Three-dimensional monitoring of RBC sedimentation in external magnetic fields

Abstract

The external magnetic fields resulting from electronic devices around humans have become more prevalent nowadays, and studying their influence on living matter is a required task. Here, we experimentally model the movement of RBCs in veins under an external magnetic field; we monitor the sedimentation of multiple RBCs at different distances from a surrounding wall. The monitoring is performed in 3D by incorporation of digital holographic microscopy (DHM). DHM not only provides a 3D quantitative phase image of an RBC but also, through its numerical refocusing feature, 3D trajectories of several cells in the field of view can be obtained. Our results show that the magnetic field facilitates the sedimentation of cells, and the effect is higher in proximity to the walls. This influence is attributed to the presence of magnetic field-sensitive materials included in RBCs.

1. Introduction

Red blood cells (RBCs) are crucial for the transport of oxygen from the lungs to various tissues and organs of the body. The shape and size of RBCs allow them to flow easily through the narrowest of blood vessels, ensuring efficient delivery of oxygen to all parts of the body. Blood sedimentation tests are commonly used in clinical laboratories to measure the rate of settling of RBCs in vessels over a specific period of time. These tests are simple and low-cost, but they have moderate sensitivity and specificity [1,2].

RBCs are susceptible to external magnetic fields (MFs) as they contain hemoglobin and therefore strong external magnetic forces can have a significant impact on their behavior [1]. On the one hand, this effect can be beneficial; reducing high blood viscosity is a direct approach to lowering the risk of certain diseases and mitigating the potential hardening and thickening of arterial walls, and to this end, a strong MF in the blood flow direction can be applied. This occurs as RBCs aggregate along the field direction and form short microscopic chains. Exposure for 1 min to 1.3 T MF is shown to reduce blood viscosity by around $20\mathrm{\%}$ to $30\mathrm{\%}$ [3]. Another application of MF is the separation of RBCs from the blood, which is based on the fact that reduced hemoglobin exhibits paramagnetic properties [4]. The benefit of employing magnetic separation is that it is a purely physical process and does not require the use of additives that could contaminate the blood. On the other hand, however, the effect of external MF can be harmful. The aforementioned positive features of MF on blood have two important aspects: (1) the MF exposure is performed for a limited duration, and (2) the application of MF is under control. If these conditions are not met, the effect of MF can be naturally harmful. This, indeed, happens nowadays as the use of electronic devices around humans has become more prevalent, and they result in the production of external MFs.

Given the above reasons, therefore, it is crucial to investigate how MFs affect the behavior of RBCs in flowing fluid. The behavior of RBCs in sedimentation, which is called the erythrocyte sedimentation rate (ESR), is a ubiquitous hematology technique in medicine as a marker of systemic illness [3]. ESR involves placing whole blood in an upright test tube and monitoring the rate of fall over time, and it can indicate and monitor an increase in inflammatory activity within the body caused by one or more conditions such as autoimmune disease, infections, or tumors. Furthermore, at the microscopic level, the sedimentation of RBCs is considered a rather easy-to-implement experimental modeling of RBC in a flowing fluid and has been the subject of some predated research. In [5] it is shown that RBCs exhibit distinct shapes under the influence of various factors such as elastic parameters and gravity [6]. They observed three main deformed shapes of RBCs including parachute-like, teardrop-like, and fin-tailed spherical shapes under different strengths of gravity and bending rigidity. The RBC sedimentation has been also studied by computer simulations using multi-particle collision dynamics.

The sedimentation of all objects on microscopic scales is shown to dramatically depend on the proximity of the object to the surrounding walls [7]. This can be justified by considering the particle-particle and particle-wall hydrodynamic interactions which impose an additional coefficient in Stoke’s formula, and the coefficient depends on the size and distance of the sedimenting object and its viscoelastic properties. The above conclusions can be extended to the case of RBCs according to their size, shape, and structure, and, indeed, the dependence is the key point behind the ESR diagnosing test. In [8] we showed the sedimentation behavior of RBCs in non-Newtonian fluids and compared their behavior with the behavior of conventional colloidal micro-particles. Moreover, we showed the slippery conditions of the surrounding walls, their roughness, and also the roughness of the surface on which the sediment particles can cause different falls [9]. These findings provide valuable information on the dynamics of the sedimentation of the RBC and lay the foundation for further investigation in more complex scenarios. Considering this line of studies, in this paper, we address the RBC sedimentation in an external MF.

