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Abstract
Label-free detection of intracellular substances for living cancer cells remains a significant hurdle in cancer pathogenesis research. Although the sensitivity of light polarization to intracellular substances has been validated, current studies are predominantly focused on tissue lesions, thus label-free detection of substances within individual living cancer cells is still a challenge. The main difficulty is to find specific detection methods along with corresponding characteristic parameters. With refractive index as an endogenous marker of substances, this study proposes a detection method of intracellular refractive index distribution (IRID) for label-free living colon cancer (LoVo) cells. Utilizing the circular depolarization decay model (CDDM) to calculate the degree of circular polarization (DOCP) modulated by the cell allows for the derivation of the IRID on the focal plane. Experiments on LoVo cells demonstrated the refractive index of single cell can be accurately and precisely measured, with precision of 10−3 refractive index units (RIU). Additionally, chromatin content during the interphases (G1, S, G2) of cell cycle was recorded at 56.5%, 64.4%, and 71.5%, respectively. A significantly finer IRID can be obtained compared to the phase measurement method. This method is promising in providing a dynamic label-free intracellular substances detection method in cancer pathogenesis studies.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Cancer remains a major global health threat. Regardless of the type of cancer, it originates from cytopathy, leading to transformation of normal cells into neoplastic ones. Therefore, label-free detection of intracellular substances for living cancer cells is critical for revealing the mechanisms of cancer development. Traditional techniques, such as microscopic examination [1], flow cytometry [2], and advanced tools like super resolution microscopy [3] have been used for the detection of cancer cells. However, these methods require intrusive cell labeling with reagents or fluorescent markers, which alter cellular properties, limit multicolor labeling, lead to phototoxicity and photobleaching over time, and restrict to only detect predefined cellular structures or substances. Given these limitations, there is rising demand for non-invasive detection methods that avoid labeling and other potentially damaging procedures in recent years [4–14].
The light field generated by the interaction between light and cells, called cell’s “fingerprint”, carries the information about external morphology and internal substances of cell [4]. Characteristics of the light at a fixed wavelength include intensity, phase, and polarization. In terms of intensity measurement, in 2000, V. P. Maltsev et al. developed a scanning flow cytometer to testify the dependency between particle size and intensity at certain angles [4]. Su et al. implemented feature extraction techniques on forward and sideward light scattering images, which enabled the recognition of leukemia [5,6], senescent [7], and lung cancer cells [8] when integrated with various machine learning algorithms. By 2020, Goda developed intelligent sorting system for label-free cells based on Raman scattering imaging [9]. In 2022, Zhang et al. established the volume inversion method for cell membrane and nucleus based on the forward light scattering images [10]. These studies have demonstrated that intensity of the scattered light is predominantly decided by volume and morphology of cell membrane and nucleus, resulting in the weak scattered light from subcellular organelle being overcovered. In Among many phase measurement studies, Kemper et al., 2011, introduced digital holographic microscopy for cell morphology assessment, employing Michelson’s interference principle [11]. In 2017, high-throughput label-free single cell screening was demonstrated with quantitative phase imaging (QPI) methods [12]. Recently, Fan et al. achieved phase imaging of red blood cells and yeast cells through non-interferometric QPI, employing a solution to the transport of intensity equation (TIE) [13,14]. However, the observed phase represents the optical path difference caused by the cell, which is the integral of the product of refractive index and thickness, thus complicating the decoupling of refractive index of distinct intracellular substances and components.
Although polarization as vector feature of light has a relatively short history in biomedical analysis, it contains more information about the subwavelength structure and substances of the sample [15,16]. Recent studies in the development of polarization devices and detectors have accelerated its application. It has been demonstrated that the changes in refractive index of scatterers with identical scattering properties cause different polarization characteristics [17,18]. The tissues of lung [19] and skin cancer [20] typically exhibit heightened refractive index due to an increased chromatin content. The analysis of polarized light modulation by these cancerous tissues suggested that degree of circular polarization (DOCP) serves as an effective classification tool between normal and cancerous tissues. From the perspective of wave property of light, the refractive index serving as an endogenous marker can comprehensively depict different intracellular substances. Refractive index, connected to biophysical parameters, can uncover disease progression such as cancer [21] and infection [22]. Yet, the application of polarization detection for refractive index within suspended living cancer cells has been rarely reported to the best of our knowledge. The polarization techniques primarily focus on the full measuring of vectorial transformations imposed on light by the sample (Mueller matrix) or the vector characteristics of the light beam (Stokes vector) [15]. However, advanced polarization methods are gradually changing to partial instead of full measurement since certain characteristics of biomedical samples can be captured by partial vectors, propelling the need of detection methods for specific sample features in polarization imaging methodology. For instance, Ma et al. extracted partial parameters from the Mueller matrix to identify human papillary thyroid carcinoma tissues [23], cervical cancer tissues [24], and hair follicle microstructures [25]. Similarly, Mu et al. derived diameters of microspheres and nucleus sizes of gastric cancer tissue samples from partial parameters of the Stokes vector [19].
