We present a spatio-temporal analysis of cell membrane fluctuations to distinguish healthy patients from patients with sickle cell disease. A video hologram containing either healthy red blood cells (h-RBCs) or sickle cell disease red blood cells (SCD-RBCs) was recorded using a low-cost, compact, 3D printed shearing interferometer. Reconstructions were created for each hologram frame (time steps), forming a spatio-temporal data cube. Features were extracted by computing the standard deviations and the mean of the height fluctuations over time and for every location on the cell membrane, resulting in two-dimensional standard deviation and mean maps, followed by taking the standard deviations of these maps. The optical flow algorithm was used to estimate the apparent motion fields between subsequent frames (reconstructions). The standard deviation of the magnitude of the optical flow vectors across all frames was then computed. In addition, seven morphological cell (spatial) features based on optical path length were extracted from the cells to further improve the classification accuracy. A random forest classifier was trained to perform cell identification to distinguish between SCD-RBCs and h-RBCs. To the best of our knowledge, this is the first report of machine learning assisted cell identification and diagnosis of sickle cell disease based on cell membrane fluctuations and morphology using both spatio-temporal and spatial analysis.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Sickle cell disease (SCD) belongs to a group of inherited red blood cell disorders. According to the National Institutes of Health [1, 2], people affected with SCD have abnormal hemoglobin, called hemoglobin S or sickle hemoglobin in their red blood cells (RBCs). Hemoglobin is a protein that is responsible for transporting oxygen throughout the body. Individuals suffering from SCD inherit two abnormal hemoglobin genes, one from each parent. Healthy RBCs (h-RBCs) contain normal hemoglobin and have a biconcave disk shape, allowing them to squeeze through the micron sized blood vessels to supply oxygen to various parts of the body. In SCD, hemoglobin can form stiff rods within the RBCs, creating crescent or sickle shaped RBCs and hindering oxygen transportation. The lack of oxygen delivery in the body can cause sudden, severe pain, known as a pain crisis, which may result over time in chronic organ damage or failure.
Optical technologies are becoming increasingly popular standalone modalities for disease diagnosis as these are usually less invasive in nature. Recently, digital holographic microscopy (DHM) [3–13] and quantitative phase imaging (QPI) based techniques have been used to study the morphology and mechanical properties of RBCs for disease diagnosis. DHM is an interferometry-based approach to image biological samples [6–16]. The system generates a hologram which can then be numerically reconstructed, forming a three-dimensional (3D) image of the height or optical path length (OPL) profile of the cell. DHM and QPI techniques are label-free and can non-invasively and quantitatively measure the optical path delays in phase objects, such as biological cells and sparse tissue samples. Some DHM and QPI based techniques may be complicated, bulky, and sensitive to mechanical noise. However, DHM and QPI have proven to be extremely powerful 3D imaging tools due to their single-cell profiling and label-free imaging capabilities. In , it was demonstrated that healthy RBC and sickle cell disease RBC (SCD-RBCs) membranes may fluctuate at different rates providing additional information for cell identification.
In this paper, we perform classification of healthy RBCs and sickle cell disease RBCs using spatio-temporal analysis with a compact and low-cost 3D printed shearing interferometer. The prototype consists of a laser source, a microscope objective, glass plate and an imaging sensor. In addition, this setup allows for a stable, common-path DHM system based on shearing geometry [7–9] and uses the cell membrane fluctuations in the lateral and axial directions as features for classification. We conducted a prospective, limited clinical research study at a single institution using peripheral blood from consenting sickle cell patients and healthy control volunteers. This study was conducted in accordance with UConn Health and UConn Storrs Institutional Review Board policy standards. To be eligible for participation, each subject had to be at least 18 years of age and have not received a blood transfusion in the previous 3 months. We enrolled a total of 14 subjects, 8 with sickle cell disease (2 females and 6 males) and 6 healthy volunteers without sickle cell disease or any hemoglobinopathy trait (4 females and 2 males). For the healthy controls, the mean age, in years, and standard deviation was 37 and 9 respectively, while the mean age and standard deviation of subjects with SCD-RBCs-was 32 and 8, respectively. Approximately 6-8 ml of blood was drawn from each human subject. The time between drawing blood and measurement was less than two hours. The mean and standard deviation of the hemoglobin was 13.1 g/dL and 1.6 g/dL for the healthy controls, respectively, while it was 8 g/dL and 1.4 g/dL for the SCD subjects, respectively. The demographic data and clinical results by electrophoresis are presented in Table 1.