In the aforementioned investigations, toward a 3D insight of the phenomena we incorporated digital holographic microscopy (DHM). DHM technique combines conventional microscopy with laser interferometry to create a digital hologram. In DHM, an interference pattern is recorded between the light scattered from the specimen and a reference wave. This digital hologram contains information about the specimen’s optical properties and can be used for various applications, such as 3D imaging and quantitative phase microscopy in a non-destructive, non-invasive, single-exposure, and label-free manner. The possibility to capture digital holograms, i.e., volumetric data at on-demand frame rates and for arbitrary time scales from few milliseconds to hours allows for a better understanding of the dynamics and interactions happening at a small scale, which obviously have numerous applications in various fields like biology, chemistry, and engineering [10–16]. Moreover, given that DHM system is built on a microscope, its combination with the optical manipulation methods provides further capability to investigate 3D morphometry of optically immobilized cells, which is a more realistic fashion for single cell level studies [17–22].

As we will discuss in detail, DHM possesses a couple of significant benefits: (1) The reconstruction of digital holograms provides full field complex amplitude and, therefore, the phase information of the object under imaging. The phase map, in turn, provides the 3D image, which if considered in time, provides a quantitative 3D monitoring of dynamics. This, indeed, is highly useful in biological and fluidics-related phenomena like sedimentation. (2) Using the whole complex field one can obtain a focused intensity image of 3D samples at any desired image plane on demand. Unlike other 3D imaging techniques like confocal microscopy, DHM does not require scanning or electro-mechanical adjustments to capture images of particles outside the focal plane. This makes DHM a convenient and efficient method for detecting and tracking the collective behavior of micro-objects. This feature is equivalent to the physical refocusing process of a microscope. However, it is performed numerically and as a post-process stage. Therefore, it is possible to track the dynamics of several objects in 3D over time by the acquisition of successive digital holograms and the follow-up reconstruction and numerical refocusing. It seems incorporating both of these two features together makes DHM an excellent approach for investigations on RBC and similar microscopic objects, which require examining the morphometry as well as the trajectory of multiple cells in a single exposure. It is remarkable that flow measurement techniques such as astigmatism particle tracking velocimetry, on the other hand, are limited to spherical particles and cannot provide a complete 3D image of moving micro-objects [11].

The paper is organized as follows. In Section 2 we present the sample preparation details and the experimental procedure. In Section 4 the experimental results are presented and discussed, and the paper is concluded in Section 5.

2. Material and methods

2.1. Sample preparation

For the RBC experiments, freshly collected human blood from healthy donors is obtained from the Blood Bank of Zanjan, Iran. The blood fresh samples are centrifuged at 3000 g for 10 min at 4 ^∘C temperature to separate their plasma and buffy coat. The upper layers including the buffy coat are removed by careful aspiration. In order to prepare sufficiently dilute samples, the collected RBCs are resuspended in a physiological solution (NaCL, 150 mM) three successive times. The samples eventually contain $0.5\mathrm{\%}$ hematocrit value, which is the suitable concentration for microscopic single-cell experiments such as the present study. The RBC specimens are kept in a water bath at 37 ^∘C before the experiments to minimize the effect of temperature changes. All the experimental protocols are conducted in accordance with the regulations and policies of the Zanjan Blood Bank.

