Binary classification of cells from week 1 and 5 using logistic regression trained and tested with cells from the same sample .
Holographic cytometry (HC) has been developed as an ultra-high throughput implementation of quantitative phase microscopy (QPM). While QPM has been well developed for studying cells based on endogenous contrast, few implementations have imaged cells in flow or provided high throughput measurements. Although QPI offers high resolution imaging, experiments are limited to examining a single cell at a time. The HC approach enables high throughput by imaging cells as they are flowed through microfluidic devices. Stroboscopic illumination is used in an off-axis interferometry configuration to produce holographic images of flowing cell samples without streaking artifact. The ability to profile large number of cells using individual images has been demonstrated in red blood cell and cancer cell samples. The large volume of data provides suitable training data for developing machine learning algorithms, producing excellent accuracy in classifying cell type. Analysis of the adherent cells to flow also produces diagnostically useful information in the form of biomechanical cell properties. Introduction of a new parameter, disorder strength, a measure of the variance of phase fluctuations across a cell, provides an additional window into the cell mechanical properties.
- high throughput cell screening
- quantitative phase imaging
- red blood cells
- cancer cells
Quantitative phase microscopy (QPM) has been developed as a means to visualize the structure, dynamics and function of biological cells without exogenous contrast agents. The approach achieves
While there are many methods to obtain QPM images, the approach used in holographic cytometry (HC) is
The phase due to a sample can produce an image based on optical path length (OPL). The change in optical path length is related to the measurement of optical phase as:
Where is the refractive index, is the physical height of the cell and is the wavenumber, equal to for wavelength . In earlier work with using machine learning to classify QPM images of malaria infected cells , a set of 23 morphological descriptors were defined based on OPL as well as geometrical features of a binary mask defining the cell shape. Additional parameters included metrics such as the gradient of the OPL and statistical measures of a histogram distribution of OPL values. This approach was highly accurate in discriminating stage of malaria infection, providing 99.7% accuracy in identifying the schizont stage.
Another approach for quantifying cell morphology based on QPM images is to sum up the OPL values across the cell to produce a metric termed Optical Volume (OV). To calculate OV, the following equation integrates across the OPL in each pixel :
In previous work establishing the utility of OV, we demonstrated that it is an
2. HC: high throughput QPM
While QPM has been widely used for cell analysis, typically only a handful of cells can be imaged at once due to the field-of-view (FOV) size limitation. Manual translation of sample stage to finding a good FOV and manual refocusing further restrict system throughput. Such limitations hinder QPM’s ability to rapidly analyze large quantities of cells for disease diagnosis. For comparison, commercial imaging flow cytometry systems can capture 300–1000 cells/sec . However, typical flow cytometry require a laborious immunophenotypic staining process and the lacking or overlapping of certain epithelial cell markers may compromise diagnostic judgment .
HC has been developed as a label-free, high throughput QPM modality that offers comparable acquisition rate (∼420 cells/sec) to commercial imaging flow cytometers. Figure 2 illustrates the classic Mach-Zehnder interferometry system setup used to capture off-axis holograms. Light from a laser diode is divided into sample and reference arms using a 1 × 2 fiber coupler. Light in the sample arm is collimated and directed to the sample. To enable high throughput of cell images, customized microfluidic channels are integrated into the QPM system. The illumination extends across multiple parallel channels in the microfluidic element. Light transmitted through the sample is imaged using a 20× microscope objective and a tube lens to create an image at the sensor plane. To enable imaging across a large number of channels a machine vision line scan array is used. This 2D sensor array (4096 × 96) captures the light from channels in one direction with interference fringes produced along the shorter dimension. The light from the reference arm is collimated and combined with the sample arm light using a beam splitter to produce an off axis interferogram.
Stroboscopic illumination is achieved using a 350 μs laser pulse, implemented using an acousto-optic modulator, to coincide with the duration of image acquisition, resulting in an overall framerate of 300fps. To avoid streaking effects, data acquisition rates are adjusted to ensure that the maximum distance traveled by cells during the pulse is less than diffraction-limited resolution.
