3.1.

Experimental Setup

The detailed experimental setup for measuring E-fields with various illumination angles has been described in previous works.^40,43 Briefly, complex E-fields images are recorded by Mach–Zehnder interferometry. A laser beam from a He-Ne laser ($\lambda =633\mathrm{nm}$, 10 mW, unpolarized light, Throlabs, Newton, New Jersey) is split into two arms. One arm can be tilted by a galvano mirror (GVS012, Throlabs) and illuminates samples with various angles of illuminations. The diffracted beam from the sample is collected by a high NA objective lens (UPLSAPO, $100\times$, $\mathrm{NA}=1.4$, Olympus Inc., Center Valley, Pennsylvania) and a tube lens ($f=200\mathrm{mm}$). Then, the beam is further magnified by an additional $4f$ lens system so that the total lateral magnification is $210\times$. The diffracted beam from the sample interferes with a reference beam and generates spatially modulated interferograms, which are recorded by a high-speed CMOS camera (1024 PCI, Photron USA Inc., San Diego, California). Typically, 600 2-D holograms of the sample, illuminated by plane waves with illumination angles ($-70\mathrm{deg}$ to 70 deg at the sample plane), are recorded for the reconstruction of one tomogram.

The complex amplitude (amplitude and phase) of the E-fields images is then extracted from the measured interferograms using the field retrieval algorithm (see Ref. 51 for field retrieval algorithms). Diffraction tomograms are mapped in 3-D Fourier space using multiple 2-D E-field images, and then reconstructed by using a 3-D inverse Fourier transformation (refer to Supporting Materials for the MatLab code used for the reconstruction). The projection tomograms are reconstructed from the sequential E-fields maps with various illumination angles via inverse Radon transformation.

Due to the limited angle of acceptance of the imaging system, or NA, there is missing information in the 3-D Fourier spectrum for both the projection and diffraction algorithms [Fig. 1(b) and 1(c)]. Even with the high NA objective lens, only a fraction of the scattered light from the sample can be utilized for optical imaging. To fill this information due to the limited NA, the iterative constraint algorithm^43,52 was executed to the tomograms reconstructed from both the projection and diffraction algorithms. The following constraints were invoked in the interactive algorithm in the present study:

Applying the iterative algorithm fills the information corresponding to the missing angles with appropriate values. All data analysis was performed using custom-made scripts in MatLab (MathWorks Inc., Natick, MA) on a desktop computer (Inter Core i5-2600 CPU, 3.4 GHz, 8 GB RAM). The MatLab codes used for optical tomographic reconstruction based on diffraction algorithm are included in Supporting Information S1. The computation times for reconstructing a 3-D RI tomogram (size of $380\times 380\times 380$ matrix) are typically 100 and 200 s for the projection and diffraction algorithms, respectively. The iterative algorithm takes approximately 100 iterations for the diffraction algorithm, corresponding to $\sim 3000$-s computation time, whereas the projection algorithm takes approximately 15 iterations (3000-s computation time.)

3.2.

Sample Preparation

P. falciparum (3D7) parasites were maintained in leukocyte-free human $\mathrm{O}+$ erythrocytes (Research Blood Components, Boston, Massachusetts), stored at 4°C for no longer than two weeks under an atmosphere of 3% ${\mathrm{O}}_2$, 5% ${\mathrm{CO}}_2$, and 92% ${\mathrm{N}}_2$ in RPMI 1640 medium (Gibco Life Technologies, Carlsbad, California) supplemented with 25 mM HEPES (Sigma-Aldrich, St. Louis, Missouri), 200 mM hypoxanthine (Sigma-Aldrich), 0.209% ${\mathrm{NaHCO}}_3$ (Sigma-Aldrich) and 0.25% albumax I (Gibco Life Technologies). Cultures were synchronized successively by a concentration of mature schizonts using plasmagel flotation⁵³ and sorbitol lysis 2 h after merozoite invasion to remove residual schizonts.⁵⁴ The sample preparation procedures and the methods were approved by the Institutional Review Board.

Upon measurement, Pf-RBC samples were first diluted in phosphate-buffered saline (PBS) solution to approximately ${10}^6\mathrm{RBC}/\mathrm{ml}$. Ten microliters of the diluted samples were sandwiched between two cover glasses. Measurements were performed at 14 to 20 h (ring stage), 20 to 36 h (trophozoite stage), and 36 to 48 h (schizont stage) following merozoite invasion.

