Dielectric characterization of Babesia bovis using the dielectrophoretic crossover frequency

Coinfection with the tick‐transmitted pathogen Babesia spp. is becoming a serious health problem because of the erythrocyte invasion through Ixodes scapularis tick. The transmission of this protozoan by blood transfusion often results in high morbidity and mortality in recipients. A novel way to detect parasitized erythrocytes is by utilizing dielectrophoresis, an electrokinetic technique on a microfluidic platform, to improve the diagnostics of Babesia spp. The differences in the dielectric properties of Babesia spp.–infected erythrocytes versus healthy erythrocytes were exploited to design a fast and cost‐effective diagnostic tool. One crucial factor for a successful diagnostic platform via dielectrophoretic separation is the dielectric characterization of Babesia‐infected erythrocytes, which is investigated in this paper. The influence of medium conductivity and erythrocytes phenotype and genotype over the first crossover frequency (fco1) are used to quantify the dielectric properties of the infected cells. A sigmoidal curve was plotted via curve fitting of the single‐shell model, which has been proven appropriate for parasitized cell populations where considerable cell geometry variation occurs. The difference in these curves is relevant for the separation of cells population. Microliters of sample and reagent were used throughout this experiment; the scale, results obtained, and simplicity of the system often make it very suitable for point‐of‐care babesiosis disease diagnostics.

the former Yugoslavia. Since then, babesiosis has been considered a potentially life-threatening zoonotic disease [4,5]. B. bovis parasites are endemic in tropical and subtropical regions worldwide and cause anemia due to extensive hemolysis and other related symptoms [6]. This parasite actively interacts with the host cell both internally and externally, and during the invasion process, its behavior resembles that of other apicomplexan parasites, including Plasmodium falciparum, Plasmodium yoelii, and B. divergens, which also invade erythrocytes [1,[7][8][9]. B. bovis and Toxoplasma gondii move in a spiral or helical pattern, searching for erythrocytes to attack and causes a depression in the plasma membrane, which deforms the cell. This invasion results in ridge formation on the surface of erythrocytes, leading to modifications in their adhesive, mechanical, structural, and functional properties [10]. This deformation often leads to changes in the cells' morphology and the dielectric properties of the infected cells. The changes triggered in the subcellular components, such as the cell membrane and cytoplasm, regulate the dielectric properties (conductivity, σ, and permittivity, ε), thus affecting the bioelectric signals that aid in the detection of infected cells.
One of the standard identification techniques many physicians use to detect B. bovis parasites in whole blood is to consider the patient's travel history, geographical region, and whether blood transfusion was received within the past 6 months [5]. The first clinical diagnostic test for babesiosis involved microscopic examination of Giemsa or Acridine Orange stained blood smears, still a preferred technique, because of its quickness and affordability [11]. However, the low parasitemia at the early stage of infection can make it challenging to visualize parasites, requiring trained professionals to investigate multiple blood samples [12]. To detect Babesia spp. infection in blood donors presents a unique set of challenges due to the intraerythrocytic nature of the parasite and a lack of knowledge on the minimum parasite burden in the asymptomatic chronic phase of infections [13]. Other approaches for babesiosis diagnosis include polymerase chain reaction, which detects Babesia microti nucleic acids, and indirect fluorescent antibody assay that detects B. microti as an antigen [14,15]. Out of all the available diagnostic tests, the Grifols Procleix Babesia assay is the only FDA-approved test that can detect Babesia spp. in screening blood donors currently [16]. Although it has a high sensitivity and can detect the pathogen in the early stages of infection, it is expensive, time-consuming, and can only identify a few Babesia spp. parasites, such as B. microti, B. divergens, B. duncani, and B. venatorum [17]. To address these limitations, this study employs a dielectrophoresis (DEP) technique to detect parasitized erythrocytes by estimating the dielectric properties of the infected cells using the single-shell model [18,19]. By exploiting the difference in dielectric properties among Babesia spp. infected erythrocytes, and healthy cells, a tool can be designed for rapid and cost-effective diagnosis [16,20]. One critical factor for the success of this DEP detection platform is the dielectric characterization of Babesia-infected erythrocytes, the focus of this paper.

