# Modeling of an Impedimetric Biosensor with Ultrasonic-Assisted Cell Alignment for the Detection of Yeast

Authors: Jian Tian; Jiangan Xie; Zhonghua He; Dui Qin; Xiuxin Wang
Journal: Journal of Sensors
 (2022)

---

## Abstract

Yeast is an integral part of our environment. The detection of yeast is of great significance in many fields. The impedance-based sensor with interdigital microelectrodes is a promising method to establish a simple and portable detection system. However, the positions of yeast cells greatly influence the impedance variation and eventually the sensitivity of detection. In this study, an impedimetric biosensor with ultrasonic-assisted cell alignment for yeast detection was proposed. In order to verify the feasibility of this biosensor, finite element modeling was conducted using the software COMSOL. The acoustic pressure field and the acoustic radiation force exerted on yeast cells were investigated. Cell positions in the microfluidic channel were determined using the fluid particle tracking module. After that, the impedance between the microelectrodes was calculated. Yeast suspensions with different cell concentrations were used as the tested samples for the simulation. The proposed sensor showed a higher sensitivity than the conventional impedimetric biosensor on which the cells were randomly located. It can be used for the detection of microorganisms. This finite element modeling provided an effective approach for the design of biosensors.


---

## Body

## 1. Introduction

Yeast is a kind of fungus widely existing in our living environment. Yeast contamination can cause spoilage of foods, including dairy products, vegetables, and fruits [1]. Thus, yeast detection is helpful for food quality control and environmental monitoring. Besides, yeast plays an important role in alcohol fermentation and winemaking [2]. Online detection of yeast is of great significance to improve yields and reduce costs in the fermentation industry.Numerous approaches have been developed to detect and quantify yeasts. The methods based on cell cultivation [3, 4] are time-consuming. Guo et al. [5] employed the enzyme-linked immunosorbent assay for the detection of yeasts in food. The process was laborious. O’Connor and Glynn [6] identified yeasts in biological samples using fluorochrome-labeled oligonucleotide probes. The method required complex sample pretreatments, such as cell fixation and permeabilization. Many researchers used flow cytometry [7, 8] to detect and enumerate yeasts with high throughput. However, this method relied on large instruments and skilled operators. Molecular techniques, such as polymerase chain reaction [9, 10], have high sensitivity and specificity but are expensive [11]. Biofunctionalized resonant photonic grating sensors [12] were used for yeast detection. The method needed an expensive and complex optical system to measure the resonance wavelength shifts. Raman spectroscopy was applied to detect yeasts in apple juice by Mizrach et al. [13]. The method required complicated data analyses. Park et al. [14] developed terahertz slot antenna arrays for the detection of yeasts. The method was nondestructive and label-free. However, an expensive femtosecond laser was required for generating polarized THz pulses. In another research [15], yeasts were concentrated with chitosan-modified magnetic nanoparticles and detected using the hydrophobic carbon dots. Although the sensitivity was high, the synthesis of the reagents was cumbersome. Martyniak et al. [16] combined the fluorescent staining with an image cytometer for yeast analysis. However, the cell staining process required professional technicians.Due to the advantages of low cost, saving time and reagents, and easy operation, electrical impedance spectroscopy has been used for the dynamic detection of microorganisms [17]. Tubía et al. [18] developed a biosensor to detect spoilage yeast in wine using immunological reactions and impedance spectroscopy. Stilman and his colleagues [19] detected yeast strains in food samples such as yoghurt and beer by combining surface-imprinted polymers with impedance spectroscopy. Kiani et al. [20] fabricated a biochip for the determination of yeast concentration in different media based on impedance measurements. Yao et al. [21] studied the dielectric properties of yeast cells by impedance spectroscopy to detect the status and concentration of the cell suspension. The impedance spectroscopy was also used to monitor the biomass produced during the industrial brewing processes [22, 23]. Van Wyk and Silva [24] determined the yeast amount during beer fermentation using impedance technology. Krommenhoek et al. [25] designed a micromachined impedance sensor for the online monitoring of yeast cell concentration. They found that the permittivity change of the cell suspension depended linearly on the biomass concentration over a wide range.Many research studies were aimed at improving the sensitivity of impedance spectroscopy in the detection of target analytes by using interdigitated electrodes [26, 27]. Simic et al. [28] developed an interdigitated flexible sensor on the paper substrate for bacterial detection. There was a strong correlation between the sensor impedance and the bacterial concentration. Varshney et al. [29] embedded gold interdigital microelectrodes into a microfluidic flow cell to fabricate an impedance biosensor for the rapid detection of pathogens. Interdigital electrode sensors had great advantages in the detection of microorganisms. However, the three-dimensional finite element simulation showed that the random distribution of microbial cells on the microelectrode surface limited the detection ability [30, 31]. Therefore, it is of great significance to apply an effective method to concentrate microbial cells and confine the cell distribution. This may improve the detection performance of the impedance biosensor based on interdigital microelectrodes.The constant negative potential has been used to attract microorganisms to the target electrode surface [32]. In addition, dielectrophoretic [33] and electrohydrodynamic forces were also applied to focus particles for biosensor enhancement [34]. Wu et al. [35] detected the microorganisms by electrical impedance spectroscopy with asymmetric-polarization AC electroosmotic trapping. In their work, the microorganisms aggregated at the electrode surface. It was suggested that the cells located between two microelectrodes might produce more significant changes in suspension impedance than the cells located above the microelectrodes [30].Acoustophoresis has been widely adopted for trapping, separation, concentration, and washing [36]. Micron-sized particles, including cells, can be manipulated by acoustic radiation forces in the ultrasonic field [37, 38]. Nakao et al. [39] applied a kilohertz-order ultrasound standing wave technique to generate scaffold-free three-dimensional aggregates of cells in a cell culture dish. Johansson et al. [40] developed a method for manipulating particles in a continuous flow by the surface acoustic wave excitation.In order to enhance the performance of the impedance-based yeast detection, the present study proposed an impedimetric biosensor with ultrasonic-assisted cell alignment for the detection of yeast. This biosensor combined electrical impedance spectroscopy with acoustophoresis. The ultrasonic field was applied to enrich yeast cells and confine them to the gaps between two adjacent microelectrodes. Additionally, the numerical simulation of this sensor was conducted by the software COMSOL. To the best of our knowledge, there are few reports on the combination of electrical impedance technology with ultrasonic particle manipulation for yeast detection. The biosensor proposed in this work integrated interdigital microelectrodes into a microfluidic device. It had the advantage of small demand for samples and reagents. This was helpful for developing an easy-to-use, rapid, and efficient detection method of yeasts.


## 2. Background Theory

### 2.1. Forces on a Suspended Particle

For the aqueous suspensions of biological particles with diameters larger than 2μm, the acoustic radiation force plays a more important role than the streaming-induced drag force in acoustophoresis [41]. In the present study, yeast suspensions were modeled as single-cell dispersions, where the cells were represented by spherical particles with several microns in diameter. The interaction between cells was ignored. The COMSOL Particle Tracing Module was applied to investigate the motion of cells suspended in the microchannel. The behavior of the cells was governed by Newton’s law of motion. To determine the time-dependent position of cells, the acoustic radiation force, the streaming-induced drag force, and the gravity were taken into account. In the standing wave field, the time-averaged acoustic radiation force on a spherical particle Fac is related to the gradients of the time-averaged kinetic and potential energy densities [42–44]. The kinetic energy density is a function of the acoustic velocity, and the potential energy density is a function of the acoustic pressure. The acoustic radiation force is given by
(1)Fac=V∇3ρp−ρm2ρp+ρm⋅ρmv22−1−βpβm⋅p22ρmcm2,where V is the volume of the cell, ρp is the density of the cell, ρm is the density of the medium, cm is the sound velocity in the medium, p and v are the magnitudes of the pressure and velocity fields, the angled brackets denote time average, and βp and βm represent the compressibilities of the cell and medium, respectively. The Stokes drag force is given by
(2)Fdrag=6πηrvpm,where η represents the dynamic viscosity of the medium, r is the radius of the cell, and vpm is the particle velocity relative to the medium [41, 45].