2.2. Experimental procedure

The experimental setup utilized in this study is based on a Mach-Zehnder transmission mode off-axis DHM system and is equipped with an MF generation apparatus. The 3D scheme of the setup is shown in Fig. 1. A linearly polarized He-Ne laser beam (MEOS, 632.8 nm, 5 mW) by the use of a spatial filter (SF) is spatially filtered to have a clean diverging beam, which is then collimated by lens L1. The collimated beam is divided into reference and object beams by the non-polarizing 50:50 beam splitter BS1. The object beam is reflected from BS1 and passes through the sample (S). The sample chamber is a single seated 3.5 ml quartz cuvette (Azzota) with a cross-section of 10 mm × 10 mm and is filled up with a physiological solution to 1 mm below its upper surface. It is mounted vertically in the center of an MF-producing coil (MFC). MFC consists of a couple of coils each with 200 wrapped copper wires of 0.9 mm thickness around an iron cylindrical core of 23 mm diameter. The distance between the two counter-looking heads is 43 mm, and the sample is placed between the two heads where a uniform MF is generated. The MF generator is pre-calibrated using a Tesla meter. Microscope objective MO1 collects the diffracted beam from the sample and through the mirror M1 sends it to the beam splitter BS2. The placement of the sample cuvette is adjusted carefully so that besides positioning the imaged cells in the middle of the open area of the MFC device, the focal point of the objective MO1 also coincides with it. The reference beam is transmitted through BS1 and is reflected from M2 toward BS2. A neutral density filter (NDF) is used to adjust the intensities of the interfering beams in order to achieve high-contrast holography fringes. Moreover, a microscope objective (MO2), similar to MO1, is placed in the reference arm in a distance to the camera, toward matching the curvature of the object and the reference beams and to minimize their optical path differences. Matching the curvatures of the interfering waves guarantees the quality of the fringes in terms of linearity, uniformity, and appropriate fringe density. The two reference and object beams meet with each other at BS2, and by the tube lens (L2) the hologram, i.e. the interference of the reference beam which has no structure, and the object beam which carries the information about the object is formed on the recording camera (DCC1545M, Thorlabs, 8-bit dynamic range, pixel pitch 5.2 μm).

Fig. 1.

Off-axis DHM setup equipped with a magnetic generator; SF: spatial filter, L: lens, BS: beam splitter, NDF: neutral density filter, M: mirror, S: sample, MO: microscope objective, MFC: magnetic field coil. Inset: enlarged sample and infusion arrangement.

During the experiments, under a controlled infusion rate, the RBC-contained suspension is injected carefully into the upper surface of the cuvette by the use of a syringe pump, and the single RBCs start sedimenting freely. In the inset, an enlarged view of the sample and infusion arrangement is shown. The end part of the syringe needle is bent to prevent its influence on the uniformity of the applied MF and its end is right below the free surface of the pre-filled physiological solution to avoid possible fluidic perturbation on the sedimentation of cells. The central part (both in vertical and horizontal directions) of the cuvette is kept on the optical axis to minimize the upper surface perturbations, the bottom surface influence, and the effects of the rear walls of the cuvette. Hence, the only flat wall of the cuvette that may have influence is the one placed toward MO1. In our experiment, we systematically consider the proximity effect of this wall on the RBC sedimentation. The flow rate is carefully adjusted to fulfill two conditions: (1) appearing of few RBCs in the field of view at different distances from the wall, (2) the cell-to-cell hydrodynamic interaction of RBCs should be avoided by increasing the number of RBCs in the field of view. The camera has recorded successive holograms at a 25 fps frame rate since the beginning of the experiments. We conduct a control experiment in which the MF is switched off. Then, MFs of 8, 13, and 16 mT strengths are applied in the direction of the sedimentation and the phenomenon is live monitored through hologram recording. The recorded holograms are subjected to numerical processing for hologram reconstruction, quantitative phase imaging, and multi-object 3D tracking.

2.3. Numerical processing

In digital holography the interference pattern resulted from the superposition of the sample beam with a definite reference beam is recorded by the digital camera and stored on a computer as a digital hologram [23]. The 3D trajectory of sedimenting micro-spheres and RBCs may be obtained through numerical reconstruction of the recorded holograms. Their velocities can also be extracted by knowing the recording frame rate and the time of their sedimenting process. The reconstruction process includes simulating the illumination of the recorded holograms by the reference laser beam followed by diffraction into the plane where the image is planned to form. The angular spectrum propagation approach in scalar diffraction theory is shown to be a suitable method to perform the aforementioned processes [24,25]. It provides the complex amplitude of the reconstructed object wavefront at an arbitrary plane located at $z=d$ :

$$E_s^F(x,y,d)=F{T}^{-1}\{{[FT\{E_s(x,y,0)\}]}^F{e}^{ikd\sqrt{1-{\lambda }^2{u}^2-{\lambda }^2{v}^2}}\}.$$ (1)

where, $FT$ denotes the Fourier transformation, $\lambda$ is the wavelength of the laser beam, u and v are the spatial frequencies in x and y directions, respectively, $E_s(x,y,z=0)$ is the light-wave at the hologram’s plane, and the superscript F shows the spatial frequency filtering in the Fourier plane. Details of the method can be found in [9].

