Enhanced detection of malaria infected red blood cells through phase driven classification

Abstract

Digital holographic microscopy (DHM) has emerged as a powerful, label-free technique for visualizing and analyzing biological samples. By extracting the intrinsic optical properties of red blood cells (RBCs), DHM enables the detection of infection-induced morphological and biophysical changes. Traditional classification methods often rely on feature-specific analysis, which can lead to misclassification when a single parameter fails to differentiate between uninfected and infected cells. In this study, we present a novel features-based approach that integrates multiple features to classify Plasmodium falciparum-infected RBCs obtained using lensless inline DHM. Our analysis shows that phase-based features classification provides a more reliable indicator of infected RBCs compared to morphological features. Additionally, our features-based approach outperforms feature-specific methods that rely on individual attributes. The parasitemia detection rate improved from 48% (feature-specific method) to 61% (phase-based features method) on the same sample set, demonstrating enhanced detection accuracy. Furthermore, the proposed method achieved high specificity (98–100%), ensuring reliable identification of uninfected cells. Although our method slightly underestimates the parasitemia detection rate compared to Giemsa staining (90%), it offers a significant advantage as a real-time, label-free imaging tool, presenting a promising avenue for rapid and automated malaria diagnosis.

Introduction

Malaria, an acute mosquito-borne disease caused by Plasmodium parasites, remains a major global health challenge¹. Plasmodium falciparum, one of the five species of malaria parasites affecting humans, is the deadliest and most prevalent parasite in sub-Saharan Africa². Following the invasion of a red blood cell (RBC) during infection, the parasite develops and replicates, before egressing from the host cell and reinvasion. Infection and development distinguish the host cell morphology from healthy/uninfected RBCs (uRBCs), which can be used for diagnosis³.

Several imaging modalities have been developed to capture morphological information^4–12. Quantitative phase imaging (QPI) is a label-free imaging technique that extracts phase information from interference or intensity variations. This allows for the biophysical and morphological characterization of biological cells^13–16. Digital holographic microscopy (DHM), a specific type of QPI technique, captures structural details in the form of interference patterns (or holograms)^17–19. The reconstruction of amplitude and phase information from the hologram via numerical methods enables precise measurement of biophysical parameters and has been employed in biological cell imaging and disease identification^20,21. Lensless inline digital holographic microscopy (LiDHM) is a version of DHM that enables high-resolution and large field-of-view (FOV) imaging of biological samples without traditional optical lenses. It incorporates a partially coherent light source, enabling portable, cost-effective, and speckle-free imaging systems for point-of-care applications^22,23.

Moon et al.. employed digital lateral shearing interferometry to generate gradient phase and amplitude data, identifying key features for distinguishing uRBCs from infected RBCs (iRBCs)²⁴. Anand et al.. utilized a digital holographic interferometric microscope to analyze the correlation coefficient of the cross-sectional thickness distribution of RBCs. While these methods have shown promise, their accuracy and computational efficiency remain insufficient for clinical application²⁵. Kim et al.. reconstructed 3D optical refractive index (RI) tomograms of iRBCs at various stages of infection, enabling detailed feature quantification but at the cost of extensive computation time²⁶. Similarly, Park et al.. trained machine learning models on 23 morphological features derived from phase images to classify RBCs, but their approach required prior blood fractionation²⁷. Ugele et al. developed a flow cell system for analyzing sphered erythrocytes via DHM; however, their reliance on morphological parameters limits robustness²⁸.

Advances in computational power, reconstruction algorithms, and the integration of machine learning (ML) methods, such as support vector machines and random forests, to directly learn the mapping between holograms and their corresponding object waves^29–34, and to enhance detection accuracy and decision-making of iRBCs^5,6,25,35,36. However, the application of DHM for malaria faces several challenges. The reliability of classification models often hinges on pixel morphological parameters such as eccentricity, perimeter, sphericity, and surface area^3,37–48. These features, however, may not be as effective for RBC classification since the size of the cell often remains unchanged during infection. In addition, these measurements are highly sensitive to factors such as image segmentation quality, noise, and the precision of cell boundary detection⁴⁹. Such sensitivities introduce variability and undermine the robustness of these models. Furthermore, many current approaches are computationally intensive, limiting their scalability for analyzing large datasets or practical use in resource-limited settings.