### 2.2. Electric Field and Current

In the impedance scanning of cell suspensions, the excitation signal can be introduced through a group of interdigital microelectrodes, and the generated current flows out through another group of interdigital microelectrodes. The potential distribution in the cell suspension can be described by the following equation:(3)−∇⋅σ+jωε0ε⋅∇φ=0,j=−1,where σ is the electrical conductivity, ω is the angular frequency of the excitation signal, ε0 is the dielectric constant of vacuum, ε is the relative dielectric constant, and φ is the electrical potential. The mathematical form of the boundary conditions is
(4)φ=U,onS1,φ=0,onS2,σ+jωε0ε⋅∂φ∂n⇀=0,onS3,where n⇀ is the outward unit normal vector of the boundary surface, S1 is the surface of the excitation electrode, S2 is the surface of the ground electrode, and S3 is the other interface between the cell suspension and the walls of the microchannel [30, 46]. A time-dependent electric field with the frequency ω will produce an electric current density:
(5)J=−σ+jωε0ε∇φ,where J is the current density.


## 2.1. Forces on a Suspended Particle

For the aqueous suspensions of biological particles with diameters larger than 2μm, the acoustic radiation force plays a more important role than the streaming-induced drag force in acoustophoresis [41]. In the present study, yeast suspensions were modeled as single-cell dispersions, where the cells were represented by spherical particles with several microns in diameter. The interaction between cells was ignored. The COMSOL Particle Tracing Module was applied to investigate the motion of cells suspended in the microchannel. The behavior of the cells was governed by Newton’s law of motion. To determine the time-dependent position of cells, the acoustic radiation force, the streaming-induced drag force, and the gravity were taken into account. In the standing wave field, the time-averaged acoustic radiation force on a spherical particle Fac is related to the gradients of the time-averaged kinetic and potential energy densities [42–44]. The kinetic energy density is a function of the acoustic velocity, and the potential energy density is a function of the acoustic pressure. The acoustic radiation force is given by
(1)Fac=V∇3ρp−ρm2ρp+ρm⋅ρmv22−1−βpβm⋅p22ρmcm2,where V is the volume of the cell, ρp is the density of the cell, ρm is the density of the medium, cm is the sound velocity in the medium, p and v are the magnitudes of the pressure and velocity fields, the angled brackets denote time average, and βp and βm represent the compressibilities of the cell and medium, respectively. The Stokes drag force is given by
(2)Fdrag=6πηrvpm,where η represents the dynamic viscosity of the medium, r is the radius of the cell, and vpm is the particle velocity relative to the medium [41, 45].


## 2.2. Electric Field and Current

In the impedance scanning of cell suspensions, the excitation signal can be introduced through a group of interdigital microelectrodes, and the generated current flows out through another group of interdigital microelectrodes. The potential distribution in the cell suspension can be described by the following equation:(3)−∇⋅σ+jωε0ε⋅∇φ=0,j=−1,where σ is the electrical conductivity, ω is the angular frequency of the excitation signal, ε0 is the dielectric constant of vacuum, ε is the relative dielectric constant, and φ is the electrical potential. The mathematical form of the boundary conditions is
(4)φ=U,onS1,φ=0,onS2,σ+jωε0ε⋅∂φ∂n⇀=0,onS3,where n⇀ is the outward unit normal vector of the boundary surface, S1 is the surface of the excitation electrode, S2 is the surface of the ground electrode, and S3 is the other interface between the cell suspension and the walls of the microchannel [30, 46]. A time-dependent electric field with the frequency ω will produce an electric current density:
(5)J=−σ+jωε0ε∇φ,where J is the current density.


## 3. Structure of the Biosensor

The structure of the biosensor is shown in Figure1. The biosensor was composed of a quartz substrate, the interdigitated microelectrodes, a microfluidic chamber, the coupling gel, and an ultrasonic transducer. The dimensions of the interdigitated microelectrodes are shown in Figure 2. The microfluidic chamber was fabricated using acrylic plastic (PMMA). On the top wall of the microfluidic chamber, the inlet and outlet with a diameter of 2 mm were added. The ultrasonic transducer was fabricated using a PZT-4 piezoelectric ceramic. The piezoelectric ceramic was excited at a frequency of 5 MHz. The coupling gel was used to enhance the transmission efficiency of ultrasonic waves from the piezoelectric ceramic to the microfluidic chamber. This structure formed a plane wave resonator where a standing wave was produced in the fluid medium. Under the influence of radiation forces, the cells would move toward the pressure nodal planes. The width of the microfluidic chamber and the frequency of ultrasonic waves were determined to make sure that the lateral positions of the pressure nodes were between two adjacent microelectrodes. The anti-yeast antibody was immobilized onto the bottom surface of the microfluidic chamber using a well-established method [47]. The detection process of yeasts was as follows: firstly, the yeast suspension was dropped into the liquid inlet of the biosensor chip, and the suspension filled the microfluidic cavity and flowed to the liquid outlet by capillary effect. Then, the excitation signal of the ultrasonic transducer was generated, and the yeast cells were captured at specific locations in the microfluidic chamber. Thirty seconds later, the ultrasonic excitation signal was turned off. The biosensor was allowed to stand for 15 minutes so that the suspended yeast cells settled on the bottom surface of the microfluidic chamber and were bound to the antibody. Fresh normal saline was pumped into the microfluidic chamber to wash away particles that did not bind to antibodies. Finally, an AC voltage was applied to the interdigital microelectrodes. The yeast cell concentration was quantified by analyzing the impedance spectrum.Figure 1
The structure of the biosensor. (a) A schematic of the biosensor chip. (b) A cross-sectional view of the biosensor chip.
(a)(b)Figure 2
The dimensions of the interdigitated microelectrodes. The area marked by a red rectangle is enlarged at the right.