4.1.

3-D RI Tomograms of Pf-RBCs Based on Diffraction Algorithm

The 3-D RI tomograms of 26 Pf-RBCs were measured throughout the full intraerythrocytic states (8, 13, and 5 cells for ring, trophozoite, and schizont stages, respectively) For each individual Pf-RBC, 600 E-field holograms with various illumination angles ($-70\mathrm{deg}$ to $+70\mathrm{deg}$) were measured from which both projection and diffraction tomograms were reconstructed by respective algorithms. The projection and diffraction tomograms from the representative Pf-RBCs at each intraerythrocytic state are shown in Figs. 2Fig. 3–4.

Fig. 2

Refractive index (RI) maps of a Pf-RBC at the ring stage. (a–c) $x–y$ cross-sectional slices of RI distribution mapped with the projection algorithm at (a) 1 μm above the focal plane, (b) the focal plane, and (c) the $x–z$ plane at the center. (d–f) Slices of RI distribution mapped with the diffraction algorithm. Green arrow indicates malaria parasite. Each dashed line stands for corresponding slices. Scale bar indicates 5 μm.

Fig. 3

RI maps of a Pf-RBC at the trophozoite stage. (a–c) $x–y$ cross-sectional slices of RI distribution mapped with the projection algorithm at (a) 1 μm above the focal plane, (b) the focal plane, and (c) the $x–z$ plane at the center. (d–f) Slices of RI distribution mapped with the diffraction algorithm. Black arrow indicates hemozoin. Scale bar indicates 5 μm.

Fig. 4

RI maps of a Pf-RBC at the schizont stage. (a–c) $x-y$ cross-sectional slices of RI distribution mapped with the projection algorithm at (a) 1 μm above the focal plane, (b) the focal plane, and (c) the $x-z$ plane at the center. (d–f) Slices of RI distribution mapped with the diffraction algorithm. Black arrow: hemozoin and blue arrow: plasmodium vacuoles. Scale bar indicates 5 μm.

Each figure shows cross-sectional maps of the 3-D RI tomograms reconstructed by either the projection (upper row) or the diffraction algorithm (lower row) at various planes: 1 μm above the focal plane (left column), the focal plane (center column) along the axial direction, and $x-z$ plane at the center of the sample (right column). Since the cytoplasm of RBCs consists mainly of Hb, cytoplasmic Hb concentration for individual RBCs can be calculated from the measured RI.⁸ The RI of Hb solution is directly related to the concentration of Hb.^55,56 The real part of the RI $n$ is proportional to the cytoplasmic Hb concentration $C$ as

The 3-D RI tomograms of Pf-RBCs at the ring stage clearly show a ring-shaped internal structure inside the host Pf-RBC, which corresponds to an invaded parasite having an RI smaller than that of the cytoplasmic area (green arrows, Fig. 2). At the focal plane, both diffraction and projection algorithms provide comparable structures. However, above and below the focal plane, the tomogram reconstructed with the projection algorithm shows blurry cell boundaries that are extended in the axial direction, whereas the diffraction tomogram shows more distinct cell boundaries. More importantly, cross-section images reconstructed by the projection algorithm provide incorrectly elongated shapes in the $z$-direction [Fig. 2(c)]. This is due to the omission of light diffraction in the projection algorithm; light diffraction at the RBC boundaries can be only taken into account in the diffraction reconstruction algorithm. Considering the complex shape of the RBC membrane and the RI difference between the surrounding medium and the cell cytoplasm ($\sim 0.04$ to 0.06, depending on the Hb concentration), the plane wave impinging into the RBC may exhibit both refraction and reflection, thus resulting in significant diffraction of the transmitted beam. The RI tomogram of Pf-RBCs not only shows morphological information regarding the cell and its subcellular structures, but also enables us to obtain the biochemical information of the Pf-RBCs; the cytoplasmic RI can be directly translated into quantitative information about Hb concentration and total Hb contents.⁸

The effect of light diffraction becomes more significant in the later stages. The 3-D RI tomograms of the Pf-RBCs at the trophozoite stage show more difference between the reconstructions with the projection and diffraction algorithms (Fig. 3). Distinct differences can be observed, especially for the extremely high RI values in the cytoplasm, indicating the hemozoin structure (black arrows, Fig. 3). As they grow inside the host RBCs, the parasites metabolize Hb and produce hemozoin—an insoluble crystallized form of free heme, the nonprotein component of Hb, having a high RI ($n\ge 1.42$). At the trophozoite stage, the overall shape of the Pf-RBCs membrane becomes more complex, and malaria byproducts are newly generated as substructures with significantly high RI values and with a high spatial gradient.

