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Transient bioimpedance monitoring of mechanotransduction in artificial tissue during indentation


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Fig. 1

Schematic of the microfluidic system with integrated bioimpedance sensor. Not to scale.
Schematic of the microfluidic system with integrated bioimpedance sensor. Not to scale.

Fig. 2

Photo of patterned substrate showing microfluidic system. Insets: SEM images of sections of microfluidic system: (left) inlet; (center) micropillars; (right) microfluidic channels).
Photo of patterned substrate showing microfluidic system. Insets: SEM images of sections of microfluidic system: (left) inlet; (center) micropillars; (right) microfluidic channels).

Fig. 3

Schematic and geometry of the impedance sensor.
Schematic and geometry of the impedance sensor.

Fig. 4

The equivalent circuit for the impedance of the leads. RL and CL represent the load impedance, ZL.
The equivalent circuit for the impedance of the leads. RL and CL represent the load impedance, ZL.

Fig. 5

The materials surrounding the conductivity sensor.
The materials surrounding the conductivity sensor.

Fig. 6

Equivalent circuit of the multiple layers surrounding the sensor.
Equivalent circuit of the multiple layers surrounding the sensor.

Fig. 7

Fluorescence microscopy images of cells stained with a live-dead assay encapsulated into the alginate hydrogels.
Fluorescence microscopy images of cells stained with a live-dead assay encapsulated into the alginate hydrogels.

Fig. 8

Measured force during small strain indentation experiments on acellular alginate. Legend denotes final indentation depth.
Measured force during small strain indentation experiments on acellular alginate. Legend denotes final indentation depth.

Fig. 9

Measured resistivity of acellular alginate during small strain indentation experiments calculated from eq. 32. Legend denotes final indentation depth.
Measured resistivity of acellular alginate during small strain indentation experiments calculated from eq. 32. Legend denotes final indentation depth.

Fig. 10

Measured relative permittivity of acellular alginate during small strain indentation experiments calculated from eq. 33. Legend denotes final indentation depth.
Measured relative permittivity of acellular alginate during small strain indentation experiments calculated from eq. 33. Legend denotes final indentation depth.

Fig. 11

Measured force during large strain indentation experiments on acellular alginate. Legend denotes final indentation depth.
Measured force during large strain indentation experiments on acellular alginate. Legend denotes final indentation depth.

Fig. 12

Measured resistivity of acellular alginate during large strain indentation experiments calculated from eq. 32. Legend denotes final indentation depth.
Measured resistivity of acellular alginate during large strain indentation experiments calculated from eq. 32. Legend denotes final indentation depth.

Fig. 13

Measured relative permittivity of acellular alginate during large strain indentation experiments calculated from eq. 33. Legend denotes final indentation depth.
Measured relative permittivity of acellular alginate during large strain indentation experiments calculated from eq. 33. Legend denotes final indentation depth.

Fig. 14

Measured force during small strain indentation experiments on alginate hydrogel encapsulated fibroblasts. Legend denotes final indentation depth.
Measured force during small strain indentation experiments on alginate hydrogel encapsulated fibroblasts. Legend denotes final indentation depth.

Fig. 15

Measured resistivity of alginate hydrogel encapsulated fibroblasts during small strain indentation experiments calculated from eq. 32. Legend denotes final indentation depth.
Measured resistivity of alginate hydrogel encapsulated fibroblasts during small strain indentation experiments calculated from eq. 32. Legend denotes final indentation depth.

Fig. 16

Measured relative permittivity of alginate hydrogel encapsulated fibroblasts during small strain indentation experiments calculated from eq. 33. Legend denotes final indentation depth.
Measured relative permittivity of alginate hydrogel encapsulated fibroblasts during small strain indentation experiments calculated from eq. 33. Legend denotes final indentation depth.

Fig. 17

Measured force during large strain indentation experiments into alginate hydrogel encapsulated fibroblasts. Legend denotes final indentation depth.
Measured force during large strain indentation experiments into alginate hydrogel encapsulated fibroblasts. Legend denotes final indentation depth.

Fig. 18

Measured resistivity of alginate hydrogel encapsulated fibroblasts during large strain indentation experiments calculated from eq. 32. Legend denotes final indentation depth.
Measured resistivity of alginate hydrogel encapsulated fibroblasts during large strain indentation experiments calculated from eq. 32. Legend denotes final indentation depth.

Fig. 19

Measured relative permittivity of alginate hydrogel encapsulated fibroblasts during large strain indentation experiments calculated from eq. 33. Legend denotes final indentation depth.
Measured relative permittivity of alginate hydrogel encapsulated fibroblasts during large strain indentation experiments calculated from eq. 33. Legend denotes final indentation depth.

The mean coefficients for the relaxation modulus and time constants as calculated by fitting to the small strain indentation data given in figures 8 and 14. Errors given to one standard deviation.

Acellular TissueCellular Tissue
G (kPa)15.83±0.916.61±1.4
G0 (kPa)69.91±6.682.29±18.5
G1 (kPa)36.05±5.251.98±14.6
G2 (kPa)15.03±1.113.69±2.5
T1 (s)7.61±0.95.22±1.0
T2 (s)60.27±11.975.35±2.2

Values from characteristic impedance measurement. Errors to one standard deviation.

ShortedOpenCharacteristic
ImpedanceImpedanceImpedance
Magnitude (Ω)153.03±0.014564.6±0.1835.76±0.02
Phase (degs)-184.1±0.15.5±0.1-89.3±0.1

The properties of the free ions assumed to be in the alginate/S-DMEM hydrogel. Composition due to 50 % S-DMEM as given in [78]. Diffusivities from [79].

IonValenceConcentration (mmol/L)Diffusivity (x10-9 m2/s)
Na+154.761.334
K+12.681.957
SO42-$\text{SO}_{4}^{\,\,\,2\text{-}}$20.411.065
Ca2+20.900.792
Cl-159.242.032
Mg2+20.410.706