Label-free refractive index mapping of human sperm cells

Abstract

In intracytoplasmic sperm injection (ICSI), a single sperm cell is chosen and injected into an oocyte in a dish. The selection process is guided by subjective evaluation of experienced clinicians using non-quantitative optical microscopy techniques, where the cells are mostly transparent and thus their internal morphology is not well visualized. Since staining cannot be applied to enhance imaging contrast during ICSI, label-free interferometric phase microscopy (IPM) offers an alternative solution for providing the missing information. The quantitative phase maps acquired by IPM are proportional to the product between the refractive index (RI) and the average thickness of the sample. However, so far, refractometry of human sperm cells has not been fully achieved. In this paper, to perform refractometry of individual human sperm cells, we first solve the coupling problem between the RI and the thickness profile of the cell by quantitative phase imaging in two media with different RIs. We then combined IPM with fluorescence microscopy to achieve molecular specificity as a learning step. We utilized fluorescence microscopy to localize the nucleus within the RI profile of the cell, enabling refractometry of the different structures within the sperm cell head. This approach allowed us to obtain the integral RI values of the nucleus and the acrosome, demonstrating that these two organelles can be distinguished based on their RI differences. A machine learning model was trained using spatial, morphological, and textural features extracted from the label-free quantitative phase images. The model achieved high classification performance, with a sensitivity of 89% and specificity of 94%, demonstrating its potential for automated identification of subcellular structures within sperm cells. The presented study is expected to help in better morphological characterization of sperm cells, improving their selection for fertilization.

1. Introduction

One in every six couples encounters infertility issues, while male factors contribute to approximately 50% of all cases [1]. The World Health Organization (WHO) defines infertility as the inability to conceive naturally over the course of one year [2]. Assisted reproductive technology (ART) includes procedures such as in vitro fertilization (IVF) and intracytoplasmic sperm injection (ICSI) to achieve conception. Recent data indicates that over 2.5 million fertilization cycles are conducted each year, with an approximate success rate of 33% [3]. In ICSI, a single sperm cell is selected manually and subjectively by a trained clinical embryologist using a micromanipulator and injected directly into the oocyte [4]. The WHO has established criteria for assessing male fertility through sperm sample imaging, primarily focusing on sperm morphology and motility [5]. However, internal sperm morphology should be assessed without the use of exogenous stains, as such staining is cytotoxic and cannot be applied to human sperm cells in ICSI procedures.

Off-axis interferometric phase microscopy (IPM) can be applied to provide a solution to this problem. IPM is a stain-free optical imaging technique that enables in vitro imaging of cells by capturing an interferogram or a digital hologram. This is achieved by superimposing the light that passes through the sample with a clear reference beam. The interferograms are digitally processed to obtain the quantitative amplitude and phase maps of the sample [6]. This map corresponds to the optical thickness or optical path delay (OPD) of the cell, which is proportional to the product of the cell thickness and its integral refractive index (RI) [7]. While other phase imaging modalities-e.g., differential phase contrast, transport-of-intensity, or Fourier ptychographic microscopy, allow qualitative measurement, IPM allows direct integral RI measurement on all cell points.

The RI profile has a great potential for being an indicator used for medical diagnostics and biological research, as RI is an intrinsic optical property closely linked to cellular mass and its distribution, offering valuable insights for various biological models [8]. However, the geometric thickness and RI of the cell are coupled in the measurement obtained by IPM, making it challenging to distinguish each property individually. Additionally, the RI might not be fully indicative for the location of cell organelles. As shown in previous studies, for certain cells, the RI of the nucleus might even be lower than that of the cytoplasm [9–11].

Various methods have been proposed to address the RI-thickness coupling problem. One such approach involves conducting two interferometric measurements, each of which with a different surrounding medium [12–15]. This method generates two quantitative phase profiles, providing two equations with two variables for each spatial location on the measured cell.

In parallel, several studies have suggested integrating fluorescence emission measurements with IPM to enhance molecular specificity in the cell organelles and analyze cellular processes such as proliferation and mitosis. Furthermore, it has been demonstrated that IPM systems can be coupled with confocal fluorescence microscopy to facilitate simultaneous data acquisition [16–22].

The sperm head consists of two main components, the nucleus and the acrosome, which differ in their concentration and composition of proteins, nucleic acids, and other biomolecules [23]. The results for the refractometry of the nucleus and the acrosome fall within the expected range, as the acrosome is primarily a vesicle-like structure filled with hydrolytic enzymes essential for breaking down the zona pellucida during oocyte penetration, while the nucleus, that is densely packed with DNA-associated proteins, enzymes, and lipids, is expected to have a higher RI [24].