On the other hand, the optical phase of the cell undergoes significant alterations due to structural changes caused by the parasite^50–54. For RBCs, this phase information corresponds to their shape, refractive index, and intracellular composition, providing a quantitative basis for disease diagnosis and monitoring^50–54. Thus, by focusing exclusively on the phase information of the reconstructed images, we conducted RBC classification to detect Plasmodium falciparum-infected cells. Furthermore, we introduced a novel features-based classification framework that leverages domain knowledge to identify and prioritize relevant morphological and biophysical features of RBCs. The results demonstrate that, compared to traditional morphology-based methods, the phase-based approach achieves a more accurate and efficient detection of infected cells. Furthermore, the features-based classification significantly outperforms conventional feature-specific techniques. Through rigorous testing, we show that it achieves higher accuracy, sensitivity, and specificity, establishing it as a robust and scalable tool for malaria detection. By addressing the key limitations of existing methods, this approach offers a practical, efficient, and accurate solution for real-world diagnostic applications, particularly in resource-constrained environments.

Methods

Compliance with guidelines

All methods were carried out according to institutional guidelines and regulations.

Ethical approval

This study was deemed not subject to human subjects’ research guidelines by the Harvard Longwood Campus Institutional Review Board, because the researchers do not have access to identifying information for donors of the commercially purchased human blood used in the investigation.

Informed consent

The blood was commercial (Research Blood Components), and they obtained informed consent.

Sample preparation and measurement

A fraction of RBCs from a healthy donor are infected with the Plasmodium falciparum HB3 strain, adhering to strict ethical and biosafety standards. After 48 h, the cells reach the trophozoite and schizont stages, where they exhibit magnetic susceptibility due to the accumulation of paramagnetic hemozoin. Infected RBCs are then isolated via magnetic-activated cell sorting (MACS), a technique developed by Miltenyi Biotec. The MACS-purified samples typically consist of ~ 85–90% schizont-stage iRBCs and ~ 10–15% uRBCs, with negligible early-stage iRBCs. Both healthy and MACS sorted samples were imaged using brightfield microscope and custom-built LiDHM setup. For brightfield imaging, thin blood smears were prepared and stained with Giemsa dye to confirm infection.

The LiDHM setup, illustrated in Fig. 1, uses a partially coherent LED light source (Thorlabs, LED525E, 2.6 mW @ 20 mA, wavelength λ = 525 nm) passed through a 50 μm pinhole for spatial filtering, ensuring a clean and coherent illumination beam. A drop of the RBC sample was carefully placed on a microscope slide and covered with a coverslip to ensure uniform distribution and minimize air bubbles. The sample was then positioned approximately 1 mm above the Raspberry Pi HQ camera, which was located ~ 10 cm from the pinhole. The camera, with an active area of 4056 × 3040 pixels and a pixel size of 1.55 μm, enabled high-resolution imaging. The sample is then placed in the optical path of the LiDHM to record holographic images. Placing the sample close to the camera sensor allowed for full utilization of the field of view, spanning approximately 30 mm². Holographic images recorded by the setup captured the phase information of the RBCs. Phase reconstruction and analysis were performed via Python software, which leverages libraries such as NumPy, OpenCV, and sci-kit-learn for efficient image processing and classification.

Fig. 1.

Experimental setup of lensless, inline digital holographic microscopy. A partially coherent LED light source passed through a pinhole for spatial filtering. The RBC sample is placed on a microscope slide and positioned above the Raspberry Pi HQ camera, which captures the holograms. A Python-based algorithm is used for phase reconstruction and analysis.

Image acquisition, processing, analysis, and classification

The overall process from imaging to classification is composed of four integrated steps: (1) hologram recording and reconstruction, (2) cell segmentation and detection, (3) cell labeling and feature extraction, and (4) classification.

Step 1—Hologram acquisition and reconstruction

Figure 2a shows a region of interest (ROI) from the full FOV of a digital hologram of a healthy sample captured by LiDHM. The holograms were first preprocessed by autofocusing measures, including Tenengrad variance and Laplacian-based sharpness, to computationally refocus at multiple depths and identify the optimal focal plane for each cell. Then, the object information was reconstructed using our recently developed phase-support constraint on phase-only function (PCOF) algorithm⁵⁵. This process mitigates twin-image artifacts and enhanced the fidelity of the reconstructed phase images, as shown in Fig. 2b.

Fig. 2.

Image processing of the proposed method. (a) Hologram of the cropped region of interest (ROI) of the RBC sample, (b) reconstructed phase image via the PCOF method, (c) binary image for segmentation, (d) labeled cells via the watershed method, (e) marked image multiplied by the reconstructed phase image to isolate RBCs from the background, and (f) unwrapped phase image annotated for feature extraction.