This paper proposes, for the first time to our best knowledge, a method of determining intracellular refractive index distribution (IRID) of label-free living colon cancer (LoVo) cells in suspension, based on circular depolarization decay model (CDDM). By using CDDM for the calculation of degree of circular polarization (DOCP) modulated by the cell, the IRID on the focal plane can be derived. Simultaneously, a cell optical thickness normalization model is established to address the issue of unknown cell size as well as size inconsistency. Specifically, circularly polarized light is applied to illuminate the label-free living LoVo cells suspended in culture medium, while analyzing the DOCP of the outgoing beam with polarization cameras. The characteristic parameter depolarized length, derived from DOCP based on CDDM, enables the derivation of the IRID of single LoVo cell on the central plane through linear mapping between depolarization length and the refractive index range of cancer cells. Experimental results of LoVo cells demonstrated the measurement of the refractive index of single cell with a precision of 10−3 refractive index units (RIU) and the chromatin content during the G1, S, G2 phases of cell cycle at 56.5%, 64.4%, and 71.5%, respectively. Measured IRID presented consistency with the pathological characteristics of cancer cells. In addition, we performed dynamic tracking experiments on LoVo cells. Compared against phase measurement method based on transport of intensity equation (TIE), the proposed method can derive much finer IRID. This method can be technically well compatible with conventional microscopy and paves a new way for monitoring the cellular kinetic behavior and revealing mechanisms of cancer development.
2. Theory
During the transmission of light, the oscillation direction of the electric field vector is called polarization. The polarization state of the light wave can be quantitatively described by the Stokes vector with four parameters (S0, S1, S2, S3), as shown in Eq. (1) [15]:
The Stokes vector is obtained through intensity measurements, with each parameter derived from the intensities of two mutually orthogonal polarized light components. The total intensity S0 is the sum of horizontal (IH) and vertical (IV) components. S1, S2, and S3 correspond to the difference of intensity between three pairs of orthogonally oriented directions (horizontal and vertical, 45° and 135°, right-handed and left-handed), respectively. Combinations of different parameters of the Stokes vector can describe the different properties of light. For example, the DOCP describes the ratio of circularly polarization component to the whole light, as shown in Eq. (2):
which has been demonstrated to be positively correlate with refractive index [18].2.1 Depolarization mechanism of cell
As a universal scattering theory, Mie scattering theory is applicable to all homogeneous spherical scatterers. Mie theory is approximated to Rayleigh scattering theory when the size of scatterers decreases [26]. The dimensionless parameter X = dπnm/ λ can be employed to distinguish between Mie scattering and Rayleigh scattering, where d is the diameter of the scatterers, nmthe refractive index (usually represented by n) of the medium, and λ the wavelength of the incident light. When X >>1, implying that the scatterers’ size is significantly larger than the wave length, Mie scattering occurs. Conversely, Rayleigh scattering happens with the scatterers’ size much smaller than λ (X <<1). Scattering induces alterations in the polarization state of light, which is known as depolarization, and depolarization depends not only on the size of scaterers (whether it belongs to the Mie or the Rayleigh scattering region), but also on the refractive index of the scatterers.
Mie depolarization results in the change of the light’s polarization plane, leading to an accelerated decay for line polarization light. Conversely, scatterers undergoing Rayleigh depolarization exhibit isotropy characteristics of Rayleigh scattering, where the amplitudes of two mutually perpendicular polarization components of the polarized light are changed with the case of multiple scattering. Thus, circularly polarized light is more sensitive to Rayleigh depolarization [20]. According to relevant research findings [20,27], it has been reported that when the size parameter X and relative refractive index ratio m (m = ns/ nm, nsand nm are the refractive index of scatterer and medium respectively) of the scatterers satisfy the relationships of (m-1) X ≤ 2.5 and m-1<<1, anomalous depolarization phenomenon arises, resulting in Rayleigh optical depolarization of certain scatterers within the Mie scattering region. Figure 1(a) reveals that the depolarization boundary demarcates the region of Mie (pink) and Rayleigh (purple) depolarization mechanisms. Compared with the scattering boundary (X = 1, blue dotted line), it further uncovers the parameter range causing anomalous Rayleigh depolarization within the Mie scattering region.