A morphologically normal sperm nucleus is typically smooth, symmetric, and oval-shaped, with no large vacuoles or surface irregularities. Its dimensions generally fall within a defined range, approximately 4.47 to 5.03 μm in length and 3.08 to 3.48 μm in width [25]. According to WHO criteria, the acrosome should be distinctly visible and occupy approximately 40% to 70% of the total area of the sperm head [5]. Previous studies have shown that sperm cells with morphologically abnormal nuclei are associated with reduced fertility potential. Similarly, abnormal acrosome morphology has been linked to decreased fertilization success, as it can hinder the sperm ability to penetrate the egg, emphasizing the clinical relevance of identifying both internal structures during sperm assessment. For these reasons, the sperm nucleus and acrosome size measurements are recommended by the WHO for chemically labeled sperm cells used in male fertility evaluation [25,26]. These two organelles are the most functionally significant subcellular structures relevant to fertilization, and their internal properties are not visually accessible using conventional label-free imaging. In contrast, abnormalities in the sperm tail are generally detectable using brightfield microscopy, which is routinely employed in IVF clinics. Since these features are already clinically visible without staining, applying interferometric imaging to them may not provide added diagnostic value. For these reasons, we focused on the nucleus and acrosome RI mapping.

Chemical labeling cannot be used during human IVF, and thus, so far, the WHO guidelines could not be fully implemented during human IVF. However, since label-free interferometric imaging has been recently implemented in clinical settings [27,28], RI measurements in sperm cells have become attainable for sperm cell selection in IVF. Since the cell RI may not be distinctive per each cell organelle, in order to apply the WHO morphological evaluation based on interferometric imaging, RI mapping is needed, especially for the nucleus and the acrosome. Cell refractometry has been previously performed for bovine sperm [29,30], which is different in structure and behavior compared to human sperm. Bovine sperm heads are larger, measuring approximately 9.1-9.2 µm in length and 5.0–5.2 µm in width, compared to the smaller and more variable human sperm heads measuring approximately 4-5.5 µm long and an average width of 3 µm [30,31]. This size difference directly reflects differences in nucleus and acrosome dimensions. In addition, morphological criteria for normal cells apply to 70% of bovine sperm, whereas only over 4% in human samples according to WHO guidelines [5]. This difference makes identification and localization of appropriate cell for fertilization more difficult and previous RI measurements done in animal sperm cells generally irrelevant for human IVF.

In contrast to these previous studies, our study presents human sperm refractometry. Furthermore, we combined IPM with confocal fluorescence microscopy allowing us to verify the sperm cell organelle locations and calculate the characteristic RI values of the different organelles. After trying to use regular fluorescence microscopy, which induces multi-plane fluorescence signals and unclear organelle borders, we switched to confocal fluorescence microscopy to accurately define the borders of the relevant organelles within the sperm head. The goal was to reject out-of-focus planes and obtain an in-focus fluorescence signal that would allow us to generate a precise mask of the nucleus for further training the machine learning model.

The method involves imaging the same cell in two solutions with different RIs, allowing for the decoupling of the cell integral RI and the cell thickness. A set of pixel-wise OPD-based features was then extracted from the OPD images, capturing local intensity, spatial, and textural information. These features were used to train a machine-learning model to predict the location of the nucleus within the sperm cell head without the fluorescent image counterpart, providing more reliable identification of subcellular sperm structures, with the potential to support better informed sperm selection in IVF procedures.

2. Methods

2.1. Theory

Off-axis IPM records the complex wave front of the sample by creating a slight angle between the sample and reference beams. The digital camera records the off-axis interference pattern, defined as following:

$$I_{sensor}={|E_s|}^2+{|E_r|}^2+2|E_s||E_r|\text{cos}({\phi }^{\prime }),$$ (1)

where $E_s$ represents the sample beam, $E_r$ represents the reference beam, and ${\phi }^{\prime }$ represents the phase shift between the beams. By subtracting the phase created by the off-axis angle in the reference beam, we can retrieve $\phi$ , which is the quantitative phase of the sample. It is proportional to the OPD of the sample, at pixel $(i,j)$ , as follows:

$$\phi (i,j)=\frac{2\pi }{\lambda }\cdot OPD(i,j),$$ (2)

where λ is the illumination wavelength. The reconstructed OPD at each pixel can be written as follows [22]:

$$OPD(i,j)=[n_{cell}(i,j)-n_m]\cdot h_{cell}(i,j),$$ (3)

where $n_{cell}(i,j)$ is the integral RI of the whole cell at pixel $(i,j)$ , $n_m$ is the RI of the surrounding medium at pixel $(i,j)$ , and $h_{cell}(i,j)$ is the thickness of the whole cell at pixel $(i,j)$ .