THEORY
H. A. Pohl first mentioned DEP in his publication "The Motion and Precipitation of Suspensoids in Divergent Electric Fields" while studying the usefulness of DEP for removing suspended solid particles from polymer solutions [21,22]. This phenomenon can be observed in both alternating current (AC) and direct current (DC) when a nonuniform electric field is applied to an uncharged particle in a fluid, causing the particle to exhibit an electrokinetic motion toward the position of maximum field strength, which is caused by the dielectric polarization effects of the applied electric field. This phenomenon is known as dielectrophoresis. Blood cells that experience strong DEP motion typically experience a DEP force of about 1 × 10 −11 N, which is 40 times greater than the gravitational settling force and around 2 × 10 5 times larger than the maximum Brownian diffusion force [23]. The knowledge of passive electrical properties such as dielectric constant and conductivity of various cellular components like cell membrane, cytoplasm, and the nucleus is claimed to add to a better understanding of cell functions [24]. The primary electric properties of these components reflect the cell's ability to maintain ion balances and are also a measure of metabolic work and biological organization. The basic dielectric properties of a cell include cell membrane capacitance, cytoplasmic conductance, dielectric constant, and membrane resistance. The polarization forces produced by an inhomogeneous (nonuniform) electric field caused the motion of suspended particles relative to that of the solvent. Dielectric analysis of cell suspensions was first applied to red blood cells (erythrocyte) of a canine, and the specific membrane capacitance of 0.8 µF/cm 2 was estimated from dielectric theory based on an electrical model in which a conducting homogenous sphere covered with a single thin shell was able to conduct [25]. A single-shell model of a cell is well applicable for characterizing the electrical properties of mammalian erythrocytes, which include neither the nucleus nor cytoplasm organelle [19,25]. The membrane separates the internal phase (cytoplasm) from the environment (medium). R is the cell's radius, Ɛ is the dielectric constant, and is the conductivity. , i, and med represent membrane thickness, cell interior, and medium, respectively.
Two distinct phenomena can be observed during DEP: positive DEP (pDEP) and negative DEP (nDEP). pDEP is observed when the suspended cells tend to move toward the higher electric field region under the influence of a nonuniform electric field gradient, and nDEP, on the other hand, is when the cells move toward the lower electric field region. During the transition from nDEP to pDEP and vice versa, the cells experience a zero DEP force at a particular frequency referred to as the "crossover frequency." The cell DEP behavior is primarily dominated by extracellular factors, including the cell's membrane and cytoplasm electrical properties, cell morphology, and solution conductivity. The net magnitude and direction of the resulting DEP force depend on the cell's relative polarizabilities and surrounding medium [26].
The time average of the DEP force of conventional DEP on a spherical particle can be described theoretically as [27]: where R is the radius of the particle, is relative permittivity, and is the permittivity of free space (8.85 × 10 −12 F/m); [̃] is the real part of the Clausius-Mossotti (CM) factor, ⃗ is the root-mean-square of the applied electric field, and ∇ is the gradient operator. The DEP force is proportional to the volume of the target cells and the applied field magnitude. When the permittivity of the cell particle and the medium is known, the CM factor is given bỹ= * − * * + 2 * where * and * are the complex permittivity of the cell particle and surrounding medium, respectively. At low frequencies, the DEP force depends on the conductive properties of the particle and suspending medium, whereas at higher frequencies, the permittivity values are more important. Equation (2) is a complex version of the CM factor; it considers the conduction and dielectric energy loss of the cell suspended and the medium. The positive value of the CM factor implies that the cells experience pDEP when the induced dipole moment is directed in the direction of the applied AC electric field E. On the other hand, the negative value of the CM factor implies nDEP when the induced dipole moment is directed in the opposite direction to the field E. For example, bioparticles exhibit a conductivity associated with mobile ions in their structures, and their suspending medium is usually a conducting electrolyte. When AC fields are applied, these conduction losses are accommodated * or * , given by Ref. [28], where * is the complex permittivity of the particle, and * is the complex conductivity of the particle: * = 0 − and * = + where j is the imaginary vector (j = √ −1), and is the angular frequency ( = 2 ) of the applied AC field.
A positive value for CM indicates that the particles will attract toward the point electrode. In contrast, a negative CM value implies that the particles will repel away from the point electrode, see Figure 1C. DEP dependence on R 3 indicates a ponderomotive (particle volume-dependent) effect: ) is called the Maxwell-Wagner relaxation time constant. represent the medium permittivity and particle permittivity, respectively, and represent particle conductivity and medium conductivity, respectively. Equation (4) describes the polarizability of the particles under consideration, and it is often referenced in scientific papers dealing with the dielectric properties of particles [26,27].
To explore field-induced polarization of dielectric particles in a microdevice using a point-and-planar electrode, AC signals were applied to the electrodes using a signal generator at a fixed peak-to-peak voltage of 8 V pp . The frequency was varied from 10 kHz to several MHz until a crossover frequency was obtained [29]. The cells subjected to the nonuniform field tend to move toward the region where the electric field is minimum (nDEP) or maximum (pDEP), depending on the suspending medium characteristics, dielectric properties of the cells, and the frequency of the applied electric field.
The crossover frequency, f xo, is characteristic of the value Re[f̃C M ] = 0, implying that no net dielectrophoretic force is exerted on the cell particle. The crossover frequency is given by