Step 2—Cell segmentation

To accurately segment individual RBCs from the background, adaptive thresholding was employed, leveraging local intensity variations within the image. A neighborhood window size of 25 pixels was used to calculate the local threshold for each region, ensuring sensitivity to varying illuminations and contrasts across the image. The choice of an appropriate window size was guided by image characteristics, such as the size of features (RBCs) and the degree of intensity variation. This approach enables the reconstruction of phase images into binary masks, where pixels representing RBCs are distinguished from the background, facilitating precise segmentation for subsequent analysis. Figure 2c depicts the binary image generated for the cropped region shown in Fig. 2a, demonstrating successful segmentation of the RBCs.

Watershed segmentation, a common method for separating touching objects in microscopy images, was applied to distinguish overlapping cells and remove artifacts from the analysis. While this approach improved segmentation, some overlapping cells persisted and were excluded during feature extraction to ensure data accuracy. To further refine the segmentation, morphological operations such as erosion and dilation were applied, enabling precise boundary detection between adjacent RBCs. The final segmented regions, isolated individual RBCs from the background, are shown in Fig. 2d,e.

Step 3—Feature extraction and labeling

Feature extraction allows for the quantitative characterization of cells and forms the basis for classifying cells as infected or uninfected. Our selection of features is based on morphology (or the number of pixels) and the optical phase (or optical path length). The optical path length is represented by the integral, which is influenced by the sample’s thickness and refractive index. The optical phase (φ), or phase shift of light passing through the sample, is given by:

1

where is the wavelength of the light, is the sample’s refractive index, and is the refractive index of the medium. The sample thickness can be obtained as

and the refractive index of the cell as

2

The morphological features include surface area (SA), eccentricity (E), extent (Ext), and sphericity (Sph), which are derived from image analysis and provide valuable insights into the shape, size, and geometry of RBCs. The surface area is a two-dimensional area covered by the RBC, which represents the projected size of the cell. The projected surface area is defined as:

3

where N_pixels is the number of pixels within the measured area of the RBCs, ps is the pixel size of the sensor, and SF is the scaling factor of the LiDHM system used for RBC imaging.

Eccentricity measures how elongated the object is and is calculated as the ratio of the distance between the foci of the ellipse and its major axis length. It ranges from 0 (perfect circle) to 1 (highly elongated). It can be expressed as:

4

where a is the length of the semimajor axis and b is the length of the semi-minor axis. The extent is another feature that quantifies how much space the cell occupies within its bounding box.

Sphericity, which measures how closely the shape of a cell approaches that of a perfect sphere, often depends on the surface area and volume of the object. It ranges from 0 to 1 (1 being perfectly spherical).

The total dry mass utilizes both morphological and optical phase features.

5

where is the refraction increment. For each segmented cell, these features were extracted to quantify the cell characteristics. Python-based libraries, e.g., SciKit-Image, OpenCV, and facilitate the automated processing of larger datasets, streamlining the workflow for feature extraction and analysis. Figure 2f represents an unwrapped phase image annotated for feature extraction.

Step 4—Thresholding

(A) Feature-specific thresholding: Typically, a healthy RBC exhibit a smooth phase map around the thicker peripheral regions and lower phase values in the thin center. The uniformity of the phase distribution reflects the normal biconcave shape and consistent refractive index of hemoglobin within the cell. The reconstructed phase map, as shown in Fig. 3, demonstrates these characteristics, providing a clear profile. Figure 3a shows a ROI of the recorded hologram of a healthy RBC. Figure 3b depicts a doughnut/biconcave shape of a normal RBC, whereas Fig. 3c, d show the 3D and phase map profiles of the cells. Baseline thresholds and population-level statistical characteristics were established using phase profiles. In addition, phase shift was used to calculate the refractive index and the dry mass of the cell.

Fig. 3.

Recorded hologram and reconstructed phase image of a healthy RBC sample. (a) Hologram of a region of interest (ROI). (b) Reconstructed phase image with a scalebar of 5 μm. (c) 3D mesh of uRBCs. (d) The line profile (blue line) of the selected cell in (b) shows the cross-sectional profile of the normal RBC.

The thresholds were determined via statistical measures, including the mean and standard deviation (µ ± 2σ), as well as the 1/e² width of the feature distribution. Feature-specific low (LT) and high (HT) threshold values were derived from kernel density estimates (KDE) plots and histograms. These values are presented in Table 1, along with the percentage of cells that fall within these thresholds.

Table 1.

Feature-specific thresholding.