To solve the RI–thickness coupling problem in the OPD measurement, it has been proposed to perform interferometric measurements of the same cell in two different surrounding media with known RIs, $n_{m1}$ , $n_{m2}$ , obtaining two OPD profiles as follows:

$$\{\begin{array}{l}OP{D}_1(i,j)=h_{cell}(i,j)\cdot [n_{cell}(i,j)-n_{m1}]\\ OP{D}_2(i,j)=h_{cell}(i,j)\cdot [n_{cell}(i,j)-n_{m2]}.\end{array}$$ (4)

Thus, we obtain two equations with two variables for each pixel $(i,j),n_{cell}(i,j)$ and $h_{cell}(i,j)$ , allowing the uncoupling of the integral RI from the thickness profile of the cell [12–14] as follows:

$$\{\begin{array}{c}{n}_{cell}(i,j)=\frac{OP{D}_2(i,j)\cdot n_{m1}-OP{D}_1(i,j)\cdot n_{m2}}{OP{D}_2(i,j)-OP{D}_1(i,j)}\\ h_{cell}(i,j)=\frac{OP{D}_1(i,j)}{[n_{cell}(i,j)-n_{m1]}}.\end{array}$$ (5)

Regardless, the nucleus location can be determined by integrating quantitative phase imaging with fluorescence microscopy [16–21]. The sperm cell head contains two main components: acrosome and nucleus [23], where their OPD profiles can be expressed as follows:

$$OPD(i,j)=\{\begin{array}{c}[n_{nuc}(i,j)-n_m]\cdot h_{nuc}(i,j),\mathrm{\forall }(i,j)\in nucleus\\ [n_{acr}(i,j)-n_m]\cdot h_{acr}(i,j),\mathrm{\forall }(i,j)\in acrosome.\end{array}$$ (6)

where $h_{nuc}(i,j)$ and $n_{nuc}(i,j)$ are the thickness and RI distributions of the nucleus, respectively, $h_{acr}(i,j)$ and $n_{acr}(i,j)$ are the thickness and RI distributions of the acrosome, respectively, and $n_m$ is the RI of the surrounding medium. Therefore, by using Eq. (5) the integral RI of the nucleus and the acrosome can be expressed as follows:

$$n_{cell}(i,j)=\{\begin{array}{c}\frac{OP{D}_2(i,j)\cdot n_{m1}-OP{D}_1(i,j)\cdot n_{m2}}{OP{D}_2(i,j)-OP{D}_1(i,j)},\mathrm{\forall }(i,j)\in nucleus\\ \frac{OP{D}_2(i,j)\cdot n_{m1}-OP{D}_1(i,j)\cdot n_{m2}}{OP{D}_2(i,j)-OP{D}_1(i,j)},\mathrm{\forall }(i,j)\in acrosome.\end{array}$$ (7)

We applied this process on human sperm cells, as explained below.

2.2. Cell preparation

We obtained human sperm samples from donors, following approval from Tel Aviv University's Institutional Review Board (IRB), with signed consent obtained from the sperm donors. The raw semen was incubated at room temperature for 20 minutes before isolating the sperm cells using the PureCeption By-Layer Kit (ORIGIO, CooperSurgical, Måløv, Denmark), following the manufacturer's instructions. Following the isolation process, the cells were centrifuged at 2000 rpm for 20 minutes at ${23}^{\circ }\text{C}$ , and the supernatant was removed, leaving only the bottom pellet. 100 μL of phosphate-buffered saline (PBS) was added to the pellet to wash the cells, followed by gentle resuspension to ensure proper mixing. Afterward, 100 μL of the resuspended sample was transferred to a test tube containing 10 mL of PBS for further dilution and processing. The cells were centrifuged at 1500  rpm for 7 minutes at ${23}^{\circ }\text{C}$ , and the supernatant was removed again, leaving only the 100 μL of the bottom pellet.

To ensure the fluorescent stain effectively bound to the DNA within the nucleus, staining was performed before cell fixation. The cells were then labeled with 10 μL/mg Hoechst 33342 dye (Sigma-Aldrich, St. Louis, MO, USA) and incubated in the darkness for 30 minutes.