Fig. 1. Analysis of optical depolarization mechanism for biomolecules. (a). Schematic diagram of depolarization mechanism based on two key parameters (size parameter X and relative refractive index ratio m). The depolarization boundary (m-1)X = 2.5 separates the Rayleigh depolarization (purple) and the Mie depolarization (pink). Two depolarization mechanisms transition near the depolarization boundary (Note: Fig. 1(a) is adapted from Ref. [20]). (b). Important organelles within cells. (c). The biomolecules that make up the important organelles.
Cell structure and corresponding depolarization properties need to be analyzed before studying the depolarization properties of cells. Cell structure primarily includes membrane, cytoplasm, nucleus, chromatin and various organelles like nucleolus, mitochondria, lysosomes, ribosomes with the refractive index ranging from 1.37 to 1.44 [28–32], as illustrated in Fig. 1(b). Despite the numerous organelles within cell, they can be decomposed into biomolecules, such as proteins, lipids, nucleic acids and sugars, as shown in Fig. 1(c), which are mostly tens of nanometers in size and have refractive index ranging from 1.37 to 1.44. Considering culture medium used as the background medium (nm≈1.340) [13], depolarized region of these molecules falls within the red dashed box of Fig. 1(a) in the Rayleigh depolarization region. Therefore, optical depolarization of intracellular structures and components can be interpreted as Rayleigh optical depolarization of biomolecules, which strongly affects circularly polarized light.
2.2 Depolarization mathematical model of cell
With label-free living LoVo cells in suspension as the object of study, the CDDM needs to be analyzed according to the geometric characteristics of cell. Equation (1)-(7) are executed for each point (x, y) within each cell. As depicted in Fig. 2(a), the cell is focused by polarization imaging system to obtain the DOCP on the focal plane (the central plane of cell). Representing the proportion of circularly polarized light in the light, DOCP mentioned in Eq. (2) of the light scattered by a cell can be expressed as CDDM shown in Eq. (3) [17,18,33]:
where τ is the optical thickness of the scatterers, and ξc, the characteristic parameter needed to be solved, represents the circularly depolarization length required for circularly polarized light to be fully depolarized by the cell. τ is defined as τ = d / l, where d represents the distance traversed by light through the cell to the focal plane as represented in Fig. 2(a), and l (l = ∑sc + ∑a = ∑t-1) is the total mean free path. Given the stochastic distribution of intracellular substances, l can be assumed as same throughout the cell, leading to the exclusive correlation between τ and d.Fig. 2. Analysis of mathematical model for cell. (a). Schematic of spatial model of measured cell. (b). Schematic of cell’s geometry from the upward view of Fig. 2(a) facing the incident light. The red point is the geometric center of the cell, and the blue point represents the arbitrary position inside the cell. (c). Normalized τ.
