1.

Introduction

The most severe form of human malaria is caused by the parasite Plasmodium falciparum (Pf). The infection is accompanied by profound changes in the mechanical properties of the infected host red blood cells (RBCs), contributing to reduced blood flow in the microcirculation and vasoocclusion.¹ A precise assessment of the mechanical properties of infected red blood cells (IRBCs) is thus essential for an improved understanding of the disease, for the assessment of potential treatments, and for improved diagnostic purposes. At the single-cell level, micropipette aspiration, optical tweezers, and magnetic traps offer powerful tools for precise measurements of cell compliance.² These methods have either low throughput efficiencies or are limited in the information they yield. They are also difficult to incorporate into online diagnostic tools. Bulk methods such as ektacytometers have fast acquisition, but deliver only ensemble measurements^{2, 3} liable to deliver false negative results when samples contain small subpopulations of IRBCs among many uninfected cells. We report here the development and use of a novel hematological tool for the detection of IRBCs, a microfluidic optical stretcher, tested in Pf cultures. We show that the technique is ideally suited for the quantification of alterations in the mechanical properties of RBCs during early stages of infection. The method combines the sensitivity of traditional single-cell measurement techniques with the potential for high throughput analysis.

The optical stretcher can determine IRBC elasticity in a noncontact mode by trapping cells directly between two divergent counterpropagating laser beams.^{4, 5} Figure 1 illustrates the schematics of the setup used. The capillary and optical fibers are supported and aligned by a cross-shaped photolithographic pattern on a glass slide [Fig. 1]. The trapped cell is stretched along the axis of the laser beams by simply modulating the light intensity.⁴ The stretching forces are generated by the momentum transfer that occurs at the interface between the sample cell and the surrounding medium due to a change in refractive index. These surface forces pull the cell apart, analogous to a tug-of-war situation. The resulting stretching force can be 1 to 2 orders of magnitude larger than the net trapping forces, the latter arising from the asymmetric force field for cells positioned slightly off the center in the trap.⁴ Spheroidal cell shapes greatly facilitate theoretical modeling, and consequently the only quantitative measurements of erythrocyte mechanical properties with the optical stretcher have been performed in the past on osmotically swollen erythrocytes.⁴ To measure erythrocyte deformability without altering its original shape, the analysis of surface forces becomes more involved, but is tractable in principle using finite element method (FEM) calculations.⁶ An alternative approach, taken here, is to employ a simplified phenomenological model to quantify cell compliance. Here we use the simple Kelvin-Voigt model, assuming only a global viscosity $\eta$ and elasticity constant $E$ for the whole cell. According to this model, the strain $\epsilon \left(t\right)$ following an instantaneous constant stress $\sigma$ can be described as:

Fig. 1

(a) Schematic of the optical stretcher illustrating the photolithographical SU8 pattern used for aligning the fibers and capillary. Two lights delivering opposing fibers are automatically aligned when placed into the grooves, which are narrower than the fiber diameter. The superposition of the light creates a stable trap. Cells can be trapped and stretched, depending on the light intensity. (b) Sequence of operation during experiments. After a cell is positioned in the trap, the capillary flow is halted. The image acquisition is started and after one second the stretcher light intensity is instantaneously stepped up for approximately one second. The cells stretch and relax according to the light intensity. (c) Example of an uninfected RBC in the trap at low light power. The image analysis routine automatically locates the cell boundaries and displays corresponding cell edge pixels. (d) The same cell as in (c), elongated due to increased power in the optical stretcher. (e) Deformation behavior of uninfected RBCs compared to IRBCs. Cohorts (squares, $n=32$ ) and controls (triangles, $n=46$ ) behave similarly and exhibit small standard errors, whereas the IRBCs (circles, $n=24$ ) show $a$ greatly reduced compliance and larger standard errors.

2.

Materials and Methods

3.

