We report a technique for simultaneous label-free quantification of cytoplasmic hemoglobin Hb concentration and dynamic membrane fluctuation in individual red blood cells (RBCs). Spectroscopic phase microscopy equipped with three different coherent laser sources and a color detector records three wavelength-dependent quantitative phase images in a single shot of a color-coded hologram. Using molecular specific dispersion, we demonstrate the extraction of Hb concentration and the dynamic membrane fluctuation from individual RBCs.
© 2012 OSA
Measuring the concentration of specific molecules in living cells and tissue is crucial to understand the molecular activity of cellular pathophysiology. The molecular concentrations in cellular metabolism are significantly relevant to molecular activities; the concentrations are highly regulated and controlled in normal physiological conditions, but also can be severely altered in abnormal physiological conditions related to diseases. Currently, staining agents including fluorescent dyes, fluorescence proteins, and functionalized quantum dots have been widely used to selectively label and quantify molecular concentrations of interest . Although the use of staining agents provides high molecular sensitivity, the quantification of molecular concentration using these exogenous agents requires careful consideration of factors including interference with normal metabolic biochemical activities, photo-bleaching/blinking issues, and non-specific binding to other molecules. Another technique for measuring molecular concentration is Raman spectroscopy. Combined with confocal microscopy, in-elastic Raman scattering signals provide a means of determining the molecular concentration in living cells non-invasively . However, measuring the Raman scattering signal is time-consuming and requires expensive laser sources.
The refractive index (RI), an intrinsic optical property of any material including biological samples, can be used for quantifying the concentration of a specific molecule. For example, by measuring the refractive index via reflectometers, the sugar content of an aqueous solution can be measured . On the other hand, surface plasmon resonance biosensors detect molecular activity by utilizing the refractive index of the target molecule . Quantitative phase imaging (QPI)  or digital holographic microscopy (DHM) techniques [6–9], interferometry-based light microscopy techniques measuring complex electric field of a sample, have meanwhile been employed to measure the molecular concentrations of specific molecules inside living cells or tissue. QPI or DHM techniques has become an important tool for imaging biological samples [5–15], and extensively used for several biophysical studies, including the measurement of cellular dry mass  and cell growth , the light scattering spectroscopic studies of biological samples [11, 18–21], the imaging of the structure and dynamics of RBCs [22–27], eukaryotic cells [28, 29], immune cells , neuron cells , and yeast cells .
One approach to measure the molecular concentrations of specific molecules inside living biological samples using QPI or DHM technqieus is to introduce two different immersion media with different refractive indexes in order to decouple the refractive index and the thickness of the cell [7, 8, 33]. The wavelength-dependent RI, obtained by dispersion measurement in QPI, has been employed to determine the molecular concentration in solution and in tissue sections , to decouple the molecular concentration of hemoglobin (Hb) proteins and cellular thickness from the phase delay induced by a specimen , and to measure refractive index dispersion in deep UV ranges . Tomographic reconstruction after measuring multiple quantitative phase images at different angles of illumination has also been used to retrieve the RI [25, 27, 29].
Recently, it has been shown that a combination of quantitative phase information with bright field absorption measurement acquired in the Soret band  and nonlinear phase dispersion spectroscopy using spectral-domain phase microscopy and spectroscopic optical coherence tomography  can simultaneously measure the Hb concentration and topography of an RBC. Unfortunately, despite recent developments in optical non-invasive techniques to measure molecular concentrations in living cells based on RI measurement, the speed of measurement has been stymied by technical limitations; the current available techniques are not suitable for measuring fast dynamic changes of molecular concentrations. This speed constraint is unfortunate, because optical measurement of molecular concentrations using QPI has much to offer the world of biology and medicine with its unique non-invasiveness, sensitive and quantitative measurement, and avoidance of exogenous labeling agents.