Due to the unknown sizes of cells, in other words, d is unknown, we propose a cellular optical thickness normalization model. As depicted in Fig. 2(a), d reaches maximum ‘dmax’ at the geometric center of the cell, corresponding to the red point in the upward view facing the incident light as depicted in Fig. 2(b). Arbitrary position on the focal plane in Fig. 2(b) has a distance of r to the center (rmax is the longest distance from center to the outer edge of the cell), which corresponds to d in Fig. 2(a). Obviously, d is inversely proportional to r. The value of r at arbitrary position in Fig. 2(b) can be determined once the cell’s region is extracted. To resolve the issue of unknown d, the normalization of τ is implemented through the ratio r / rmax, with the expression of normalized τ is shown in Eq. (4):
τ is 1 when the incident light passes through the center of the cell in Fig. 2(b) corresponding to dmax in Fig. 2(a), and 0 at the edge of cell with rmax in Fig. 2(b) matching d = 0 in Fig. 2(a). For the arbitrary position on the focal plane within the cell, τ is approximated by the equation of τ2 + (r / rmax)2 = 1. The normalized optical thickness of a LoVo cell is shown in Fig. 2(c), which is calculated after extracting the cell region from an experimentally acquired cell image. Through Eq. (5): ξc inside a cell can be inverted from the DOCP, which is also normalized to avoid effects of different experimental conditions. The characteristic parameter ξc at any (x,y), expressed as ξc = ξc(X, m), indicates that it is influenced by the size parameter X and the relative refractive index m, as mentioned in Section 2.1, and is applicable to any scatterers with different X and m. However, defining ξc(X, m) through a mathematical expression proves to be difficult, and to our best knowledge, the value of ξc is typically inferred from DOCP. Extensive research and simulations demonstrate that under constant X, ξc increases with the rise of m in the condition of m-1<<1, subsequently leading to a corresponding increase of DOCP [17,19,26,32]. The analysis presented in Section 2.1 elucidates that various organelles can be broken down into biomolecule assemblies, each approximately in the scale of tens of nanometers [34–36]. Thus, those biomolecules are likely to possess similar size parameter X. Given this assumption, ξc is exclusively related to m. Considering the difficulty of clearly defining of expression for ξc, we approximate the relationship between ξc and m with a linear relationship. Based on the linear mapping, m can be obtained from ξc, and subsequently refractive index n(x, y) at any position of (x, y) is further derived from m as shown in Eq. (6):3. Materials and methods
3.1 Cell samples
The cell samples used in the experiments were living human colon cancer cell line (LoVo cells) in culture medium, purchased from Wuhan Procell Life Science & Technology Co., Ltd. (Wuhan, China). LoVo cells were cultured in Ham’s F-12 K medium supplemented with 10% fetal bovine serum and 1% penicillin/streptomycin, in a humidified incubator at 37°C with 5% CO2. Polarization imaging of cells were performed by placing a drop of cell suspension on a slide and clamping it to the sample holder of the experimental system.
3.2 Experimental system
The experimental system and schematic diagram are shown in Fig. 3(a). The LED point light source (3W, 620 nm, $\Delta \lambda$=20 nm, Daheng Optics, China) is collimated by Lens1 and subsequently modulated into RCP by the polarization state generator (PSG), which consists of polarizer (P) and true zero-order quarter-wave plate (QWP1). The living cell sample, positioned on a slide, is held by a three-dimensional displacement stage (sample holder in Fig. 3(a)). The 4f system, composed of objective lens (OL, N PLAN 50X/0.75, Leica, Germany) and tube lens with a focal length of 200 mm (Lens2) is employed for magnification and imaging the light field on the focal plane. Reflected by the reflector, magnified beam is split into the transmitted and reflected beams by the unpolarized beam splitter prism (BS, R:T = 50:50, Shenzhen LUBON Technology, China), with the transmitted beam analyzed by the polarization camera1 (PC1, 2448 × 2048pixels, VCXU.2-50MP, Baumer, Switzerland) and reflected beams passing through the true zero-order quarter-wave plate (QWP2) analyzed by the polarization camera2 (PC2, 2448 × 2048pixels, VCXU.2-50MP, Baumer, Switzerland).
Fig. 3. (a). Experimental system and schematic diagram. (b). Principle of DoFP polarization imaging. (c). Intensity components acquired by two polarization cameras.
The polarization cameras are based on the division of focal plane (DoFP) polarization imaging technique as shown in Fig. 3(b), with every 4 pixels forming a polarization unit (including 0°, 45°, 90°, 135° channels). PC1 and PC2 are aligned to perform simultaneous single-shot imaging of the same cell to realize dynamic measurement. IV and IH are obtained from the 0° and 90° channels of PC1, and summed to get S0. IR and IL are obtained from the 90° and 0° channels of PC2, and subtract to get S3, as shown in Fig. 3(c).
