MASTER’S THESIS
HYDROGEL-BASED 3D SEMI-CIRCULAR MICROVAS- CULAR BBB-ON-CHIP WITH INTEGRATED SENSORS FOR BARRIER FUNCTION ASSESSMENT THROUGH TEER MEASUREMENTS
L.E. de Heus
Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) BIOS Lab on a Chip
Exam committee:
dr. L.I. Segerink (chairman)
ir. M.P. Tibbe (daily supervisor)
dr.ir. A.M. Leferink (External member)
“Not everything that can be counted counts, and not everything that counts can be counted.”
Albert Einstein
Abstract
Background: Realistic models that optimally mimic the blood-brain barrier (BBB) are essential for researches regarding drug passage across the barrier that aim for de- veloping adequate neuropharmaceuticals. Over the past decade, in vitro BBB models have evolved from static two-dimensional (2D) Transwell systems towards dynamic hydrogel-based three-dimensional (3D) BBB-on-chip systems with physiologically relevant matrix stiffness. However, this next generation BBB models lacks integra- tion of a measurement setup for assessing barrier function using trans endothelial electrical resistance (TEER). Here, we propose a hydrogel-based 3D microvascular BBB-on-chip with integrated sensors for barrier function assessment through TEER.
Method: Although a fully functional device was not achieved during the scope of this thesis, an initial concept design was optimized in an iterative process, af- ter which individual components were developed an experimentally tested with preliminary studies. Hyaluronic-based hydrogels suitable for this application were identified by their ability to adopt channel features from a mould and subsequently seal on a chemically functionalized glass substrate. To investigate the suitability of the selected hydrogel for cell culture purposes, human cerebral endothelial cells (hCMEC/D3) were cultured on hyaluronic-based hydrogels complemented with gelatin to promote cell adhesion. Cell behaviour was quantified and qualified by assessing metabolic activity and cell morphology, respectively. Finally, the devel- oped sensor comprised of electrodes incorporated in a glass slide was characterized using hydrogel-based electrolytes with increasing conductivity.
Results and discussion: The optimized novel hydrogel-based chip design proved appropriate for imprinting hydrogels with channel features that subsequently could be aligned with electrodes integrated in a glass substrate. Sealing of the open chan- nels on the glass substrate was not achieved. hCMEC/D3 cultured on 5% hyaluronic- based hydrogel complemented with gelatin at a final concentration of both 0.5 and 1.0 mg/ml showed a healthy characteristic cobblestone-like morphology with simi- lar cell viability. Measured resistance values roughly followed the trend for increas- ing conductivity and electrode spacing as expected from the theoretical cell constant, however appeared to lose sensitivity for high conductivity values.
Conclusion: During the scope of this thesis, first steps were made in achieving a
hydrogel-based microfluidic chip with integrated sensors. Open channels could be
fabricated in hyaluronic-based hydrogel, which proved suitable for endothelial cell
culture. Moreover, preliminary tests with the electrode configurations showed its
potential for ultimately TEER measurements on chip. Future research on channel
sealing is vital for completing the device such that it facilitates cell culture and TEER
measurements.
Acknowledgements
I would like to thank a lot of different people for their help during my master’s
thesis. First of all, I would like to thank Albert van den Berg for giving me the
opportunity of writing my master’s thesis in the BIOS Lab-on-a-Chip group. I would
like to thank all the members of the examination committee, Loes Segerink, Anne
Leferink and Martijn Tibbe. During the meetings with Loes, I always gained a lot
of knowledge but mostly interest in a for me new topic, electrodes, which I really
appreciate. I would like to thank Anne for her overall guidance and sometimes
the push in the right direction, which I am very grateful for. And ofcourse, a big
thanks to Martijn. I really enjoyed working with you! For me, it was the perfect
combination between doing research while at the same time having a lot of fun and
ofcourse listening to the best music in the labs. You always kept me motivated and
focused whenever I needed. Besides the committee, I would like to thank Johan
Bomer and Hans de Boer who helped me with the design and fabrication of the
electrodes and holders. I would like to thank everyone of the BIOS Lab-on-a-Chip
group for the laughs and inspiring talks in the coffee corner, during the trips to the
fish stand, the weekly football matches, or any other activity during this amazing
time. And last but definitely not least, I would like to thank Rob, who had to cope
with me during the last months.
