Supplemental Materials
Microfluidic Platform for Assessing Pancreatic Islet Functionality through Dielectric
Spectroscopy
K. Heileman1, J. Daoud1, C. Hasilo2, M. Gasparrini2, S. Paraskevas2 and M. Tabrizian1,a)
1
Biomedical Engineering Department, McGill University, Montreal, QC,
H3A 2B4, Canada.
2
Department of Surgery, McGill University, Montreal, QC, Canada H3A 0G4, Canada
a)Correspondence:
Dr. Maryam Tabrizian, Biomedical Engineering Department, McGill
University, Montreal, QC,
H3A 2B4, Canada.
Fax: +1-514-398-7461; Tel: +1-514-398-8129.
E-mail: Maryam.Tabrizian@mcgill.ca;
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S1 Microfluidic Device Assembly
Figure S1 Microfluidic device assembly steps. Left: The patterning and deposition of the
gold electrodes on the glass substrate and the subsequent patterning of the Su-8 2050 wells.
Right: Patterning of Su-8 2050 on silicon substrates to create a PDMS mold followed by soft
lithography of the PDMS channel layer. Finally the PDMS channel layer is bonded to the Su8 2050 well layer to complete the microfluidic device assembly.
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S2 Shear Stress Simulations
Figure S2 COMSOL simulation of the wall shear stress profile on the microfluidic
device. The geometry consists of a microfluidic channel segment and a single well. The
flow rate in the simulation was 10µl/min.
To find the conditions to minimize the shear stress experienced by the islets, fluid
dynamic simulations were performed using the MEMS module of COMSOL
Multiphysics 3.5 (Burlington, MA). Microfluidics and general laminar flow was
selected with no slip boundary conditions. High shear stress in microfluidic devices has
been shown to affect islet functionality, affecting in particular the peripheral islet cells,
which experience larger fluid forces 1. The shear stress can be optimized by adjusting
the microfluidic design and the flow rate. For COMSOL simulations, the geometry used
was a section of the microfluidic channel and a single well (fig. S2). The material filling
the geometry was set to approximate the properties of water at 37°C (as the GSIR assay
was performed in an incubator) with a density of 993 kg/m3 and a dynamic viscosity of
0.692 mPa·s. Pump flow rates (1, 5, 10, 15, 20, and 40 μl/min) were translated into
microfluidic channel fluid velocities experimentally using dye. These fluid velocities
were applied to the inlet in the simulation. The outlet pressure was fixed at 0 Pa. To
approximate the shear stress on the microfluidic device walls, equations were applied to
the velocity profile obtained from the simulation at all boundaries. First, the wall shear
rate (𝛾̇) was found for Cartesian coordinates in 3D using the eq. 2 2:
𝜕𝑢 2
𝜕𝑣 2
𝜕𝑤 2
𝜕𝑣 2
𝜕𝑢
𝜕𝑢
𝛾̇ = [2 ∗ ((𝜕𝑥 ) + (𝜕𝑦) + ( 𝜕𝑧 ) ) + (𝜕𝑦 + 𝜕𝑥) + ( 𝜕𝑧 +
𝜕𝑤 2
𝜕𝑣
𝜕𝑤 2
) + (𝜕𝑧 + 𝜕𝑦 ) ]1/2
𝜕𝑥
(1)
Here u, v, and w are the x, y, and z components of the velocity. The shear stress (τ) was
then calculated as a product of the dynamic viscosity of water (μ) at 37°C and the wall
shear rate (𝛾̇), as in eq. 3.
𝜏 = 𝜇 ∗ 𝛾̇
(2)
At a flow rate of 10μl/min, the shear stress along the well walls is ~100mPa, hence this
was selected as the experimental flow rate. The shear stress heat map for this flow rate
is shown in figure S2, which shows that the well provides the islet with an environment
which is sheltered from the shear stresses experienced in the channel. In the venous
system, the shear stress range is 1–6 dyne/cm2 (100–600 mPa), which is much lower
than the shear stress range in the arterial system3. Because islets are composed of
endocrine cells and, unlike endothelial cells, are not directly exposed to blood flow, the
shear stress they are exposed to should be significantly smaller. Previous microfluidic
devices have maintained shear stress on islets within a physiological range of 1–14
dyn/cm2 (100–1400 mPa)1. Thus, 10µl/min was selected as the experimental flow rate.
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S3 Modeling of Mass Exchange on the Microfluidic Device
Figure S3 Modeling of mass exchange on the microfluidic device. (A) Images of a single
well on the microfluidic device, with dye washing out after a dye-free solution has been
introduced. The dye is used as a model for glucose. (B) Simulations of diffusion and
convection for glucose at different time points for a single slice of a 3D segment of the
microfluidic channel and well.