Features	1/e2 Threshold			µ ± 2σ Threshold
	LT	HT	% of cells	LT	HT	% of cells
SA (m2)	121.52	158.00	91	113.96	165.56	94
Ecc	0.13	0.31	91	0.10	0.35	97
Ext	0.73	0.79	95	0.71	0.80	98
Sph	0.85	0.91	93	0.87	0.91	99
Mass (pg)	31.84	78.87	89	22.10	88.61	98
RI	1.36	1.39	90	1.36	1.40	99
Δφ (rads)	0.51	1.19	90	0.37	1.34	99

(B) Features-based thresholding: In addition to feature-specific thresholding, we designed and implemented a novel features-based thresholding strategy to enhance classification accuracy. For example, in phase-based thresholding, all cells with phase values confined within statistically defined LT and UT were systematically identified. Within these subsets of cells, the minimum (min) and maximum (max) values of remaining of the features—SA, Ecc, Ext, Sph, RI, and Mass—were computed. These min and max values were then used to define refined thresholds, effectively replacing the broader statistical limits and enabling more precise classification. Similarly, for surface area-based thresholding, all cells with SA values confined within the LT and UT were extracted. Within this subset, the min and max values of other features—Ecc, Ext, Sph, ϕ, RI, and Mass—were computed.

Table 2 shows the phase-based, surface area-based, mass-based, and refractive index-based thresholding for the sample obtained via features-based thresholding, as discussed above. Importantly, the min and max values of the features Ecc, Ext, and Sph under the µ ± 2σ and 1/e² curves are nearly identical. This is because all the cells are counted in each case. However, the phase values in the phase-based threshold and the surface area values in the surface area-based threshold represent the LT and UT.

Table 2.

Phase-based, dry mass-based, refractive index-based, and surface area-based thresholding.

Values under 1/e2 curve
	Phase-based			Surface area-based			Mass-based			Refractive index-based
	Min	Max	%	Min	Max	%	Min	Max	%	Min	Max	%
SA (m2)	121.59	174.27	100	121.59 (LT)	157.69 (HT)	91	121.59	174.27	100	121.59	174.27	100
Ecc	0.06	0.38	100	0.06	0.38	100	0.06	0.38	100	0.06	0.38	100
Ext	0.70	0.81	100	0.70	0.81	100	0.70	0.81	100	0.70	0.81	100
Sph	0.88	0.89	100	0.88	0.89	100	0.88	0.89	100	0.88	0.89	100
Mass (pg)	30.54	91.40	98	30.54	98.43	100	32.86 (LT)	78.86 (HT)	89	30.54	91.40	98
RI	1.36	1.39	90	1.36	1.40	100	1.36	1.39	97	1.36 (LT)	1.39 (HT)	90
Δφ (rads)	0.52 (LT)	1.19 (HT)	90	0.52	1.42	100	0.52	1.28	97	0.52	1.19	90
Values under µ ± 2σ curve
SA (m2)	120.01	175.28	100	120.01 (LT)	165.35 (HT)	94	120.01	175.28	100	120.01	175.28	100
Ecc	0.06	0.38	100	0.06	0.38	100	0.06	0.38	100	0.06	0.38	100
Ext	0.70	0.81	100	0.70	0.81	100	0.70	0.81	100	0.70	0.81	100
Sph	0.88	0.91	100	0.88	0.91	100	0.88	0.91	100	0.88	0.91	100
Mass (pg)	23.61	98.03	100	23.61	98.43	100	23.61 (LT)	88.55 (HT)	98	23.61	98.03	100
RI	1.36	1.40	99	1.36	1.40	100	1.36	1.40	99	1.36 (LT)	1.39 (HT)	99
Δφ (rads)	0.40 (LT)	1.32 (HT)	99	0.40	1.42	100	0.40	1.40	99	0.40	1.32	99

Step 5—Classification

For classification, we used MACS-sorted RBCs to ensure a controlled sample for analysis. The classification was based on baseline thresholds established from healthy/uninfected samples of the same donor. Figure 4a shows a hologram of ROI-reconstructed RBCs from which phase information was extracted. Cells with feature values within the LT and UT were labeled uRBCs, while those exceeding the UT were classified as iRBCs. Cells with feature values below the LT were considered noise and excluded from further analysis – except for sphericity. As shown in Table 1, the healthy sample exhibit sphericity in the range of 0.85–0.91. Upon infection, the sphericity value drops below LT rather than exceeding the UT. Therefore, cells with sphericity values below the LT were not considered noise and were instead retained for classification as potential iRBCs. Parasitemia, representing the proportion of infected cells, was calculated as the ratio of iRBCs to the total cell count (uRBCs + iRBCs), expressed as a percentage. Since this method is label-free, no external validation using Giemsa-stained microscopy was performed. Instead, parasitemia was estimated and compared between feature-specific and features-based thresholds.

Fig. 4.