## 4. Finite Element Simulations

### 4.1. Geometric Configuration

Finite element analysis was conducted to validate the feasibility of the proposed biosensor. The software COMSOL Multiphysics version 5.5 was applied to set up and analyze the acoustic-electric coupling model. Because of the symmetry of the biosensor structure, the model was set up as a 2D problem. The geometric configuration (cross-section of the biosensor) is shown in Figure3. The width and height of the quartz substrate were 3.75 mm and 0.2 mm, respectively. The microfluidic chamber was simulated by a rectangle with dimensions of 1.9×0.15 mm. The width and height of the PMMA plastic block were 3 mm and 0.2 mm, respectively. PMMA (Young’s modulus 3 GPa, Poisson’s ratio 0.4) was considered an isotropic material. The interdigitated microelectrodes consisted of 6 gold digital electrode pairs with a 110 μm digit width. The gap between two adjacent fingers was 40 μm. The rectangular cross-section of the ultrasonic transducer was 732 μm wide and 200 μm high. Yeast cells were simplified into spheres with a shell [48]. The diameter of the cell was randomly distributed with a mean of 8 μm. Electrical characteristic parameters of yeast cells were obtained from the literature [49]. As the thickness of the cell membrane was much smaller than the size of the microfluidic chamber and the conductivity of the membrane was smaller than that of the surrounding medium, the contact impedance boundary condition was used to reduce the number of mesh elements and save computing resources. The contact impedance boundary condition is defined as
(6)n⋅J=1dσ+jωεrε0U1−U2,where n is the unit normal vector of the cell membrane boundary, J is the current density, d is the thickness of the outer shell of the bacterial cell, σ and εr are the electrical conductivity and relative dielectric permittivity of the shell, respectively, U1 is the potential of the intracellular medium, and U2 is the potential of the extracellular medium [50].Figure 3
The geometric configuration of the 2D biosensor model. The line segments marked with “-” and “+” indicate the ground electrodes and positive electrodes, respectively.


### 4.2. Mesh Generation

In order to investigate the convergence of the solving process, the maximum length of the computational mesh elements near the microfluidic chamber wall,Lb, was changed into a series of different values and the trend of solution results was depicted. The maximum length of mesh elements in other domains was set to be 5Lb, as shown in Figure 4(a). Lb ranged from λ/10 to λ/500, wherein λ represented the ultrasonic wavelength in the fluid. The convergence for a solution s was evaluated by using the following function [51]:
(7)Cs=∫s−sref2dydz∫sref2dydz.Figure 4
(a) Computational mesh elements. The maximum size of the mesh elements near the solid-liquid boundary isLb, and the maximum size of the mesh elements in other domains is five times larger. (b) A semilogarithmic plot of the convergence index C for pressure field solutions obtained with varied mesh element sizes. The threshold of C=0.01 (denoted by the straight dashed line) was selected to ensure the accuracy of the numerical solutions and make the computational cost acceptable.
(a)(b)The letterC is the convergence index, s is the solution, and sref is the reference solution obtained when Lb equals λ/600. Figure 4(b) shows the changing trend of the convergence as the maximum mesh element size decreases. In order to get a suitable convergence index value, the parameter Lb=1.2μm (i.e., λ/Lb=250) was chosen for the present study, leading to 218353 triangular elements.


### 4.3. Acoustic Field

The acoustical system was simulated in the frequency domain by coupling fundamental physics interfaces, the electromechanical, solid mechanical, and acoustic pressure modules. In order to simplify the model, the adhesive and couplant at the interface of materials were ignored. The bonding between different materials was assumed to be perfect. Figure5 shows the computational domains and the boundaries. The domain in the microfluidic chamber (Ω3) was modeled by the acoustic pressure module. The PMMA structure (Ω2) and the piezoelectric ceramic (Ω1) were analyzed by the module for solid mechanics of linear elastic materials. Besides, the piezoelectric ceramic was modeled by coupling solid mechanics with electrostatic physics. The ultrasonic transducer was activated by a 5 MHz sine-wave voltage signal with an amplitude of 30 V (peak-to-peak). The interaction between fluid and solid is described by the following equations (on the fluid-solid interface):
(8)σ⋅n=−pn,an=−n∇pρ,where σ is the stress vector, n is the unit normal vector of the fluid-solid surface, p is the pressure, an is the normal acceleration applied to the fluid, and ρ is the density of the fluid. The fluid medium of the cell suspensions used in the present study was the saline solution (0.9% NaCl).Figure 5
The computational domains and the boundaries.The bottom wall of the microfluidic chamber (H-I) was modeled with a hard boundary condition because the quartz substrate had a relatively high stiffness compared to the PMMA material. Therefore, at the bottom wall, the normal component of the fluid velocity was set to be zero. The boundaries F-H, F-G, and G-I were the acoustic-structural coupling boundaries. The fixed boundary conditions were applied to the boundaries D-E, E-H, and I-J. The boundary condition applied to the boundary A-D was the roller support. The boundaries A-B, B-C, and C-J were the stress-free boundaries of the solids. In the electrostatic module, the electric potential at the boundary A-D was kept at zero, and a 30 V voltage was applied to the boundary B-E. The boundaries A-B and D-E were set with zero charge.


### 4.4. Particle Tracing

The standing wave was applied in they-direction. The cells moved under the control of the acoustic radiation force, the streaming-induced drag force, the gravity, and the buoyancy. The trajectory could be described by a pair of time-dependent coordinates, yt,zt. The cell motion for 30 seconds was investigated. The density of yeast cells ρp used in this study was 1.1 g/mL [52]. Particle tracing was conducted in the time domain by using the Particle Tracing for Fluid Flow module. The computational domain was the region Ω3 shown in Figure 5. Acoustic radiation forces exerted on the cells, the cell velocity, and locations were predicted from the acoustic pressure distribution obtained in the previous calculation steps. A normal distribution of the cell diameter (mean 8 μm) with a standard deviation of 1 μm was applied for the simulation. Initial positions of the cells were randomly selected and distributed uniformly in the computational domain. The cell number was determined by multiplying the cell concentration and the volume of the microfluidic chamber. The compressibility of the cell was 384 TPa-1 [53].


### 4.5. Impedance Measurement

After the piezoelectric excitation, the yeast cells were aligned between two neighboring fingers of the interdigitated microelectrodes. Then, the device was left to stand for 15 minutes, and the suspended cells fell onto the bottom of the microfluidic chamber. The position coordinates of cells were obtained from the Particle Tracing for Fluid Flow module and used to build the electrical model. In order to simplify the geometry of the model and save computing resources, a single shell model for the yeast cell was used in the present study. Some material parameters used in this study are listed in Table1. Impedance characteristics of the cell suspension were simulated in the frequency domain by using the Electric Currents module. The 30 mVpp AC voltages with frequencies ranging from 1 Hz to 1 MHz were applied to the interdigital electrodes marked with “+,” as shown in Figure 3. Other electrodes marked with “-” were set to ground potential. The walls of the microfluidic chamber were regarded as electrically nonconductive. The impedance of the saline solution without cells was taken as a control. Normalized impedance variations (NIV) corresponding to suspensions of different cell concentrations are defined as
(9)NIVf=Zf−Z0fZ0f,where Z0f is the impedance of the control at the frequency f, Z denotes the modulus of Z, and Zf is the impedance of the cell suspension. The impedance spectra of suspensions with concentrations of 5×103/mL, 1×104/mL, 2×104/mL, and 4×104/mL were simulated. The mean and standard deviation of the impedance were calculated from the simulation results obtained with 10 different randomly selected initial position distributions of yeast cells.Table 1
Material parameters.
MaterialSaline solutionYeast cellPMMACell membraneCytoplasmDensity (kg/m3)1004.611001150——Speed of sound (m/s)149015052590——Compressibility (TPa-1)4443841.3——Young’s modulus (GPa)——3——Poisson’s ratio——0.4——Viscosity (mPa·s)0.893————Conductivity (S/m)1.6——10−71Relative permittivity80——580Thickness (nm)———5—


