bits/pixel) with custom software made with National Instruments LabVIEW 8.5, microscopic objective (lens 10 × ), and green LED with the wavelength of 517 nm.