Figure 3A and B shows the approach for creating the microfluidic element. A master mold is created using SU-8 photoresist comprising an array of parallel channels. Each channel is 40 μm wide and 30 mm long. Polydimethylsiloxane (PDMS) is cured on top of SU-8 mold for 2 hours at 80°C and subsequently plasma bonded onto glass coverslips. Inlets and outlets are punctured into PDMS slab, where metallic tubes are inserted for flow, shown in Figure 3C.
Interferograms of flowing cells are captured in video format and the complex field information describing red blood cell (RBC) height is reconstructed from the OPL data. Each complex field image is passed through digital refocusing algorithm [3, 4] which propagates the cell image to the plane by using an algorithm to determine the minimum variance in amplitude. A randomly selected empty frame with no cells apparent is used for background subtraction. Additional background noise is then removed by applying a 3rd-order polynomial fit to non-cell regions of the phase image. A segmentation algorithm is implemented so that single whole cells can be isolated for postprocessing classification, while partial cells and debris can be excluded.
3. Imaging RBCs
3.1 Flowing through constrictive microfluidic channels: storage lesion
RBCs are an ideal sample for QPM studies due to their almost uniform refractive index distribution and homogeneous structure. RBC membrane flexibility and deformability are important metrics that can be used to assess RBC’s ability to transport gases within the body. Impaired deformability is often associated with diseases such as sickle cell disease or diabetes [7, 8]. In severe cases of the disease, poorly deformable RBCs may block blood flow to vital organs or promote splenic sequestration .
In one study , QPM was used to examine the biophysical deformability of RBCs from different storage periods, where mechanical stress was induced by flowing cells through custom-made constricted microfluidic channels. When squeezed through the channels, RBCs experience a water discharge that affects the overall cell height. Figure 4 illustrates how the RBC deforms as it flows through the constricted channels and the optical volume (OV) values that are calculated from each time point. Note that the OV values appear to increase as the outflow of water results in a material with
Figure 5 shows that HC measurements detect a consistent increase in OV of RBCs in the same blood bag over longer storage times. Water efflux and increased hemoglobin concentration may be a possible explanation to the gradual OV changes seen over storage periods . The increase in OV during squeeze is an outcome of increased cell height within confined space.
This study finds that water content exchange in RBCs under mechanical stress changes over time, showing a significant drop by day 29, as shown in Figure 6. This finding agrees with previous study which has shown that RBC stiffness significantly increases after week 4 . The increased stiffness in RBC would explain the decrease in the volume change that is induced through mechanical confinement. Interestingly, this could also be an indication that, compared to the initial mixture of young and old RBCs that is expected to be encountered in circulating blood, there are now a greater proportion of old RBCs present within the blood bag. ∆OVSP could thus, become a useful metric for evaluating aging RBCs. Coupled with constrictive microfluidics, QPM has the potential to be applied as a diagnostic tool for monitoring stored blood bag health.
3.2 High throughput RBC study
HC can provide cell morphology data without the need for time-consuming and costly staining processes and provides, otherwise inaccessible, 3D information on cell structure and dynamics. Its nanoscale sensitivity to membrane changes has been used to study the subtle biophysical changes in RBCs over different storage periods . This previous study used 25 morphological descriptors, extracted from single cell phase images, to visualize cell structural variations at different time points. Notably, OV is a useful parameter that can differentiate between the different cell conditions.
Over 9 million single cell images were analyzed and a decreasing shift in OV is observed across blood bags from 3-week to 5-week storage, shown in Figure 7. One possible explanation to this phenomenon is that regular discocytes have gradually transformed to smaller-sized, deformed RBCs such as echinocytes, spheroechinocytes, and spherocytes, seen in previous studies [12, 13, 14]. The consistent decrease in OV over storage time can be potentially pinpointed to increase in deformed RBC population, which according to one study, increases from 4.9% on day 3 to 23.6% by day 42, in just a span of 5 weeks .