Following the staining procedure, the sperm cells were fixated to preserve their morphology and spatial arrangement throughout the imaging cycles. Fixation was performed by adding 12 mL of a 4:1 methanol-to-acetic acid solution. Initially, 5 mL of the fixative was added to the stained cells, followed by centrifugation at 2000 rpm for 5 minutes at ${23}^{\circ }\text{C}$ . After centrifugation, the supernatant was discarded, and the pellet was resuspended in 0.5 mL of fixative solution.

To prepare the dry samples, 10 $\mu \text{L}$ of the fixated sperm cell solution were placed on 50 × 24 mm microscope slide and left in a fume hood for 40 minutes to allow complete evaporation of the fixative solution. To prepare the sample in suspension, an adhesive (Grace Bio-Labs, Bend, OR, USA), 21.6 × 21.6 × 0.12 mm depth, which was placed on the dry sample microscope slide, and 60 μL of PBS was added to it.

2.3. Optical setup

The multimodal optical system used is shown in Fig. 1. It consists of a commercial inverted microscope (Olympus PlanApo N 60×/1.42 oil), along with an epi-illuminance fluorescence spinning-disk confocal imaging unit (CSU-X1, Yokogawa, Tokyo, Japan) and a custom-built external interferometric module integrated at the microscope's output.

Fig. 1.

Scheme of the combined IPM-confocal fluorescence system used for imaging. The IPM beams appear in red; The fluorescent excitation beam appears in blue; The fluorescent emission beam appears in purple; The BFM beam appears in gray. CO, condenser lens; MO, microscope objective; BS, beam splitter; L1, L2, L3, L4, L5, L6, L7, L8 lenses; SD spinning disk; DM dichroic mirror; C1, C2, digital cameras; DG, diffraction grating; Ma, mask; C, compensation glass; M, mirror; BE, blue emission; BF, brightfield.

To generate the OPD images, we used shearing interferometry with a constant off-axis angle module [32]. Helium-Neon (HeNe) laser beam at 633 nm passes through the condenser lens CO to illuminate the sample as a plane wave. The beam passes through the sample and is magnified by microscope objective MO (Olympus PlanApo N 60×/1.42 oil). By using beam splitter BS, the beam is reflected out of the microscope, passes through the lenses L1 (f = 200 mm), L2 (f = 100 mm), L3 (f = 100 mm) and enters to the interferometric module. As described in Fig. 1, the module consists of diffraction grating DG with 100 lines/mm, which produces two laterally shifted sample beams. The diffracted beams are then focused by lens L4 (f = 150 mm). A mask is positioned at L4 focal plane to choose the zeroth and a single first diffraction order beams and a glass plate phase compensator C is placed in the path of the first-order beam. The two diffraction orders are then directed into L5 (f = 300 mm). Subsequently, the beam passes through an additional magnifying 4f configuration composed of L6 (f = 50 mm) and L7 (f = 180 mm). Finally, an off-axis image hologram is created on an ultrafast digital camera C2 (FASTCAM Mini AX200, Photron; square pixels of 20 $\mu \text{m}$ each, 1024 × 1024 pixels), which is then used to generate the OPD map.

For fluorescence confocal imaging, excitation laser light is generated by a multi-line laser source LC (VS-Laser Control, Visitron Systems, Puchheim, Germany), which includes a 405 nm laser for Hoechst excitation. The spinning-disk (SD) includes dichroic mirror (DM) separating the excitation light from the emitted fluorescence. The Hoechst-labeled nucleus emits blue fluorescence, which is magnified by MO and transmitted via BS back to the SD and DM. DM then redirects the emitted light toward tube lens L8 (f = 200 mm), projecting it onto camera C1 (acA2440-75um, 5 Megapixels, 2448 × 2048 square pixels of 3.45 µm, Basler, Ahrensburg, Germany), which captures the spatial distribution of the Hoechst fluorescence signal.

In parallel, for bright-field microscopy (BFM), LED light enters the microscope and passes through the condenser lens CO. The beam then traverses the sample and is magnified by the microscope objective MO. The transmitted light is subsequently projected onto camera C1, capturing the brightfield image. To ensure the same cell is imaged in two different surrounding media with two different RIs, the (X, Y, Z) coordinates of the stage are recorded for each cell.

Examples of the acquired images using the system are presented in Fig. 2.

Fig. 2.

