2.1.

Optical Setup

The optical setup used in this study combines IVM and OCT for simultaneous image acquisition. A scheme of the setup is shown in Fig. 2. The principle of image acquisition was previously described elsewhere.¹³ In this paper’s configuration, the optical resolution of the IVM, limited by the numerical aperture of the system, amounts to approximately $4\mu \mathrm{m}$. With a field of view of $1.7\times 1.3{\mathrm{mm}}^2$, the pixel resolution leads to $1.06\mu \mathrm{m}/\text{pixel}$, yielding an oversampling by a factor of 4. The speed of the system was set to 12.5 fps. IVM imaging is performed by using a dark field illumination with a ring of 24 light-emitting diodes (LEDs) surrounding the objective lens and yielding an incidence angle of 45 deg. Color image acquisition was achieved utilizing a $1600\times 1200$ pixel complementary metal oxide semiconductor camera (Sumix, United States) with a pixel size of $4.2\times 4.2{\mu \mathrm{m}}^2$. The optics was designed to yield a telecentric ray propagation in object space to prevent changes in magnification due to axial movement of the object. OCT images were simultaneously acquired by IVM. The free-space optical resolution is $8\mu \mathrm{m}$ in the lateral direction and $10\mu \mathrm{m}$ in the axial direction. Oversampling yields a voxel size of $4\times 4\times 5{\mu \mathrm{m}}^3$ with a lateral depth scan rate of 12 kHz and a maximum field of view of $10\times 10{\mathrm{mm}}^2$.

Fig. 2

Optical setup for combined IVM and optical coherence tomography (OCT) imaging. A fiber coupler and a single-mode fiber (SMF) connect the near-infrared (NIR) light source (SLD) with the interferometer, integrated in the scanner head, and with the spectrometer. The NIR light is coupled into the interferometer by the collimator (C) and divided into reference and sample beam by a beam splitter (BS). The sample beam is deflected by a scanner unit (SU) for $x$ and $y$ directions and focused by an objective lens (OL) onto the sample. The backscattered light is superimposed with the reference light, first focused by the reference lens (RL) and then reflected by the reference mirror (RM), coupled into the SMF and transmitted to the spectrometer, where it is spectrally resolved. A dichroic mirror (DM) separates the light for intravital microscopy (IVM), which is then focused with the camera lens (CL). The IVM image is acquired by a complementary metal oxide semiconductor camera, which is also integrated into the scanner head. A ring light, consisting of 24 super high light-emitting diodes (LEDs), is positioned at the front of the scanner head above the sample for IVM-illumination (light pathway indicated by dashed lines and dark gray color).

2.2.

Lung Tissue Preparation

As an animal model for the study of image formation of subpleural alveoli with IVM and OCT, we used a preparation method for in vivo experiments.^19,20 According to the guidelines of the governmental authorities, we utilized mice post mortem instead of living animals. Mice were anesthetized and sacrificed via exsanguination. To gain optical access to the upper alveoli, a thorax window was prepared by removing three ribs of the chest above the middle lobe of the right mouse lung. After introducing a thoracic catheter into the chest and resealing the window with a transparent wrapping film, the intrathoracic pressure was reconstituted by sucking out the excess air. Ventilation was performed utilizing a trachea tube and a customized ventilator capable of air- and perfluorodecalin-(F2 Chemicals Ltd., United Kingdom) based liquid ventilation.¹⁷ IVM as well as OCT images were acquired at constant pressures set by the ventilator for air as well as liquid ventilation within physiological limits (12 mbar peak pressure).

2.3.

Simulation

For the simulations, the ray tracing software TracePro® was used. To minimize computational effort, two kinds of tracing techniques were applied, reverse and direct ray tracing. Reverse ray tracing was performed by using the rendering or radiance ray tracing option in TracePro®, see also Fig. 3(a). This was utilized to obtain intensity images or radiance maps of the model for a given point of view set by the eye position of the virtual camera. Since this method only traces ray paths that contribute to the image formation, the number of rays traced can be reduced up to a factor of 2500. For these kinds of simulations, the light source was modeled as a light ring under 45 deg with Lambert properties. The simulated image was obtained by placing a virtual pinhole camera far above the model (100 mm). For each analysis pixel, 150 to 200 rays were traced from the fixed point at the camera position through a random position on the analysis plane to the model until they reached a light source. Analysis pixel size was set to $0.75\mu \mathrm{m}\times 0.75\mu \mathrm{m}$. For direct ray tracing, see Fig. 3(b) which reveals the traveling paths of the rays, a light sheet (incidence angle 45 deg, 100,000 to 500,000 rays) illuminated the model. Reflection, transmission, and refraction of the rays were traced according to the optical properties and the geometry of the model including wave properties such as Fresnel reflections. Rays leaving the model in a normal direction were selected with a ray selecting plane far away from the model, resulting in angles of $\pm 0.2\mathrm{deg}$ relative to the normal on the pleura. These ray paths are displayed and the intensity is analyzed when the rays leave the model.