Single-shell model
The single-shell dielectric model mathematically describes biological cells' electrical properties [26], which links these Step-by-step procedure for fabricating poly(dimethylsiloxane) (PDMS) point-and-planar microwell (PPM) device for dielectrophoresis (DEP) experiments; (B) experimental setup and PPM PDMS microdevice, (C) this demonstrates negative dielectrophoresis (nDEP) and positive dielectrophoresis (pDEP) phenomena using bovine red blood cells. In the nDEP case, the cells appear less dense around the point electrode as they are being pushed away. In contrast, in the pDEP case, the cells move toward the point electrode, causing them to become denser around it.
properties to the cell's structure and composition. In this model, the cell is considered an idealized homogeneous spherical particle with a radius of r, representing the cytoplasm, and complex permittivity enclosed by a thin shell of thickness , with R = r + , representing membrane. The cytoplasm conductivity is denoted by , and * , * are cytoplasm and membrane complex permittivity, respectively: * cyt = cyt − cyt , and * mem = mem − mem (6) The complex permittivity of the cell, * , is [27,30] where = ( + ) = ∕ .
When the cell membrane is assumed to be a lipid bilayer, and the cell cytoplasm has a physiological ionic conductivity, then ≫ ≫ , ℎ * ≫ * [26]. The interfacial polarization between membrane and cytoplasm results in dispersion with a characteristic relaxation time , that is, at a characteristic dispersion frequency (≈ 1 MHz) [26,31]: The approximation of specific cell membrane capacitance (C sp-mem ) and total membrane conductance, * , can be defined as [26,32] sp−mem A cell membrane acts as a capacitor because it is constructed like a thin dielectric between two conductors (the outer and inner electrolytes) [33]. For a cell of radius R suspended in an electrolyte of conductivity , the specific membrane capacitance C sp-mem can be determined from the measurement of the DEP lower (first) crossover frequency f xo1 using the following equation: The time-averaged DEP force approximation for a viable spherical cell can be improved by including the mem-brane's specific conductance, [34]: This relationship can be simplified further if G mem ≤ 600 S/m 2 , to the form [34]: Using Equation (12), ( × 1 ) versus ( ) is plotted to give a linear profile (y = mx + c) of the slope, m, and intercept c: The single-shell model was previously used to characterize the dielectric responses of red blood cells [23,35,36]. This study utilized experimental crossover frequencies obtained at various medium conductivities to generate a curve based on the linear model described in Equation (13). These crossover frequencies were then applied to the relationships described in Equations (9) and (14) to estimate the dielectric properties of infected erythrocytes. A previous study [25,36] similarly calculated specific membrane capacitance and conductance of cells using Equation (9) and derived membrane permittivity and conductivity from the slope and axis intercept of the linear dependency shown in Equation (13). These properties can potentially enable the development of diagnostic platforms for detecting multiple infections in a noninvasive, cost-effective manner and could be used as point-of-care solutions in developing and underdeveloped countries.