From the complex amplitude of the object wavefront, both the intensity and phase of the image can be computed:

$${\varphi }_s(x,y,z)=\arctan \left[\frac{\text{Im}\{E_s^F(x,y,z)\}}{\text{Re}\{E_s^F(x,y,z)\}}\right],$$ (2)

$$I_s(x,y,z)={|E_s^F(x,y,z)|}^2.$$ (3)

Equation (2) gives the phase map of the object, which includes the 3D information of phase objects such as RBCs. The phase map is proportional to the optical path length, $\varphi (x,y)=\frac{2\pi }{\lambda }n(x,y)L(x,y)$ , where $n(x,y)$ is the refractive index of the medium and $L(x,y)$ is the physical length that the light beam propagates, e.g. the thickness of RBCs at each $(x,y)$ point. The phase distribution changes when either the shape or the refractive index of the object under study is changed. Assuming negligible changes of the refractive index of the object the phase distribution directly leads to the surface 3D profile of it. The phase obtained from Eq. (2) is in the range of $[\frac{-\pi }{2},\frac{\pi }{2}]$ , which makes discontinuities throughout the phase map. The discontinued phases are converted to continuous phase maps by the unwrapping process. We use Goldstein’s branch-cut unwrapping algorithm in this paper [26]. Besides, the possibility to numerically calculate the intensity of the image leads to an important advantage of DHM over conventional microscopy which is called numerical refocusing. In the reconstruction process, by varying the parameter d, it is possible to change the image formation plane. In bright-field microscopy, the intensity image at different axial planes is obtained by adjusting the distance of the sample from the microscope objective. Therefore, if a part of the sample is not sharply imaged, by mechanical or electronic adjusting the stage or the microscope objective sharp and focused image is obtained. Thanks to the numerical refocusing feature this task is done numerically in DHM though re-calculation of intensity image, Eq. (3). A single digital hologram can be reconstructed to extract the axial position of multiple objects in the field of view. According to Eq. (3), a sharp image of each object can be achieved by proper numerical propagation, and since the propagation distances (d) for all the objects are known, their axial distance to each other will be determined. Given that their lateral (x and y) position is also known, by DHM 3D position of several objects distributed in a volume can be tracked. This feature of DHM is, therefore, a treasure for studying several dynamic phenomena in microfluidics. It is remarkable that the 3D position tracking capability of DHM along with its 3D image acquisition of individual objects makes DHM a unique methodology for the aforementioned applications. Sedimentation of RBCs, which is considered here, is a concrete example. Figure 2 shows the main stages of 3D image reconstruction and numerical re-focusing. Figure 2(a) is a hologram of multiple sedimenting RBCs in different depths, and Fig. 2(b) is the “reference hologram”, which is free of RBCs and is taken before sedimentation onsets. In Visualization 1 ^{(7.3MB, avi)} successive digital holograms of sedimenting RBCs are shown. Acquisition of reference holograms allows for subtracting the effect of contaminations of the chamber wall, camera sensor, and other surfaces, optical aberrations of the elements in the optical setup train, and other noises, from the final complex amplitude data. To this end, the identical reconstruction procedure of the main digital hologram is repeated for the reference hologram. Figure 2(c) shows the spectrum of the recorded digital hologram. Only the spatial frequencies of the “+1” term (shown by the red square in Fig. 2(c)) are cropped and the rest of the frequencies are filtered out [9]. After applying a frequency shift to the center of the Fourier domain, proper numerical propagation, and then getting back from Fourier space, the complex amplitude is calculated, which provides the 3D image of the RBCs as well as their intensity images. Figure 2(d) shows the 3D image of one of the sedimenting RBCs, and in Fig. 2(e) we show that by proper numerical propagation, the RBCs at different depths can be sharply imaged and tracked.