The 3-D RI tomograms of the Pf-RBCs in the schizont stage show significantly decreased RI in the cytoplasm (Fig. 4), which is consistent with a previous report.⁸ The 3-D RI tomograms reconstructed with the diffraction algorithm clearly show plasmodium vacuoles generated by the parasites (blue arrows). By contrast, the tomogram reconstructed with the projection algorithm does not provide high-resolution details on these subcellular structures.

The structural and biochemical alterations resulting from the parasitization of the host Pf-RBC inevitably cause significant light diffraction from the sample. Severe structural alterations in the schizont stage Pf-RBCs can result in more light diffracted in the Pf-RBCs. In addition, significant reorganization of Hb proteins can also contribute more light diffraction; most of the cytoplasmic Hb is digested by the parasites, and then converted into hemozoin with high RI values. The use of the diffraction reconstruction algorithm could provide more precise 3-D RI tomograms. On the other hand, the projection algorithm does not support the appearance of light diffraction from the sample. As shown in Figs. 2–4, the reconstruction with the diffraction algorithm provides more precise 3-D RI tomograms of the Pf-RBCs with finer details. For comparison purposes, the projection and diffraction tomograms from healthy RBCs are also shown in Fig. 5. Similar to the Pf-RBCs, the tomograms of the healthy RBCs reconstructed by the diffraction algorithm show less distortion in their shapes than the ones obtained with the projection algorithm.

Fig. 5

RI maps of a healthy RBC. (a–c) $x–y$ cross-sectional slices of RI distribution mapped with the projection algorithm at (a) 1 μm above the focal plane, (b) the focal plane, and (c) the $x–z$ plane at the center. (d–f) Slices of RI distribution mapped with the diffraction algorithm. Scale bar indicates 5 μm.

Based on the tomograms of the Pf-RBCs reconstructed by the diffraction algorithm, 3-D isosurfaces are rendered, as shown in Fig. 6 (see also Multimedia movies). The cell membranes of the Pf-RBCs are represented for the outer surface having the cytoplasmic RI; subcellular structures such as hemozoin, plasmodium vacuoles, and malaria parasites are also visualized as surfaces by connecting the specific refractive indices. The 3-D RI tomogram reconstructed with the diffraction algorithm shows the shapes and locations of the parasites as well as other associated structures in high detail. Rendering was performed by commercial software (Amira 5, Visage Imaging Inc., San Diego, California). The structures of Pf-RBCs depicted in 3-D RI tomograms are comparable with those obtained with high-resolution scanning electron microscopy.^4,5

Fig. 6

Rendering of the RI isosurfaces of Pf-RBCs at (a) the ring (Video 1, QuickTime, 4 MB) [URL: http://dx.doi.org/10.1117/1.JBO.19.1.011005.1], (b) the trophozoite (Video 2, QuickTime, 6 MB) [URL: http://dx.doi.org/10.1117/1.JBO.19.1.011005.2], and (c) the schizont stage (Video 3, QuickTime, 6 MB) [URL: http://dx.doi.org/10.1117/1.JBO.19.1.011005.3]. The length of arrows corresponds to 1 μm.

4.2.

Cytoplasmic Volumes Calculated by Different Reconstruction Algorithms

Compared with the projection tomogram, the diffraction tomograms of 3-D RI of the Pf-RBCs not only provide high-resolution structural details, but also enable the determination of biochemical information about the Hb content with higher precision. To quantitatively compare the effects of using the different reconstruction algorithms with respect to chemical information, we calculated the cytoplasmic volume and mean cellular Hb concentration (MCHC) values of the Pf-RBCs with both the projection and diffraction tomograms. The cytoplasmic volume and MCHC values are important parameters for hemodiagnosis.