Device fabrication
The device was fabricated using a standard rapid prototyping technique, as illustrated in Figure 1. The process involved using a 10:1 ratio of Sylgard 184 silicone base and curing agent [25,[36][37][38], and the resulting poly(dimethylsiloxane) (PDMS) device was cured and cut into 1-in. squares with a 3 mm microwell created using a biopsy punch. The PDMS microwell contained two platinum electrodes with a fixed interelectrode distance of 50-60 µm. These electrodes were arranged perpendicularly in a point-and-planar configuration, making up the point-and-planar microwell (PPM) platform. This platform is biocompatible, economical, easy to use, and has low thermal conductivity, making it ideal for fabricating devices that require only one material [39]. The platinum wire electrodes used had a high purity of 99.95% and were highly corrosion-resistant. Finally, the device, consisting of two platinum electrodes, a glass slide, and PDMS, was bonded to a glass slide [40] using a plasma wand from Electro-Technic Products. According to reports in Refs. [41,42], triangular electrodes generate a stronger DEP force, with the maximum value near the tip of the electrode. COMSOL simulations in Ref. [41] demonstrated that utilizing bovine erythrocytes at 8 V pp with all electrode shapes (triangle, square, and semicircle) at a spacing of 25 µm resulted in electrolysis. However, cell movement was too slow at the 125 µm electrode distance [25,36]. Therefore, to ensure equal DEP force acting on the cell population, the device's interelectrode distance was maintained at 55 ± 5 µm throughout the experiment. Figure 1A demonstrates the step-by-step procedure for fabricating the PPM PDMS device, and the electrode distance is held at the desired spacing using a calibrated inverted Nikon Eclipse microscope. The applied AC electric field induces a nonuniform electric field, causing the cells' motion due to the polarization of bioparticles. Cell movement within the region of the two electrodes in the microwell device was observed under a microscope with a high speed video camera to determine the crossover frequencies of the cells at different medium conductivities ( Figure 1C).

Cell culturing and suspension in DEP media
The Mo7 strain of B. bovis was cultured in vitro using the Levy and Ristic method [43]. Our previous studies utilized this strain to produce B. bovis-parasitized erythrocytes [18,35]. B. bovis-infected erythrocytes were incubated in a microaerophilous phase using 24-well suspension plates at 10% (v/v) packed cell volume obtained by gravity separation of whole blood to isolate packed erythrocytes only. The cultures were maintained in M-199 culture medium (Gibco, 22340020) supplemented with 50 g/mL gentamicin (Gibco, 15710-049), 1% (v/v) fungizone (Gibco, 15290-026), 20 mM N-Tris(Hydroxymethyl) Methyl-2-aminoethane sulfonic acid (Sigma Aldrich, T5691), and 40% (v/v) bovine serum and incubated at 37 • C in a 5% CO 2 in air-humidified atmosphere. Subcultivation was performed by splitting/dilution with fresh normal bovine erythrocytes and M-199 medium when parasitemia levels reached around 2%-3%. Parasitemia was monitored by microscopic examination of Giemsa-stained thin smears under a 100× microscope oil objective. The results indicated that parasites produced in vitro were morphologically identical to parasites from the blood of infected cattle and were susceptible to antibabesial drugs [43].
Furthermore, the infected cells were suspended in a dextrose medium prior to the DEP experiments. To prepare the 50 g/mL dextrose medium solution, 25 g was weighed using a Mettler Electronic Weighing Balance (model XSR104) and dissolved in 50 mL deionized water. Potassium chloride salt (KCl) was added to the solution to achieve the desired conductivity value, which was adjusted to nine different levels ranging from 0 to 0.06 S/m. The pH and conductivity of the media (buffer) were measured using a Mettler Toledo multiparameter. The packed infected red blood cells were washed twice in phosphate-buffered saline (pH 7.2) and then suspended in the media prepared for the DEP experiment. Approximately 5 µL of the cell suspension was measured and transferred into the fabricated PPM device within the confines of a 1300 Series A2 Bio-Safety Cabinet. The medium has low conductivity to prevent possible heat generation that could lead to erythrocyte lysis during exposure to AC field. Low conductivity solutions are typically used in DEP-based cell manipulation to maximize the DEP force and minimize the Joule heating effect [26]. As a result, low-conductivity media are frequently used in DEP-based cell manipulation studies [44][45][46].