Fig. 2.

(a) Hologram of multiple sedimenting RBCs in different depths (See Visualization 1 ^{(7.3MB, avi)} ). (b) Associated reference hologram. (c) The Fourier spectrum of the recorded digital hologram, from which only the spatial frequencies of the “+1” term are kept and the rest is filtered out. (d) The 3D reconstructed image of a sedimenting RBC. (e) Numerical refocusing for depth tracking of sedimenting RBCs.

3. Theoretical description

To model the sedimentation behavior of a RBC under an external MF several acting key forces have to be considered. For simplicity, we consider spherical shapes for the sedimenting objects. Considering the experimental arrangement, we assume that the MF is non-uniform and aligned with gravity. The main forces that a sedimenting RBC experiences include the magnetic force, the gravitational force, the hydro-dynamical force exerted by the fluid, and the force due to the proximity to the flat wall. In the experiments, we image an area that is away from both the free surface of the fluid and the container basement. Accordingly, their influencing forces are neglected. The gravitational force on the RBC is its weight:

$$F_g=mg,$$ (4)

where, m is the mass and g is the gravitational acceleration of the Earth. For the RBC of volume V and density ${\rho }_{\text{RBC}}$ sedimenting in a fluid of density ${\rho }_{\text{fluid}}$ , the net acting effect of gravitation, $F_{\text{sed}}$ , may be written as:

$$F_{\text{sed}}=V({\rho }_{\text{RBC}}-{\rho }_{\text{fluid}})g.$$ (5)

Moreover, a moving RBC in a stream experiences a drag force. In a low Reynolds number fluidics, the drag force is given by Stokes’ law:

$$F_{\text{drag}}=6\pi \eta av,$$ (6)

where $\eta$ is the viscosity of the fluid, a is the radius of the moving sphere, and v is the velocity. However, it is shown that in proximity to the fluid container walls, the formulae of Eq. (6) is modified as [7,27]:

$$F_{\text{drag}}=6\pi \eta a{v}_h,$$ (7)

where, $v_h=\frac{v}{{\lambda }_h}$ is the hindered sedimenting velocity of the sphere and ${\lambda }_h$ is the correction factor for a sphere of radius a sedimenting at the distance h from a flat wall:

$$\frac{1}{{\lambda }_h}=1-\frac{9}{16}(\frac{a}{h})+\frac{1}{8}{(\frac{a}{h})}^3-\frac{45}{256}{(\frac{a}{h})}^4-\frac{1}{16}{(\frac{a}{h})}^5+O{(\frac{a}{h})}^6.$$ (8)

It predicts that as the $\frac{h}{a}$ becomes larger, the correction, $\frac{1}{{\lambda }_h}$ , approaches 1, and the drag force equation is changed to the Stokes’ law. On the other hand, in very small particle-wall distances, i.e., in the order of the particle size or less, the drag force increases dramatically.

The potential energy U of a magnetic object with volume V in a MF $\mathbf{B}$ , and with magnetic susceptibility $\chi$ , which measures how much the object becomes magnetized in the presence of an MF, is given by:

$$U=-\frac{1}{2}\chi V\mathbf{B}\cdot \mathbf{B}$$ (9)

The force ${\mathbf{F}}_{\text{mag}}$ acting on the object is derived from the gradient of the potential energy:

$${\mathbf{F}}_{\text{mag }}=-\mathrm{\nabla }U=-\mathrm{\nabla }(-\frac{1}{2}\chi V\mathbf{B}\cdot \mathbf{B})=\frac{1}{2}\chi V\mathrm{\nabla }(\mathbf{B}\cdot \mathbf{B})=\frac{1}{2}\chi V\mathrm{\nabla }{B}^2.$$ (10)

Using the identity $\mathrm{\nabla }\left(B^2\right)=2\mathbf{B}\cdot \mathrm{\nabla }\mathbf{B}$ , Eq. (10) becomes:

$${\mathbf{F}}_{\text{mag }}=\chi V\mathbf{B}\cdot \mathrm{\nabla }\mathbf{B},$$ (11)

which applies also to the arrangement of the present study, i.e., a sedimenting object of volume V under exposure to a MF. For a uniform MF, $\mathrm{\nabla }B$ will be zero.