Experimental observations and computer modeling was performed to ensure the
microfluidic device provides sufficient mass exchange around the islets. Good mass
transfer is essential to ensure islets receive sufficient and equitable stimulation with
glucose. Dye was used as a model for mass transfer between the channels and the wells.
The dye is composed of tratrazine, with a diffusion coefficient of 4.9 ± 0.8x10-10 m2/s4,
which overlaps slightly with that of glucose (5.7x10-10 m2/s). Green dye was perfused at
a flow rate of 10μl/min on the microfluidic device for 36 minutes, after which ethanol
was perfused. The well that took the longest to clear did so in 3 minutes (figure S3A).
We then determined using dye that for a flow rate of 10 μl/min, fluid takes ~15s to travel
from the device inlet to outlet. Hence, we can assume that the final well on the device
would take around 3 minutes plus an additional 15 seconds to equilibrate after
introducing a new glucose concentration to the inlet. Therefore the temporal stimulation
gradient across the device arising from introducing a glucose concentration lasts for a
short period compared to each stimulation period (36 minutes). The Péclet number was
determined for the well, using the equation:
Pe = Lu/D
(3)
Where Pe is the Péclet number, L is the characteristic length of the well (200μm), u is
the flow velocity (10mm/s), and D is the diffusivity of glucose (5.7x10-10 m2/s). The
resulting Péclet number was 3509, showing that convection is more significant for
glucose transfer than diffusion. High Péclet numbers are typical for microfluidic
devices.
For more precise modeling of mass transfer, COMSOL multiphysics 5.0 was used to
model glucose as the dilute species. The geometry was in 3D with the same dimensions
as figure S2. The aim of the simulation was to investigate how much time was needed,
after introducing a high glucose concentration (16.7 mM) to the channel segment, for
the well to reach this concentration. First, the velocity profile for a flow rate of 10μl/min
was obtained using the laminar flow module. Water was used as the carrier fluid, with
a density of 993 kg/m3 and a dynamic viscosity of 0.692 mPa·s (properties of water at
37°C, since the GSIR assay was performed in an incubator). The flow velocity was set
to 10mm/s (determined experimentally with dye for a flow rate of 10μl/minute). The
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velocity profile was then applied to the transport of diluted species module to obtain the
concentration distribution in the channel. The diffusion coefficient was selected as
5.7x10-10 m2/s, which is similar to that of glucose. The initial glucose concentration in
the geometry was 0mM while the inlet supplied a constant glucose concentration of 16.7
mM. The simulation showed that within 20 seconds, the glucose concentration within
the well reached equilibrium with the channel (figure S3B). This equilibrium
concentration was verified for all slices across the geometry to account for convection
and diffusion in all directions. Therefore, the simulation suggests rapid and sufficient
mass transfer and stimuli delivery through diffusion to the islets within the chambers.
This result is beneficial, considering that the microfluidic device geometry promotes
more equal mass transfer across all islets, for two reasons. First, a single narrow channel
is placed above the wells, reducing lateral gradients in concentration. Second, because
the sizes of the wells were close to the sizes of single islets, islet aggregation was
reduced, which maximized islet surface exposure.
S4 Dielectric spectroscopy simulations
Figure S4 COMSOL simulation of dielectric impedance spectroscopy interrogation of
two islets within wells along a microfluidic channel segment. (A) Simulated changes in
capacitance and conductance spectra for islets with different cell membrane permittivity. This
simulation shows the efficacy of the platform to detect changes in cell membrane permittivity
and capacitance in response to stimuli. (B) Diagrams of current density distribution and
streamlines in a microfluidic channel segment at indicated frequencies. At higher frequencies,
the electric field penetrates the islets, allowing interrogation of islet electrical parameters such
as the cell membrane permittivity.
Dielectric spectroscopy simulations of the microfluidic platform were performed in
COMSOL, using an AC/DC module to optimize the chip geometry for dielectric
measurement of islet dielectric parameters during stimulation. The geometries of the
channels, wells, and electrodes were the same as those designed and described in fig.
S2. The simulation was performed on two wells containing islets represented as 200μm
spheres (fig. S4). Electric fields resulting from a potential difference of 1V were applied
to the electrodes, situated at the bottoms of the wells. The frequency in the simulation
was swept from 10kHz to 1GHz, yielding the respective capacitance and conductance
spectra of the islet spheres. The dielectric parameters used were extracellular media
permittivity and conductivity of εa=80 and ka=1 S/m, respectively; intracellular
cytoplasm permittivity and conductivity of εa=80 and ka=1 S/m, respectively; and
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membrane permittivity and conductivity of εm=5-50 and km=0 S/m, respectively. Fig.