Fig. 3

Simulation setup and model of alveolar tissue. (a) Reverse ray tracing image is obtained with a virtual camera and an illumination with a light ring. (b) In direct ray tracing, rays are traced from a 45-deg light sheet through the model until they leave the model in normal direction. The virtual camera in (a) as well as the ray selection plane in (b) are located far away from the model, which corresponds to a detection of rays leaving the model in normal direction ($\pm 0.2\mathrm{deg}$ to the normal on the pleura). (c) Modeling of alveolar tissue by using hexagonally shaped alveoli. Abbreviations are: alveolus (A), pleural surface (PS), tissue (T).

For the simulation, our simplified model of alveolar tissue uses typical geometries found for a mouse lung²¹ and consists of six hexagonal structures which were placed in a ring around a seventh center alveolus, see Fig. 3(c). These structures were filled with air and the refractive index of the tissue was set to 1.38.²² Parameter variation included a shift of the center alveolus downward and fluid filling of the center alveolus [refractive index 1.31 according to the manufacturer information for perfluorodecalin (F2 chemicals Ltd., United Kingdom)].

3.1.

Experimental Investigations on Liquid-Filled Lung Tissue

A typical IVM image of a partially liquid-filled in situ mouse lung is displayed in Fig. 4(a). Representative characteristics of the IVM images are given by bright reflexes lining bubble-like structures in the air-filled area (triangle with solid contour) and forming more or less a double ring. The bright reflexes are currently used as a border for the discrimination between alveolar lumen and tissue.^2–4,7 At the transition to liquid filling, the bright reflexes show decreased intensity at the side facing the liquid-filled area compared to the side facing the air-filled region [asterisk in Fig. 4(a)]. The double ring structure finally disappears in the liquid-filled space as a result of the index matching. The corresponding OCT cross section in Fig. 4(b) additionally shows the depth information of the tissue at the position marked with the white-dotted line in Fig. 4(a). Alveolar lumina appear as dark circular structures within the scattering tissue, which is visible in grayscale. The OCT data in Fig. 4(b) perfectly reveal the transition between the liquid-filled and the air-filled alveolar area (marked with an asterisk). The alveolar structures are still recognizable in the liquid-filled region in contrast to the appearance in the IVM image of Fig. 4(a). Additionally, Fig. 4(c) shows an en face section through the 3-D OCT data stack [marked with the curved dash-dotted line in Fig. 4(b)], which illustrates data points located $20\mu \mathrm{m}$ below the pleura visceralis [marked with pv in Fig. 4(b)]. Similar to the depth cross section of Fig. 4(b), Fig. 4(c) reveals the presence of alveoli within the liquid-filled region of the tissue. Since the OCT images in Figs. 4(b) and 4(c) still show alveoli, we have to realize that IVM images give no information about whether alveoli are collapsed or filled with liquid.

Fig. 4

Partially liquid-filled lung area acquired with IVM (a) and OCT (b), (c) and (d) using the in situ mouse model at a constant positive airway pressure of 8 mbar after 35 min of liquid ventilation. The view in (c) shows a section through the dash-dotted line in (b), which is formed by all points of the OCT data stack, which are located $20\mu \mathrm{m}$ below the pleura visceralis (pv). The position of the OCT depth cross section (b) is marked with the dotted line in (a) and (c), the abbreviation $m$ denotes the surrounding medium above the lung surface, which is air. The index matching caused by the liquid-filling leads to a loss of contrast for IVM resulting in vanishing of alveolar structures, but an increase in contrast and penetration depth for OCT [marked with asterisk in (a) (b) and (c)]. Liquid-filled structures are still detectable with OCT in contrast to IVM images. One typical bright circular structure in IVM is indicated by a triangle with solid contour. Such structures are more pronounced in the case of a slightly underlying neighbor alveolus (triangle with dotted contour); see also the enlarged inset (d) within (b) with indicated alveolar borders. $\text{Scale bar}=100\mu \mathrm{m}$.