3.3 Calibration of experimental system
In practice, potential errors may arise from inaccuracies in the marked angle of the polarizer’s transmission axis and the fast axis of QWP. Furthermore, the monochromaticity of the LED light source might result in the phase delay of the QWP differing from the ideal state, necessitating the system error calibration. Different from the measurement of Muller matrix, the vector property of the light is the measurement object of this method, especially the characteristic of DOCP. Polarization state of light modulated by PSG is analyzed by polarization camera and movable QWP2. Ideally, when air is used as a sample, the light should be close to circularly polarized light with DOCP of 1. The strictly polarization calibrated polarization camera were employed to calibrate P, so it can be assumed that there is no angular error in P. During the error calibration process, QWPs were rotated to ensure that the light is closer to the ideal circularly polarized light and the DOCP is closest to 1. Under these circumstances, the initial angles ε1, ε2 and the phase delays σ1, σ2 of QWP1, QWP2 (fast axis angle calibrated by manufacturer) served as the sources of system error. Therefore, the mathematical model representing the whole system can be expressed as Eq. (8):
4. Results
4.1 Processes for deriving intracellular refractive index distribution
Figure 4 illustrates the implementation of this method with two LoVo cells as samples, with the primary procedures of extracting cellular region and determination of IRID based on DOCP. The original intensity images of LoVo cells, presented in Fig. 4(a), are equalized and filtered to facilitate the extraction of cell’s boundary. The extracted cell’s boundary is drawn on the original image with red line, as shown in Fig. 4(b).
Fig. 4. Processes for deriving IRID. 1 and 2 represent two LoVo cells. (a). Original intensity image. (b). Boundary of cell plotted on the original intensity image. (c). Normalized DOCP. (d). Intracellular distribution of ξc. (e). IRID of LoVo cell.
According to the intracellular region determined by the cell’s boundary, the intracellular DOCP is calculated based on the light intensity components acquired from two polarization cameras and normalized as shown in Fig. 4(c). This method works on the intracellular region without concern about the background, which is set to 0. The normalized optical distance is determined based on the intracellular region’s coordinates, and then the depolarization length ξc shown in Fig. 4(d) can be calculated according to Eq. (5). The final IRID is derived through the Eq. (7), where the nmin and nmax are the refractive index of cytoplasm (1.37) and nucleolus (1.44), respectively [27–31], as shown in Fig. 4(e). The culture medium with 10% fetal bovine serum is regarded as the background with refractive index of 1.34 [13]. Each image in Fig. 4 contains 400 × 400 pixels, with each pixel representing the actual area of 69 × 69nm2 after 50X magnification by 4f system.
4.2 Average of intracellular refractive index
In many previous studies, cells were regarded as a unit for the measurement of overall refractive index [37–39]. Consequently, in this method, the average of IRID (represented by navg) represents the n of an individual cell to compare with existing research findings. Considering that cells could not serve as a sample with standard refractive index, repeated measurements were employed to test the measurement accuracy of the experimental system. Each of 30 LoVo cells was measured 10 times, and the mean and standard deviation of the navg of intracellular region were counted. The maximum standard deviation observed among the 30 cells was 0.001 refractive index units (RIU), which meant that the system had a measurement precision of 10−3 RIU under the conditions of our experiment. The measurement resolution mainly depended on the system’s capability to resolve DOCP, and the experimental system’s resolution in this paper was estimated to be 2∼4 × 10−3RIU. It is small enough to contrast with the refractive index difference between major cellular organelles with the order of 10−2 RIU [21].
Utilizing the processing algorithm in Section 4.1, a total of 1,011 LoVo cells were polarimetric imaged and processed to derive the IRID. Ignoring the cell membrane thickness of a few nanometers which had negligible effect on the refractive index, the IRID was averaged to obtain the navg of individual cell. The distribution of navg for the 1011 LoVo cells is depicted in Fig. 5, with mean values(µ) marked by the blue dashed line and standard deviations (σ) of 1.393 and 4.155E-3, respectively. The dotted green lines in Fig. 5 indicate the refractive index of cancer cells ranging from 1.380 to 1.400 reported in many previous studies [21,40], which is referred to as normal range in this paper. Notably, approximately 98% of the LoVo cells in the experiment demonstrated navg values falling within this range, providing compelling evidence for the validity and accuracy of our method.
Fig. 5. The distribution of average refractive index (navg) of 1011 LoVo cells. The normal range refers to the refractive index range (1.380-1.400) of cancer cells reported in many previous studies.
A more comprehensive analysis of the statistical distribution is imperative. The box plot in Fig. 6(a) reveals that the maximum and minimum navg for LoVo cells are 1.408 and 1.379, respectively, with a median of 1.394. Cells with navg ranging from 1.388 to 1.399 account for 80% of the total samples, excluding the largest 10% and smallest 10%. To further elucidate the distribution of navg, a red distribution curve (DC) is fitted in Fig. 6(b). A bar chart enumerates the number of samples within different ranges of navg, showing the highest probability of 94.5% within the range of 1.386 to 1.400. The proportions of cells with navg below 1.386 and above 1.4 are 3.56% and 1.94%, respectively, indicating that the majority of LoVo cells exhibit navg within the range of 1.386 to 1.400. The comprehensive statistical data for LoVo cells is summarized in Table 1.