As shown in Table 1, all healthy controls had a normal hemoglobin level and distribution of hemoglobin A and A2 indicating healthy controls produce normal adult hemoglobin. Conversely, all subjects with sickle cell disease had low total hemoglobin levels (as expected) and hemoglobin electrophoretic results consistent with sickle cell disease (i.e., no hemoglobin A production, normal A2 levels, and varying degrees of hemoglobin F and hemoglobin S). All hemoglobin F production was endogenous as no subjects were taking hydroxyurea, a medication that is known to stimulate hemoglobin F production.
After obtaining blood samples from each subject, we prepared thin blood smears and sequenced digital holograms of red blood cells using the proposed 3D microscope. A blood-smear of human blood containing either h-RBCs or SCD-RBCs was prepared and imaged using the compact DHM setup and a video containing hologram frames was recorded. Once a video hologram was captured from the portable setup, cells were manually segmented and a 3D reconstructed OPL profile of each cell is created for each time frame followed by the formation of a spatio-temporal data cube to measure the dynamic fluctuations of the cells. We performed statistical analysis on dynamic features including computation of 2D mean and standard deviations (STD) maps for every location on the cell membrane of the data cube along the time axis. Once the 2D maps were generated, the standard deviation for each 2D map was computed. Moreover, optical flow (OF)  was used to extract cell fluctuation information between subsequent frames in the temporal 3D reconstructions. The STD of the magnitude of the OF vectors across all frames were then computed. In addition, spatial features were extracted from the OPL profiles based on seven morphological cell features including mean optical path length (M-OPL), coefficient of variation (COV), Optical volume (OV), projected area (PA), ratio of PA to OV, skewness and kurtosis . These additional features were used along with the three spatio-temporal features in order to further improve the classification accuracy. Using this information, all features were inputted into a pre-trained random forest classifier  to determine whether the sample under inspection is SCD-RBC or h-RBC. An advantage of the proposed system over previous works [7, 10, 13] is that SCD-RBCs may appear similar (morphological similarity) to healthy RBCs, potentially compromising the accuracy of classification by morphological features; however, differences in hemoglobin cause the cells fluctuate at different rates. By including features related to cell motility (membrane fluctuations) for classification, improved classification may be possible.
2. Material and methods
2.1 Experimental system
For the 3D printed DHM setup, a collimated laser beam passes through a sample which is then magnified by an objective lens (40X magnification). A fused silica glass plate (3-5mm thick) inclined at an angle of 45° splits the beam (from the objective) into two beams due to reflections from the front and the back surface of the glass plate generating two laterally shifted object wavefronts. The portion of the wavefront unmodulated by the object provides the reference beam and the wavefront modulated by the object acts as an object beam. These beams interfere over the sensor and digital holograms are recorded. Also, the lateral shear caused by the glass plate helps to achieve off-axis geometry which enhances the reconstructions and simplifies the numerical processing of the digital holograms in comparison to in-line DHM setups such as Gabor holography . The fringe frequency is fs = S/r λ where S denotes the lateral shift induced by the glass plate, λ is the wavelength of light source and r is the radius of curvature of the wavefront [20, 21]. Moreover, the relationship between shift (S), glass plate thickness (t), incidence angle on glass plate (β) and refractive index of glass (n) is given as follows: S/t = Sin(2β) (n2 - sinβ)-1/2. Hence a glass plate thickness of 3-5 mm is enough for our experiments, allowing for spatial filtering the spectrum and satisfying the Nyquist criteria for sampling. In order to have more control over the off-axis angle, a wedge plate can be used.