Note the following three peculiarities in IVM images in the transition zone between liquid and air filling: first, double ring structures are present in the air-filled space of the tissue and disappear within the liquid region of the lung, although open alveoli are still present. Second, the bright reflexes are less pronounced at the side of those alveoli, which are located directly at the border between liquid and air filling. These alveoli are still filled with air, but have a neighbor alveolus which is filled with liquid. Third, the bright reflexes in the air-filled space are much more pronounced in the case of alveoli whose adjacent alveolus is placed slightly below them, as indicated by the triangle with a dotted contour in Fig. 4(b) as well as in the enlarged inset given in Fig. 4(d). This behavior leads to the hypothesis of total internal reflection (TIR) between adjacent alveoli, which shall be further studied in the following theoretical section.

3.2.

Theoretical Considerations

In IVM, the lung is usually illuminated with a circular light and the camera is positioned in the middle of the ring light. To avoid a direct reflex from the pleura of the lung, the illumination is performed under a certain angle of incidence. The current opinion in IVM studies is that the reflexes visible in the camera image arise from the alveolar walls^2–4 or partial reflection at the boundary between tissue and alveolar lumen, which is filled with air.⁷ Since the distance between the bright reflexes of neighboring alveoli is greater as would be expected for an alveolar septum, the latter hypothesis of partial reflection seems to be more reasonable. This case is illustrated in Fig. 5(a). Using Fresnel equations for a plane wave, the relative power of light reaching the camera along the displayed pathway can be quantified by approximately 2% when assuming an incidence angle of $\alpha =45\mathrm{deg}$ and a refractive index of the tissue of $n_{\text{Tissue}}=1.38$.²² Furthermore, this model does not describe the presence of double rings as well as the loss of brightness of the outer ring when located next to a liquid-filled alveolus.

Fig. 5

(a) Current model for the formation of the IVM images: rays from a light source are refracted at the pleura, partially reflected at the tissue–air interface of an alveolus located below the pleura and finally reaching the camera perpendicular through the pleura. (b) Proposed model of rays forming total internal reflexes (or nearly total internal reflexes) near the border of alveoli by two reflections. The illuminating ray enters under an entrance angle of $\alpha$ (not drawn). The transmitted ray hits alveolus 1 under an angle (${\alpha }_{\text{Out}}+\beta$) at a point where the surface of the alveolus is tilted by $\beta$ relative to the pleura. The reflected part reaches alveolus 2 under the angle $\gamma$ and is reflected toward the camera.

To explain a double ring structure, a second process of light propagation should be considered, yielding a brighter outer ring in addition to the inner ring resulting from partial reflection with weaker intensity as mentioned above. Higher intensities for the outer ring would be obtained, for instance, by two times TIR or a mix of TIR or partial reflexes with high incidence angles (nearly TIR), further called multiple internal reflection (MIR), by suggesting a light path between neighboring alveoli as illustrated in Fig. 5(b). The occurrence of MIR depends on the surface angle $\beta$ of the first alveolus, which is defined as the angle between the surface normal of alveolus 1 and the optical axis toward the camera, and the corresponding reflection angle $\gamma$ of the second alveolus, respectively. Assuming identical curvatures for both alveoli, the expected relative power of light at the camera position can be calculated via Fresnel equations. The diagram in Fig. 6(a) displays the resulting normalized power in dependence of the surface angle $\beta$ and the corresponding height of the second alveolus fulfilling the angle condition for the pathway sketched in Fig. 5(b). The graph shows that TIR on both alveoli only appears within a given range for $\beta$ (between 16 deg to 28 deg) as well as an upward shift of alveolus 2 toward the pleura compared to alveolus 1. The normalized power in dependence of angle $\beta$ can be found in Fig. 6(b) assuming unpolarized incident light. Even for no displacement of alveolus 2, the normalized power on the camera amounts to approximately 10%. Taking an upward shift of alveolus 2 into account, the relative power even reaches 94%. Both conditions result in a much higher intensity than the partial reflex and are likely to happen since the conditions for this process are met within a broad range of alveolar surface angles and relative heights. Thus, the model of multiple internal reflections between adjacent alveoli perfectly explains the appearance of a bright outer ring surrounding the inner partial reflex at the alveoli.

Fig. 6

(a) Normalized power reaching the camera after being transmitted at the pleura, reflected at both alveoli and transmitted through the pleura again as a function of both the surface angle $\beta$ and the vertical displacement between alveoli with identical curvatures. A positive value means that alveolus 2 is located nearer to the pleura. The gray value shows the amount of light being transmitted for unpolarized light where black is 1 and white is 0. (b) Amount of light detected at the camera as a function of the surface angle $\beta$ of alveolus 1 by meeting the angle conditions for the pathway shown in Fig. 5(b). The resulting tilt angle $\gamma$ is independent from the height or radius of curvatures of the alveoli. For different tilt angles ($\beta$ and its corresponding $\gamma$), various conditions can be found for the event of total internal reflection (TIR) (normalized power approximately 0.94). One of these is illustrated for equal curvatures of alveoli and varying height of alveolus 2.