## 4.1. Geometric Configuration

Finite element analysis was conducted to validate the feasibility of the proposed biosensor. The software COMSOL Multiphysics version 5.5 was applied to set up and analyze the acoustic-electric coupling model. Because of the symmetry of the biosensor structure, the model was set up as a 2D problem. The geometric configuration (cross-section of the biosensor) is shown in Figure3. The width and height of the quartz substrate were 3.75 mm and 0.2 mm, respectively. The microfluidic chamber was simulated by a rectangle with dimensions of 1.9×0.15 mm. The width and height of the PMMA plastic block were 3 mm and 0.2 mm, respectively. PMMA (Young’s modulus 3 GPa, Poisson’s ratio 0.4) was considered an isotropic material. The interdigitated microelectrodes consisted of 6 gold digital electrode pairs with a 110 μm digit width. The gap between two adjacent fingers was 40 μm. The rectangular cross-section of the ultrasonic transducer was 732 μm wide and 200 μm high. Yeast cells were simplified into spheres with a shell [48]. The diameter of the cell was randomly distributed with a mean of 8 μm. Electrical characteristic parameters of yeast cells were obtained from the literature [49]. As the thickness of the cell membrane was much smaller than the size of the microfluidic chamber and the conductivity of the membrane was smaller than that of the surrounding medium, the contact impedance boundary condition was used to reduce the number of mesh elements and save computing resources. The contact impedance boundary condition is defined as
(6)n⋅J=1dσ+jωεrε0U1−U2,where n is the unit normal vector of the cell membrane boundary, J is the current density, d is the thickness of the outer shell of the bacterial cell, σ and εr are the electrical conductivity and relative dielectric permittivity of the shell, respectively, U1 is the potential of the intracellular medium, and U2 is the potential of the extracellular medium [50].Figure 3
The geometric configuration of the 2D biosensor model. The line segments marked with “-” and “+” indicate the ground electrodes and positive electrodes, respectively.


## 4.2. Mesh Generation

In order to investigate the convergence of the solving process, the maximum length of the computational mesh elements near the microfluidic chamber wall,Lb, was changed into a series of different values and the trend of solution results was depicted. The maximum length of mesh elements in other domains was set to be 5Lb, as shown in Figure 4(a). Lb ranged from λ/10 to λ/500, wherein λ represented the ultrasonic wavelength in the fluid. The convergence for a solution s was evaluated by using the following function [51]:
(7)Cs=∫s−sref2dydz∫sref2dydz.Figure 4
(a) Computational mesh elements. The maximum size of the mesh elements near the solid-liquid boundary isLb, and the maximum size of the mesh elements in other domains is five times larger. (b) A semilogarithmic plot of the convergence index C for pressure field solutions obtained with varied mesh element sizes. The threshold of C=0.01 (denoted by the straight dashed line) was selected to ensure the accuracy of the numerical solutions and make the computational cost acceptable.
(a)(b)The letterC is the convergence index, s is the solution, and sref is the reference solution obtained when Lb equals λ/600. Figure 4(b) shows the changing trend of the convergence as the maximum mesh element size decreases. In order to get a suitable convergence index value, the parameter Lb=1.2μm (i.e., λ/Lb=250) was chosen for the present study, leading to 218353 triangular elements.


## 4.3. Acoustic Field

The acoustical system was simulated in the frequency domain by coupling fundamental physics interfaces, the electromechanical, solid mechanical, and acoustic pressure modules. In order to simplify the model, the adhesive and couplant at the interface of materials were ignored. The bonding between different materials was assumed to be perfect. Figure5 shows the computational domains and the boundaries. The domain in the microfluidic chamber (Ω3) was modeled by the acoustic pressure module. The PMMA structure (Ω2) and the piezoelectric ceramic (Ω1) were analyzed by the module for solid mechanics of linear elastic materials. Besides, the piezoelectric ceramic was modeled by coupling solid mechanics with electrostatic physics. The ultrasonic transducer was activated by a 5 MHz sine-wave voltage signal with an amplitude of 30 V (peak-to-peak). The interaction between fluid and solid is described by the following equations (on the fluid-solid interface):
(8)σ⋅n=−pn,an=−n∇pρ,where σ is the stress vector, n is the unit normal vector of the fluid-solid surface, p is the pressure, an is the normal acceleration applied to the fluid, and ρ is the density of the fluid. The fluid medium of the cell suspensions used in the present study was the saline solution (0.9% NaCl).Figure 5
The computational domains and the boundaries.The bottom wall of the microfluidic chamber (H-I) was modeled with a hard boundary condition because the quartz substrate had a relatively high stiffness compared to the PMMA material. Therefore, at the bottom wall, the normal component of the fluid velocity was set to be zero. The boundaries F-H, F-G, and G-I were the acoustic-structural coupling boundaries. The fixed boundary conditions were applied to the boundaries D-E, E-H, and I-J. The boundary condition applied to the boundary A-D was the roller support. The boundaries A-B, B-C, and C-J were the stress-free boundaries of the solids. In the electrostatic module, the electric potential at the boundary A-D was kept at zero, and a 30 V voltage was applied to the boundary B-E. The boundaries A-B and D-E were set with zero charge.


## 4.4. Particle Tracing

The standing wave was applied in they-direction. The cells moved under the control of the acoustic radiation force, the streaming-induced drag force, the gravity, and the buoyancy. The trajectory could be described by a pair of time-dependent coordinates, yt,zt. The cell motion for 30 seconds was investigated. The density of yeast cells ρp used in this study was 1.1 g/mL [52]. Particle tracing was conducted in the time domain by using the Particle Tracing for Fluid Flow module. The computational domain was the region Ω3 shown in Figure 5. Acoustic radiation forces exerted on the cells, the cell velocity, and locations were predicted from the acoustic pressure distribution obtained in the previous calculation steps. A normal distribution of the cell diameter (mean 8 μm) with a standard deviation of 1 μm was applied for the simulation. Initial positions of the cells were randomly selected and distributed uniformly in the computational domain. The cell number was determined by multiplying the cell concentration and the volume of the microfluidic chamber. The compressibility of the cell was 384 TPa-1 [53].


## 4.5. Impedance Measurement

After the piezoelectric excitation, the yeast cells were aligned between two neighboring fingers of the interdigitated microelectrodes. Then, the device was left to stand for 15 minutes, and the suspended cells fell onto the bottom of the microfluidic chamber. The position coordinates of cells were obtained from the Particle Tracing for Fluid Flow module and used to build the electrical model. In order to simplify the geometry of the model and save computing resources, a single shell model for the yeast cell was used in the present study. Some material parameters used in this study are listed in Table1. Impedance characteristics of the cell suspension were simulated in the frequency domain by using the Electric Currents module. The 30 mVpp AC voltages with frequencies ranging from 1 Hz to 1 MHz were applied to the interdigital electrodes marked with “+,” as shown in Figure 3. Other electrodes marked with “-” were set to ground potential. The walls of the microfluidic chamber were regarded as electrically nonconductive. The impedance of the saline solution without cells was taken as a control. Normalized impedance variations (NIV) corresponding to suspensions of different cell concentrations are defined as
(9)NIVf=Zf−Z0fZ0f,where Z0f is the impedance of the control at the frequency f, Z denotes the modulus of Z, and Zf is the impedance of the cell suspension. The impedance spectra of suspensions with concentrations of 5×103/mL, 1×104/mL, 2×104/mL, and 4×104/mL were simulated. The mean and standard deviation of the impedance were calculated from the simulation results obtained with 10 different randomly selected initial position distributions of yeast cells.Table 1
Material parameters.
MaterialSaline solutionYeast cellPMMACell membraneCytoplasmDensity (kg/m3)1004.611001150——Speed of sound (m/s)149015052590——Compressibility (TPa-1)4443841.3——Young’s modulus (GPa)——3——Poisson’s ratio——0.4——Viscosity (mPa·s)0.893————Conductivity (S/m)1.6——10−71Relative permittivity80——580Thickness (nm)———5—