The MCHC values of each Pf-RBC calculated from the reconstructed RI tomograms do not show statistical differences between the projection and diffraction algorithms. This can be readily understood by the fact that, in principle, both algorithms should give comparable RI values of an object at the focal plane since the effect of diffraction of the propagated beam is minimized at the focal plane. The cytoplasmic volumes, however, show significant differences between the projection and diffraction algorithms (Fig. 7). Overall, the mean cytoplasmic volumes calculated from the projection algorithm are 33% higher than those calculated from the diffraction algorithm. In addition, the values retrieved with the diffraction algorithm showed narrower distribution among the Pf-RBCs. The difference in the values of cytoplasmic volume calculated by different reconstruction algorithm can be explained by the fact that, in the projection algorithm, the diffraction of light is not considered except at the focal plane, and thus, the reconstructed shapes of the RBC membrane can be severely distorted.

Fig. 7

Cytoplasmic volumes calculated by different reconstruction algorithms. Circular symbols represent individual Pf-RBCs. Dashed lines connect the values of the same cell calculated with the different algorithms. The cross symbols represent the median values, and the vertical lines indicate standard deviations.

4.3.

Volumes of Pf-RBC, Cytoplasm, and Parasitophorous Vacuole at Individual Cell Level

To address the structural alterations of Pf-RBC during intraerythrocytic cycle, we calculate the volumes of host Pf-RBC, RBC cytoplasm, and parasite at individual cell levels, from the measured 3-D RI tomograms reconstructed by diffraction algorithm based on the Rytov approximation (Fig. 8). Since the 3-D RI tomograms provide quantitative information about morphologies of individual Pf-RBCs, the volumes of Pf-RBC, cytoplasm, and parasite are measured at the individual cell level.

Fig. 8

Measured values of (a) Pf-RBC volume, (b) cytoplasmic volume, and (c) parasite volume over intraerythrocytic cycle. Measured values from previous reports were also shown for comparison purpose.

The whole host Pf-RBC volumes were calculated by integrating volumes inside individual Pf-RBCs. The cytoplasmic volumes were obtained by integrating volumes in which RI values are within a specific range ($1.34\le n\le 1.42$) in order to select cytoplasm-containing Hb solution, and the space corresponding to parasitophorous vacuoles (with hemozoin inside) was excluded. Then, the volumes for parasitophorous vacuole were calculated by subtracting the whole host Pf-RBC volumes from cytoplasmic volumes.

Despite the large cell-to-cell variations in the measurements, it is clear from the results that the total volumes of Pf-RBCs increase as the intraerythrocytic stage progresses. The mean values of the total Pf-RBCs volumes are $117.6\pm 17.7$ fl (ring), $106.9\pm 17.4$ fl (trophozoite), and $132.7\pm 29.7$ fl (schizont) [Fig. 8(a)]. This increase of total Pf-RBC volumes is caused by the enlargement of parasite volumes even though cytoplasmic volume, corresponding to host cell water volume, decreases. Cytoplasmic volumes (host cell water volume) are measured to be $105.0\pm 18.3$ fl (ring), $65.3\pm 20.7$ fl (trophozoite), and $56.0\pm 14.0$ fl (schizont) [Fig. 7(b)]. The mean values of the parasitophorous vacuole volumes are $12.7\pm 8.3$ fl (ring), $40.3\pm 16.0$ fl (trophozoite), and $75.90\pm 30.3$ fl (schizont) [Fig. 7(c)].

Our results are in good agreement with the previous measurements obtained with independent techniques (Fig. 8). Zanner et al. reported cytoplasmic volumes and Pf-RBC volumes measuring diffusive water permeability using stopped-flow spectroscopy.⁵⁷ Elliott et al. measured the transport of lactate and pyruvate in Pf-RBC,⁵⁸ and employed serial thin-section electron microscopy and 3-D reconstruction⁵⁹ in order to measure whole Pf-RBC volumes as well as parasite values. Recently, Esposito et al. measured total RBC volumes using confocal microscopy.⁶⁰ More recently, Hanssen et al. determined parasitophorous volumes of Pf-RBCs using cryo x-ray tomography.⁴ Although the previous techniques have measured the values at different time scales with different sensitivities, their values of the total Pf-RBCs volumes are 75 to 100 fl (ring), 130 to 150 fl (trophozoite), and 50 to 160 fl (schizont). Previously measured cytoplasmic volumes are 75 to 100 fl (ring), 25 to 100 fl (trophozoite), and 10 to 80 fl (schizont) [Fig. 8(b)]. The previously measured values of the parasitophorous vacuole volumes are 5 to 20 fl (ring), 5 to 50 fl (trophozoite), and 30 to 100 fl (schizont). In addition, our measured values are also consistent with mathematical model simulations.⁶¹

4.4.