Contents
Abstract v
Acknowledgements vii
1 Introduction 1
1.1 Report structure . . . . 3
2 Theory 5 2.1 Hyaluronic-based hydrogel . . . . 5
2.2 Fabrication of hydrogel-based microfluidic chips using soft-lithography in tissue engineering . . . . 5
2.3 TEER . . . . 7
2.3.1 In vivo TEER measurements . . . . 7
2.3.2 In vitro TEER measurements . . . . 9
Cell constant . . . 11
3 Design optimization 15 3.1 Hydrogel-based microfluidic chip . . . 15
3.1.1 Initial concept . . . 15
3.1.2 Observed limitations . . . 15
3.1.3 Proposed adaptations . . . 16
3.2 Electrode configuration . . . 17
3.3 Optimized novel design . . . 19
3.3.1 Strengths and limitations . . . 19
4 Hydrogel chip fabrication by soft-lithography 23 4.1 Introduction . . . 23
4.2 Experimental methods . . . 24
4.2.1 Silicon mould fabrication . . . 24
4.2.2 Hydrogel preparation . . . 24
4.2.3 Surface functionalization . . . 26
4.2.4 Hydrogel chip fabrication . . . 26
4.2.5 Analysis channel feature transfer . . . 27
4.2.6 Analysis sealing hydrogel channels . . . 27
4.3 Results and Discussion . . . 28
4.3.1 Hydrogel channel fabrication . . . 28
4.3.2 Channel feature transfer . . . 28
4.3.3 Sealing hydrogel channels . . . 32
4.4 Conclusion . . . 33
5 Endothelial cell morphology and viability on hyaluronic-based hydrogel 35 5.1 Introduction . . . 35
5.2 Experimental methods . . . 36
5.2.1 Hydrogel preparation . . . 36
5.2.2 hCMEC/D3 cell culture . . . 36
5.2.3 Fluorescent staining . . . 36
5.2.4 Viability assay . . . 36
5.3 Results and Discussion . . . 37
5.4 Conclusion . . . 40
6 Electrode characterisation 41 6.1 Introduction . . . 41
6.2 Experimental methods . . . 41
6.2.1 Electrode fabrication . . . 41
6.2.2 Hydrogel preparation . . . 43
6.2.3 Two terminal impedance spectroscopy . . . 43
6.2.4 Data analysis . . . 43
6.3 Results and Discussion . . . 44
6.3.1 Theoretical cell constant . . . 44
6.3.2 Experimental resistance . . . 44
Experimental vs. theoretical cell constant . . . 47
Resistance vs. ion concentration . . . 48
Resistance vs. electrode spacing . . . 49
6.4 Conclusion . . . 52
7 Future outlook 53 7.1 Channel sealing . . . 53
7.1.1 Sacrificial hydrogel element . . . 53
7.1.2 Glass functionalization with molecular hydrogel coating . . . . 54
7.2 TEER measurements . . . 55
7.3 Implementation controllable shear stress variable . . . 56
8 Conclusion 57 Bibliography 59 A Hydrogel chip fabrication 63 A.1 Silicon mould fabrication . . . 63
A.2 Exploring limited sealing of hyaluronic-based hydrogel on tyramine
functionalized glass slide . . . 63
B Electrode characterisation 65 B.1 Reconstruction K
cellfrom Linderholm et al. . . . 65 B.2 Raw impedance data . . . 66 B.3 COMSOL model electrode characterisation . . . 69
C Future outlook 71
C.1 COMSOL model TEER . . . 71 C.2 COMSOL model shear stress . . . 73
D 3D view final designs 75
List of Abbreviations
BBB Blood-brain barrier
TEER Trans Eendothelial Electrical Resistance
2D two-dimensional
2D three-dimensional ECM Extracellular matrix
hCMEC/D3 human Cerebral Microvascular Endothelial Cell /D3 cell line EC Endothelial Cells
HA-ta Hyaluronic Acid - tyramine Dex-ta Dextran - tyramine
Gel-ta Gelatin - tyramine HRP Horse Radish Peroxidase PBS Phosphate Buffered Saline
RT Room Temperature
PDMS Polydimethylsiloxane
PMMA Poly (methyl methacrylate)
Chapter 1
Introduction
The world’s population’s average age and life expectancy is increasing, accompa- nied with the rising trend in prevalence of chronic diseases, such as neurodegener- ative diseases. According to Alzheimer’s Disease International, 46.8 million peo- ple were estimated to suffer from Alzheimer’s disease in 2015, a number that is expected to increase even more. [1] Consequently, the development of adequate neuropharmaceuticals is required. However, drug delivery into the central nervous system (CNS) exposes a major challenge, since molecular diffusion into the brain tissue is hindered by the so called blood-brain barrier (BBB). This barrier partitions brain interstitial fluid from peripheral blood. It is composed of highly specialized endothelial cells forming the brain capillaries that are closely interacting with astro- cytes, pericytes, microglia and a base membrane. Restricted uptake of compounds is highly controlled by the endothelial cells with their characteristic continuous tight junctions, lack of fenestrae, low pinocytic activity and high concentration of efflux transporters. [2] Therefore, the identification of neuropharmaceuticals suitable for drug delivery across the BBB remains a major challenge.