## 5. Results and Discussion

### 5.1. Acoustic Pressure Distribution and Radiation Force

When the 5 MHz drive voltage with an amplitude of 30 Vpp was applied, a pressure distribution was formed in the microfluidic chamber. It was solved using the acoustic pressure module and displayed in Figure 6. The colors indicate the pressure magnitudes. The maximum acoustic pressure is 2.0841×105Pa. The excitation signal results in about 6 wavelengths and 13 pressure node planes in the y-direction. The pressure node plane near the side wall of the microfluidic chamber is distorted because of the edge effect.Figure 6
The pressure distribution in the microfluidic chamber.The acoustic radiation forces on the cells with a diameter of 8μm were estimated from the pressure field. The acoustic radiation force in the y-z cross-section of the microfluidic chamber is shown in Figure 7. The y-components of the acoustic radiation forces (ARFy) range from -3.24 pN to 2.04 pN. The z-components of the acoustic radiation forces (ARFz) range from -1.35 pN to 1.85 pN. Figures 7(a) and 7(c) illustrate the distributions of normalized ARFy and ARFz, respectively. In Figures 7(b) and 7(d), the amplitudes of normalized ARFy and ARFz versus the positions along the horizontal (in Figure 7(a)) and vertical (in Figure 7(c)) white lines in the subfigures are displayed. As can be seen, the cells will be trapped in some vertical planes where the ARFy is zero. According to the directions of ARFy near the planes, the y-coordinates of the trapped cells will be around 0.032, 0.176, 0.327, 0.47, 0.63, 0.78, 0.93, 1.08, 1.24, 1.39, 1.55, 1.71, and 1.84. This means the cells will be localized at the pressure nodes between the adjacent microelectrode fingers. There are no stable localized positions in the z-direction. In the derivation of Equation (1), the particle radius was assumed to be much smaller than the ultrasonic wavelength. The ultrasound with the frequency of 5 MHz was applied for cell manipulation, resulting in a wavelength of 300 μm (much larger than the cell diameter of 8 μm). The above hypothesis was satisfied.Figure 7
The distribution of acoustic radiation forces in they-z cross-section. (a) The distribution of normalized y-components of the acoustic radiation forces. (b) The amplitude of normalized ARFy versus the positions along the horizontal white line in (a). The black arrowheads indicate the direction of ARFy near the pressure nodes (orange dots) where the cells will be trapped. (c) The distribution of normalized z-components of the acoustic radiation forces. (d) The amplitude of normalized ARFz versus the positions along the vertical white line in (c).
(a)(b)(c)(d)


### 5.2. Acoustophoretic Cell Tracks

According to the distribution of the acoustic radiation force, the locations of the yeast cells at different time points could be predicted. Simulations were implemented in the transient mode from 0 s to 30 s with a time step of 0.2 s. Figure8 shows the trajectories of cells in the microfluidic chamber. The colors indicate the velocity of the cells. It is shown that the cells move to 13 pressure node planes from adjacent zones.Figure 8
The trajectories of the cells in the microfluidic chamber.In order to determine a suitable ultrasonic treatment time for cell alignment, the locations of cells with different diameters (4μm, 8 μm, and 10 μm) at different time points of ultrasonic action were investigated. In Figure 9, the results under a cell concentration of 2×104/mL are displayed.Figure 9
Locations of cells with different diameters at different time points of ultrasonic action.


