1. Introduction

Most of the biological samples are relatively transparent. Since the microscopic techniques can detect only the intensity and color of the light of field-sample interaction, staining methods are used to provide contrast through such samples. The optical phase changes by a transparent sample provide valuable structural information of the samples, and methods such as phase contrast and differential interference contrast microscopy have been utilized to image boundaries of phase objects within the sample [1]. However, these techniques are inherently qualitative. Several attempts have been presented to resolve this problem with more quantitative approaches. Among various techniques, holography has been emphasized and developed more than others [2]. Holography is capable of three dimensional (3D) information recording. Optical reconstruction is also possible via visual 3D observation. Conventional holography suffers from drawbacks such as the need for photographic development of holograms and extra facilities for quantitative 3D analysis. Digital holography can be a solution for these shortcomings. It works based on recording the holograms by digital image sensors followed by their numerical reconstruction [3,4]. Subsequent reconstruction of the hologram contains the information about the phase object. In recent years, extensive research has been dedicated to the expansion of different applications of digital holography [5–7]. A significant advantage of holography is its capability to integrate with conventional microscopes to perform digital holographic microscopy (DHM) [8,9]. DHM provides high resolution quantitative phase contrast imaging that is suitable for non-invasive investigations of living cells and many other industrial life sciences and medicine applications [10,11].

In this paper, for the first time, we utilize DHM technique for myelin figures (MF) imaging. MFs are multilamellar cylindrical tubes of membrane lipids. In living cells, such tubules are generated via a highly regulated transduction of physical forces [12]. Morphologically similar membrane tubules also form when plasma membranes are deformed by binding with bacterial toxins in their extra-cellular space, e.g., shiga and cholera toxins [13–15]. Multilamellar tubules of MFs, are found in healthy and diseased cells as transient and long-lived structures originating from concentrates of dense lipid plaques [16–18]. Case in point of such cells and biological organelles include Histiocyte cell in lung [19,20], aged red blood cell [21], Mesangial cell and Podocytes in kidney [22]. A prominent example is the existence of MFs in pulmonary lining. They have been implicated in the formation of extra-cellular lipid-protein coat at the alveolar surface, whose primary function is to facilitate decrease in the surface tension when lungs deflate [23–25]. These extra-cellular MFs form when intracellular lamellar bodies secreted into the alveolar lumen experience chemical stresses due to changes in pH and ion (e.g., Ca++ and Mg++) concentrations [23,25].

Generally, stacks of lipid amphiphilic molecules in excess water and at the presence of an external stress/force have great capability for the formation of multilamellar cylindrical tubes. For example lamellar bodies in lung convert to multilamellar tubular configuration in response to stress [23]. A dry plaque of lipid would make many MFs after applying the stress caused by hydration. Even the hydrated stack lipids can make MF at the presence of sufficiently strong external flow [26].

Cylindrical tubes also have an important role in long-distance communication between biological cells and in pathologies [27]. They have also been used in studying the physical properties of some amphiphiles such as lipid bilayers by pulling out tethers [28–31].

So far, imaging of MFs was mostly focused on Fluorescence [32] or Phase Contrast microscopy [33] and to a lesser extent on Scanning Electron Microscope (SEM) [34]. To the best of our knowledge, there is no report of using DHM in studying the myelin figure features. Sample preparation is difficult for SEM imaging and it cannot be used for studying the dynamics of myelin figures. When studying the dynamics using Fluorescence or Dark/Bright field microscope, accuracy and focusing problems exist due to the MF movement in all directions as well as their frequent coiling [35]. Also alteration in the volume of the myelin figures cannot be measured by these methods. However, DHM can give us the opportunity to quantitatively consider the structure and dynamics of the myelin figures such as precise evolution of volume, thickness and length of MFs in time.

In this paper, we study the growth of myelin figures employing DHM technique at the presence and absence of linear thermal gradient. The results indicate that thickness of a myelin figure does not alter significantly during its growth. However, it may change at the early stage of the protrusion (< 10 sec.) Our work indicates that length of the myelin figure grows as $L\propto \sqrt{t}$ at the absence or presence of thermal gradient (L = length, t = time). However, thermal gradient facilitate and fasten its growth toward the higher temperature region. Our work provides evidence for the growth based on collective diffusion of lipid molecules in hydrophilic solution [36,37].

2. Materials and methods

1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) was purchased from Avanti polar lipid. The solution of POPC and chloroform was prepared at concentrations of 10 mg/ml and one microliter drop of the solution was placed in the DHM stage. The drop was air dried at room condition and placed in vacuum for 12 hours for complete evaporation of chloroform. Myelin figures were formed upon hydration of the dry drop.

A special chamber was built in order to conduct temperature gradient on the stage. As shown in the inset of Fig. 1, the chamber consists of a heat source, a cooling pipe and channels for water injection. The heat source includes a thin wire which can be heated by applying electric current via a controlled DC power supply. One side of the chamber is connected to a zero degree water tank via a rectangular shaped capillary as a cooling system. Water constantly passes through the capillary so that the temperature in the cold part remains fixed.

 

Fig. 1 Schematic DHM setup; M: mirror; BS: beam splitter; MO: microscope objective.

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A syringe tip connected to an injection pump was used to flow deionized water into the chamber with a rate of 20 ml/h. The chamber is inserted on the stage of the digital holographic microscope.

The DHM setup is based on a Mach–Zehnder interferometer configuration to allow off-axis holography of a transparent sample, as shown schematically in Fig. 1. A white light illumination source (KL1500 compact, Olympus), collecting lens L1, condenser C, microscope objective MO1 (100X, Olympus) and camera (Thorlabs-DCC1545M) were used to build a conventional home-made inverted microscope. The samples were first viewed through this microscope to adjust the best focus before the holography experiments.

3. Results and discussions

The temperature gradient obtained in our set-up and used in the experiments is shown in Fig. 2(a). Minimum and maximum points correspond to the location of hot and cold sources, respectively. Growth of the myelin figures are considered in the direction of cold source to the hot source. The results were compared with the identical room temperature experiment. Figure 2(b) shows a typical image of MFs observed by conventional microscopy. This figure corresponds to t = 10 s after MF formation.

 

Fig. 2 (a) Temperature gradient used in the experiments; (b) Conventional microscopy image of myelin figures recorded 10 sec. after hydration of the parent lipid dry drop. The arrow indicates the direction of the thermal gradient from low to high temperature. As thermal gradient can act as an external force, it facilitates the growth of MFs.

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As shown in Fig. 1, laser light emitted from a He-Ne laser (λ = 632.8 nm) after being expanded by beam expander BE is split into object wave and reference wave by beam splitter BS1. Very low laser power ensures that the absorption of laser by the sample and consequent thermal change is negligible. The beam going through mirror M1 is the reference wave, which is sent to camera through MO2 (to adjust the beam curvature) and BS2. The object beam goes through the condenser onto the chamber; and after scattering from the transparent object though MO1, M2, and BS2 goes to the camera to interfere with the reference wave. The interference pattern of the two beams is recorded as a digital hologram and has 3D information of the sample being studied. The recorded holograms will then be reconstructed numerically by computer. The reconstruction process is performed by simulating the diffraction from the digital hologram when illuminated by the reference wave.

As shown in Fig. 1, laser light emitted from a He-Ne laser (λ = 632.8 nm) after being expanded by beam expander BE is split into object wave and reference wave by beam splitter BS1. The beam going through mirror M1 is the reference wave, which is sent to camera through MO2 (to adjust the beam curvature) and BS2. The object beam goes through the condenser onto the chamber; and after scattering from the transparent object though MO1, M2, and BS2 goes to the camera to interfere with the reference wave. The interference pattern of the two beams is recorded as a digital hologram and has 3D information of the sample being studied. The recorded holograms will then be reconstructed numerically by computer. The reconstruction process is performed by simulating the diffraction from the digital hologram when illuminated by the reference wave.

We utilized the angular spectrum propagation approach in scalar diffraction theory for numerical reconstruction of the holograms [11]. The propagation can be written as

The objects under study in our case are almost transparent and hence we are interested in measurement of phase changes during the experiments. Several holograms were recorded at a rate of 5 frames per second (fps) in various states of MFs growth. Figure 3 shows the reconstruction process and results for a typical hologram of a MF. Figure 3(a) is the recorded hologram of MF at t = 3 s after it started to be formed, and Fig. 3(b) is the Fourier spectrum of the hologram containing two separated images from which one is selected to derive intensity and phase information. Figures 3(c) and 3(d) are the associated phase and intensity patterns of the hologram, respectively. In order to remove the background contaminations from the sample container and the fluid for every sample, we recorded a reference hologram in which no MF is presented. This ensures that the phase changes in various times in MF growth process are only due to its growth. Figure 3(e) is the filtered phase image of the MF subtracted by phase of the reference hologram. Figures 3(f) to 3(h) are different illustrations of the phase information of the reconstruction. Figure 3(f) is the 2D map of a region of interest indicated in Fig. 3(e). As can be seen, the phase of the MF and the rest of the field of view have different value ranges. By a simple RGB to binary transformation of the map, the surface covered by the MF can be calculated. Assuming negligible changes for refractive index, the thickness along an arbitrary line across the MF can also be calculated as shown in Fig. 3(g). 3D map of the phase is shown in Fig. 3(h). The process shown in Fig. 3 should be repeated for all the holograms recorded at a rate of 5 fps for each sample. Changes in thickness, length, surface, or volume of the MF can be used to follow its growth.

 

Fig. 3 (a) Hologram of a MF at t = 3 s after its formation starts; (b) Fourier spectrum of the hologram; Associated phase (c) and intensity (d) patterns of the hologram; (e) Filtered phase image of the MF subtracted by phase of the reference hologram; (f) 2D phase map of a cropped part of the reconstructed image; (g) 1D profile of the MF along the line indicated in panel (f); (h) 3D phase map of the MF; (i) to (l): recorded hologram and reconstructed, 1D, 2D and 3D phase map of a coiled MF. Information such as volume, surface, and thickness of the MF can be derived from the reconstruction of holograms. The field of view was 85 µm × 60 µm.

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Due to the frequent coiling of myelin figures, studying the dynamic characterization of myelin figure via direct measurement of its length by conventional microscopy can hardly be accurate. Figures 3(i) to 3(l) show a recorded hologram and corresponding reconstructed images of a coiled MF. Coiling is evident from the reconstructed images, showing the capability of the DHM method for measurements in such cases. In our DHM technique, we consider the evolution of the volume of the myelin figure in time. Figure 4(a) shows the volume vs. time of a myelin figure at the presence and absence of thermal gradient. Note that the curves indicate the average value of several measurements (more than 20) of various MFs. Red squares show the case in which no temperature gradient is presented, and blue circles show the effect of applying a gradient of temperature in our experiment. Note that the applied temperature gradient is shown in Fig. 2(a) and the direction of MF growth is toward the higher temperature. Figure 4(b), indicates that the thickness of the myelin figure does not change significantly during the growth. However, at the very early stage, in the first ten seconds, more instability is observed in the thickness. In Fig. 4(c), the length of the myelin figure is derived from the values of volume and thickness.

 

Fig. 4 The effect of temperature gradient on MF growth employing DHM technique. (a) Evolution of volume in time; (b) Thickness of myelin figures does not alter significantly during the growth; (c) Length of myelin figures vs. time at the presence and absence of thermal gradient.

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As indicated by the curve fittings, the length of the MF at both presence and absence of the thermal gradient follows the diffusive model of the MF growth [36,37], in which the length evolution is described as .. for the early stage of the growth. Note that, in our experiment, the growth of the individual MFs was measured rather than the group of MFs. There are some other reported experiments in which the length of the myelin grows differently (e.g., $L\propto t,orL\propto t^{(p)}p\sim 1$) by changing the experimental conditions and the geometry (e.g., applying mechanical puncturing) [26,38]. To the best of our knowledge, the growth of the MFs under thermal gradient has not been studied yet. In this work we showed that applying thermal gradient as a possible external stress does not influence the general length-time relation at the early stage of the growth. However, the thermal gradient increases the rate of the growth, as shown in Fig. 4(c). In this experiment, the MF under thermal gradient grew as $L=0.61\sqrt{t}-0.20$ and the MF protruding from similar stacked lipid without thermal gradient grew with about three times slower slope as $L=0.23\sqrt{t}-0.11$. Moreover, it was reproducibly observed that MFs under thermal gradient grow for more extended time as $L\propto \sqrt{t}$ and have longer final length.

4. Conclusion

Digital Holographic Microscopy provides a non-destructive and quantitative phase contrast imaging suitable for high resolving investigations of living cells. In this paper, DHM technique was introduced as an accurate technique to study the quantitative dynamics of myelin figures. Specifically, measurements of the volume, thickness and length of the myelin figures, which can hardly be estimated precisely by other microscopy techniques, were presented by DHM method. Our microscope setup was able to provide linear temperature gradients within an acceptable range. After analyzing the results from the numerical reconstruction of the recorded holograms, we discussed the configurational changes and the growth rate at the presence and absence of the thermal gradient.