The net force acting on the RBC is the sum of these forces. Since the MF and gravity are in the same direction, the magnitude of the net force can be written as:

$$F_{\text{net}}=F_{\text{sed}}+F_{\text{mag}}-F_{\text{drag}}.$$ (12)

Combining the above equations and solving v in the restraining force equation, taking into account the changes due to the MF, and finally by a rearrangement of the equations the sedimenting velocity can be expressed as:

$$v=\frac{V({\rho }_c-{\rho }_f)g+\chi VB\mathrm{\nabla }B}{6\pi \mu a{\lambda }_h^{-1}}.$$ (13)

Since the field experiences more variations in the proximity of the walls [28] the presence of the magnetic force $F_{\text{mag}}$ in the numerator of the fraction shows that if the magnetic coefficient $\chi$ and the gradient of the MF, $\mathrm{\nabla }B$ , are significant, they can increase the sedimenting velocity v. Moreover, given the dependence of the correction factor ${\lambda }_h$ on the sedimenting object size and the position of the object with respect to the wall, there will be competition between the aforementioned factors on the object’s sedimenting behavior.

4. Result and discussion

The sedimentation experiments are performed for RBCs under exposure of MFs of different strength and their digital holograms are recorded as a movie. The study of the sedimentation behavior of RBCs is based on applying the whole reconstruction procedure on all the frames and obtaining the trajectories of multiple RBCs. For each MF strength, at least seven RBCs in different axial positions are tracked. We examine four different cases; no MF, and MF strengths of 8, 13, and 16 mT. In Fig. 3 we show the trajectories of three RBCs at different distances to the flat wall of the chamber for each case. The MFs are separated by different colors: gray, green, red, and blue wall and dots represent MF strengths of 0, 8 mT, 13 mT, and 16 mT, respectively. Darker dots indicate closer distances of the sedimenting objects, and the circle markers indicate the closest measured sedimenting objects. In order to gather all the trajectories information the X direction includes successive ranges of [0,200μm]. The lateral positions of the RBCs are simply obtained by tracking the center of mass of their reconstructed intensity images or even the hologram, and their axial distances to the container wall are obtained through numerical focusing as explained in Subsection 2.3. The size of the shadow projection of the data points, sketched on the below surface, indicates the level of deviation of the sedimenting particles from the perpendicular direction. It shows that with the application of the MF, the RBCs experience less deviation from the vertical sedimenting path than in the case without the field, and this deviation is much smaller at closer distances to the flat wall. The vertical size of the tracking field-of-view is 100 μm, therefore, different numbers of data points for different MFs or RBC-to-wall distances mean different sedimenting velocities. We quantify these differences and specifications via post-processing measurements and present the results in different graphs. The results are shown in Figs. 4–6. Given the 3D trajectory of all the individual particles and knowing the capturing speed of the holograms, one can measure their velocities. We measure the instantaneous velocity of a sedimenting particle by measuring the sedimented distance between two successive frames and multiplying by the frame rate. The distances in pixels are converted into μm by pre-calibration of the setup by means of a USAF-1951 test target. Figures 4(a) to 4(d) show the measured settling velocities versus time for B=0, 8 mT, 13 mT, and 16 mT, respectively. In the inset of the figures, the distances of the examined RBCs from the wall are shown, which, considering the experimental conditions, are not identical for different experiments. Darker color data points correspond to closer-to-wall RBCs. The RBCs with distances between a few microns to tens of microns are chosen and presented. Sedimenting velocities in general increase as B increases, which is expected as the MF and the gravity are in the same direction. Moreover, the increase in stronger MFs can even overcome the proximity effect [7]. However, the fluctuations in the velocity decrease in the proximity of the wall, while it increases by increasing B and the increase is more pronounced in closer distances. Indeed, the distance to the wall is an effective parameter; for example, the required time to sediment in 100 μm, varies from 0.1 s for h=8 μm in B=16 to 0.6 s for h=90 μm in B=13. These experimental findings may be attributed to the possible increase in the gradient of the MF near the wall which leads to higher velocities according to Eq. (13). In Fig. 4(b) all the hs distances are short and they behave similarly. In Fig. 4(d) the RBCs are closed to the wall, however, they are under exposure to higher MF strength.