Previously, a white-light source with color filters was used for quantitative phase image measurement at different colors , which is a simple and practical method for dealing with spectroscopic phase images. However, the use of color filters and a white-light source is not suitable for dynamic spectroscopic measurement, because (i) there is an inevitable time delay between each phase image measurement at different wavelengths and (ii) the spectral power density of a white-light source is not sufficient and requires long exposure time during the measurement, which prevents the usage of this approach for fast dynamic spectroscopic measurement. Also noteworthy is that there are overlaps between the spectral responses of each color channel in Bayer color pixels, and thus the use of white light is not ideal since it will generate large crosstalk between different color channels. Here we present dynamic spectroscopic phase microscopy (dSPM), a new technique that can simultaneously measure the concentrations of specific molecules in living cells and their volumes at high speed. dSPM integrates three different coherent lasers and a color charged coupled device (CCD) in spectroscopy phase microscopy . Since three wavelength-dependent quantitative phase images can be recorded in a single shot of a color-coded hologram, the measurement speed is only limited by the acquisition speed of the detector. Using dSPM, we demonstrate that cytoplasmic hemoglobin Hb concentration and dynamic membrane fluctuation in individual RBCs can be simultaneously measured. The present technique offers a sufficiently general means of measuring the dynamically changing molecular concentrations in living cells as well as cytoplasmic Hb concentrations in individual intact RBCs.
The quantitative phase images of a biological cell measured in transmission geometry can be expressed as5]. For the case of a RBC, Eq. (1) can be simplified as35]. Since non-Hb molecules do not have a distinct dispersion at visible wavelengths, can be approximated as an wavelength-independent constant as . In addition, by using a priori knowledge on from the literature [39, 40] or calibration , only three unknowns remain in the quantitative phase images: C, , and h(x,y). Hence, at least three quantitative phase measurements at different wavelengths are required to retrieve these three unknowns, as delineated below:
We note that Eq. (4) is a nonlinear equation where unknowns are coupled to each other. To uniquely determine the unknowns, we perform an iterative calculation minimizing the values for the standard deviation of and inside the cell area. The cytoplasm of an RBC consists of a homogenous solution of proteins, and we can assume that Hb and non-Hb proteins are uniformly distributed throughout the entire cell volume. In order to solve this non-linear equation, we can consider it as an optimization problem with the objective function and acceptable constraints as follows,
We employed the conventional interior-point nonlinear optimization algorithm minimizing contrained multivariable function within MatLab® (Mathworks Inc.) software; typically < 50 iterative calculations were required to solve this nonlinear equation via the optimization algorithm. This calculation corresponds to < 13 min computation time in a desktop computer (Intel Core i5-2500K CPU, 3.30GHz).
3. Experimental setup
The experimental setup for dSPM is shown in Fig. 1(a) . The setup consists of two parts: combined laser sources with three different wavelengths and diffraction phase microscopy (DPM) for measuring quantitative phase images. DPM employs a common-path geometry for quantitative phase imaging and have extensively used for the several biological studies [41, 42]. Three laser sources with different wavelengths [633 nm (He-Ne laser, Thorlabs. Inc., 5 mW), 532 nm (Diode-pumped solid-state laser, Shanghai Dream Lasers Inc., 100 mW), and 450 nm (Laser Diode, Edmund Optics Inc., 20 mW)] were combined using dichroic mirrors to be aligned into a single optical path. To minimize photodamage to the biological samples, the laser powers were reduced to 20.5 µW (633 nm), 28.0 µW (532 nm), and 45.0 µW (450 nm) at the sample plane. The combined laser beam illuminates the sample. The electric field containing sample information is first projected to the image plane through the objective lens (Olympus UIS2, 20 × , NA = 0.5) and tube lens (f = 200mm, Thorlabs, AC508-200-A), and the electric field is further magnified by a 4f lens system.