S4a presents simulation plots showing that by changing the membrane permittivity εm—
representing a stimulation resulting in a change of membrane capacitance—of the islet
from 5 to 50, the recorded capacitance and conductance spectra experienced significant
shifts. In addition, as depicted in fig. S4b, the simulations showed that the overall current
densities and current density streamlines were focused at low frequencies, slowly
penetrating and expanding into the low-conductivity cell membrane with higher
frequencies. This further allowed for a more precise determination of the electrical
properties of sub-islet structures. These results indicate that the chosen device
geometries are well suited for detecting shifts in membrane dielectric parameters.
Detecting these membrane permittivity changes is necessary in order to observe
membrane fusion events associated with islet insulin release/secretion, which result
from cellular responses to stimuli, such as the glucose challenge for functionality
assessment. Hence, the electrode size and spacing—in turn giving rise to a localized
electric field gradient—and islet chamber diameter and channel widths were optimal for
dielectric spectroscopy measurements of islet processes. The results of the dielectric
spectroscopy simulations are complemented by previous studies of interdigitated
electrodes, which show that with our dimensions, almost 100% of current passes within
a height of 400 μm above the electrodes 5. Hence the electric field is concentrated in the
region around the islets, improving signal quality.
S5 Dielectric modeling of islet morphology using analytical cell model
Figure S5 The vesicle inclusion model applied to islets. E and k are permittivity and
conductivity, respectively. The subscripts a, m, iv, mv, and av represent extracellular media,
outer shell, intercellular space, cell membrane, and cytoplasm, respectively. R and Rv denote
islet and cell radii, respectively. Measuring the dielectric parameters in order to investigate
cellular electric properties leads to more precise and temporal characterization of islet
response to stimuli. (A) Vesicle inclusion model showing cell electrical parameters for the
entire islet (left and centre) and an individual islet cell (right). (B) Effects of the varying cell
electrical parameters on the dielectric spectra using the vesicle inclusion model.
To understand the cause of the shifting dielectric spectra, computer simulations were
performed using the vesicle inclusion model, as illustrated in figure S5A, to observe the
effects of changing cell dielectric parameters on the dielectric spectra. The conductivity
and permittivity of the cell membranes (kmv and Emv, respectively) and cytoplasm (kav
and Eav, respectively) were increased by a factor of 100 in each experiment. The initial
conditions were as follows: cytoplasm, intercellular space, and extracellular solution
conductivities of kav, kiv, ka=1 S/m, respectively; cell membrane conductivity of kmv=1e5
S/m; cytoplasm, intercellular space, and extracellular solution permittivities of Eav, Eiv,
Ea=80, respectively; cell membrane permittivity of Emv=5; cell volume fraction of
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Pv=0.9 within the outer shell and P=0.1 for the shell volume fraction in the extracellular
solution; cell membrane thickness of dmv=5 nm; and cell radius and outer shell radius of
Rv=5 μm and R=75 μm, respectively. In addition, it is important to note that the vesicle
inclusion model assumed an outer shell composed of a basement membrane with highly
conductive characteristics similar to those of the extracellular solution: outer shell
conductivity and permittivity of km=1 S/m and Em=80, respectively, as well as an outer
shell thickness of dm=50 nm – analogous to properties observed physiologically 6. The
internal permittivity of the vesicle inclusion, namely the inclusions encapsulated by the
outer shell, was determined using the Hanai effective media approximation (EMA) to
account for the large volume fraction of the cells within the islet. In addition, the
permittivity of the entire suspension of shells was determined using the Pauly–Schwan
EMA. This vesicle inclusion model was thoroughly investigated for modelling plant
protoplasts7 and frog embryogenesis8. The results of changing the permittivity and
conductivity of the cell membrane and the cytoplasm are represented in figure S5B. As
depicted by the indicated shifts in the graph, the model showed that increasing the cell
membrane permittivity shifts the spectra backward above 100kHz, while increasing the
cytoplasm permittivity shifts the spectra forward/upward above 100kHz frequencies.
Increasing the cell membrane conductivity shifts the spectra downward below 1 MHz,
while increasing the cytoplasm conductivity shifts the spectra forward/upward above
100kHz. These shifts in dielectric spectra due to changing cell dielectric parameters,
were similar to those observed in a previous computer modeling study using the double
shell model for cells (to account for cell membrane and nucleus) 9. Of particular
importance is that the permittivity of the cell plasma membrane had a much greater
effect on the dielectric spectrum than the permittivities of the nuclear envelope,
cytoplasm, and nucleoplasm did9.
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