As studies regarding the drug development towards neuropharmaceuticals con- tinue, realistic models are essential to investigate drug passage across the barrier.
Currently, the gold standard for testing drug compounds in pharmaceutical indus- try are in vivo animal models. [3] Advantages of animal models are that they provide an elaborate view on the overall response, including the cellular, tissue, organ and systemic level. Nevertheless, as a result of species-to-species variations, successful outcomes of animal studies do not guarantee similar results in human studies. [4]
In addition, animal studies are costly, labour-intensive and ethically questionable.
Therefore, researchers focus on developing in vitro BBB models that both anatomi- cally and physically mimic the BBB.
Due to the BBB’s complexity, a lot of research is done on simplified in vitro mod-
els. In the past years, multiple Transwell
Rsystems aiming at mimicking the BBB
have been investigated and developed. In these systems, endothelial cells are seeded
in the upper compartment and astrocytes in the lower compartment, partitioned by a
porous membrane. Morphological and physiological characteristics of the cells and
the entire barrier, such as the permeability and transendothelial electrical resistance
(TEER) could be determined, allowing proper evaluation of the BBB model. [5], [6]
Although Transwell
Rsystems are easy to use, facilitate various assays to quantify or qualify barrier functionality and are relatively cheap, they lack, amongst others, the implementation of flow generated shear stress, one of the main factors responsible for endothelium alignment and tightness in the BBB. [7], [8]
BBB-on-chip systems are able to address the aforementioned shortcoming. Gen- erally, these chips are comprised of two perpendicular channels, representing the apical and basolateral compartment, separated by a semi-permeable membrane on which partitioned two-dimensional (2D) growth of endothelial cells and astrocytes or pericytes exposed to shear stress is facilitated. Similar to the Transwell
Rset up, these systems allow for easy morphological characterization of cells using mi- croscopy and barrier function assessment through TEER measurements and perme- ability assays. [9], [10] Further improvements on this design have been reported by Sellgren et al. [11] They inserted collagen hydrogel loaded with astrocytes in the basolateral channel to mimic the physically relevant stiffness of the brain extracel- lular matrix (ECM), which is known to affect astrocyte activation and subsequently their ability to modulate BBB function. [12] However, one major limitation of this general BBB-on-chip design is the creation of a 2D endothelium instead of a three- dimensional (3D) vessel-like structure.
Currently, the focus in BBB-on-chip designs increasingly shifts towards integrat- ing 3D structures, mostly by using hydrogels that have stiffnesses in the same order of magnitude as brain ECM. Brain microvasculature has predominantly been mim- icked by circular shaped channels in collagen hydrogels produced by viscous finger patterning and using microneedles. [13], [14] These designs enabled implementa- tion of shear stress and allowed qualification and quantification of barrier functions by imaging and permeability assays using fluorescently labelled compounds. How- ever, TEER measurements on these 3D brain microvasculatures on chip have not been reported to date.