Images of sperm cell acquired using the multimodal imaging system presented in Fig. 1. (a) Brightfield image of the cell. (b) Fluorescence image of the labeled nucleus. (c) Digital holograms of the sperm cell in different media (air and PBS). The white scale bar indicates $5\mu \text{m}$ .

2.4. Image processing

2.4.1. OPD reconstruction

Digital reconstruction of the sample's OPD from the captured hologram was performed using the off-axis Fourier-based algorithm implemented in Python program [33]. This algorithm involves applying a two-dimensional (2D) Fourier transform to the off-axis sample hologram, followed by cropping one of the cross-correlation terms and performing a 2D inverse Fourier transform. The argument of the resulting complex wave-front matrix represents the wrapped phase of the sample. To compensate for beam curvatures and stationary aberrations in the beam profile, the wrapped phase extracted from a hologram captured without a sample was subtracted from the sample’s wrapped phase. The Miguel’s phase unwrapping algorithm [34] was then applied to resolve 2π phase ambiguities. Finally, the unwrapped quantitative phase map was multiplied by the wavelength and divided by 2π to obtain the OPD map of the sample. Figure 3 shows the reconstructed OPD images of a sperm cell acquired in PBS media surrounding (a) and in air (b).

Fig. 3.

Reconstructed OPD images from the digital holograms presented in Fig. 2. (a) OPD image of the sperm cell in PBS media surrounding. (b) OPD image of the same sperm cell in air. The color bar represents the OPD values in nm. The white scale bar indicates $5\mu \text{m}$ .

2.4.2. Image registration

The RI of the nucleus and the acrosome was reconstructed from images taken using two different cameras, hence, image registration was needed. In order to perform the image registration, silica beads (5-µm spheres, silicon dioxide, Sigma-Aldrich) were imaged both by IPM and BFM using the commercial microscope and the same camera used for the confocal microscopy images. The scaling factor was extracted by measuring the diagonal between the two beads. Further next, prior to the imaging of the cells using IPM and confocal microscopy, BFM images of the cells were taken. The stages of the image registration were resizing the IPM images to the same size of the BFM images, rotating them, and calculating the pixel shift to align the images. The pixel shift calculation process began with segmentation, binarization and hole filling. Next, the connected components were labeled, and the largest region in each image was identified. The centroids of these regions were then computed, and the shift vectors between the centroids of the images were found. Finally, the images were shifted accordingly to bring the cells into the same spatial reference frame. This process just has to be performed once. The parameters found in this registration process were used to perform the registration on the confocal fluorescence images and the OPD images.

2.4.3. Pixel-wise organelle classification via machine learning

As a preparatory step for training a machine learning model, we first constructed a dataset containing only the pixel-wise information corresponding to the sperm cell regions surrounded in PBS, using the OPD maps acquired through the methods described above. To determine for each individual pixel whether it belongs to the nucleus or not, we extracted features and labels at the pixel level. To capture local structural variation and spatial context, each feature was computed not only from the pixel itself but also from its surrounding pixels. This allowed us to represent local changes in morphology and texture that were critical for distinguishing subcellular regions. The labels for each pixel were derived from the corresponding nucleus fluorescence images, which were used to segment and localize the nucleus within each cell.

Let $OP{D}_c(i,j)$ be the OPD value of the cell at pixel $(i,j),$ and $N_{i,j}$ be the indices of the 3 × 3 pixels centered around pixel $(i,j).$ The following parameters are based directly on the OPD map defined in Eq. (3), without prior uncoupling of the cellular thickness profile from the integral RI:

Local mean: Average value of $OP{D}_c$ at $N_{i,j}$ :

$${\mu }_{local}=\frac{1}{9}{\sum }_{(i,j)\in N_{i,j}}OP{D}_c(i,j).$$ (8)

Local standard deviation: Standard deviation of $\text{OP}{\text{D}}_{\mathrm{c}}$ at ${\text{N}}_{\text{i},\text{j}}$ :

$${\sigma }_{local}=\sqrt{\frac{1}{9}{\sum }_{(i,j)}{(OP{D}_c(i,j)-{\mu }_{local})}^2}.$$ (9)

Total OPD: The sum of the $OP{D}_c$ values at $N_{i,j}$ :

$$TotalOPD={\sum }_{(i,j)\in N_{i,j}}OP{D}_c(i,j).$$ (10)

Variance of OPD: A parameter that measures how a set of $OP{D}_c$ values is spread out:

$$VarOPD=\frac{1}{9}{\sum }_{(i,j)\in N_{i,j}}{(OP{D}_c(i,j)-{\mu }_{local})}^2.$$ (11)