The extracted morphological parameters are passed through a logistic regression algorithm. The highest accuracy level achieved by the binary classification algorithm is 85.6%, shown in Table 1. These measures show that the analysis can discriminate the storage time even though each sample has a blend of young and new cells.
|Classification performance Avg ± std. (%)||Sample A||Sample B||Sample C||Sample D||Sample E|
|Week 01||90.8 ± 0.3||82.0 ± 0.4||83.2 ± 0.4||77.3 ± 0.3||71.6 ± 0.2|
|Week 05||81.5 ± 0.3||78.1 ± 0.3||75.3 ± 0.4||85.1 ± 0.3||80.4 ± 0.2|
|Accuracy||85.6 ± 0.1||79.5 ± 0.1||79.0 ± 0.1||82.6 ± 0.1||78.2 ± 0.1|
The HC system proves to be effective in characterizing millions of cells at an individual single image level. This study demonstrates the potential of HC system to be used as a screening tool that can provide rapid classification of cell types.
3.3 High throughput study of cancer cells
Cadmium is a group 1 carcinogen commonly found in food, water and surrounding environment . Evidence show that chronic exposure to cadmium promotes cancer progression in epithelial cells . In another HC study, it has been shown that HC is capable of differentiate between large number of carcinogen-exposed cells and normal healthy cells. Thousands of single cell images were collected from a Cd-treated cell line, normal epithelial cell line, and cancer cell line. This study aimed to evaluate QPI’s diagnostic ability in identifying carcinogen-exposure at the single cell level.
The vast amount of cell data comprised individual phenotype profiles for each cell type, which when combined with machine learning and convolutional neural network (CNN), provides rapid and highly accurate classification on the carcinogenic status of cells. The system’s high performance demonstrates its potential to be developed into an abnormal cell screening diagnostic tool.
Many morphological parameters exhibit similar trends – the Cd-treated cell line show intermediate parameter values that are in between healthy cells and cancer cells, this is especially the case for OV, shown in Figure 8. Since the Cd-treated cell line overlaps more with the cancer cell line than with the normal epithelial cell line, it is likely that there are more biophysical similarities between Cd-treated cells and cancer cells. These similar traits may be monitored in future applications for identifying carcinogen exposure.
Large numbers of morphological parameters and single cell images are used as training set for logistic regression and CNN. Both algorithms exhibited extraordinarily high sensitivity (98.7%–99.5%) and high mean accuracy levels (98.5%–99.3%) for abnormal cell detection, shown in Table 2. Majority of misclassified cases occurred in the Cd/normal cell line binary classification. Thus, logistic regression results further validate that Cd-treated cells are more similar to cancer cells than they are to their healthy past selves.
|25 parameters logistic regression|
|MCF10A/BT474||99.5 ± 0.49||99.0 ± 0.84||99.3 ± 0.51|
|MCF10A Cd/BT474||90.0 ± 2.87||91.38 ± 1.96||90.7 ± 1.52|
|MCF10A/MCF10A Cd||98.7 ± 1.11||98.3 ± 0.97||98.5 ± 0.50|
It is also evident that not all morphological parameters contribute equally to perfecting the algorithm’s performance. Among the 25 morphological parameters, 4 descriptors depicted the most phenotypic differences. Table 3 shows the logistic regression performance with only 4 parameters as training set. With such a relatively high accuracy level (∼92%) in identifying normal/abnormal cells, it is likely that HC can be utilized in real-time applications where only a few parameters will be enough to provide a preliminary rapid diagnosis.
|Area, optical volume, major axis length, mean phase logistic regression|
|MCF10A/BT474||94.6 ± 1.92||89.0 ± 89.0||91.8 ± 1.34|
|MCF10A Cd/BT474||73.0 ± 2.45||70.4 ± 1.74||71.7 ± 1.41|
|MCF10A/MCF10A Cd||91.9 ± 3.06||92.4 ± 2.26||92.2 ± 1.84|
Figure 9 demonstrates the classification performance of the CNN. The deep learning model achieved an accuracy level of up to 97.7%. It is also noted that majority of the misclassified cases rise from algorithm mistaking a Cd-treated cell for cancer cell or vice versa. The performance characteristic of the CNN again confirms the previous finding – morphological similarities between Cd-treated cells and cancer cells are dominant and apparent.