### 5.3. Impedance Spectrum

The coordinates and radius of the yeast cells were imported from the Particle Tracing for Fluid Flow module and used as parameters for setting up the electrical model. The impedance spectrum was simulated in the frequency domain from 1 Hz to 1 MHz with a step of 500 Hz. Both the magnitude of the impedance and the phase angle were calculated. Figure10 shows the impedance spectra obtained with and without ultrasonic treatments for samples of different cell concentrations. The impedance spectra were simulated with cell concentrations of 5×103/mL, 1×104/mL, 2×104/mL, and 4×104/mL, respectively. The magnitude of the impedance increased as the cell concentration rose. The magnitude of the impedance decreased with the increase in frequency. As shown in Figures 10(c) and 10(d), the phase angle decreases gradually from a value close to zero to a negative one when the frequency increases. The larger the cell concentration, the more the phase angle decreases. The effect of cell dielectric properties on the impedance becomes remarkable at the high frequency. The changes in the impedance of the cell suspensions with ultrasonic-assisted cell alignment are bigger than those without ultrasonic treatments. Normalized impedance variations at 16 kHz [29] were used to investigate the performance of the impedimetric biosensor.Figure 10
The impedance spectra obtained with and without ultrasonic treatments for samples with different yeast cell concentrations. Different colors stand for the data obtained with different cell concentrations. The impedance of the saline solution without cells was taken as the blank control. (a) The magnitudes of the impedance of different samples without ultrasonic treatments. (b) The magnitudes of the impedance of different samples with ultrasonic-assisted cell alignment. (c) The phase angles of different samples without ultrasonic treatments. (d) The phase angles of different samples with ultrasonic-assisted cell alignment.
(a)(b)(c)(d)Figure11 shows the normalized impedance variations obtained from samples with different cell concentrations and different treatments. In Figure 11(a), for the samples without ultrasonic treatments, the normalized impedance variations are 0.154±0.0165, 0.2419±0.0351, 0.4141±0.0182, and 0.7706±0.0455 (n=10), when the cell concentrations are 5×103/mL, 1×104/mL, 2×104/mL, and 4×104/mL, respectively. After the ultrasonic-assisted cell alignment, the normalized impedance variations increase to 0.1932±0.0194, 0.3028±0.0337, 0.4879±0.0242, and 0.8324±0.0316 (n=10) for the samples with cell concentrations of 5×103/mL, 1×104/mL, 2×104/mL, and 4×104/mL, respectively. The impedance increased as the cell concentration increased. This was because the conductivity of the yeast cell was lower than that of the saline solution and the volume proportion of the liquid medium was reduced when the cell concentration increased. The result was consistent with some reports in the literature [28, 54]. At the same cell concentration, the ultrasonic-assisted cell alignment led to a bigger impedance variation. It could be explained that the acoustic field made the cells gather between the adjacent electrodes, resulting in a higher local concentration, and the electric field intensity reached the maximum in the area between the adjacent electrodes. As can be seen in Figure 11(b), there is approximately a linear relationship between the cell concentrations and the normalized impedance variations. For the samples without ultrasonic treatments, the relationship can be represented by an equation: NIV=1.859×10−5C+0.03734 (R2=0.9930), where NIV is the normalized impedance variation and C is the cell concentration. For the samples with ultrasonic-assisted cell alignment, the equation is NIV=1.98×10−5C+0.06619 (R2=0.9801). The impedimetric measurement with ultrasonic-assisted cell alignment had a higher sensitivity. This indicated that the impedimetric biosensor in the present work was feasible for the detection of yeast.Figure 11
Normalized impedance variations simulated with different cell concentrations and different treatments. The error bars represent the standard deviation of results (n=10). (a) The histogram of the normalized impedance variations. The black bars indicate the data from samples without ultrasonic treatments, while the grey bars stand for the data from those with ultrasonic treatments. (b) The linear regression between the cell concentrations and the normalized impedance variations.
(a)(b)From Figure11(b), it can be seen that there is a positive intercept for zero cell concentration. However, in theory, when the cell concentration is zero, the normalized impedance variation should be zero. This discrepancy can be explained in two aspects. Firstly, due to the existence of saturation, the relationship between the impedance change and the yeast cell concentration is not completely linear in a large concentration range. In the case of low cell concentration, this relationship is approximately linear. Fitting the relationship between the impedance change and the yeast cell concentration with a linear equation will bring some errors. Secondly, in this study, the random distributions of the cell size and initial position were introduced into the model. This resulted in the variation of impedance data at the same cell concentration. The variation would lead to obvious errors in linear regression.The present study proposed an impedimetric biosensor with ultrasonic-assisted cell alignment for the detection of yeast. Its feasibility was preliminarily verified by the finite element simulation. In the present study, the acoustic field was analyzed by using a simplified 2D model. The pressure distribution in the longitudinal direction of the chamber was assumed to be homogeneous. The actual sound field distribution was three-dimensional, and there was a deviation between the simulation result based on the 2D model and the real value. When a standing wave was generated in the microchamber, the following relation was satisfied:nλ/2=W. The letter n stands for the mode of the vibration, λ is the ultrasonic wavelength, and W represents the width of the microchamber. Cells were trapped in the “pressure node” plane or the “antinode” plane, depending on the density and compressibility of the cell and the fluid medium. The positions in the y-direction where the cells were trapped could easily be influenced by the ultrasonic frequency and the dimension of the microfluidic chamber. This problem needs to be considered in the experimental process. Future studies will take into account optimizing the geometry structure of the microfluidic chamber and interdigital electrodes, including the width of the microelectrode finger and the distance between the fingers [30, 55].The model in this study did not take into account the cell-cell interactions. Forces between yeast cells might lead to agglomerations, especially when the cell concentration was high. This could result in the discrepancy between the impedance estimated by using the numerical model and that measured in experiments. In addition to the acoustic radiation force, the Stokes drag force, and the cell interaction forces, a force of attraction between the cell and the wall of the microfluidic chamber might play a role when the cell was very close to the wall. However, this attraction force was small compared to the acoustic radiation force.Additionally, in the fluid medium, cells would cause the scattering of sound waves and then affect the distribution of the sound pressure field. The change of the acoustic field caused by the existence of cells was neglected in this study. The distribution of the cell size could affect cell locations at the end of the acoustophoresis. A larger cell would take a shorter time to be positioned in the right place [56]. A small cell size led to a small acoustic radiation force, which made the cell unable to be located between interdigital microelectrodes in a short time, thus affecting the measured impedance value. However, in this study, the ultrasonic treatments lasted 30 s, and there was a 15-minute period for the cells to fall onto the bottom surface of the microfluidic chamber. The time was long enough for capturing most of the cells in the right place.During the impedance spectrum measurement, the linearity condition should be fulfilled by applying an excitation signal of sufficiently low amplitude. A perturbation of high amplitude may cause the distortion of the impedance spectrum, leading to incorrect conclusions. However, when the excitation amplitude is too small, the signal-to-noise ratio is low [57]. In our work, the amplitude of the sinusoidal voltage was 30 mV (peak-to-peak). Kramers-Kronig transforms [58] were applied to test the linearity of the measurement system. The impedance spectroscopy data obtained in our work was fitted to a modified Randles equivalent circuit with a constant phase element [28]. The fitting error was small. Kramers-Kronig tests were conducted using the commercial software ZView v4.0e (Scribner Associates). The electrical impedance spectra obtained by Kramers-Kronig transforms were in good agreement with the original data. It was reasonable to assume that the linearity criterion was satisfied in our impedance measurement system. Besides, in another study [54], a sinusoidal voltage of 50 mV was applied across the interdigitated microelectrodes of a biosensor to measure the impedance of bacterial suspensions. The excitation amplitude in our work was smaller.Another problem should be considered. Yeast cells are not completely spherical. Their behavior under the acoustic field in a fluidic medium is complicated. The effect of cell rotation on measurement results should be paid attention to. Numerical simulations using a cell geometry model with more fine structures will be conducted to verify the performance of the detection system further.An overview of the reported methods based on biosensors for yeast detection is presented in Table2. Tubía et al. [18] fabricated an interdigitated microelectrode sensor functionalized with antibodies and measured the impedance spectrum of the culture medium to monitor the growth of yeasts. This biosensor was suitable for the real-time detection of cell metabolic activity rather than the actual cell concentrations. Abdallah et al. [12] used biorecognition elements to modify the surface of a resonant photonic grating sensor and detected biofouling in fuel systems with a low limit of detection (17 cells/mL). The limit of detection of the method proposed in our work is estimated to be 16 cells/mL, according to FDA guidance [59]. The ability of our method for detecting yeast cells is comparable to that of their method. The advantage of our method may come from the lower detection cost because the detection process requires no expensive instruments, such as spectrometers. Another study [60] used superparamagnetic nanoparticles modified with affinity bioreceptors to enrich yeast cells. Enzyme molecules were bound to the cells. After that, amperometric detection of the yeasts was conducted by carbon screen-printed electrodes. This method had a very low detection limit and a wide linear range. However, the enzyme activity can be affected by sample properties such as the temperature and pH value. Terahertz slot antennas [14] were applied for the detection of individual yeast cells. The sensitivity was high, although the linear range was limited. Other research studies [20] have also promoted the development of yeast cell detection. Compared with the published biosensors, the sensor proposed in this paper has the advantages of low cost, easy operation, low reagent consumption, and easy integration into portable devices.Table 2
Comparison of the different biosensors used for the detection of yeasts.
MethodLimit of detectionCalibration rangeApplicationsAdvantagesReferenceInterdigitated microelectrode sensor functionalized with antibodies——Monitoring the growth of spoilage yeastsIn situ and real-time detection[18]Resonant photonic grating sensor functionalized with biorecognition elements17 cells/mL79-7.94×107 cells/mLThe detection of yeast contamination in fuel systemsHighly sensitive and rapid detection[12]Core-shell superparamagnetic nanoparticles modified with affinity bioreceptors and screen-printed electrodes for measuring the electrochemical process5 colony-forming units/mL10-106 colony-forming units/mLQuantification of the yeast content in wineDisposable, sensitive, highly selective[60]Impedance biochips—3.3×107‐1.7×108 cells/mLDetermination of yeast concentration in DI water and in glucoseContinuous detection[20]Terahertz slot antennas—0-50 cellsDetection of individual yeast cellsSensitive, nondestructive, label-free, on-site detection[14]According to Figure11, the impedance spectrum changes significantly with the change of yeast cell concentration. However, the model in this study did not consider the influences of the electric double layer at the interface between the interdigital microelectrodes and the electrolyte, the electrical characteristics of the antibody layer on the bottom of the microfluidic chamber, the kinetics of the cell-antibody binding, and the parasitic capacitance on the impedance spectrum. This limitation should be remedied in future studies. The specificity of the sensor needs to be further verified by experiments.