Recorded hologram and reconstructed phase image of malaria-infected RBCs. (a) Hologram of a cropped region of interest (ROI) with a scalebar of 15 μm. (b) Reconstructed phase image annotated for feature extraction and labeling. The red square lines indicate iRBCs, whereas the blue square lines represent uRBCs. (c) Surface plot of the reconstructed phase image of (b). (d,e) Surface plots of the iRBCs and uRBCs, respectively, and (f) corresponding intensity profiles. Table shows the surface area, mass, and phase values of all 12 cells identified in (b). The presence of the parasite alters the morphological features, resulting in a corresponding change in the cell.

Results

We used the 1/e² thresholds for our phase-specific classifier model for classification. For example, cells with phase values within the range of 0.51 radians and 1.19 radians were labeled “Uninfected,” (presumable negatives - PN_S) whereas cells with a phase value greater than 1.19 radians were labeled “Infected,” (presumable positives - PP_S). This classification was applied to each cell. Figure 4b,c show a phase map of RBCs with phase values, which are displayed in radians on a color scale ranging from 0 (blue) to 2 (red). In Fig. 4b, iRBCs are circled with red boxes, and exhibit more intense colors (yellow, orange, and red), as depicted in Fig. 4d, whereas the uRBCs, blue boxes, have lower phase values, appearing in cooler colors (blue to green), as shown in Fig. 4e. The intensity/phase profile in Fig. 4f illustrates the changes in the phase of the RBCs, where the presence of the parasite alters the optical path length of the cell, resulting in a corresponding change in the phase. The surface area, mass, and phase values of all 12 cells identified in Fig. 4b are listed in the table shown in Fig. 4. Even though various cells are identified as uninfected and infected by each feature, only one cell (#9) is classified as infected by all three features. On the other hand, several cells have been classified as uninfected by all three features.

Table 3 presents the classification for the full FOV based on threshold values that are listed in Table 1. The phase feature has a notably greater parasitemia value (48%), suggesting that the phase, which reflects optical path length changes in the cell’s internal structure due to parasitic infection (hemozoin crystals), is a more sensitive indicator. Furthermore, the refractive index and total mass, derived from phase measurements, show similar trends, reinforcing the importance of phase-based indicators in detecting parasitemia. While sphericity, extent, and eccentricity also show higher parasitemia values (46–56%), these morphological features are prone to high false positives in parasitemia classification. As discussed previously, from Table 1, the sphericity threshold range is 0.85–0.91. That means cells whose values are below 0.85 are classified as iRBCs. However, cells that are not well resolved during the phase reconstruction process, such as those that are damaged or fragmented, may also exhibit low sphericity values and are classified as iRBCs. Therefore, while these morphological features can offer useful information, their susceptibility to these artifacts makes them less reliable than phase-based indicators, which are more directly linked to the optical changes caused by the presence of the parasite.

Table 3.

Classification and parasitemia using statistical threshold.

	1/e² threshold-based classification				µ ± 2σ threshold-based classification
Features	Total RBCs	uRBCs PNS	iRBCs PPS	% Parasitemia	Total RBCs	uRBCs	iRBCs	% Parasitemia
SA (um2)	2044	1870	174	9	2076	2004	72	3
Ecc	2208	969	1239	56	2073	1409	664	32
Ext	1953	877	1076	55	2073	1338	735	35
Sph	1953	1055	898	46	2073	687	1386	67
Mass (pg)	2200	1343	857	39	2243	1773	470	21
RI	2185	1147	1038	48	2243	1691	552	25
Δφ (rads)	2185	1147	1038	48	2076	1539	537	26

A correlation matrix helps identify which features, such as phase, surface area, or eccentricity, provide independent diagnostic information and which are redundant. Figure 5 presents a feature correlation heatmap, giving a visual summary of the linear relationships among features extracted from RBCs. Phase, total mass, and refractive index have a strong positive correlation (0.9), indicating redundancy among them. Consequently, we prioritized the phase feature, as it represents the most direct measurement for classification. The extent and sphericity also show a high positive correlation (0.85), indicating their close relationship. Eccentricity is inversely correlated with sphericity (− 0.81) and extent (− 0.71), highlighting distinct morphological differences. The surface area, on the other hand, showed weak correlations with most features, except for total mass (0.5), suggesting its role as an independent diagnostic feature.

Fig. 5.

Feature correlation heatmap illustrating the relationships among the extracted morphological and optical properties of RBCs. The color intensity represents the strength and direction of the correlation between features, with red indicating a strong positive correlation, blue indicating a strong negative correlation, and values near zero (light colors) indicating weak or no correlation. Key observations include a strong positive correlation between the phase value, total mass, and refractive index, as well as an inverse relationship between eccentricity and sphericity. The surface area shows weak or no correlation with the other features. These insights guide feature selection and contribute to understanding the interactions between features, aiding in the classification of infected versus uninfected RBCs.