Fig. 6. Analysis of the statistical distribution for LoVo cells. (a). Box-plots of navg. (b). Statistical distribution of navg.
Table 1. Summary statistics of LoVo cells refractive indexa
4.3 Analysis of chromatin at different phases of interphase
Abnormal nucleus-cytoplasmic ratio (the increasement in nucleus volume exceeds that of the whole cell), increased chromatin content accompanied by the coarsening of chromatin granules, are typical features of cancer cells. Numerous studies have indicated that nucleus filled with chromatin typically exhibits a refractive index at least 1.400 [31,32]. Additionally, the nucleolus, with the highest refractive index within the nucleus, ranges from 1.42 to 1.44 [28,31,32]. Consequently, the region with n exceeding 1.400 can be identified as the region of nucleus, coinciding with the region of chromatin. Chromatin, primarily composed of genetic material and histones, doubles in content during interphase of cell cycle, resulting in increase of both n and cell size. The interphase is divided into three phases (G1, S, G2 phases) as shown in Fig. 7(a) [41]. Polarization experiments are performed on individual cell, so this method is not applicable to cells in mitosis (M phase).
Fig. 7. IRID of LoVo cells of different phases of interphase. (a). Schematic representation of the cell division cycle. (b-d). Representative results of G1/S/G2 phase, respectively.
Based on cell synchronization techniques [42], cells of G1, S, G2 phases were obtained. Six groups of cells were collected (two groups per phase). For two group of cells in the same phase, one group as experimental samples was used for polarization experiments, and the other as a control group for external validation of phase. Validation of cell cycle phases of LoVo cells was performed using classical propidium (PI) station and conventional fluorescence detection. DNA intercalation of PI can determine the DNA content corresponding to DNA ploidy and differentiate between the G1, S and G2 phases of the cell cycle [41]. Three control groups were verified to belong to G1, S, G2 phase, respectively. Three experimental groups of cells were used to perform polarization experiments to obtain IRID. IRID of 600 LoVo cells, comprising 200 cells per phase (G1/S/G2), were analyzed to calculate the percentage of region with refractive index exceeding 1.400, which corresponds to the chromatin content or the nuclear cytoplasmic ratio. The cells exhibited in Fig. 7(b)-(d) are taken as examples to illustrate the characteristics of IRID of cells belonging to G1, S, G2 phase, respectively. A notable trend is illustrated: as chromatin increase from G1 to G2 phase, the refractive index also increases significantly, with both the nucleus and the whole cell size expanded. The average chromatin content of G1, S and G2 phase were 56.5%, 64.4% and 71.5%, respectively. The chromatin characteristics measured by this method are consistent with the characteristics of chromatin during interphase, which demonstrates the potential of our method to discriminate between G1, S and G2 phases, but the specific determination basis and parameters need to be further investigated. From the measured IRID, the chromatin exhibited a dispersed, granular state, especially with the increase of chromatin during the S and G2 phases, which is perfectly consistent with the characteristics of chromatin in clinical cancer cells [43–45]. This also proves the correctness of our method to derive the IRID.
4.4 Dynamic tracking measurement
The implementation of the vertical optical system and the dual camera alignment approach depicted in Fig. 3 empowers our system to measure dynamic samples. Consequently, we conducted tracking experiments on label-free living LoVo cells. The original intensity images of two adjacent cells (cell #1 and cell #2) are shown in Fig. 8(a). The IRID at four different moments (0s, 1s, 3s, 6s) are presented in Fig. 8(b1-b4), where cell #2 undergoes greater displacement and rotation than cell #1. As the measurements continue, the cells also move along the z-axis, causing a deviation of the focal plane from the center plane of cell. This deviation in the measuring plane results in slight change in the IRID. Tracking the IRID of dynamic live LoVo cells without invasive manipulation is a great advantage of this experimental system. It can be extended to other cancer cells and is easily integrated with commercial microscopy.
Fig. 8. Dynamic tracking experiments of living LoVo cells. (a). The raw intensity image of two adjacent cells. (b1-b4). Results of IRID at different moments.