Figure 1(a) illustrates a schematic of the proposed digital holographic microscope (DHM) based on shearing geometry for cell identification and disease diagnosis. A laser source (λ = 633 nm) illuminates the sample under inspection and a microscope objective magnifies the sample. A fused silica glass plate splits the beam, generating two laterally sheared object beams. These two sheared beams interfere over the imaging sensor (CMOS or CCD), and interference fringes are observed. Figure 1(b) shows the 3D printed prototype employing shearing geometry. Moreover, the dimensions of the system shown in Fig. 1(b) are 90mm × 85mm × 200mm.
Figure 2(a) depicts the thickness profile of a blood smear from a healthy volunteer and Fig. 2(b) shows a thickness profile for a blood smear from a patient with SCD. It can be seen from Fig. 2(a) that most of the healthy RBCs are round while in Fig. 2(b) some of the RBCs from a SCD patient are round, but the depressions in the RBCs’ center are not as prominent and a few RBCs are elongated, or sickle shaped. Accurate SCD diagnosis with respect to the state of health of RBCs is difficult using visual inspection. Moreover, visual inspection is not regarded as a valid medical diagnostic test by medical professionals and lab tests are necessary for an accurate medical diagnosis of sickle cell disease. Even though the patient with SCD may have round shaped RBCs, all RBCs produced by a patient with SCD will contain abnormal hemoglobin. Morphological similarities between the healthy and SCD-RBCs may pose a problem for accurate classification tasks, hence by including features related to cell motility (membrane fluctuations), improved classification may be possible. Figure 3(a) shows a pseudo-color 3D height reconstruction for an h-RBC and Fig. 3(b) shows a pseudo-color 3D reconstruction for a round shaped SCD-RBC [see left in Fig. 3(b)] and a crescent shaped SCD-RBC [see right in Fig. 3(b)].
2.2 Off-axis DHM reconstruction algorithm
Once the video containing hologram frames has been recorded, the 3D OPL reconstruction is generated from each of the hologram frames (i.e. with object and background (Ho)). Thereafter, a Fourier transform of every digital hologram frame is taken, filtered by digital filtering of the real part of spectrum in Fourier domain, and then inverse Fourier transformed, which outputs the phase map. Additionally, we also recorded a hologram frame containing background only (HR) information i.e. a hologram frame of the glass slide containing no cell (just blood plasma). We inverse Fourier transform the filtered spectrums separately to get object plus background phase (ΔΦο from Ho) and background phase (ΔΦR from HR). In order to get the phase information due to object only we subtract the phase map of the object and background from the phase map with background only (i.e. ΔΦ = ΔΦR −ΔΦο). This process also removes most of the system related aberrations. After the background phase subtraction, cells are manually segmented to allow for computation of features from the individual cells. The phase was then unwrapped using the Goldstein’s branch cut method  to get the unwrapped phase ΔΦUn. After phase unwrapping, we compute the optical path length (OPL) using the linear relationship given by: where λ is the source wavelength. Height (Δh) information can be calculated from the OPL by when object and surrounding media’s refractive indices are known and Δn = nRBC – nplasma, is the refractive index difference between the cell and the surrounding plasma. It is worth mentioning that average refractive index of a healthy RBC is given by nRBC = 1.42 , while the average refractive index for plasma is given by nplasma = 1.34 , the refractive index varies for individual SCD-RBCs due to stiffening of hemoglobin. Thus, accurate 3D height reconstructions are difficult to compute in SCD case. Therefore, we have computed 3D OPL reconstructions for feature extraction (used in classification) as Δn is not required.