To validate the correlation matrix coefficients and visualize feature differences, we generated probability density distributions for all extracted features. As shown in Fig. 6, these features are compared between iRBCs (red curves) and uRBCs (blue curves). The phase, mass, and eccentricity features demonstrate strong discriminatory potential, making them effective markers for differentiating between infected and uninfected cells. Notably, the refractive index and phase plots are nearly identical, indicating a high degree of correlation between these two features, as reflected in the correlation matrix. Since both features capture similar information about the structural and optical changes induced by malaria infection, using either the phase or refractive index could be sufficient in a classification model, reducing redundancy without compromising accuracy. Therefore, RI-based features were excluded from the final classification model. Conversely, features such as surface area and sphericity significantly overlap between the two groups, limiting their utility as standalone indicators for classification. Given the varying levels of discriminatory power among features, a features-based strategy offers a more robust and reliable method for accurately classifying infected RBCs, leveraging the complementary strengths of the most promising features while minimizing redundancy. Furthermore, utilizing the phase is more practical, as DHM directly provides phase information, whereas the refractive index must be inferred by assuming the sample’s thickness. This additional assumption can introduce uncertainties, making phase a more reliable and straightforward choice for classification.

Fig. 6.

Kernel density estimation (KDE) curves comparing several features of healthy RBC samples (blue curves) and infected RBC samples (red curves). The features include the surface area, eccentricity, extent, sphericity, mass, phase, and refractive index. The density plots illustrate the probability distributions of these features, highlighting differences between the two groups. The vertical lines indicate threshold values (lower and upper) for each feature, aiding in understanding typical ranges and abnormalities. The MACS-purified samples used in this study typically consisted of ~ 85–90% schizont-stage iRBCs and ~ 10–15% uninfected.

Table 3 clearly shows that feature-specific classification is not optimal—the % of parasitemia is low. Therefore using features-based threshold and optimized features using correlation map, we adopted a two-step process to improve the classification: (i) identifying cells classified as uninfected by all selected features (presumably negative - PN_F). The min-max values, obtained via features-based threshold, of each feature were used, and a logical AND operation was employed to identify cells that simultaneously met the threshold criteria for all selected features. These cells were classified as “uRBCs.”

and (ii) detecting infected cells from the remaining population based on a specific feature, the remaining subset of cells is subjected to feature-specific statistical thresholds (LT and UT) to classify as “iRBCs”. For example, a cell is classified as infected if its phase value (f) φ exceeds a UT (presumably positive - PP_F). This two-step process ensures both conservative features-based filtering and sensitivity to phase feature-specific abnormalities. The same procedure was applied to surface area and total mass in Tables 4 and 5 for comparison analysis.

Table 4.

Classification and parasitemia detection using features-based thresholds.

	Classification using values under 1/e2 curve
Features-Based	Total RBCs	uRBCs (PNF)	iRBCs (PPF)	% Parasitemia using sum of iRBC & uRBC	% Parasitemia using Total Cell Count	Cells that are Not Classified
SA (m2)	1972	897	174	16	9	901
Mass (pg)	1967	647	824	56	42	496
Δφ (rads)	1981	603	935	61	47	443

Table 5.

Classification evaluation metrics.

	Feature-specific		Features-based		Metrics evaluation
	uRBC PNS	iRBC PPS	uRBC PNF	iRBC PPF	PFNF	PFPF	Sensitivity	Specificity
SA (m2)	1781	172	897	174	884	2	16	100
Mass (pg)	1138	815	647	824	491	9	63	99
Δφ (rads)	1028	925	603	935	425	10	69	98

Compared to feature-specific classification, Table 4 shows that features-based classification increased the detected parasitemia from 48 to 61% for phase-derived features. A detailed comparison of Tables 4 and 5 reveals that the number of infected RBCs remains the same across both methods. The key difference lies in the classification of uninfected RBCs. Feature-specific classification identified 1147 cells as uninfected, whereas the combined features-based method classified 603 cells as uninfected. As a result, when only uRBCs and iRBCs are considered, the calculated parasitemia is 61%. However, when all detected cells are included in the calculation, parasitemia is 48%. This suggests that the features-based approach refines classification by reducing the misclassification of uninfected cells, thereby yielding a more sensitive estimation of parasitemia.

