Bacterial media, reagents and materials

Low salt LB medium contained 0.5 g/L NaCl, 10 g/L tryptone, and 5 g/L yeast extract, supplemented with 1–5% fetal bovine serum. Antibiotics tested in this study include ampicillin, ofloxacin, ciprofloxacin, vancomycin, and tobramycin. The sensors and receiver plate were fabricated on a flexible polyimide flex circuit board (Custom ordered from PCBWay Prototype to volume production Factories, Shenzhen, China). Oil-based polyurethane protective spray coating was purchased from MINWAX (New York, NY). Permittivity data were measured using an EIS analyzer (Model E4990A-20, Keysight, Santa Rosa, CA).

Sample preparation

Overnight bacterial cultures were grown in 25 mL low salt LB medium at 37 °C for 16 h with shaking at 200 rpm. To test antibiotic susceptibility, overnight cultures were used to inoculate low salt LB medium with a starting OD600 of 0.001. Three hundred µL of the inoculant was then aliquoted to a 96-well plate with LC sensor inserts and quickly transferred to a 30 °C culture room for growth monitoring.

Broth microdilution AST

A 96-well plate was inoculated with 200 µL of low salt LB medium with designated antibiotics at different concentrations and bacteria with a starting OD600 of 0.0001. The inoculated microplates were transferred to a 30 °C culture room for 16 h of incubation and then visually inspected to determine MIC.

Permittivity calculation

In order to calculate the complex permittivity of a bacterial culture, an equation can be derived from parameters of the LC sensor and the resonant frequencies collected from the EIS [28,29,30]:

$$\varepsilon =\frac_}_}-_+\frac___}$$

(1)

In which \(_\) is the permittivity of free space, \(_\) is the permittivity of substrate material, \(_\) is the zero-inductance frequency of the system, and C1, R1 are components of the sensor circuit (Fig. 1C). Additionally, \(k\) is the cell constant of the IDC defined by:

$$k=\frac\left(N-1\right)K\right)}^\right]}^\frac}\right]}$$

(2)

All parameters needed to calculate k can be found based on the sensor design (Fig. 1B), except for the elliptic integral of the first kind expressed as K[A]. Using Eqs. 1 & 2, a permittivity vs time plot was generated. Thus, the permittivity changes in the system can be tracked to monitor bacterial growth, allowing rapid assay of antibiotic susceptibility.

Signal processing

The resonant circuit consists of two sides, including a circuit with a coil and an IDC on the sensor side, and a detection coil and a signal generator/analyzer (Fig. 1C) on the scanner side. Circuit analysis [31] could be used to obtain the following equation from this circuit:

In this equation, Zint is considered as the background impedance of the system and is subtracted using the built-in function of the EIS. Zsensor can be represented using the frequency domain as:

$$_=j\omega _+\frac_}__}$$

(4)

Substituting Eq. (4) into Eq. (3), and combining with the subtraction of background noise \(_\) mentioned above, the representation of total impedance on the scanner side becomes:

$$_=\frac^^_}_-^___\right)}^+^_}^}+j\frac^^(\omega __\left(_-^___\right)-\omega _\right)}_-^___\right)}^+^_}^}$$

(5)

It is important to note that in this equation, ω (frequency), M (mutual inductance), and L2 (inductance of sensor coil) are all known parameters that can be controlled either by changing the input or the design of the IDC. This means only two parameters, the R1 and C1, are unknown and can be solved using Eq. 5 after setting the imaginary part of the impedance to 0 at the zero-reactance frequency (Eq. 6) and taking the derivative of the real part of the Eq. (3) to set ω to resonant frequency (Eq. 7).

$$_=\sqrt-\frac^^}}$$

(6)

With these two frequencies calculated, the complex permittivity of the IDC can be calculated with the two equations mentioned above (Eqs. 1 & 2).

Electromagnetic coupling analysis of the sensor

Two identical coils both with 0.035 mm wire thickness, 0.06 mm wire width, 0.06 mm wire gap, 50 turns with 25 turns on each side of the polyimide flex PCB was brought together within 1.2 mm distance separated by a 0.9 mm thick polystyrene plastic well bottom of a standard 96-well plate. Power was supplied to the receiver coil by the impedance EIS at 50 µA current level with frequencies ranging from 1 MHz to 12 MHz. Figure 2E shows the COMSOL simulation of the magnetic coupling of the two coils. The frequency sweep was performed with the EIS at a resolution of 1600 points, and the absolute impedance and phase shift of the system were recorded before and after the sensor was brought within the coupling range of the two coils (Fig. 2F). The result shows that the polystyrene 96-well plate is magnetically transparent enough to have a negligible effect on the coupling of the two coils.

Fig. 2

Implementation of the LC sensor system in 96 well-plate. A Design of a single sensor. B The orientation of the folded sensor fitting in a single well of a 96 well-plate. C Picture of a fabricated sensor before folding. D Picture of a 96 well-plate well with a sensor folded and inserted. E COMSOL simulation of magnetic coupling between the receiver coil and the sensor coil across a piece of polystyrene plastic, showing the 96 well plate bottom is magnetically transparent and will not prevent the coils from coupling. F The frequency sweep data before and after the sensor is coupled to the receiver coil. The line represents the absolute impedance \(\left|Z\right|\) of the system

Construction of the sensor system

Bacterial cultures were diluted and aliquoted into a standard 96-well plate with a sensor inserted in each well. A receiver coil connected to a Keysight E4990A-20 EIS on the bottom of the 96 well plates wirelessly communicates with the sensor and scans a spectrum of electrical wavelength to identify the resonance frequency between the sensor and the receiver coil. The resonance frequency of the system was recorded every 5 min, combined with the parameter of the sensor to calculate the permittivity of the bacterial culture. The permittivity readout is plotted as a time series, and the slope of the curve over the initial 30 min was used to access the sensitivity score of bacteria to each tested antibiotic. The baseline of the sensitivity score is determined by acquiring the time sequence slope in sterile medium (for growth detection) or antibiotic-free cultures (for AMR detection).

All experiments were performed with cultures incubated at 30 °C without shaking, and with an inoculation OD600 of 0.001 unless noted otherwise. The positive and negative ends of the receiver coil are situated in a diecast aluminum electromagnetically insulated box, which is connected to the EIS via a pair of twisted and insulated stranded copper wires.

The sensor was first mounted onto a double-sided adhesive sheet and had the single-layer protective polyurethane spray coating applied. The entire sheet of coated sensors was then left in a desiccator for 48 h to ensure complete evaporation of solvent and curing of the coating material. Individual sensors were then removed from the sheet with adhesive backing, rolled up as cup sleeves and placed inside of the wells. To avoid interference from protein and bacteria settling effect in a static culture environment, the sensing component of the sensor is placed vertically to the bottom, lining the wall of the well. Finally, the entire 96-well plate was placed in a UV Clave ultraviolet sterilization chamber for a one-hour sterilization cycle. Three sensors were randomly selected to establish a baseline for each batch of sensors to verify successful coating. On the EIS platform, a MATLAB program was used to trigger the equipment every 5 min for a 35 min duration, the program then took the readout, searched for the resonance frequency, and saved it as time series for further analysis. The file generated by the MATLAB program is written in VBScript to interface with the EIS to perform a preset 1600 points sweep within a 1 MHz range near the initial resonance frequency. The experimental setup is shown in Fig. 2B.