RESULTS AND DISCUSSION
As shown in Table 1, previous studies [25,[47][48][49][50] have reported erythrocytes to be treated as a single shell [51], and the single-shell model has been used to describe their dielectric responses effectively [3,35,52,53]. The spectra of various healthy cells were similar to previous research, suggesting a high degree of homogeneity in the normal erythrocyte population.
Although an oblate spheroid model has been used to model normal erythrocytes, a spherical approximation is more suitable for parasitized cell populations with significant variations in cell geometry [36,47]. Therefore, this study used the single-shell model to estimate the dielectric properties of B. bovis. In a previous study, impedance spectroscopy was employed as a label-free detection method TA B L E 1 Dielectric properties of normal erythrocytes from data published by other researchers.  for B. bovis on a microfabricated flow cytometer [3]. In contrast, DEP was used here to characterize B. bovisinfected erythrocytes. The impedance spectroscopy results revealed a shift in the phase angle for parasitized cells when the signal phase increased from −90 • to 0 • at 8.7 MHz. Two additional peaks indicating subpopulations were observed when comparing the histogram of an infected sample with that of the healthy sample, as shown in Figure 2. The parasitized erythrocyte subpopulation peak was located between −30 • and 0 • , whereas no peak in that region was found in the histogram of the negative control. The population peak of the uninfected erythrocytes was positioned at a signal phase between −55 • and −30 • . Despite measuring cells dielectrically using impedance spectroscopy, the previous study did not include the analysis of cell dielectric properties, such as internal and membrane permittivity and conductivity, as they were estimated using the DEP method for blood cells in this study. According to the findings, the dielectric properties of cells indicate the invasion of B. bovis on erythrocytes. These results are consistent with previous reports on F I G U R E 3 (a) Dielectrophoretic crossover frequency characteristics of Babesia bovis infected and healthy erythrocytes as a function of radius × crossover frequency versus medium conductivity. The (•) points reflect the experimental data, whereas the (♦) points represent data extracted for normal erythrocytes by inserting the single-shell oblate spheroid dielectric specific capacitance and conductance obtained by Gascoyne et al. [48] into Equation (14). The (•) points in (b) reflect the min-max normalized data. The straight lines show least-square linear fits to the data described above.

TA B L E 2
Average experimental first crossover frequency and respective membrane capacitance estimated using the single-shell model. P. falciparum [47,48], as B. bovis causes similar alterations in cellular dielectric response. However, the extent of these changes may be lower because they are more pronounced in malaria-infected erythrocytes [35]. The cellular DEP responses varied between infected and normal cells. To measure the dielectric properties of B. bovisinfected erythrocytes, a DEP experiment was conducted using medium conductivity values ranging from approximately ∼0.001 ≤ ≤ 0.05 S/m. The frequency was swept from 1 kHz to 50 MHz, and the crossover frequency was determined for each sample run, as shown in Table 2. Table 2 presents the average crossover frequencies for nine samples at various medium conductivity levels. The resulting plot of the × cell radius against is illustrated in Figure 3. The normalized plot is highly similar to the × cell radius vs. reported for P. falciparum by Gascoyne et al. [48].
When the specific membrane capacitance, membrane conductivity, and cell geometry remain independent of the suspending medium conductivity ( ), and ≪ , a plot of * cell radius against is linear for >∼ 0.01 S∕m when using a single-shell model. Using Equation (14), C sp-mem was calculated from the slope [34,54]. The best-fit line of the plot exhibited a linear response to the medium conductivity function, , with a slope of 5.37 Hz m 2 /s, a positive intercept of 0.9297 Hz m, and an R 2 value of 0.8772, indicating a strong linear relationship between crossover frequency and medium conductivity.
B. bovis and P. falciparum are two apicomplexan parasites that are phylogenetically distant but share several cell biological features [3,53]. Parasite-mediated modifications to the host cytosol and plasma membrane are required for intraerythrocytic survival [53,55,56]. Given their similarities, they are expected to have very similar dielectric properties. The dielectric properties of human erythrocytes were significantly altered by P. falciparum, and these properties were utilized for enrichment by free-flow fractionation [3,57]. Moreover, the life cycles of B. bovis and P. falciparum are very similar, implying that changes in the dielectric properties of B. bovis-infected cells should be comparable to those observed in P. falciparum-infected cells [58,59].
In this study, to achieve more accurate analysis and remove experimental or technical biases, experimental data were normalized by using the xo × cell radius. Normalization is crucial in data processing, especially in biological samples, to account for the sample-to-sample variation observed [60]. In a similar study, Weng et al. normalized the crossover frequencies as a function of particle diameter to facilitate the comparison of trends [61] and previously published experimental results [39,[62][63][64]. To eliminate the impact of the measurement scale, we TA B L E 3 The dielectric properties of (i) erythrocytes infected with Babesia bovis were estimated using the normalized xo × cell radius at a medium conductivity range of 0.01 ≤ ≤ 0.05 S/m medium conductivity, and (ii) the dielectric properties of Plasmodium falciparum-infected erythrocytes were estimated based on published data.