2.3 Temporal stability of the prototype
The proposed prototype [see Fig. 1(b)] based on shearing geometry exhibits very high temporal stability [9, 12], which is desired when studying the cell membrane fluctuations, which are of the order of tens of nanometers. In order to determine the temporal stability of the proposed prototype [see Fig. 1(b)], we recorded 600 fringe patterns for 20 seconds at a frame rate of 30 Hz for a sensor area of 512 x 512 pixels (or 67 µm X 67 µm) exploiting the “windowing” functionality of the CMOS sensors, which is not available on CCD sensors. Using windowing, a user can select a region of interest (ROI) from the available sensor area. One of the advantages of windowing is the elevated frame rates, which allows dynamic cell membrane fluctuations to be recorded at higher frame rates (FPS). One reason for choosing a small ROI from the whole image is the lower computation time. After recording a movie of fringe patterns, path length changes were computed by computing the standard deviation between the reconstructed phase distributions for each frame (containing the fringe patterns) and a previously recorded reference phase distribution. We tested the proposed prototype at the UConn Health Center, where we collected and prepared the blood smears from healthy volunteers and patients suffering from SCD. Figure 4 shows a histogram of the standard deviation values using the grey colored setup [see Fig. 1(b)]. The prototype has sub nanometer stability i.e. a mean of 0.76 nm with a standard deviation of 0.426 nm, taken on a clinical bench at UConn Health. In Fig. 4, the dashed white line depicts location of statistical mean, where is the average of the standard deviations.
The mean of the mechanical noise in the system, which is due to both environmental noise and noise attributed to optical components used in the system, was found to be in the sub-nanometer range. The mean noise is less than the expected value for cell membrane fluctuations (usually on the scale of tens of nanometers) of healthy and SCD-RBCs, which is highly desired when studying membrane fluctuations.
Figure 5(a) shows a video frame from the 3D pseudo-color reconstruction for a h-RBC’s membrane fluctuations as discussed in section 2.2. Figure 5(b) is the top view of the same h-RBC, where the height fluctuations for three different locations on the cell membrane’s surface were computed. Figure 6 shows a plot of the cell membrane fluctuations for three different locations (A-C) as shown in Fig. 5(b) taken over approximately15 seconds. As shown in Fig. 6, the standard deviation, σ, of points A, B, and C are 83 nm, 69 nm, and 56nm, respectively. The standard deviations of the fluctuations are higher in the outer cell regions and lower in the cell’s center.
3. Feature extraction
We investigate time-related features for classification to utilize the cell motility and dynamics as features. To do this, a video hologram of RBCs is recorded over a time period, t. In practice, video holograms containing RBCs were recorded for approximately 20 seconds at a frame rate of 30 frames/sec resulting in approximately 600 frames. Cells are manually segmented from the phase map and reconstructed individually. After each hologram is reconstructed (i.e. OPL reconstructions), these reconstructions are stacked together to form a data cube by employing the reconstruction steps mentioned earlier in section 2.2. Figure 7 depicts the formation of the data cube and data stacks. Figure 7(a) shows a stack of 3D reconstructions for a healthy RBC at different time intervals. Figure 7(b) depicts the stack of reconstructed images as a spatio-temporal data cube. Each pixel stack (tower) represents the optical path length (OPL) changes on the cell membrane at different interval of times t. Thus, the new data set contains information of the cell for the x-direction, y-direction, and axial OPL fluctuations over time. From the feature data cube, the mean and standard deviation (STD) of each spatio-temporal pixel stack was taken across t. More specifically, the first spatio-temporal feature is computed by creating a 2D mean map, shown in Fig. 8(a), generated by finding the mean for each pixel stack individually. Thereafter, we compute the standard deviation from the 2D mean map. In a similar fashion, the second spatio-temporal feature is determined by first computing the standard deviation (STD) for each pixel stack individually, generating a 2D STD map, as shown in Fig. 8(b). Thereafter, the STD of the 2D STD map is computed.
To extract information about the cell motility between subsequent frames (3D OPL reconstructions), i.e. the cell’s lateral movement in time t, the optical flow  algorithm was used. This algorithm generates feature vectors corresponding to the magnitude and direction of the movement of an object’s pixels between frames. For feature extraction, the mean of the magnitude vectors was computed between each subsequent frame. The standard deviation of the mean of the vectors was then used to compute the lateral motion (x-y) of the RBC over time which was used as a third spatio-temporal feature. The rationale is that SCD-RBCs are assumed to be stiffer than the h-RBCs due hemoglobinopathies . Thus, the fluctuations between subsequent frames will be abnormal for a SCD-RBC compared to an h-RBC. Figure 8(c) depicts an example of the optical flow vectors. Along with the three aforementioned spatio-temporal features, we used seven morphological features (spatial) based on optical path length (OPL) such as mean optical path length (M-OPL), coefficient of variation (COV), Optical volume (OV), Projected area (PA), ratio of PA and OV, skewness and kurtosis . Figure 9 shows density plots of all the extracted features from the cell data.