## 5.1. Acoustic Pressure Distribution and Radiation Force

When the 5 MHz drive voltage with an amplitude of 30 Vpp was applied, a pressure distribution was formed in the microfluidic chamber. It was solved using the acoustic pressure module and displayed in Figure 6. The colors indicate the pressure magnitudes. The maximum acoustic pressure is 2.0841×105Pa. The excitation signal results in about 6 wavelengths and 13 pressure node planes in the y-direction. The pressure node plane near the side wall of the microfluidic chamber is distorted because of the edge effect.Figure 6
The pressure distribution in the microfluidic chamber.The acoustic radiation forces on the cells with a diameter of 8μm were estimated from the pressure field. The acoustic radiation force in the y-z cross-section of the microfluidic chamber is shown in Figure 7. The y-components of the acoustic radiation forces (ARFy) range from -3.24 pN to 2.04 pN. The z-components of the acoustic radiation forces (ARFz) range from -1.35 pN to 1.85 pN. Figures 7(a) and 7(c) illustrate the distributions of normalized ARFy and ARFz, respectively. In Figures 7(b) and 7(d), the amplitudes of normalized ARFy and ARFz versus the positions along the horizontal (in Figure 7(a)) and vertical (in Figure 7(c)) white lines in the subfigures are displayed. As can be seen, the cells will be trapped in some vertical planes where the ARFy is zero. According to the directions of ARFy near the planes, the y-coordinates of the trapped cells will be around 0.032, 0.176, 0.327, 0.47, 0.63, 0.78, 0.93, 1.08, 1.24, 1.39, 1.55, 1.71, and 1.84. This means the cells will be localized at the pressure nodes between the adjacent microelectrode fingers. There are no stable localized positions in the z-direction. In the derivation of Equation (1), the particle radius was assumed to be much smaller than the ultrasonic wavelength. The ultrasound with the frequency of 5 MHz was applied for cell manipulation, resulting in a wavelength of 300 μm (much larger than the cell diameter of 8 μm). The above hypothesis was satisfied.Figure 7
The distribution of acoustic radiation forces in they-z cross-section. (a) The distribution of normalized y-components of the acoustic radiation forces. (b) The amplitude of normalized ARFy versus the positions along the horizontal white line in (a). The black arrowheads indicate the direction of ARFy near the pressure nodes (orange dots) where the cells will be trapped. (c) The distribution of normalized z-components of the acoustic radiation forces. (d) The amplitude of normalized ARFz versus the positions along the vertical white line in (c).
(a)(b)(c)(d)


## 5.2. Acoustophoretic Cell Tracks

According to the distribution of the acoustic radiation force, the locations of the yeast cells at different time points could be predicted. Simulations were implemented in the transient mode from 0 s to 30 s with a time step of 0.2 s. Figure8 shows the trajectories of cells in the microfluidic chamber. The colors indicate the velocity of the cells. It is shown that the cells move to 13 pressure node planes from adjacent zones.Figure 8
The trajectories of the cells in the microfluidic chamber.In order to determine a suitable ultrasonic treatment time for cell alignment, the locations of cells with different diameters (4μm, 8 μm, and 10 μm) at different time points of ultrasonic action were investigated. In Figure 9, the results under a cell concentration of 2×104/mL are displayed.Figure 9
Locations of cells with different diameters at different time points of ultrasonic action.