In this study, a hydrogel-based 3D semi-circular microvascular BBB-on-chip is
proposed, with integrated sensors for barrier function assessment through TEER
measurements. Using soft-lithography, open channel features are aimed to be trans-
ferred into a hyaluronic-based hydrogel and sealed on a glass substrate. Upon en-
capsulating astrocytes or pericytes in the hydrogel, this chip would allow for a co-
culture with human brain endothelial cells lining the channel wall. The total de-
sign enables visualization of morphological and physical characterizations using im-
munofluorescence staining of cell specific proteins whereas permeability assays pro-
vide insight in the diffusion through the endothelial cell layer. Moreover, incorpo-
ration of electrodes in the glass substrate aims at facilitating a standardized method
for assessing barrier function by measuring TEER according to the leaky cable the-
ory as performed by Crone et al. [15] During the scope of this thesis, first steps were
made in achieving this goal. We have developed a combination of devices that allow
for channel feature transfer in hyaluronic-based hydrogels that subsequently could
be aligned with electrodes integrated in a glass substrate. The hydrogel proved
suitable for conventional endothelial cell culture purposes, which was concluded from the characteristic cobblestone morphology and active remodeling capacity of the hCMEC/D3 cell line. Subsequently, preliminary tests were performed for char- acterization of the proposed electrode configuration and showed to potentially be suited for impedance spectroscopy measurements in the developed device. Future research on channel sealing is crucial for completing the device such that it facili- tates cell culture in the hydrogel-based microfluidic chip and subsequently allows for performing TEER measurements.
1.1 Report structure
In this master thesis, Chapter 2 will elaborate on theory about previous work regard-
ing the hyaluronic-based hydrogel and hydrogel-based microfluidics in general, and
some background on methods to determine the TEER of endothelium in vivo as well
as in vitro. In Chapter 3, the design of the hydrogel-based chip fabrication method
is shortly discussed together with the design of the integrated electrodes. Since a
complete functional hydrogel-based microfluidic chip was not achieved during the
scope of this thesis, experiments done on imprinting channel structures in hydro-
gel together with channel sealing, endothelial cell morphology and viability on the
hydrogel and characterisation of the electrode configuration are addressed individ-
ually in Chapter 4, 5 and 6, respectively, each with individual results, discussions
and conclusions. The final chapter gives an outlook on future work.
Chapter 2
Theory
2.1 Hyaluronic-based hydrogel
Hydrogel-based BBB models are mostly comprised of collagen type-I. [14], [16] How- ever, this abundant ECM component is hardly present in the brain tissue. Therefore, a more relevant hydrogel type is hyaluronic acid, one of the main components of the brain ECM. [17] To date, various applications of hyaluronic acid (HA)-based hydrogels in tissue engineering have been reported, with an enormous variety of modifications and crosslinking mechanisms that allow for highly tunable hydrogel properties suitable for, amongst others, cartilage repair [18]. The hyaluronic-based hydrogel utilized in this thesis is composed of dextran and hyaluronic acid both functionalized with a tyramine group (Dex-ta and HA-ta), which allows for enzy- matic crosslinking by horse radish peroxidase (HRP) with (H
2O
2) as oxidant of HRP.
[18]
2.2 Fabrication of hydrogel-based microfluidic chips using soft-lithography in tissue engineering
Fabrication of channel features in hydrogel-based microfluidic chips has not only been investigated for blood-brain barrier model purposes, but also for creating in vitro microvessels in general. Micromoulding methods used to obtain channel fea- tures in a hydrogel are typically stamping, casting or injecting hydrogel in a mould, after which the imprinted open channels are sealed by various mechanisms includ- ing shortly melting the imprinted hydrogels [19], chemical crosslinking [20] or ap- plying pressure [16].