Fig. 3.

The trajectories of three RBCs at different distances to the flat wall of the chamber under different MF exposure: gray, green, red, and blue colors or the wall and the dots represent MF strengths of 0, 8 mT, 13 mT, and 16 mT, respectively. Darker dots indicate closer distances of the sedimenting objects and the circle markers indicate the closest measured sedimenting objects. Shadows projected on the surface are also shown.

Fig. 4.

Settling velocities versus time for (a) B= 0, (b) B= 8 mT, (c) B= 13 mT and (d) B= 16 mT, respectively.

Fig. 6.

The velocity vs. distance to the wall for the four different MFs.

In order to separate the influence of affecting parameters and the $B-h$ interplay, in Fig. 5(a) we present the sedimenting velocities of the farthest and nearest RBCs to the wall for each MF strength and in Fig. 5(b) we present the sedimenting velocities of RBCs at identical distances to the wall under different MFs. Moreover, in Fig. 6 we show the velocity vs. distance to the wall for the four different cases. It illustrates that in higher B more RBCs tend to sediment in the proximity of the wall, which is a result of the aforementioned higher proximity effect in stronger MFs.

Fig. 5.

(a) The sedimenting velocities of the farthest and nearest RBCs to the wall for each MF strength. (b) The sedimenting velocities of RBCs at identical distances to the wall under different MFs.

The effect of external MF on the sedimentation behavior of RBCs is due to the presence of hemoglobin which is susceptible to MF. DHM capabilities, which provide complete space and time information of the dynamic processes, enable reviewing all aspects of the sedimentation data to ensure apparent effect of the MF in increasing the erythrocyte sedimentation rate. The results are in agreement with the model and simulation predictions, which demonstrated that MFs influence the flow stream and the behavior of RBCs, including the motion and the deformation of the cell [29]. The present study experimentally simulates the RBC motion in veins, stating that the external fields of the strengths of the order of the fields near power plants can cause significant changes in the cell flow and therefore in the blood viscosity. Hence, our findings suggest potential risks of external MFs and the requirement for further researches for assessment of the influence of the external MFs resulting from electronic devices around humans on living matter. For example, measurement of the clinical level MF effects, and investigation of the cumulative effects of prolonged exposure to lower-intensity MFs from everyday electronics seem some of the required tasks. Moreover, the methodology can be extended to similar fluidics and biomedicine investigations in which 3D tracking of dynamics of multiple microscopic objects is a required task; more importantly, in the cases where 3D tracking and 3D imaging are simultaneously needed.

5. Conclusion

In conclusion, using digital holographic microscopy (DHM), we investigated the sedimentation of multiple RBCs at different distances from a surrounding wall and under exposure to external magnetic fields (MFs). Electronic devices nowadays are found everywhere around humans, resulting in MFs, and, in turn, may have a harmful influence on health. The present arrangement is an experimental model for the movement of RBCs in veins and addresses the microscopic effects of external MF with the strengths of the order of the fields near power plants. 3D dynamic monitoring of the RBCs is performed by incorporating the numerical refocusing feature of DHM. Our results show that MF facilitates sedimentation of cells, and the effect is higher in proximity to the walls. These effects, in agreement with previous numerical predictions, are due to the presence of hemoglobin which is MF-susceptible. These results collectively suggest potential risks of external MFs and the requirement for further researches for assessment of the influence of the external MFs resulting from electronic devices around humans on living matter. Clinical level MF effects as well as the cumulative effects of prolonged exposure to lower-intensity MFs from everyday electronics are some of the issues to be subjected for future researches. On the other hand, the present DHM methodology, which provides 3D tracking and 3D imaging simultaneously, can be extended to similar fluidics and biomedicine investigations in which 3D tracking of the dynamics of multiple microscopic objects is needed.

Disclosures

The authors declare no conflicts of interest.

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.