3-D RI Tomograms of In Situ Formation of Hemozoin Crystals

To further show the capability of 3-D optical tomograms with the diffraction reconstruction algorithm, we perform in situ 3-D imaging and structural analysis of the residual bodies containing subcellular hemozoin in Pf-RBCs. Hemozoin is a disposal product formed by the malaria parasites as a result of the metabolization of Hb. It accumulates as cytoplasmic crystals in the food vacuole of developing parasites. As Pf-RBCs mature from ring stage to trophozoite stage, hemozoins become detectable as brown birefringent crystals via light microscopy⁶². No hemozoin is observed at the ring stage.

The shape and size of hemozoin provide metabolic information of individual Pf-RBCs.⁶³ Different structural characteristics of hemozoin crystals have been observed for Plasmodium species.⁶⁴ From the measured 3-D optical diffraction tomograms of the Pf-RBCs, we analyzed hemozoin structures and their optical properties in 16 Pf-RBCs (12 trophozoites and 4 schizonts). By selecting positions having RI values higher than a threshold value ($n\ge 1.42$), we retrieved the 3-D volumes of RI corresponding to the residual bodies containing hemozoin in the Pf-RBCs [Fig. 9(a)]. In order to investigate the structural characteristics of the hemozoin crystals quantitatively, we calculated the volume and surface area of hemozoin from the Pf-RBCs. The measured values for the volume and surface area are $1.08\pm 0.48$ fl and $7.25\pm 3.56{\mu \mathrm{m}}^2$, respectively, for trophozoite stage, and $0.68\pm 0.27$ fl and $4.47\pm 1.29{\mu \mathrm{m}}^2$, respectively, for schizont stage. These values are consistent with previous studies using independent experimental methods. Gligorijevic et al. used spinning disk confocal microscopy and measured the volumes of hemozoin crystals in the range 0.2 to 0.7 fl.⁶³ Hanssen et al. employed x-ray microscopy and measured the volumes of hemozoin crystals during gametogenesis in the range of 0.6 to 0.8 fl.⁴ Although the magnitudes of the measured values for the volume and surface area are in agreement with the previous reports, we note that the decrease in the measured values from trophozoite to schizont stage is not consistent with previous works. This can be partly attributed to the limited number of samples ($n=12$ and 4 for the number of cells in trophozoite and schizont stage, respectively). Moreover, the sphericity $\psi$ of hemozoin was found to be $0.79\pm 0.11$ (trophozoite) and $0.83\pm 0.09$ (schizont), which was calculated from the volume and surface area as $\psi ={\pi }^{1/3}{(6V_p)}^{2/3}/A_p$.

Fig. 9

Characterizations of in situ hemozoins. (a) 3-D renderings of representative hemozoins inside Pf-RBCs. The length of arrows corresponds to 1 μm. Three isosurfaces with representative RI values are rendered according to the color bar. No hemozoin was observed during the ring stage. (b) Hb concentration in hemozoin. (c) Hemozoin volume. (d) Hemozoin contents. (e) Sphericity of the hemozoin. The cross symbols represent the median values, and the vertical lines indicate standard deviations.

In addition, 3-D RI tomogram reconstructed with the diffraction algorithm provides complex RI values $n^{*}=n^{\prime }+i{n}^{\prime \prime }$; the real part of RI is a conventional value for RI $n$ that relates the speed of light in the material, whereas the imaginary part of RI corresponds to the absorption coefficient. Absorption coefficient $\kappa$, which describes how much a material absorbs light so that illuminated light intensity $I_0$ is attenuated to $I$ after passing a material with a thickness $l$, $I=I_0\exp (-\kappa l)$. $\kappa$ and $n^{\prime \prime }$ are related by Beer–Lambert law as $\kappa =4\pi n^{\prime \prime }/\lambda$. The absorption coefficients of the hemozoins are calculated from the imaginary part of RI: $n″$ of in situ hemozoin was found to be $0.048\pm 0.005$ (trophozoite) and $0.045\pm 0.008$ (schizont), while the rest of Pf-RBCs are nearly transparent at the wavelength used ($\lambda =633\mathrm{nm}$). The measured $\kappa$ is comparable with the previous report ($n″=0.052$; estimated from Ref. 65 with the size of hemozoin is $\sim 0.6\mu \mathrm{m}$) where an UV-VIS absorption spectrometer was used.

The concentration of hemozoin $c$ is calculated from the measured $\kappa$ based on Beer–Lambert law: