Computational Model of Optical Scattering by Elastin in Lung

Tristan B. Swedish*, Joseph P. Robinson*, Maricris R. Silva†, Andrew Gouldstone†,

David Kaeli*, Charles A. DiMarzio*†

* Department of Electrical and Computer Engineering * Gordon Center for Subsurface Imaging Systems (CenSSIS)

† Department of Mechanical and Industrial Engineering

Northeastern University, 360 Huntington Avenue, Boston, Massachusetts 02115

ABSTRACT

Little is understood about the detailed microstructure of lung in vivo. Attempts to improve imaging are hampered by heterogeneity of the tissue. One common ex vivo technique is optical coherence tomography (OCT). Simulated OCT with a Finite-Difference Time-Domain (FDTD) computer model elucidates the relationship between captured images and the physical geometry of the lung. Parallel computation and improved processing power make accurate coherent imaging models feasible. A previous FDTD model of pulsed laser wave propagation in the lung produced images that displayed many of the properties of experimental images. The model was improved with the addition of elastin and increased computational volume. Elastin plays an important role in the simulation because the combination of its fibrous structure and high index of refraction acts as an excellent scatterer of light. This strong scattering increases the signal reported by the simulated OCT scan in areas where elastin is most abundant, improving visualization of the structure as more light is reflected back from the heterogeneous elastin network. However, scattering by elastin decreases the depth of penetration and leads to images that are more difficult to interpret. Gaining a better understanding of how lung structures affect light propagation will lead to improved signal processing, instrumentation, and the development of new probing techniques. This image modeling technique can also be applied to other imaging modalities such as confocal and other laser scanning methods.

Keywords: Optical Coherence Tomography (OCT), Confocal Reflectance Microscopy (CRM), Computational Microscopy, Lung, Alveolar Structure, Elastin, Finite Difference Time Domain (FDTD)

1. MOTIVATION

Attempts to image the microscopic structure of the lung for the purposes of studying its mechanical properties are made difficult by the lung’s complicated anatomical structure and the diverse optical properties of the tissues that compose it. Current in vivo imaging techniques lack the resolution for sub-alveolar analysis of the lung’s internal structure. Optical imaging can provide the necessary resolution, but lacks the necessary penetration to provide useful information about the lung in vivo.1 Excised lung samples collapse without the necessary surrounding tissue to maintain air pressure and keep their structure. Large sections of lung can be artificially inflated and subsequently imaged using optical

imaging techniques such as Optical Coherence Tomography (OCT), but the desired penetration depths and resolution are still not adequate to study collapse and re-inflation on alveolar scales.1 The light scattering nature of the tissue in lung complicates the problem of creating optimized imaging platforms in order to image the lung and its structure. The limit on imaging depth is not the result of absorption; light penetrates many layers of alveoli into the lung. However, the complexity of the tissue leads to reduced contrast, degraded resolution, and distortion. Understanding these effects may enable their mitigation through instrument design and image processing algorithms. Thus, there is a need for a way to evaluate new experimental imaging instruments and algorithms against some type of “ground truth.”2 One way to do this is to construct computational models that simulate light propagation for various optical systems.3

In this work, we present an anatomical model of the lung that we use in a finite difference wave propagation algorithm to generate synthetic images in different imaging modalities.

2. ANATOMICAL MODEL

Our lung model is comprised of a computational grid representing a two dimensional slice of lung. We have represented each type of tissue in our simulation with an index identified by color (Figure 1). We used histological images of excised lung samples and Confocal Reflectance Microscopy (CRM) images as references to construct the correct geometry.3 A mammalian lung is composed of branching bronchial structures that terminate in clusters of air sacs called alveoli. The visceral pleura is an elaborate network of elastic fiber which surrounds these alveolar sacs and forms the outer layer of the lung.4 Previous work utilized simplified models that focused primarily on the effect of the shape of alveoli and the refractive properties of the tissue-air boundaries between them.3 The internal structure of the tissue and the visceral pleura was ignored. In the present work a more accurate model of the lung was developed with the addition of elastin-like components and the inclusion of the visceral pleura (Figure 1A). Elastin has a very high index of refraction (1.534)5 compared to the surrounding tissue, as well as a complicated geometry that suggests that it would have interesting effects on optical imaging of lung. Our anatomical models most closely follow the dimensions of a rat lung with alveolar radii of about 30µm.6

(A) (B) Figure 1 – Anatomical models of lung used for the simulation. Each type of tissue is assigned an index represented by color in these images. Each tissue type is assigned a corresponding value for the index of refraction. (A) A lung model with a thick pleural wall. (B) A lung model with 3 distinct layers of alveoli filled with water.