Skewness of OPD: A parameter that quantifies the asymmetry of $OP{D}_c$ relative to its mean value:

$$SkewOPD=\frac{1}{9}{\sum }_{(i,j)\in N_{i,j}}{\left(\frac{OP{D}_c(i,j)-{\mu }_{local}}{{\sigma }_{local}+ϵ}\right)}^3.$$ (12)

Kurtosis of OPD: A parameter that indicates whether $OP{D}_c$ is sharply peaked or more uniformly spread:

$$KurtosisOPD=\frac{1}{9}{\sum }_{(i,j)\in N_{i,j}}{\left(\frac{OP{D}_c(i,j)-{\mu }_{local}}{{\sigma }_{local}+ϵ}\right)}^4.$$ (13)

Gradient magnitude: A parameter that quantifies the rate of change (via local derivatives) in OPD values around each pixel. It reflects how sharply the OPD varies spatially and helps identify structural boundaries within the cell:

$$Gradient=\sqrt{{\left(\frac{\partial OP{D}_c}{{\partial }_x}\right)}^2+{\left(\frac{\partial OP{D}_c}{{\partial }_y}\right)}^2}.$$ (14)

Gabor mean: This parameter measures the average response of the $N_{i,j}$ pixels to a Gabor filter, capturing local texture patterns aligned with a specific frequency and orientation:

$${\mu }_G(i,j)=\frac{1}{9}{\sum }_{(i,j)\in N_{i,j}}Re[G(i,j;f)].$$ (15)

where $Re[G(i,j;f)]$ is the real part of the Gabor filter response at pixel $(i,j)$ , for a given frequency f [35].

Gabor STD: This parameter quantifies the variability of the Gabor filter response within a local neighborhood, indicating texture complexity:

$$GaborSTD=\sqrt{\frac{1}{9}{\sum }_{(i,j)\in N_{i,j}}{(Re[G(i,j;f)]-{\mu }_G(i,j))}^2}.$$ (16)

Further next, the GLCM-based texture features [36,37] were calculated, capturing statistical patterns in the spatial relationships between pixel intensities to characterize local texture.

Energy: Let $GLCM(i,j)$ be the normalized gray-level co-occurrence matrix for the $N_{i,j}$ pixels. Energy describes the cell texture by indicating the homogeneity of the OPD distribution and the coarseness of its structural patterns:

$$Energy={\sum }_{i,j}GLCM{(i,j)}^2.$$ (17)

Entropy: This parameter describes the non-uniformity and complexity of the cell texture.

$$Entropy={\sum }_{i,j}GLCM(i,j)\cdot log(GLCM(i,j)+ϵ).$$ (18)

Contrast: This parameter indicates the sharpness of structural transitions within the cell and the depth of texture variations:

$$Contrast={\sum }_i{\sum }_j{(i-j)}^2\cdot GLCM(i,j).$$ (19)

Homogeneity: This parameter captures the uniformity of cell texture and quantifies the extent of local variations. Higher homogeneity values indicate minimal intra-regional changes and a more consistent texture distribution within the cell.

$$Homogeneity={\sum }_{i,j}\frac{GLCM(i,j)}{1+{(i-j)}^2}$$ (20)

For the task of pixel-wise classification, the classifier was developed using a Support Vector Machine (SVM), a widely used machine learning algorithm that relies on feature-based classification. SVM aims to identify an optimal hyperplane within the feature space that clearly separates different data classes [38]. It is known for achieving high classification accuracy with efficient computation [39], and its performance remains robust regardless of the dataset size or the dimensionality of the feature space. Two SVM models were trained: one using OPD-based features and the other using features extracted from brightfield microscopy images. This comparison was performed on the same features to evaluate the added value of OPD-based imaging for predicting the location of the nucleus within the sperm cell head.

Principal component analysis (PCA) was applied as a standard technique for dimensionality reduction and to improve feature separability. PCA projects the original feature set onto a new set of orthogonal axes, where each principal component is a linear combination of the original features. Previous studies have shown that combining PCA with SVM can lead to improved accuracy by reducing the number of misclassified instances [40–42]. During training, all features were used as input to PCA, which identified the most informative linear combinations of features to distinguish between the acrosome and nucleus. In this work, we selected the first 8 components to serve as the input representation.

The classification performance was evaluated using sensitivity, specificity, precision, F1-score, and the area under the receiver operating characteristic curve (AUC-ROC). Each model was trained on 80% of the data and tested on the remaining 20%. Training was performed using 10-fold cross-validation [43].

3. Results

OPD profiles of 42 human sperm cells were measured in two surrounding media with different RIs. The cells were imaged using both IPM and the 2D confocal fluorescence microscopy. The fluorescent signal was recorded in order to obtain 2D segmentation of the cell organelles in the OPD profiles. Figure 4 shows the result of the segmented OPD both for the nucleus and the acrosome in two media.

Fig. 4.

Stages in extraction of the integral RI of the sperm cell nucleus from the combined IPM/fluorescence measurements in two media. (a,e) Reconstructed OPD image of the sperm cell head in air and PBS, respectively. (b,f) Reconstructed OPD image without nucleus as found from the fluorescence image in air and PBS, respectively. (c,g) Reconstructed OPD image of the segmented nucleus in air and PBS, respectively. (d,h) Reconstructed OPD image of the acrosome in air and PBS, respectively. The color bar represents the OPD values in nm. The white scale bar indicates $5\mu \text{m}$ .

Using Eq. (6), we calculated the integral RI of each compartment and the average RI. Figure 5 shows the integral RI values for the nucleus and the acrosome for 42 cells. For the nucleus ${\text{n}}_{\text{nuc}}$ = 1.46 $\pm$ 0.05, and for the acrosome ${\text{n}}_{\text{ac}}=$ 1.38 $\pm$ 0.04. This result demonstrates that the nucleus has indeed higher RI values than the acrosome, which aligns with the expectations based on its denser protein composition compared to the vesicle-like structure of the acrosome. Furthermore, the values align with those found in previous studies in different species [30]. Although the average RI values of the nucleus and the acrosome differ significantly (p-value < 0.00005), the overlap between their distributions makes it difficult to separate the organelles based on RI alone. To address this, we trained a machine learning model based on SVM that uses additional spatial and texture features from the phase images to improve classification of the nucleus region.

Fig. 5.

Histogram of the average RI values of the nucleus and the acrosome.

The 42 OPD maps of the sperm cells surrounded by PBS medium and their paired nucleus segmented areas marked as labels were used to train the machine learning model. We applied Eqs. (8)-(20) to the cell OPD area. Figure 6 shows the histograms of each of 13 features for which the two groups of organelles compared were statistically significant. All these parameters are statistically significant based on p-values of 0.05, < 0.005, and <0.0005.

Fig. 6.

Histograms of the parameters based the OPD maps for the nucleus (blue) and the acrosome (red): (a) Local mean, (b) Local STD, (c) Gradient magnitude, (d) Total OPD, (e) Variance of OPD, (f) Skewness of OPD, (g) Kurtosis of OPD, (h) Gabor mean, (i) Gabor STD, (j) Energy (k) Entropy. (l) Contrast (m) Homogeneity. * denotes p-value < 0.05, ** denotes p-values <0.005 and *** denotes p-values <0.0005.

13 features were used as input for automatic pixel-wise classification via support vector machine (SVM) to predict the nucleus location within the OPD map. Two models were trained: one incorporating the OPD-based features (Eqs. (8)-20) of the nucleus and the acrosome, and one that uses the same features extracted from brightfield images of the same cells, where we calculated mean local, std local, total intensity, variance, skewness, kurtosis, gradient magnitude, Gabor mean, Gabor STD, energy, entropy, contrast, homogeneity. Figure 7 shows the ROC curves for each model (OPD-based vs. brightfield) across all cells. The model that included the OPD-based features achieved higher classification accuracy, with a greater area under the curve (AUC), demonstrating its improved performance over the model without the OPD-based features.

Fig. 7.

ROC curves of true-positive rate (sensitivity) versus false-positive rate (1 – specificity) for the two SVM models. (a) The blue curve represents the model trained with OPD-based features. (b) The red curve corresponds to the model trained with brightfield-based features.

The confusion matrices presented in Fig. 8 compare the performance of the two SVM models-using the OPD-based features (a) and using the brightfield-based features (b). The OPD-based model shows improved classification, with an increase in correctly identified nucleus pixels from 115 to 492 and a reduction in false positives from 214 to 36. The OPD-based features demonstrated a substantial reduction in both false positives and false negatives, resulting in improved overall accuracy. The brightfield model, on the other hand, shows higher confusion between nucleus and the acrosome, which supports the significant contribution of the OPD to distinguish the subcellular classification.

Fig. 8.