3.3.

Ray Tracing Results

To verify the hypothesis of multiple internal reflection between adjacent alveoli, alveolar tissue was simulated using reverse [Fig. 3(a)] and direct ray tracing [Fig. 3(b)], respectively, as described in the Methods section using the idealized tissue geometries depicted in Fig. 3(c). According to the findings of the experimental investigations summarized in Sec. 3.1, typical features present in the IVM images [Fig. 7(a) second row] can also be found in the reverse ray tracing simulation results [Fig. 7(a) first row]. The simulated intensity images are inverted for clarity reasons, meaning that a dark color corresponds to a high intensity. The characteristic features found for both the simulation and IVM images are: (1) double ring structures (solid arrow for bright outer ring, dash-dotted arrow for less bright reflex), (2) disappearing of liquid-filled alveoli (asterisk) and decrease of intensity of the bright ring structure adjacent to the liquid-filled region (black solid triangle), and (3) increased intensity of the outer ring of the double ring structure (triangle with solid contour) in the case of a downward shift of an adjacent alveolus (triangle with dotted contour), which goes along with decreased intensity of the outer ring of the shifted alveolus.

Fig. 7

(a) Comparison between simulation and imaging results for the alveolar model geometry [Fig. 3(c)] and mouse lung tissue, respectively. Within the simulation, all alveoli are filled with air (refractive index $n=1$) except for the case of liquid filling (center alveolus filled with liquid $n=1.31$, marked with asterisk). The axial position of the center alveolus is displayed within the simulation results ($0\mu \mathrm{m}$ corresponds to the same axial position compared to the surrounding alveoli, $11\mu \mathrm{m}$ corresponds to an axial position $11\mu \mathrm{m}$ below the neighbor alveoli). Characteristic features are the following: first, the appearance of double ring structures (solid arrow for outer ring, dash-dotted arrow for inner ring), second the vanishing of alveoli (asterisk) and the loss of intensity of the outer ring facing the liquid region (black solid triangle, please also compare the simulated intensities for the outer rings between the air-filled and the liquid-filled cases, i.e., solid arrow and solid triangle), and third the increase of intensity of the outer ring (triangle with black solid contour) if positioned next to an alveolus, which is slightly located below (triangle with black-dotted contour), combined with a decreased outer contour intensity of the lower alveolus (black-dotted contour, position assumed in the IVM image, but not visible). (b) Direct ray tracing and ray propagation for the alveolar model tissue as well as the resulting simulated intensity image revealed by the reverse ray tracing method. $\text{Scale bar}=50\mu \mathrm{m}$.

Using direct ray tracing, the beam paths, which form the intensity distribution of the reverse ray tracing results in Fig. 7(a), can be further analyzed and attributed to specific light interaction processes [Fig. 7(b)]. From this, two major sets of rays can be attributed to form the different circular structures: partially reflected rays at the surface of the alveoli (dash-dotted lines) as well as rays, which are deflected by double TIR or nearly TIR ($=\mathrm{MIR}$) first at a deeper lying alveolus and second from a neighbor alveolus positioned slightly above the first one (solid line). Comparing these pathways with the resulting intensities [first row of Fig. 7(b)], the partially reflected rays can be attributed to the less bright inner reflexes, whereas light propagating via multiple internal reflection forms strong outer rings around the inner weaker reflexes. In addition, rays that are both reflected and refracted at the corner of an alveolus can produce a slightly darker reflex almost collocated with the MIR reflex. In Fig. 7(b), such a path can be found very close to the strong solid line, but slightly shifted to the right at the left edge of the right alveolus. Strong signals can also be produced by multiple reflections at the surfaces of more than two alveoli as the dashed ray path shows, but they nearly coincide with the MIR reflex. The initial reflection might be far away from the alveolus with the last, image-relevant reflection. Altogether, these ray paths confirm the theoretical assumption of two basic processes forming the double ring structure in IVM images of lung tissue: the bright outer ring corresponds to multiple internal reflections between adjacent alveoli and the inner ring, which has lower intensity, corresponds to partial reflection at the surface of the alveoli.

3.4.