Results/Discussion

Optical stretcher measurements of cell compliance were done in three different types of cells: 1. trophozoite-containing IRBCs, 2. uninfected RBCs of the IRBC culture (cohorts), and 3. controls. A reduced compliance was observed for IRBCs, confirming previous results obtained with optical tweezers.¹⁰ Both cohorts and controls retained their normal biconcave disk-like shape. Figure 1 shows a comparison between the stretch responses of controls $(n=46)$ , cohorts $(n=32)$ , and IRBCs $(n=24)$ . Both uninfected samples display homogeneous behavior in the optical stretcher, with a similar compliance and a small standard error [Fig. 1]. In contrast, the IRBCs are less compliant, with a relative stretch amplitude $a$ reduced by almost half. The stretch response of IRBCs was much more variable than that of uninfected cohorts and controls, reflected in the much larger error bars.

The fitted curves in Fig. 1 represent the exponential strain-time relation from the Kelvin-Voigt model [Eq. 1]. The parameters for these fits and their standard errors of the mean (SEM) are shown in Table 1 .

Table 1

Fitting parameters and their standard errors of the mean describing the cell deformations. The table shows the number of stretch responses n in each experiment, the two fitting parameters a and λ , the goodness of the fit (chi-square), and the average cell diameter in the trap before stretching D .

Optical stretching of infected and uninfected red blood cells confirms results obtained with other single-cell mechanics-measurement techniques.¹¹ Measurements with optical tweezers had found IRBCs to stiffen significantly during parasite maturation, with shear moduli increasing up to ten-fold in the late schizont stage.¹¹ Here we have shown that even at an early trophozoite stage, when the increase in apparent stiffness (the relative stretching amplitude $a$ ) by a factor of $\sim 2$ is relatively modest, IRBCs can be easily detected with the optical stretcher. Also, the values found for the elasticity-viscosity ratio (the deformation rate $\lambda$ ) for uninfected RBCs are in good agreement with earlier published values in the range of $5\text{to}10{\mathrm{s}}^{-1}$ .^{12, 13} This ratio decreased by a factor of $\sim 3$ for the infected cells in our experiments.

Our study shows that uninfected cohort cells from Pf cultures and control RBCs do not have significantly different mechanical properties in vitro. This is in contrast to one clinical study³ performed with ektacytometry. Dondorp attribute the reduced deformability of red blood cells (infected and uninfected) from patients with severe malaria also to alterations in the uninfected RBCs³ (not to be confused with “uncomplicated malaria” in Ref. 3). The ekacytometer, however, cannot distinguish between infected and uninfected RBCs. The extension to uninfected RBCs is made in that study because of the low fraction of parasitized cells present $(<20\mathrm{\%})$ , and the finding that the measured deformability did not correlate with different parasitaemia levels. It remains to be elucidated whether reduced elasticity can be observed with the optical stretcher in ex vivo RBC samples from patients with severe malaria.

Quantifying the absolute elasticity modulus remains an open task. It is solvable in principle and has been demonstrated for spherical shapes.⁴ But the biconcave disk-like shape of uninfected RBCs, and the irregular shape of IRBCs require theoretical modeling and FEM simulations to extract absolute numbers for forces and elasticity moduli.⁶ However, the simplified phenomenological model used for analysis here proved sufficient for detecting the mechanical differences in diseased cells. The characteristic deformation rate $\lambda$ is independent of the actual magnitude of stress on the cell. Both parameters $a$ and $\lambda$ change significantly during infection (with the probability of the null hypothesis that the means are not different $p<0.001$ ), and establish the use of this optofluidic device in applications that involve automatic cell sorting, early stage diagnostics, or screening of drugs that reduce cell stiffening.

In summary, optical stretching is a promising novel technique to measure red blood cell mechanical properties and their changes during disease. Its main advantage is that it operates entirely in a noncontact manner and can thus render results that are free from artifacts induced by adhesion to surfaces or physical contact required in other single-cell mechanical-measurement techniques. In addition, by incorporation into a suitable microfluidic environment and automation,¹⁴ throughput rates approaching one cell per second can in principle be achieved, which compares favorably with other single-cell mechanical-measurement techniques.⁵