The electric field is then measured via common-path interferometry, which was used for the DPM setup [41, 42]. The electric field is projected onto the plane where a diffraction grating is located. After diffraction by a transmission grating (70 lp/mm), the 0th order beam passes through a spatial filter and then becomes a well-defined plane wave as a reference beam at the CCD plane. The 1st order diffraction beams are directly projected onto the CCD plane. The 1st order diffraction beams at different wavelengths may exhibit different locations at the Fourier plane between L3-4 due to dispersion. However, the optical paths for each wavelength are identical. Both the 1st diffraction beam containing the sample information and the 0th reference plane beam interfere at the CCD plane and generate spatially modulated holograms . The focal lengths of L1-4 are 150 mm, 150mm, 75mm, 400 mm, respectively. All lenses used are achromatic doublet (Thorlabs AC508 series) so as to reduce chromatic aberration. We used a color CCD camera (IMITECH, IMC-7011g) with a Bayer color filter. Since each sub-pixel in one Bayer color pixel unit corresponds to one of the RGB channels, we can convert a raw Bayer pattern image to three different spatially modulated interferograms. We used MatLab® for this demosaic process and obtained three different holograms of red, green, and blue channels from one color CCD measurement [Fig. 1(b)]. To fully utilize the dynamic range of each color channel and minimize the crosstalk between color channels, we adjusted the laser beam powers for different wavelengths at the CCD plane using neutral density filters after the image plane. We note that the strategy of using a color CCD to record three color images has been extensively used for several applications including color digital holography , three-color holographic interferometry [43, 44], color fringe projection , and optical sectioning with a color grating for structured illumination .
4. Results and discussions
4.1. Simultaneous measurement of Hb concentration and volume of an intact RBC
To demonstrate the basic principle of dSPM, we first measured individual living human RBCs and retrieved the cytoplasmic Hb concentration and volume of the cell. A single human RBC was prepared from blood obtained from a healthy individual following the standard protocol . One color-coded interferogram was then recorded using dSPM, from which three different interferograms, corresponding to red, green, and blue channels, are retrieved [Figs. 2(a) -2(c)]. From the measured interferograms at different color channels, we extract the corresponding electric field information (both amplitude and phase images) using appropriate numerical procedures. Full details of quantitative phase imaging of RBCs and the phase extraction algorithms can be found elsewhere [12, 48]. Figures 3(d) -3(f) and Figs. 3(g)-3(i) are the amplitude and phase images of the RBC at the red, green, and blue channels, respectively.
From the spectroscopic phase measurement at three different wavelengths, the cytoplasmic Hb concentration and height map of the RBC can be calculated using Eq. (5). Figure 3(a) shows the cell height map, h(x,y), and Fig. 3(b) represents the retrieved Hb concentration, C(x,y), of the RBC shown in Fig. 2. As can be seen in Fig. 3, the cell height and Hb concentration maps are generally consistent with the previous measurements [25, 35]. The cell height map shows a distinct doughnut shape (discocyte), characterizing healthy human RBCs. The retrieved Hb concentration map shows an average value of 34.5 g/dl over the entire area, which is in the normal physiological range (32-36 g/dl). The values for C are uniformly distributed inside the RBC, which is also consistent with the normal physiological condition of RBCs.
A total of 24 individual RBCs extracted from the same donor were then measured using dSPM. For each RBC, the cell height and Hb concentration maps were retrieved following the same procedure as described above. Mean cellular volume (MCV) and mean cellular hemoglobin concentration (MCHC) values, important parameters for hemodiagnosis, can be calculated as follows,
The results are shown in Figs. 4(a) -4(b). The values for MCV and MCHC were 92.7 ± 14.3 (fl) and 34.5 ± 0.7 (g/dl), respectively. These values are in good agreement with the normal physiological range (MCV ~80 – 99 fl and MCHC ~32 – 36 g/dl). Since we can retrieve MCV and MCHC of individual RBCs using dSPM, the total Hb contents per cell or mean cellular Hb contents (MCH) can be calculated as MCH = MCV × MCHC. The results are shown in Fig. 4(c). The values for MCH were 33.0 ± 5.4 pg, which is close to the normal range (27 – 31 pg).
4.2. Simultaneous measurement of dynamic cell membrane fluctuation and cytoplasmic Hb concentration
To assess the dynamic measurement capability of dSPM, we simultaneously measured dynamic cell membrane fluctuation and cytoplasmic Hb concentration. A healthy RBC was prepared and 418 consecutive color-coded holograms of the RBC were recorded at a speed of 20 frames/sec. From the first color-coded hologram, the cytoplasmic concentration map and cell height map can be decoupled using Eq. (5). The cell height map of the RBC is shown in Fig. 5(a) . Since the refractive index value Δn and cell height map were decoupled from the first hologram, cell height maps can be readily extracted from the consecutive holograms using Eq. (2). The results are shown in Fig. 5. The height changes at three different positions are traced over 20 s [Fig. 5(b)]. The points on the RBC membrane (B and C) show characteristic dynamic fluctuation in the healthy RBC membrane; the standard deviation of the height fluctuations were 86.2 nm and 56.4 nm, respectively [Fig. 5(b)]. The point on a glass substrate showed 8.5 nm, which demonstrates the temporal stability of the system.
Here, for the sake of simplicity and computational efficiency, we assumed that the refractive index of RBC cytoplasm, and thus the MCHC values, does not change over time. However, the present dSPM can also be used for the cases where the molecular concentration of Hb and cell morphology can be changed at the same time, since one-shot measurement of dSPM can decouple two quantities. The dynamic trace of the measured MCHC values provide chemical information about Hb proteins in the RBC cytoplasm  and the dynamic membrane fluctuations can be used to retrieve the deformability of the same RBC simultaneously [23, 24, 26, 48]. Other direct applications in the study of hematology will be diverse. For example, the quantification of dynamic alterations in RBCs under osmotic stress  can be accessible for direct experimental study. Two distinct isomeric shifts between oxy-Hb and deoxy-Hb inside RBCs can also be quantified while exposed to different oxygen concentrations. Abnormal Hb polymerization and consequent modification in the membrane cortex in sickle cell disease can be addressed [49, 50]. dSPM can also be used for the study of malaria; consumption of host Hb by the malarial parasite and decreased membrane deformability can be simultaneously investigated .
As demonstrate, dSPM measures spectroscopic quantitative phase images with three different wavelengths in a single hologram recording, from which Hb concentration and dynamic membrane fluctuations in RBCs can be retrieved. Since dSPM employs a common-path interferometry, the measurement accuracy is extremely high. However, dSPM also has limitations. First, dSPM is optimal for measuring thin samples. Thin biological samples such as RBCs, HeLa cell, or adherent cells can be readily addressed with the current dSPM technique. However, for studying thick samples such as biological tissues or thick cells, one may need to consider employing a depth-resolved or tomographic reconstruction modality on the top of the dSPM technique. Second, the current sDPM setup measures three color holograms, which limits the number of molecular types that can be quantified. Three color holographic measurements are sufficient for studying several RBC-related pathophysiology. However, general biological samples contain a large number of different molecular types and thus the current dSPM setup may be limited for studying biological samples when many types of molecules are involves.
In this work, we present a new technique, dynamic spectroscopic phase microscopy, to quantify dynamically changing molecular concentrations and morphology of living cells. dSPM employs three different coherent lasers combined into a single optical path and common-path interferometry used in DPM. By recording a one-shot color-coded hologram using a Bayer color imaging sensor, three spectroscopic phase image measurements can be performed. As a demonstration, we showed that the dynamic membrane fluctuation and the cytoplasmic Hb concentration of individual RBCs can be measured simultaneously. As we demonstrated in the case of RBC, this technique will find immediate applications in studying RBC-related pathophysiology. The present technique can also be used for investigating other non-red blood cells, especially when simultaneous measurement of the dynamically changing molecular concentration and cell morphology in living cells is of interest. Example applications may include measurement of cell growth/division [16, 17] or activities in neuron cells .
This work was supported by KAIST, KAIST Institute for Optical Science and Technology, the Korean Ministry of Education, Science and Technology (MEST) grant No. 2009-0087691 (BRL). YKP acknowledges support from TJ ChungAm Foundation.
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