Reported values Reference
Specific membrane capacitance, normalized the infected cells' data using min-max normalization. The min-max method linearly transforms the original data of xo * cell radius. The relationships among the original data values were maintained using min-max normalization [63]. The min-max method preserves the original values of each data point while placing them within a new range, thus retaining all relational properties within the data [65].
To estimate the dielectric properties of infected cells, we utilized MATLAB to generate the best-fit line within the conductivity range commonly used, that is, 0.01-0.1 S/m [35,36,55,66,67], after normalizing the experimental data (refer to Table 3). A least-square linear fit was performed to determine the slope and the vertical axis intercept. To account for errors, the best-fit line, also known as the regression line, was generated for the graph of normalized xo * cell radius as a function of the medium conductivity, . After normalization, the estimated specific membrane capacitance and conductance matched those reported for Plasmodia falciparum-infected erythrocytes [48,53] after normalization. The parameters of the best-fit line graph are utilized to determine the dielectric properties of B. bovis-infected erythrocytes.
In this study, Equation (9) demonstrates that the cell membrane thickness affects the membrane conductivity. The thickness of the cell membrane was assumed to be 8 nm [25,28]. The estimated dielectric properties of the cell are presented in Table 3. To determine the total area of the cell membrane, calculated cell capacitance and (where = 4 2 − ) as reported in [68,69] were used. Assuming a smooth plasma membrane capacitance of 9.0 mF/m 2 , the specific membrane capacitance of the cell can be expressed as − = 0 [70], where represents the folding factor that indicates the degree of surface wrinkling in suspension, measured as the ratio of the actual specific plasma membrane capacitance to that of a smooth sphere with the same radius. φ is independent of cell radius and varies across cell types [68]. The findings of this study indicate that B. bovis cells exhibit nonlinear behavior at higher levels of medium conductivity, which poses challenges for using simple linear regression in analysis. The R 2 values for the best-fit lines from the experimental data are 0.877 and 0.958 for linear and nonlinear regression analyses, respectively.
The parasitized erythrocytes exhibit a lower conductivity in the cell interior when suspended in a lowconductivity, isotonic medium compared to normal erythrocytes. The findings for other parameters align with the literature on P. falciparum-infected erythrocytes [36,35,47,57], as presented in Table 3 and Figure 4. The dielectric measurements obtained enable discrimination between normal and B. bovis-infected erythrocytes and offer the potential for enhancing cell separation.
The iterative fitting of single-shell models, described by Equation (12), was used to obtain the mean dielectric parameters for normal and parasitized cells. The membrane conductivity of parasitized cells is considerably higher than that of normal cells due to a loss in membrane barrier function, which results in high membrane permeability [47]. MATLAB was used in this study to plot the real part of the CM factor against frequency for healthy and B. bovis-infected erythrocytes, using the estimated data reported in Table 3, as shown in Figure 5.
Additional statistical analysis of the results was conducted using JMP Pro 2017. The generated curve showed a biased estimate as the lower part of the curve slightly deviated from linearity, and the higher conductivity region introduced nonlinearity. Our findings revealed that simple linear regression models were not well suited to the data, with an R 2 value of approximately 87%. Figure 6 highlights the part of the data that deviated from linearity. To eliminate the bias caused by nonlinearity, we considered only the middle region of Figure 6A, where there is a linear relationship, and removed the nonlinear part of the curve. We found that at higher medium conductivity values (>0.03 S/m), the cells behaved nonlinearly. Therefore, we only considered the region with a linear relationship to fit into the linear model used in this study.