Digital reconstruction of the holograms was implemented using MATLAB. For a single frame with area of 512 x 512 pixels (21 µm x 21 µm) using a 3.07 GHz Intel i7 Processor, the reconstruction takes ~3.5 seconds, however multiple frames can be processed simultaneously by utilizing parallel computing to reduce the overall processing time. Feature extraction for 25 cells with 600 frames for each cell takes approximately 1 minute. The total processing time for a patient depends on the number of cells necessary for accurate diagnosis as well as the length and frame rate of videos required to extract motility information. Optimization of these parameters as well as dedicated hardware and software may significantly reduce the overall computation time necessary for a diagnosis.
After feature extraction, classification was performed using a random-forest classifier  with 100 trees for two scenarios. The first scenario consisted of a training set containing SCD-RBC cells and healthy RBCs from all patients whereas the test set contained SCD-RBCs and healthy RBCs not used for training in the classifier. The second scenario involved training of SCD cells and healthy RBCS from a select few patients whereas the test set consisted of patients’ cells not used in the training set to determine if the patient suffers from SCD. For each scenario, cell classification was performed for three cases. In case 1, we have only used the three aforementioned spatio-temporal cell features, in case 2 we only use the seven aforementioned morphological (spatial) features based on optical path length (OPL) and in case 3 we have combined the three spatio-temporal and the seven morphological (spatial) features to further improve the classification accuracy. The data set collected consisted of randomly selected 150 cells from six healthy volunteers and 150 randomly selected cells from eight patients with SCD-RBCs. The data set was then randomly split in half for testing and training. More specifically, 75 h-RBCs and 75 SCD-RBCs were used for training and 75 h-RBCs and 75 SCD-RBCs were used for testing.
Table 2 depicts the confusion matrices for all three cases. Using only the spatio-temporal-based features, we achieved a 78.00% accuracy with a specificity of 81.33%, and a sensitivity of 74.67%. In case 2, wherein we consider only the morphology-based features, a 92.67% accuracy with a specificity of 96.00% and a sensitivity of 89.33% was achieved. The classification results for using both the spatio-temporal and the morphological-based features was 93.33% accurate with a specificity of 100% and a sensitivity of 86.67%.
A new classification model was created to determine if sickle cell disease RBC is present in a patient. A training set was created by randomly removing 2 healthy patients and 2 SCD patients from the data set to be used for testing. A random forest model was trained using only the remaining 4 healthy and 6 SCD patients, then each patient held out from the training set was tested individually using the trained random forest classifier (RFC). A patient is determined to be either healthy or suffering from sickle cell disease based on the majority vote of the RFC. If the majority of a patient’s cells are classified into a single class, the patient is said to belong to that class. More specifically, if more than 50% of the cells extracted from the patient and inputted into the RFC are classified as being SCD-RBCs, the patient is said to have sickle cell disease. Otherwise, the patient is considered healthy.
Using only the spatio-temporal-based features, the two healthy patients’ cells were classified as healthy RBCs with accuracies of 20% and 30% leading to incorrect diagnosis, whereas the two SCD patients’ cells were classified as SCD-RBC with accuracies of 72% and 96%, leading to the correct diagnosis as shown in Table 3. Using only morphology-based features, the two healthy patients’ cells were correctly classified as healthy RBC with an accuracy of 90% and 80% resulting in a correct diagnosis. The two SCD patients’ cells were classified as SCD-RBCs with accuracies of 92% and 96%, leading to the correct diagnosis. Table 4 depicts the corresponding results. When both morphology-based and spatio-temporal-based features were used, the cells from the four patients (2 healthy and 2 with SCD) were classified with 100% accuracy as healthy RBC or SCD-RBC for their respective subjects. The classification table for these patients is presented in Table 5 below.