Overall, coupled with microfluidic channels and machine learning algorithms, HC provides a path to automated cytological sample diagnosis. Particularly, in low resource settings where labor-intensive and costly histopathological diagnostics are inaccessible, HC presents a low-cost label-free alternative.
4. Measuring cell mechanical properties
Knowing cellular mechanical properties can be useful when trying to determine health and disease states. Measuring mechanical properties often requires controlled probing of the cell and recording the response, e.g., atomic force microscopy (AFM). Physical probing can also cause damage  to the cellular environment, so less invasive methods like utilizing controlled flow of media over cells to induce a shear response can be attractive. The use of microfluidic channels and syringe pumps allow for fine control of shear imparted on a cell and stress testing. Off-axis holography quantitative phase imaging (QPI) has been shown to be able to record the cells’ mechanical response over fine space and time scales [18, 19, 20, 21]. QPI allows for recovery of cell elastic properties such as stiffness and shear modulus which can also be linked to cellular microstructure.
4.1 Phase deformation informs shear stiffness
When a cell is attached to the culture substrate, perturbing the cell and recording the response acts like a stress test. Fabricated flow chambers with well know physical boundaries combined with a syringe pump capable of constant volumetric flow allows for easy estimate of the wall shear stress, , imparted on the cell under laminar flow. The measured phase deformation, change in localized phase from before applying shear stress to when the cell reaches a steady state under shear, informs how cell height changes.
Combining measured cell height with cell position in and allows for the calculation of cell center-of-mass (COM). As shown in Figure 10 tracking the 3D change in center of mass, , allows for the study of the cell’s response to shear stress.
Using a Kelvin-Voigt model, the response of the cell at a steady state can be described in a differential equation like a 1D damped spring and provide information on the viscoelastic properties of the cell .
Where is the estimated cell surface area, is shear stiffness, and viscosity, , acts as the damping element.
This has been shown to work experimentally in the 2016 publication by W. Eldridge et al. . Here two groups of human skin cancer cells, A431; one in a normal environment as a control, the 2nd group treated with toxin cytochalasin D (CD); were observed in flow chambers. Before beginning flow, the cell’s COM is constant, then once flow begins the phase displacement goes from negative to positive within the cell in the same direction as the flow, Figure 10. Under the constant volumetric flow rate the COM comes to a steady state. Cell displacement at steady-states was found to be linearly related to the shear stress, matching predictions from the Kelvin-Voigt model. Agreeing with theory  and shown in Figure 11, cells dosed with CD were found to have a reduced shear stiffness when compared to control A431 cells because CD alters actin in the cell’s cytoskeleton, and therefore microstructure, in turn altering its viscoelastic properties.
4.2 Disorder strength and microstructure
Disorder strength, , a metric for quantifying a cell’s degree of structural heterogeneity and nanoarchitecture, has been shown to be useful in differentiating cells in the early stages of carcinogenesis from normal cells even when the two types appear similar microscopically and histologically . Originally measured using partial-wave spectroscopy, has shown potential as a cancer diagnostic tool especially for pancreatic and colon cancer . Work by W. Eldridge et al.  proves can also be measured via QPI to provide information on cell stiffness and cytoskeletal organization with potential for high throughput measurements.