F I G U R E 4
The biophysical and dielectric differences between normal and plasmodium-parasitized cells (Gascoyne et al.) [57]. Green lines around the normal and parasitized erythrocytes represent the electric field lines under low alternating current (AC) frequencies.

CONCLUDING REMARKS
The membrane conductance of erythrocytes infected with B. bovis was considerably higher, at 1290 S/m 2 , compared to the conductance of normal single-shell oblate spheroids, which was reported to be 271 S/m 2 [48]. This range is approximately four times greater than normal cells and is consistent with the findings for P. falciparum-infected erythrocytes reported by Gascoyne et al. [48]. Additionally, the conductivity of the cell interior of infected cells was significantly reduced to ≤0.0343 S/m, approximately 10 times less than standard erythrocytes [25,47,49]. Studies by [20,21,64] have suggested that erythrocytes are permeable to various solutes during parasite development, indicating that the infected cells' permeability is substantial. We observed a higher membrane conductivity of B. bovisinfected RBCs (6.689 × 10 −5 S/m) compared to the reported conductivity of normal RBCs (<10 −6 S/m) [47]. However, our findings showed a slightly lower membrane conductivity of B. bovis-infected RBCs than P. falciparum-infected RBCs. This decrease could be attributed to the severity of malaria infection, which causes significant changes in the cytoskeleton, including the conversion of hemoglobin to hemozoin [35]. The process of hemozoin formation is crucial for the survival of the malaria parasite, as hemozoin crystals act as a physical barrier that prevents the immune system from recognizing infected RBCs as abnormal, as reported [72]. Defects in the cell membrane can alter its electrical properties, potentially leading to increased conductivity. Although a certain level of conductivity is expected when the cell membrane is intact and of good quality, it is not necessarily higher than when the membrane is damaged or defective. Gascoyne et al. also reported that specific membrane capacitance increased in P. falciparum-infected erythrocytes due to alterations in surface membrane morphology induced by physical or chemical agents, contributing to a larger cell surface area [71]. Therefore, it can be concluded that B. bovis parasites significantly alter erythrocyte transport properties. Moreover, the observed increase in conductance may be due to transmembrane conductance or the apparent ion outflow from the cytoplasm, which is dependent on the characteristics of the medium [48]. The differences in dielectric properties between normal and infected erythrocytes can potentially be utilized for cell sorting and developing a diagnostic platform. Figure 4 suggests that a frequency range of 150-200 kHz may allow for the DEP separation of normal and B. bovis-infected erythrocytes at 8 V pp and 0.02 S/m, with a good separation likely to occur in the 3 MHz-20 MHz frequency region, and the best separation possibly occurring between 6 and 10 MHz. As mixed infections are common in humans and animals, particularly in the endemic areas, future work will investigate and discriminate against mixed infections of two or more Babesia spp. The statistical analysis explains the difference between the main trends or fitted lines of B. bovis and normal erythrocytes. Simple linear regression analysis was used to determine significance at the 0.05 level, and the resulting p-value was <<0.05. This indicates that the difference between the slopes is extremely significant because of the different intercepts and slopes (see Figure 6B). Additionally, utilizing the DEP technique, Figure 5 demonstrates the variations in cell crossover frequencies and membrane conductance. The results indicate that the dielectric properties of erythrocytes infected with B. bovis can distinguish between parasitized and normal cells. Specifically, the infected cells showed increased membrane conductance and significantly reduced conductivity within the cell interior. The observed differences in the dielectric properties of erythrocytes infected with B. bovis suggest the potential for utilizing cell separations based on these properties, as noted in previous studies [48,49,[73][74][75]. As such, DEP is considered to be an economical diagnostic technique.

A C K N O W L E D G M E N T S
We acknowledge the statistical analysis support offered by Prof. Twist at West Virginia University.

C O N F L I C T O F I N T E R E S T S TAT E M E N T
The authors have declared no conflict of interest.

D ATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are available from the corresponding author upon request.