## 5.3. Impedance Spectrum

The coordinates and radius of the yeast cells were imported from the Particle Tracing for Fluid Flow module and used as parameters for setting up the electrical model. The impedance spectrum was simulated in the frequency domain from 1 Hz to 1 MHz with a step of 500 Hz. Both the magnitude of the impedance and the phase angle were calculated. Figure10 shows the impedance spectra obtained with and without ultrasonic treatments for samples of different cell concentrations. The impedance spectra were simulated with cell concentrations of 5×103/mL, 1×104/mL, 2×104/mL, and 4×104/mL, respectively. The magnitude of the impedance increased as the cell concentration rose. The magnitude of the impedance decreased with the increase in frequency. As shown in Figures 10(c) and 10(d), the phase angle decreases gradually from a value close to zero to a negative one when the frequency increases. The larger the cell concentration, the more the phase angle decreases. The effect of cell dielectric properties on the impedance becomes remarkable at the high frequency. The changes in the impedance of the cell suspensions with ultrasonic-assisted cell alignment are bigger than those without ultrasonic treatments. Normalized impedance variations at 16 kHz [29] were used to investigate the performance of the impedimetric biosensor.Figure 10
The impedance spectra obtained with and without ultrasonic treatments for samples with different yeast cell concentrations. Different colors stand for the data obtained with different cell concentrations. The impedance of the saline solution without cells was taken as the blank control. (a) The magnitudes of the impedance of different samples without ultrasonic treatments. (b) The magnitudes of the impedance of different samples with ultrasonic-assisted cell alignment. (c) The phase angles of different samples without ultrasonic treatments. (d) The phase angles of different samples with ultrasonic-assisted cell alignment.
(a)(b)(c)(d)Figure11 shows the normalized impedance variations obtained from samples with different cell concentrations and different treatments. In Figure 11(a), for the samples without ultrasonic treatments, the normalized impedance variations are 0.154±0.0165, 0.2419±0.0351, 0.4141±0.0182, and 0.7706±0.0455 (n=10), when the cell concentrations are 5×103/mL, 1×104/mL, 2×104/mL, and 4×104/mL, respectively. After the ultrasonic-assisted cell alignment, the normalized impedance variations increase to 0.1932±0.0194, 0.3028±0.0337, 0.4879±0.0242, and 0.8324±0.0316 (n=10) for the samples with cell concentrations of 5×103/mL, 1×104/mL, 2×104/mL, and 4×104/mL, respectively. The impedance increased as the cell concentration increased. This was because the conductivity of the yeast cell was lower than that of the saline solution and the volume proportion of the liquid medium was reduced when the cell concentration increased. The result was consistent with some reports in the literature [28, 54]. At the same cell concentration, the ultrasonic-assisted cell alignment led to a bigger impedance variation. It could be explained that the acoustic field made the cells gather between the adjacent electrodes, resulting in a higher local concentration, and the electric field intensity reached the maximum in the area between the adjacent electrodes. As can be seen in Figure 11(b), there is approximately a linear relationship between the cell concentrations and the normalized impedance variations. For the samples without ultrasonic treatments, the relationship can be represented by an equation: NIV=1.859×10−5C+0.03734 (R2=0.9930), where NIV is the normalized impedance variation and C is the cell concentration. For the samples with ultrasonic-assisted cell alignment, the equation is NIV=1.98×10−5C+0.06619 (R2=0.9801). The impedimetric measurement with ultrasonic-assisted cell alignment had a higher sensitivity. This indicated that the impedimetric biosensor in the present work was feasible for the detection of yeast.Figure 11
Normalized impedance variations simulated with different cell concentrations and different treatments. The error bars represent the standard deviation of results (n=10). (a) The histogram of the normalized impedance variations. The black bars indicate the data from samples without ultrasonic treatments, while the grey bars stand for the data from those with ultrasonic treatments. (b) The linear regression between the cell concentrations and the normalized impedance variations.
(a)(b)From Figure11(b), it can be seen that there is a positive intercept for zero cell concentration. However, in theory, when the cell concentration is zero, the normalized impedance variation should be zero. This discrepancy can be explained in two aspects. Firstly, due to the existence of saturation, the relationship between the impedance change and the yeast cell concentration is not completely linear in a large concentration range. In the case of low cell concentration, this relationship is approximately linear. Fitting the relationship between the impedance change and the yeast cell concentration with a linear equation will bring some errors. Secondly, in this study, the random distributions of the cell size and initial position were introduced into the model. This resulted in the variation of impedance data at the same cell concentration. The variation would lead to obvious errors in linear regression.The present study proposed an impedimetric biosensor with ultrasonic-assisted cell alignment for the detection of yeast. Its feasibility was preliminarily verified by the finite element simulation. In the present study, the acoustic field was analyzed by using a simplified 2D model. The pressure distribution in the longitudinal direction of the chamber was assumed to be homogeneous. The actual sound field distribution was three-dimensional, and there was a deviation between the simulation result based on the 2D model and the real value. When a standing wave was generated in the microchamber, the following relation was satisfied:nλ/2=W. The letter n stands for the mode of the vibration, λ is the ultrasonic wavelength, and W represents the width of the microchamber. Cells were trapped in the “pressure node” plane or the “antinode” plane, depending on the density and compressibility of the cell and the fluid medium. The positions in the y-direction where the cells were trapped could easily be influenced by the ultrasonic frequency and the dimension of the microfluidic chamber. This problem needs to be considered in the experimental process. Future studies will take into account optimizing the geometry structure of the microfluidic chamber and interdigital electrodes, including the width of the microelectrode finger and the distance between the fingers [30, 55].The model in this study did not take into account the cell-cell interactions. Forces between yeast cells might lead to agglomerations, especially when the cell concentration was high. This could result in the discrepancy between the impedance estimated by using the numerical model and that measured in experiments. In addition to the acoustic radiation force, the Stokes drag force, and the cell interaction forces, a force of attraction between the cell and the wall of the microfluidic chamber might play a role when the cell was very close to the wall. However, this attraction force was small compared to the acoustic radiation force.Additionally, in the fluid medium, cells would cause the scattering of sound waves and then affect the distribution of the sound pressure field. The change of the acoustic field caused by the existence of cells was neglected in this study. The distribution of the cell size could affect cell locations at the end of the acoustophoresis. A larger cell would take a shorter time to be positioned in the right place [56]. A small cell size led to a small acoustic radiation force, which made the cell unable to be located between interdigital microelectrodes in a short time, thus affecting the measured impedance value. However, in this study, the ultrasonic treatments lasted 30 s, and there was a 15-minute period for the cells to fall onto the bottom surface of the microfluidic chamber. The time was long enough for capturing most of the cells in the right place.During the impedance spectrum measurement, the linearity condition should be fulfilled by applying an excitation signal of sufficiently low amplitude. A perturbation of high amplitude may cause the distortion of the impedance spectrum, leading to incorrect conclusions. However, when the excitation amplitude is too small, the signal-to-noise ratio is low [57]. In our work, the amplitude of the sinusoidal voltage was 30 mV (peak-to-peak). Kramers-Kronig transforms [58] were applied to test the linearity of the measurement system. The impedance spectroscopy data obtained in our work was fitted to a modified Randles equivalent circuit with a constant phase element [28]. The fitting error was small. Kramers-Kronig tests were conducted using the commercial software ZView v4.0e (Scribner Associates). The electrical impedance spectra obtained by Kramers-Kronig transforms were in good agreement with the original data. It was reasonable to assume that the linearity criterion was satisfied in our impedance measurement system. Besides, in another study [54], a sinusoidal voltage of 50 mV was applied across the interdigitated microelectrodes of a biosensor to measure the impedance of bacterial suspensions. The excitation amplitude in our work was smaller.Another problem should be considered. Yeast cells are not completely spherical. Their behavior under the acoustic field in a fluidic medium is complicated. The effect of cell rotation on measurement results should be paid attention to. Numerical simulations using a cell geometry model with more fine structures will be conducted to verify the performance of the detection system further.An overview of the reported methods based on biosensors for yeast detection is presented in Table2. Tubía et al. [18] fabricated an interdigitated microelectrode sensor functionalized with antibodies and measured the impedance spectrum of the culture medium to monitor the growth of yeasts. This biosensor was suitable for the real-time detection of cell metabolic activity rather than the actual cell concentrations. Abdallah et al. [12] used biorecognition elements to modify the surface of a resonant photonic grating sensor and detected biofouling in fuel systems with a low limit of detection (17 cells/mL). The limit of detection of the method proposed in our work is estimated to be 16 cells/mL, according to FDA guidance [59]. The ability of our method for detecting yeast cells is comparable to that of their method. The advantage of our method may come from the lower detection cost because the detection process requires no expensive instruments, such as spectrometers. Another study [60] used superparamagnetic nanoparticles modified with affinity bioreceptors to enrich yeast cells. Enzyme molecules were bound to the cells. After that, amperometric detection of the yeasts was conducted by carbon screen-printed electrodes. This method had a very low detection limit and a wide linear range. However, the enzyme activity can be affected by sample properties such as the temperature and pH value. Terahertz slot antennas [14] were applied for the detection of individual yeast cells. The sensitivity was high, although the linear range was limited. Other research studies [20] have also promoted the development of yeast cell detection. Compared with the published biosensors, the sensor proposed in this paper has the advantages of low cost, easy operation, low reagent consumption, and easy integration into portable devices.Table 2
Comparison of the different biosensors used for the detection of yeasts.
MethodLimit of detectionCalibration rangeApplicationsAdvantagesReferenceInterdigitated microelectrode sensor functionalized with antibodies——Monitoring the growth of spoilage yeastsIn situ and real-time detection[18]Resonant photonic grating sensor functionalized with biorecognition elements17 cells/mL79-7.94×107 cells/mLThe detection of yeast contamination in fuel systemsHighly sensitive and rapid detection[12]Core-shell superparamagnetic nanoparticles modified with affinity bioreceptors and screen-printed electrodes for measuring the electrochemical process5 colony-forming units/mL10-106 colony-forming units/mLQuantification of the yeast content in wineDisposable, sensitive, highly selective[60]Impedance biochips—3.3×107‐1.7×108 cells/mLDetermination of yeast concentration in DI water and in glucoseContinuous detection[20]Terahertz slot antennas—0-50 cellsDetection of individual yeast cellsSensitive, nondestructive, label-free, on-site detection[14]According to Figure11, the impedance spectrum changes significantly with the change of yeast cell concentration. However, the model in this study did not consider the influences of the electric double layer at the interface between the interdigital microelectrodes and the electrolyte, the electrical characteristics of the antibody layer on the bottom of the microfluidic chamber, the kinetics of the cell-antibody binding, and the parasitic capacitance on the impedance spectrum. This limitation should be remedied in future studies. The specificity of the sensor needs to be further verified by experiments.


## 6. Conclusions

An impedimetric sensor with ultrasonic-assisted cell alignment for the detection of yeast was introduced. The modeling for this sensor was conducted by coupling the modules of Pressure Acoustics, Solid Mechanics, Electrostatics, Electric Currents, and Particle Tracing for Fluid Flow in the software COMSOL. The acoustic pressure distribution, the radiation force, the acoustophoretic cell tracks, and the impedance spectrum were investigated to clarify the working principle of the measurement system. According to the simulation results, the ultrasonic-assisted cell alignment was helpful for enhancing the detection performance. Besides, it can be combined with other technologies, such as immunochemistry and cell imprinting, to improve the detection efficiency for small particle targets. The simplified 2D model provided an effective tool for the design and optimization of biosensors. However, the experimental tests need to be carried out further to optimize the structure of the sensor.



---

*Source: 4514218-2022-09-24.xml*