5. Discussion
Here we propose a calculation method of IRID for label-free living cells in suspension based on the CDDM. The IRID of 1,011 LoVo cells were statistically analyzed with the result shown in Fig. 5 and Fig. 6. Compared with the reported n of cancer cells ranging from 1.380 to 1.400, only 2.07% of the LoVo cells in experiment were outside of the range, which demonstrated that our method can measure the refractive index of single cell correctly. The IRID results of LoVo cells at different phases (G1, S, G2) during interphase proved the correctness of our method and the potential to distinguish between different stages. Tracking experiments on living LoVo cells also demonstrated the ability to detect dynamic samples in suspension.
Current cellular refractive index measuring methods can be categorized into one-dimensional (1D), two-dimensional (2D) and two-dimensional (3D) methods from the perspective of refractive index model, as shown in Table 2. 1D methods mainly include interference refractometer, light scattering and reflection [46–48]. While these methods afford a simple and adaptable measurement system, they are limited in the assumptions of a single living cell as a spherical object filled with protein solution, and thus many details related to the intracellular organelles cannot be obtained. 2D methods mainly focus on the quantitative phase imaging (QPI) for cells, which can be achieved by both interferometric and non-interferometric techniques [11–13]. Although the phase measurement accuracy of interferometric methods is higher than non-interferometric methods, their optical structures are considerably complex and sensitive to interference. However, the phase is the coupling of refractive index and thickness information, making it difficult to decouple realistic refractive index. 3D refractive index measurements with tomography are available for a more comprehensive refractive index map, but limited to static samples and requires the time-consuming acquisition of a large number of intensity images [49]. In contrast, the experimental system of this method is very simple, flexible and less sensitive to interference, with the ability of achieving dynamic sample tracking measurement.
Table 2. Imaging modes of refractive index and various measuring method
As LoVo cells are microscopic samples, it is not possible to ensure that the same cell is measured when using two measurement systems. Therefore, LoVo cells in the same phase (G2) of cell cycle were used to compare with other method. Figure 9(a) and Fig. 9(b) present the results of IRID for LoVo cells, derived by the TIE-based QPI method (a non-interferometric technique) and this method, respectively (Note: the IRID of two different cells are not spatially correlated due to the use of different cells). It is important to note that the QPI method obtains the cell phase, which is a coupling of the refractive index and thickness of cell. Figure 9(a) shows the IRID obtained by assuming the thickness information (about 15µm) of the cell [21]. As shown in Fig. 9(c), the refractive index comparison of middle row from Fig. 9(a) and Fig. 9(b) shows that this method can derive more detailed information of refractive index, demonstrating the superior ability of this method to highlight finer details in refractive index measurements. Although a known range of refractive index is required in this method, the range of refractive index of cells is well established, posing no hindrance to the accuracy of results. Overall this method is a novel, simple and flexible for the detection of IRID for a suspending label-free living LoVo cells, with accuracy of 10−3 RIU and resolution of 2∼4 × 10−3 RIU.
Fig. 9. Comparison of IRID measurement results. (a). IRID obtained by QPI method. (b). IRID obtained by our method. (c). Comparison of the profile in middle row.
6. Conclusion
In this paper, a method of determining IRID of label-free living colon cancer (LoVo) cells is proposed based on CDDM for the first time to our best knowledge. With two polarization cameras aligned to the same cell, the components S0 and S3 of Stokes vector are acquired to calculate the DOCP. The key characteristic parameter circularly depolarization length ξc is calculated based on the CDDM, and finally the IRID on the central plane can be derived through the linear mapping relationship between ξc and m. Experimental results of cultured LoVo cells demonstrated that capability of this method in the accurate measurement of the refractive index of single cells with a precision of 10−3 RIU. The IRID statistic of LoVo at different phases demonstrated that the cell’s chromatin content of G1, S, G2 phase were 56.5%, 64.4%, and 71.5%, respectively. Results of IRID were consistent with the pathological characteristics of clinical cancer cells. Meanwhile, this method exhibited the ability of dynamic tracking measurement and could be extended to different types of living cancer cells. The simple structure of experimental system can be implemented on commercial microscope systems with minor modifications. Thus, this method has great potential for the application of clinical living cancer cells in observing cellular kinetic behavior as well as revealing mechanisms of disease development.
Funding
National Natural Science Foundation of China (No. 62375214).
Acknowledgments
This study was funded by National Natural Science Foundation of China (Grant No. 62375214). The authors would like to thank the reviewers and the associate editor for their comments that contributed to meaningful improvements in this paper.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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