Feature importance was then computed using the predictor importance estimate (PIE) to verify that the features used contributed to the training model . The PIE was computed for the random forest model used for patient level testing, wherein both spatio-temporal and morphology-based features were used. The predictor importance estimate is a measure of a feature’s influence in determining the output of a random forest classifier. To find this estimate, first the out-of-bag error is calculated at each decision tree in the random forest. The features associated with each decision tree are then indexed. The values for a particular feature in a decision tree are then permuted and a new out-of-bag error is computed. The difference between the new out-of-bag error and the original out-of-bag error is calculated to determine the model error. A lower model error indicates that a feature is not influential in predicting the output. This is then repeated for all features in a decision tree and for all decision trees. For each feature, the mean () and standard deviations (σe) of the model error is taken across all decision trees and the final predictor importance estimate is calculated for a given feature by /σe.
The higher the predictor importance estimate (PIE), the more influential a feature is in determining the output and therefore, the more information the feature contributes to the model. In Fig. 10, the importance of all 10 features is shown. The ten features in order are optical flow, standard deviation of the 2D mean map, standard deviation of the standard deviation map, optical path length (M-OPL), coefficient of variation (COV), Optical volume (OV), Projected area (PA), ratio of PA and OV, skewness and kurtosis. Feature 1 (optical flow) is the most important feature with a PIE of 2.1989. Feature 2 (Mean of the Standard deviation) is the least important with a PIE of 0.3103. From Fig. 10 we can deduce that inclusion of spatio-temporal features provides additional useful information to the classifier, which may result in improved classification accuracy. In particular, feature 1 (optical flow) outperforms all other features.
There are several advantages of the proposed approach over more traditional lab-based tests such as hemoglobin electrophoresis, including time, cost and accessibility. The electrophoretic assay takes a few hours, but oftentimes, multiple patients are batched together to reduce cost, which can extend the time to results for a patient to several days. Additionally, these tests require trained personnel and adequate lab facilities, which may not be available in third-world countries. Using our proposed approach, specially trained personnel is not necessary, and diagnosis of a patient may be capable in as little as a few minutes from the initial blood draw, which may be further reduced with optimized hardware and software. Furthermore, the proposed approach may reduce cost, as a single system is not limited in the number of patients it can be used to test.
We have presented a compact, field portable imaging system using shearing interferometry that can distinguish between healthy red blood cells (RBC) and sickle cell disease (SCD) red blood cells using a spatio-temporal analysis of cell membrane fluctuations combined with morphological cell (spatial) features based on optical path length (OPL). By testing on patients not included in the training of the classifier, we have shown this proposed system may be capable of performing diagnosis of sickle cell disease. The proposed biosensor recorded a video containing hologram frames of cells, which were segmented and reconstructed for the individual frames then stacked together to form a data cube. Feature extraction was performed on the spatio-temporal data by computing standard deviation (STD) of the mean and STD of the spatio-temporal cube over time for each location on the cell membrane. Moreover, optical flow (OF) vectors were computed to measure the lateral displacement of a cell over time. The STD of the magnitude of the OF vectors were computed. Spatial features based on the morphology of the cells were then computed based on the optical path length including mean optical path length (M-OPL), coefficient of variation (COV), Optical volume (OV), Projected area (PA), ratio of PA and OV, skewness and kurtosis. By combining the spatio-temporal features and spatial features, a pre-trained random forest classifier was able to achieve high prediction accuracy. Using this approach would be advantageous, as the proposed classification system may be capable of rapid and cost-effective testing to provide results in near real time. Future work involves a deeper analysis of motility related features for biological classification problems, automated segmentation algorithms, larger pool of patients, ROC analysis to determine the optimal cutoff value for diagnosis, and increased frame rates of hologram video acquisition as well as testing the proposed systems on different types of diseased cells with various holographic approaches [25–28].
National Science Foundation, Directorate for Engineering (NSF ECCS 1545687).
B. Javidi acknowledges support from Nikon Research Corp. of America and National Science Foundation (NSF) under Grant NSF ECCS 1545687. Adam Markman acknowledges GE under the GE Graduate Fellowship. Timothy O’Connor acknowledges GAANN Fellowship from the Department of Education. We thank Sasia Jones, MPH and Dr. Ektor Rafti for fruitful discussions and clinical research support.
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