Since ground truth labels are unavailable, we define Presumable Negatives (PN_F) as cells that are classified as uninfected by all the features. This acknowledges the inherent uncertainty in classification without absolute validation. From the set of “remaining cells” (i.e., those not classified as PN_F), Presumable Positives (PP_F) are identified using feature-specific thresholds. For instance, in the phase-based classification, PP_F refers to cells identified as infected based on UT values of the phase feature. Similarly, for surface area-based classification, PP_F includes cells classified as infected according to the UT values for surface area. We further define Presumable False Positives (PFP) as cells that are classified as infected (PP_S) by a feature-specific method but identified as uninfected (PN_F) by the multi-feature two-step process. Presumable False Negatives (PFN) refer to cells classified as uninfected (PN_S) by a feature-specific method but identified as infected (PP_F) by the two-step process. In contrast, Presumable True Positives (PTP) are those cells consistently classified as infected by both the feature-specific and the multi-feature approaches, and are therefore considered correctly identified as infected within this framework. By using Presumable Negatives (PN) instead of True Negatives (TN), we ensure a meaningful comparison of various feature-based classification approaches while recognizing that absolute classification accuracy cannot be determined without external ground truth validation (e.g., Giemsa-stained microscopy). This framework allows for the evaluation of different feature sets for parasitemia detection in a label-free manner.

The cells that are classified as neither PN_F nor PP_F by features-based classification are re-evaluated by comparing them against feature-specific thresholds. We categorized them as presumed false negatives PFN_F (PN_F – PN_S) or false positives PFP_F (PP_F – PP_S), and the results are shown in Table 5. Using this data, sensitivity and specificity for each feature were obtained. The features-based method demonstrates higher sensitivity for mass (63%) and phase (69%) but lower sensitivity for surface area (16%). However, all the features achieved high specificity (98–100%), effectively distinguishing uRBCs.

To gain a deeper understanding of the “not classified” (or unclassified) cells, density distributions for the three features-based classifications are plotted, see Fig. 7, for Uninfected (blue), Infected (red), and Not Classified (cyan). The classification boundaries, represented by dashed vertical lines, define the thresholds used to distinguish between categories, but their placement within overlapping regions suggests inherent uncertainty in classification. The presence of uninfected samples within the infected distribution suggests the potential for false positives, whereas infected samples appearing within the uninfected range indicate the likelihood of false negatives. Furthermore, the unclassified cells are located primarily near the main peak of the uninfected RBC distribution across all three features-based classifications. This explains why the PFN values are higher than the PFP values. A small number of cells fall below and above the classification thresholds, and since most unclassified cells are within the uninfected region, the lower threshold values may be too strict.

Fig. 7.

Density distributions for three features—surface area, mass, and phase—were used for the feature-based classification of RBCs into three categories: uninfected (blue), infected (red), and not classified (cyan). Each plot evaluates the ability of these features to distinguish between uninfected and infected RBCs.

The surface area plot shows significant overlap between uninfected and infected cells, suggesting a greater likelihood of misclassification, thereby limiting its effectiveness as a standalone feature. Compared with the surface area, the mass features-based model demonstrated better separation between iRBCs and uRBCs, with infected cells shifting distinctly toward higher mass values. The phase features-based classification shows the clearest separation between infected and uninfected cells, indicating that phase values may be the most reliable distinguishing feature. The distribution of iRBCs is distinctly shifted toward higher phase values, reinforcing its effectiveness in classification. Optimizing the thresholds or incorporating additional discriminative features could increase the classification accuracy and reduce misclassification errors.

Figure 8 illustrates different classification strategies based on classification step 2, which facilitates the analysis of the distinguishing properties of infected and uninfected cells. For the surface area-based classification model, Fig. 8a, the remaining cells that survived as “uRBCs” after passing through the AND logic were subjected to statistical surface area thresholds to finalize the classification. Most uRBCs (blue) are tightly clustered within the surface area range of 121–158 μm². iRBCs (red) are scattered across a wider range of surface areas, with several exceeding the defined thresholds. In Fig. 8b, which represents a phase-based classification model, uRBCs are tightly grouped within the phase range of 0.51–1.19 rads, with minimal overlap into the infected region, whereas iRBCs exhibit broader phase values, often exceeding the defined phase thresholds. Figure 8c,d are two plots of total mass vs. phase and surface area. As shown in Fig. 8c, uRBCs fall within the narrow total mass range of 31.84–78.87 pg and phase range of 0.52–1.28 rads, whereas iRBCs display a strong positive correlation between phase mass and total mass, spreading across higher total mass values. Uninfected cells cluster within narrow ranges of surface area and total mass, as shown in Fig. 8d. However, the iRBCs showed significant deviations, with larger surface areas and higher total masses than the uRBCs did. So, while morphological features for classification are useful, the significant overlap between malaria-infected and uninfected cells suggests that surface area alone may not be sufficient for accurate classification. Compared with surface area features-based classification, phase features-based classification appears to provide better separation between iRBCs and uRBCs. Since the phase is a direct measurement in the DHM system and is sensitive to structural changes in RBCs, it is a strong classifier. Mass also performs well, reflecting its dependence on phase and its sensitivity to infection-induced changes. The total mass and phase are strongly correlated, as the total mass is derived from phase information. The total mass features-based classification captures the biophysical changes in infected RBCs, such as increased mass due to hemozoin formation, making it also a robust feature for classification. Thus, the features-based classification model improves the classification accuracy of malaria-infected cells, leveraging each feature’s strengths to address overlaps and misclassifications.