Confusion matrices as obtained using the SVM classification using (a) the OPD-based features, and (b) the brightfield-based features.

Table 1 summarizes the results obtained using the SVM learning combined with PCA for each pair of cells, with the AUC and the matching working points (sensitivity/specificity) chosen on the ROC curves.

Table 1. Machine-learning classification results between the groups (PCA/SVM analysis). AUC = Area under curve.

	Accuracy (%)	Sensitivity (%)	Specificity (%)	AUC
IPM-Based Model	92	89	94	97
BFM-Based Model	65	82	60	80

4. Discussion and conclusions

Improving the assessment and selection of sperm cells is essential for increasing the success rates of ART in general and ICSI in particular. Traditional methods rely on the visual evaluation of external sperm morphology using brightfield microscopy, which is subjective and lacks the ability to reveal internal structures. Our study introduces a novel framework that enables objective, label-free subcellular analysis of human sperm cells based on their RI profiles and optical phase signatures.

To obtain this, we have presented a label-free method that combines IPM with confocal fluorescence microscopy to map and classify subcellular components of the sperm cell, particularly the nucleus and the acrosome. Dual-medium imaging, utilizing two surrounding solutions with different known RI, enabled the decoupling of the cell’s OPD into its integral RI values. We were able to measure the integral RI distributions of the nucleus and the acrosome of the human sperm cell. This was achieved by combining BFM, IPM and 2-D fluorescence microscopy. We performed imaging of human sperm cells surrounded in two media of different RIs, and it allowed us to retrieve separately the RI of the sperm cell head structures. The results are aligned with the expected RI values of the nucleus and the acrosome as the nucleus is packed with DNA and other proteins, the acrosome is vesicular and fluid-filled, exhibits an RI closer to that of water. Despite cell fixation, the RI contrast between the subcellular structures remains distinguishable, as shown by previous studies [23]. Thus, the fixation process does not compromise the primary optical signature used for classification between the organelles. The model was trained on data of sperm cells surrounded by cell medium PBS, which mimics the optical environment of IVF media and thus it helps maintaining physiologically relevant OPD contrast and supports translational applicability. Since IPM operates with a single camera exposure, it is also suitable for analyzing sperm motility [44].

Even though during this research we labeled the cell as a learning and verification stage, the classification results are solely based on a prediction done on a label-free OPD profile of the cell, that can be acquired in IVF clinics and used for sperm assessments.

The OPD-based features revealed the potential to enhance objective sperm selection in IVF clinics and guided the development of a machine learning model for identifying subcellular structures in label-free images that can be acquired in clinical settings. We extracted 13 hand-crafted features for each pixel such as local statistical descriptors, Gabor filter responses, and GLCM texture features designed to capture local structure, optical density, and texture variations that differ between the acrosome and nucleus. Pixel-wise ground truth labels were derived from fluorescence image segmentations, enabling supervised learning. Two SVM classifiers were trained: one using features extracted from label-free OPD images, and another using the same features extracted from label-free brightfield microscopy images. The models were trained using 80% of the data and evaluated on the remaining 20%, with 10-fold cross-validation used during training. PCA was applied to reduce feature dimensionality and enhance classification performance. The OPD-based model achieved a sensitivity of 89% and specificity of 94%, compared to 82% and 60%, respectively, for the brightfield-based model. Our results demonstrate that integrating OPD derived features provide stronger discriminative power for identifying subcellular regions in label-free sperm images.

This framework offers a scalable alternative to manual label-free sperm selection in clinical IVF workflows. By identifying structurally intact, morphologically optimal sperm cells at the subcellular level, our method may contribute to improved fertilization outcomes. By providing this additional layer of information, we can bridge the gap between IVF clinics and quantitative, label-free sperm analysis, enabling more objective selection criteria for assisted reproduction. Moreover, it can help reduce the subjectivity and variability in current practices, offering a path toward fully automated sperm analysis.

In conclusion, we have proposed a label-free imaging and classification approach for subcellular sperm analysis using interferometric microscopy and machine learning. Our framework accurately distinguishes between the acrosome and nucleus based on combined RI and phase-derived features. Our approach lays the foundation for automatic, objective, and label-free sperm analysis at the individual cell level, with the potential for improving IVF procedures. Future work will focus on real-time implementation, scaling to higher-throughput imaging systems, and expanding the classification framework to identify additional sperm features relevant to embryologist selection in IVF.

Funding

Zimin Foundation 10.13039/100030886.

Disclosures

The authors declare no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.