Measuring disorder strength via QPI takes advantage of the fine spatial sampling in quantitative phase images and local homogeneity in height over small length scales. Disorder strength calculated as the product of a cell’s refractive index variance, , and its spatial coherence length, .
Measurement of cell height, at pixel can be assumed to not vairy greatly over a small neighborhood e.g., 3x3 pixel region. Therefore, the local phase variance of a cell is proportional to its local refractive index variance, . Normalizing the local phase variance by the local square mean phase, , gives an equation that can be solved for refractive index variance.
Spatial coherence length can be determined by fitting the falloff of the autocorrelation of the phase fluctuation to an exponential, allowing the phase disorder strength to be calculated via:
Experimentally was measured for five different groups of cells: 1 group of HT-29 colon cancer cells, a 2nd group of HT-29 but with a CSK shRNA-mediated knock-down (referred to as CSK), 1 group of normal A431 human skin cancer cells, 2nd group of A431 cells that were treated with CD, and a single group of A549 human lung cancer cells. Figure 12 shows phase maps, phase fluctuation maps, and mean measurements for each group.
Similar to how shear stiffness was able to differentiate the two types of A431 cells in Figures 11 and 12L shows how can also differentiate the CD-treated cells from the normal A431 cells. After performing the same shear stiffness analysis from Section 4.1 on these five groups of cells and plotting the mean vs. the mean , as shown in Figure 13, the negative correlation between the two metrics is clear. The fit constant, , of 0.75 pN make sense when considering typical forces relating to cell microstructure [24, 25]. It is important to note that a single cell’s mean can calculated from a single QPI snapshot, whereas measurement requires two images of the cell: one at rest and one after being perturbed by flow. The link between and showcases the potential of for understanding more about a cell’s viscoelastic properties without perturbation.
4.3 Shear modulus and elasticity
To truly understand cell elastic properties, shear stiffness or spring constant is not enough. Elastic moduli like the Young’s modulus, , or shear modulus, , must be measured. These moduli are related according to:
where is the Poisson’s ratio. Commonly the approximation is used for cells , and therefore a linear relationship between the two moduli, , can be assumed. Shear modulus is determined by the ratio of shear stress over shear strain. As shown in Section 4.1, the shear stress, , imparted on the cell from flowing media can be controlled with a microfluidic channel and a syringe pump. Shear strain can be treated as the transverse displacement, , divided by height. The shear stiffness analysis tracks the displacement of a cell’s COM and QPI can measure localized cell height. To get a height estimate, , of the whole cell the median of over all values of and within the cell above a reasonable lower bound, in this case 5 μm, was used. Figure 14 illustrates how and are calculated.
To experimentally determine , two different types of human breast cancer cells were used: MCF7 and BT474. Each type was split into three groups based on concentration of treatment with CD: 0 μM (control), 0.2 μM, and 1.0 μM. To measure displacement, the COM of a cell was measured before flow at and again at after flow and reaching a steady state. To validate measured , the same cell groups were also examined via AFM to measure , results shown in Figure 15. In Figure 15A there is a negative trend in elasticity measured by AFM with increasing concentration of CD treatment. This agrees with the QPI measured shear modulus, as in Figure 15B not only within but across the two types of cells.
The good agreement of AFM measured and QPI measured with the hypothesized relationship proves QPI’s usefulness to measure elastic properties of a cell and shows it can be a reasonable alternative to AFM. One drawback is that to measure , the cell must be imaged twice and be perturbed by flow. Disorder strength however can be measured with a single snapshot, without perturbation, and as shown in Figure 13 is correlated with shear stiffness. Comparing measured to , Figure 16A, it can be seen that is correlated with elastic moduli of a cell. This supports the findings in Section 4.2, that cell microstructure can be related to stiffness. There is still more research to be done in , looking into other types of cells and their elasticity compared to cancer cells. When is compared across multiple experiments and cell lines, Figure 16B, there is a negative correlation with shear modulus. Also, since can be measured with single snapshot it has great potential to provide information on cell elasticity in high-throughput settings.