Fig. 8.

Scatter plots illustrate the features-based classification of iRBCs (red) or uRBCs (blue) and highlight the distribution and overlap of features. (a) Surface area-based classification with phase thresholds overlaid for reference. (b) Phase-based classification with surface area thresholds overlaid for comparison. (c) Mass-based classification versus phase reveals a strong correlation between them. (d) Mass-based classification versus surface area. These plots emphasize the utility of phase and total mass as robust classifiers and the complementary role of surface area in distinguishing infected from uninfected cells.

The current study primarily used samples enriched for schizont-stage iRBCs via MACS purification, which excludes early stages of the parasite. While this allowed for initial validation of our phase-based classification approach, future work will include early stages to evaluate its performance.

Unsupervised learning or classification methods that rely on feature thresholds can lack interpretability and underutilize domain-specific features. Having demonstrated that the features-based classification model improves the classification accuracy of malaria-infected cells, leveraging each feature’s strengths to address overlaps and misclassifications, in our future work, we plan to integrate features-based classification with supervised learning to improve accuracy. A subset of data can be confidently classified as true positives (TPs) and true negatives (TNs), serving as a pseudo-ground truth for training a supervised model. Even a small but reliable labeled dataset enhances generalization, leveraging the strengths of supervised learning for improved classification.

Conclusion

In conclusion, we demonstrated that the optical phase, which captures Plasmodium falciparum infection-induced changes in RBCs, is more effective for classification than conventional morphological features such as surface area and eccentricity. By leveraging phase information as a primary classification parameter, we achieved enhanced sensitivity and specificity in classifying malaria-infected RBCs. The correlation analysis further reinforced the strong relationship between phase, refractive index, and total dry mass, highlighting their utility as primary classification parameters. Additionally, by integrating multiple features into a unified classification framework, the proposed features-based classification approach improved parasitemia detection, increasing classification accuracy from 48 to 61% while maintaining high specificity (98–100%). This enhancement reduces misclassification errors, primarily minimizing false positives while also improving the detection of infected cells. In future studies, the studies will be extended to the circulation of the ring or the early stage of the parasite, as well as supervised classification using pseudo-ground truth training datasets generated by the features-based classification.

Abbreviations

DHM

Digital holographic microscopy

RBCs

Red blood cells

uRBCs

Uninfected red blood cells

iRBCs

Infected red blood cells

QPI

Quantitative phase imaging

LiDHM

Lensless inline digital holographic microscopy

FOV

Field-of-view

RI

Refractive index

3D

Three dimensions

ML

Machine learning

MACS

Magnetic-activated cell sorting

LED

Light emitting diode

PCOF

Phase-support constraint on phase-only function

SA

Surface area

Ecc

Eccentricity

Sph

Sphericity

Ext

Extent

UT

Upper threshold

LT

Lower threshold

ROI

Region of interest

PN

Presumable negatives

PP

Presumable positives

PFN

Presumable false negatives

PFP

Presumable false positives

PTN

Presumable true negatives

PTP

Presumable true positives

Author contributions

Conceptualization: C.K. and C.Y.; Methodology: C.K., A.P., and C.Y.; Investigation: C.K. and A.P.; Software and Data Curation: C.K.; Formal Analysis: C.K., D.H., and C.Y.; Validation: C.K., A.P., D.H., M.D., and C.Y.; Resources: M.D. and C.Y.; Writing – Original Draft Preparation: C.K.; Writing – Review & Editing: C.K., A.P., D.H., M.D., and C.Y.; Supervision: M.D. and C.Y.; Project Administration: C.Y. All authors have reviewed the manuscript.

Data availability

Data underlying the results may be obtained from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Human specimens and/or data

In this project, we used human red blood cells for the cultured growth of Plasmodium falciparum in our studies. The use of these human cells has been determined not to constitute human subjects research by the Institutional Review Board at Harvard. We purchase units of human blood from a commercial source (Research Blood Components), which are provided to us de-identified and anonymously.