Alveolar Wall Position and Edge Radii in Intravital Microscopy Images

As we have seen from the ray tracing results, the origin of the reflexes visible in the IVM images can be attributed to MIR for the bright outer circles and partial reflection for the weaker inner circles of the double ring structure. As the angle of the alveolar surface at the position of these two reflexes is reasonably known, the true position of the alveolar wall as well as the edge radius $R_i$ can be approximated when assuming a similar geometry as the model alveoli with constant curvature in the cross section. Since in most IVM setups, the camera is positioned along the normal of the pleural surface, we can also neglect pleural tilts in the mathematical derivations. For a correction of the measured alveolar outline, the following parameters have to be extracted from the IVM image [see Fig. 8(a)]: $d_i$, which is the distance between the partial and the multiple internal reflexes at a certain point $i$ on the outer ring; and $x_{\text{MIR}i}$, the corresponding position of the MIR reflex. Furthermore, the angle of incidence ($\alpha$) and the refractive index of the tissue ($n_T$) have to be known.

Fig. 8

(a) Draft of two neighboring subpleural alveoli describing the necessary geometric parameters for the calculation of the true alveolar size based on the position of the reflexes in the intensity image: $\alpha$ is the angle of incidence, $\beta$ is the angle of partially reflected rays, $\gamma$ is the angle of MIR rays, $d$ is the distance between the partially reflected and the MIR rays corresponding to one point on the bright MIR outline of the alveolus, $x_{\text{MIR}}$ is the corresponding position of the MIR point for distance $d$, $x_S$ is the corresponding expected position of the alveolar septa for distance $d$, $R$ is the radius of the curvature of one alveolus in a cross section at one MIR point, i.e., edge radius. (b) IVM image of mouse lung parenchyma used as an example for the estimation of the alveolar wall position by measuring the distances between the partial and the MIR reflexes. The results are displayed in (c) with dash-dotted lines indicating partial reflexes, solid lines indicating total internal reflexes, and dotted lines showing the position of alveolar septa. White arrows indicate additional complex structures, which could arise from partial reflexes due to folding of the upper alveolar tissue or from deeper lying borders of the alveoli (e.g., alveolar mouths). (d) Increase of segmented area after correction [area enclosed by dotted lines in (c)] relative to the area segmented from MIR-reflexes [enclosed by solid lines in (c)]. (e) Relation between the mean alveolar edge radius $R$ over the corresponding corrected area $A_{\text{corr}}$. $\text{Scale bar}=50\mu \mathrm{m}$.

The position $x_{Si}$ of the alveolar septa corresponding to a radius $R_i$ of the alveolar edge [see Figure 8(a) for comparison] can be expressed by

An example for the calculation of the true alveolar border using IVM data is shown in Figs. 8(b) and 8(c). In the presented image, the incidence angle $\alpha$ amounts to 45 deg. Using a refractive index of 1.38 for lung tissue, $\beta$ results in approximately 15.4 deg and $\gamma$ equals 46.4 deg. The partial reflexes [dash-dotted lines in Fig. 8(c)] as well as the MIR reflexes [solid lines in Fig. 8(c)] are manually retraced. Via image processing, the shortest distances $d_i$ between the dash dotted and the solid line were measured and used for calculation of the true positions $x_{Si}$ of the alveolar septa [dotted lines in Fig. 8(c)] for each point $i$ along the segmented path of the outer ring. Although this model is very simple, the calculated positions of septa from neighboring alveoli are often very near to each other, in agreement with the small thickness of alveolar septa. Deviations might be caused by a wrong assignment of reflexes, additional not segmented alveoli, more complex structures, and capillaries. The corrected alveolar area is increased by ($57\pm 3$) % as an average over 16 segmented alveoli ($\text{mean}\pm \mathrm{SEM}$), see Fig. 8(d).

For each alveolus and each point on the outline of the alveolus, the alveolar edge radius $R_i$ can be calculated using the distances $d_i$ measured from the IVM images:

By averaging over all extracted radii per alveolus, the dependence between the average edge radius and the corresponding alveolar area can be evaluated, see Fig. 8(e). Although the area seems to increase with increasing edge radius, the large spread of area values within a small range of edge radii indicates a great variety of form factors within the image. A power function was used to estimate the dependency between the one-dimensional geometry parameter $R$ and the 2-D geometry parameter $A_{\text{corr}}$ by approximating the scaling factor and the exponent of the function. The mean alveolar edge radius, calculated over 16 alveoli, amounts to $(16.9\pm 0.8)\mu \mathrm{m}$ ($\text{mean}\pm \mathrm{SEM}$). Additionally, the average equivalent alveolar diameter $D_{\mathrm{eq}}$ can be derived, which is calculated from the mean area $A_{\text{corr}}$ and is approximated by a circular geometry according to

This parameter yields a value of $(58\pm 3)\mu \mathrm{m}$ ($\text{mean}\pm \mathrm{SEM}$).