3. COMPUTATIONAL MODEL OF LIGHT PROPAGATION

Our computational model of light propagation was developed utilizing a discrete Finite Difference Time Domain (FDTD) method of solving Maxwell’s Equations in a computational grid. Each pixel in the anatomical model is assigned a value based on the index of refraction of the structure it represents. In our FDTD simulation, the index of refraction is converted into values for the dielectric constant in order to solve for the time dependent derivatives for the electric and magnetic fields in Maxwell’s equations. The spatial derivatives of the electric field are used to compute the time derivatives of the magnetic field, which are used to increment the magnetic field to its value at the next time step. Subsequently, the spatial derivatives of the newly changed magnetic field are used to compute the time derivatives of the electric field.7 By defining an initial pulse, the electromagnetic field can be visualized as the light propagates through our anatomical model in time. Using this approach, a large amount of data can be collected about the propagation of the light through different areas of the anatomical model. This approach has been proven effective in simulating CRM.8 In addition, by capturing the reflected light in an arrangement similar to an OCT system9, images of our anatomical model can be constructed utilizing our FDTD simulation (Figure 2). These images can be directly compared to experimental data. Using different configurations of the anatomical model, images can be generated with modifications in the shape and type of tissue present. In this way, structures that affect the images most can be identified empirically.

(A) (B) Figure 2 – (A) The anatomical model is divided into slices. (B) The propagation of a light pulse through each slice is simulated using an FDTD algorithm. A simulated detector captures any reflections. Combining A-scans produces an image.

Figure 3 – Comparisons of simulated light wave propagation through lung tissue with and without elastin for three time steps. The top three pictures represent a layer of tissue with no elastin present, while the bottom three include elastin.

4. OPTICAL SCATTERING BY ELASTIN IN MODEL

When a simulated light pulse is sent through a scattering layer in our anatomical model resembling an alveolar wall (Figure 3), The propagating wave can be visualized at any time. In the case of no elastin, the layer of lung tissue is a single homogenous substance with an index of refraction of 1.40, suspended in air. A single six-wavelength pulse of 930nm light is seen as reflecting off of both air-tissue boundaries with little change in the wave front shape. In the model with the same layer of tissue and added elastin, the same reflections can be observed in the air-tissue boundaries, but much more of the light is scattered by the elastin as the pulse moves through the tissue (Figure 3). The transmitted pulse loses its spatial coherence and reflections from the lower tissue layer boundary are deformed further as they move back through the elastin geometry. Increased reflections can be observed from within the tissue layer due to the highly scattering elastin network. Scattered light from the tissue volume thus provides contrast between tissue and air, which does not exist without elastin. These observations provide insight into analysis of images generated using our simulation and anatomical models (Figure 4). Simulated images of two models with the same alveolar geometry but with and without elastin look drastically different. The model without elastin produced an image in which alveoli could be identified at a superior depth as would be expected (Figure 4A). In the model with elastin, more alveolar structure can be identified because the scattering creates contrast in the whole tissue volume rather than just the Fresnel reflections from boundaries (Figure 4B). However, distinguishing individual alveoli becomes more difficult with depth. A lung’s elastin-filled visceral pleura can have varying thickness that can make imaging difficult. In an anatomical model with elastin-rich visceral pleura about 50µm thick, no identifying features could be found in simulated images (Figure 4C). Despite elastin’s highly scattering properties, greatly improved images could be produced when the alveoli were filled with water in our anatomical model (Figure 4D). This index matching technique in our anatomical models provided the best results in our simulated images. These findings agree with experiment.10 The refractive effect of the tissue-air index gap and loss of transmitted light to scattering still is a large contributor to loss of effective light for imaging.

(A) (B)

(C) (D) Figure 4 – Simulated OCT images of various anatomical lung models. (A) Model without elastin and (B) with elastin imaged to a depth of 120µm. Models (Figure 1) with an (C) extended pleural wall and (D) alveoli filled with index matching water imaged to a depth of 150µm.

5. CONCLUSION

Upon investigating the differences in light propagation for a variety of anatomical lung models, a few conclusions can be drawn. Elastin plays a critical role in the resulting images of lung using OCT. More signal is reported in the images due to the highly reflective elastin, increasing visualization of tissue structure but decreasing the depth at which alveoli can be identified. The effects of elastin become increasingly detrimental with depth, and visceral pleura with a thickness of about 50 µm can make OCT imaging difficult or impossible. Improved images can be expected for samples with thin pleural walls in experiments. The largest contributor to poor imaging depth still appears to be the refractive effects of the tissue-air boundaries and drastic improvements to imaging quality can be achieved through index matching with water. Since inflation with water is not practical for in vivo applications, an alternative approach is to account for the refraction in image processing algorithms.

7. ACKNOWLEDGEMENTS

This work was supported in part by the Gordon Center for Subsurface Sensing and Imaging Systems, CenSSIS, under the Engineering Research Centers Program of the National Science Foundation (award number EEC-9986821). The presentation of this material was made possible with the SPIE Student Travel Grant supported by the Newport Spectra-Physics Research Excellence Travel Awards Program and support from the Office of the Provost at Northeastern University under the Provost Undergraduate Research Grant.

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