With the use of microfluidics, QPM becomes a platform capable of high throughput measurements of cells at the individual level. Further, the platform allows observation of individual cells under unique mechanical conditions such as exposure to flow or mechanical constriction. To enable QPM to provide large volumes of imaging data, the HC setup has been implemented, which uses stroboscopic imaging to enable visualization of cell features without streaking due to motion. The high throughput scheme has been shown to provide the visualization of multi-million single cells within 8–16 parallel microfluidic channels. The analysis of imaging data is made feasible by composing a single vector for each cell, comprised of 25 morphological descriptors. Upon extracting these from each single cell image, a highly descriptive, phenotype profile is obtained for the given cytological specimen.
In the experiments discussed here, the HC system was demonstrated to provide insights on the deformability of RBCs under mechanical stress. The study shows that RBCs with different storage ages have distinct capabilities for exchanging water with their environment. This is observed as a refractive index increase which causes the increase in OV. The 29-day-old RBCs exhibit the smallest change in OV, and in turn less water exchange, due to channel constriction than other time points. This trend is consistent with the known properties of RBCs to become stiffer at longer storage times and thus are unable to exchange as much water content. The monitoring of water permeability could potentially be used as a predictive factor for stored blood bag quality control.
The high throughput capabilities of HC were demonstrated with experiments that examined millions of cells, generating significant volumes of data. Although direct analysis of the cell images can be instructive, the training time for direct application of machine learning algorithms can be substantial. Instead, the analysis is greatly streamlined using the 25 morphological descriptors. Studies of cultured mammalian cell lines show that distinct cellular characteristics are observed in the individual descriptors for varying phenotypes. In particular, the morphological descriptors easily distinguished the non-tumorigenic MCF-10A cells from the cancerous BT-474 cells. The Cd-treated cells displayed morphologies in between those of regular and cancer cells, suggesting that the heavy metal treatment induced potentially carcinogenic changes. Upon training with these data sets, machine learning models have been developed which exhibited high sensitivity and accuracy levels in identifying cell groups. These results suggest that HC can potentially be used for abnormal cell monitoring in disease diagnosis.
Measurement of cell mechanical properties in HC has been enabled by switching from a direct perturbation approach, in the form of a flow assay, to use of a descriptor that can be extracted from a single cell image. A cell’s disorder strength can be calculated from a single QPM image, using a simple determination of the phase variance, allowing for facile application of this measurement to many has been shown to correlate with elastic moduli, which usually require multiple images and perturbation of an attached cell, limiting the throughput to just a handful of cells. Cellular microstructure and a, showcasing its ability to differentiate cells of the same type but under different treatment. Combining the mechanical and with the fast-paced single and multi-cell measurements of a high-throughput HC system potential over time and length scales, as cells respond to mechanical or pharmacological stimuli. Also expanding disorder strength and cell mechanics measurements to a wider range of cell types.
In summary, we have presented a high throughput QPM approach termed holographic cytometry (HC). The approach uses microfluidic elements and stroboscopic illumination to obtain off-axis holographic images of cells in flow. Several experiments have been reviewed to showcase the high throughput capabilities of HC, including examination of RBCs and cancer cells, revealing excellent discrimination of phenotype based on the wealth of information obtained from morphological descriptors. Application to stored RBC’s points to a potential utility in addressing the need to monitor the age of blood units. Experiments with cancer cells show that phenotype can potentially be discerned using this label free approach. Further development of the HC approach has enabled detailed studies of cell mechanical properties. The measurement of disorder strength provides a compelling window into cell structure that has been linked to essential mechanical properties such as stiffness and shear modulus.
This work has been supported through the Army Research Office, Grant W911NF-19-1-0306.
Conflict of interest
No conflicts of interest are declared for this work.
The authors acknowledge Dr. Han Sang Park and Dr. Will J. Eldridge for their contribution to the foundational works presented in this chapter.
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