Ling et al. developed an agarose hydrogel microfluidic chip by moulding agarose on a SU-8 silicon wafer patterned with channel features. [19] (Figure 2.1a) Subse- quent heating of the moulded agarose layer as well as an additional flat agarose layer to a temperature of 71
◦C for only 3 seconds, enabled them to seal the open channels. The total method allowed for the creation of hydrogel channels with di- mensions as small as 50 μm by 70 μm, encapsulating amongst others hepatocytes.
Zheng et al. created a device in which collagen type-I was imprinted with mi-
crofluidic structures upon injecting the solution in a holder with on the bottom a
F
IGURE2.1: Examples of hydrogel-based microfluidic chips fabri- cated using soft-lithography. Adapted from A) Ling et al. [19], B)
Zheng et al. [16] and C) Qiu et al. [20].
patterned PDMS stamp. [16] (Figure 2.1b,i) In this holder, an additional outlet was integrated to allow trapped air to escape and two steel pins were inserted to define the inlet and outlet for the hydrogel channels. After gelation, the open channels were mechanically sealed on a flat collagen type-I layer (ii) by applying pressure and cells were seeded inside the hydrogel channels (iii). Medium was provided through a PDMS layer placed on the inlet and oulet that served as reservoir (iv). This design allowed for studying endothelium permeability and angiogenesis in 100 μm x 100 μm hydrogel channels.
A variation of this method was developed by Qiu et al. (Figure 2.1c) [20] Their agarose-gelatin hydrogel mixture was casted in a silicon master at 65
◦C, physically crosslinked at 4
◦C and transferred onto a 200 μm hydrogel layer that was crosslinked with a silane functionalized glass slide. The total system was finalized by chemi- cally crosslinking all layers via gelatin through carbodiimide chemistry. Using this method, they managed to fabricate microvascular-sized hydrogel channels with more complex branching geometries mimicking the capillary beds with channel diame- ters down to 20 μm. This hydrogel-based microfluidic chip facilitated endothelial cell culture in physiological relevant matrix stiffnesses, channel geometries and di- mensions corresponding to the in vivo microvascular environment.
Although numerous variations of hydrogel-based microfluidic chip devices have been reported, a common factor can be recognized in the fact that open channel structures are predominantly sealed on an additional flat layer of the same hydro- gel. The latter approach is inapplicable for the hydrogel-based microfluidic chip as proposed in this thesis, since the TEER measurement sensor requires the open hy- drogel channels to be in direct contact with the electrodes incorporated in the glass substrate. Therefore, an alternative method for sealing of the hydrogel channels is required.
2.3 TEER
2.3.1 In vivo TEER measurements
First in situ TEER values have already been reported back in 1981 and 1982 by Crone
et al. [15] They have performed a measurement technique that enabled them to
determine the electrical resistance along a frog brain capillary by injecting a small
alternating current and measuring the voltage drop along the capillary. The cur-
rent injection and voltage measuring electrode circuits were isolated by using a four
electrode set up with the current injecting and voltage measuring glass micro elec-
trodes inserted into the brain capillary and the corresponding silver/silver chloride
(Ag/AgCl) reference electrodes connected on the brain surface. An overview of
their experimental setup is depicted in Figure 2.2. This method is based on the leaky
cable theory that states that an electric current traveling through an electrolyte cylin-
der covered with an isolating layer also leaks through that ion permeable isolating
F
IGURE2.2: Experimental set up as perfomed by Crone et al. [15].
TEER measurements of frog brain capillaries was done using a cur- rent injecting and potential measuring electrical circuit. Integration of a lock-in amplifier allowed detection of the signal’s potential with a frequency corresponding to the 2.5 Hz current pulse as was injected
into the brain microvessel. Copied from [15].
layer. When applying this general definition to a microvessel, it can be interpreted as the intracapillary potential along a blood vessel decaying due to ionic permeabil- ity of the endothelial cells lining the vessel wall, thereby following an exponential function:
V ( x ) = V ( 0 ) e
−x/λ(2.1)
where V(x) is the intracapillary potential at distance x from the current injecting electrode (V(0)) and λ is the so called length constant. This constant is a measure for how rapidly the potential drops in longitudinal direction and is related to the TEER, blood resistivity (ρ), cross sectional area (A) and circumference (C) of the cor- responding vessel according to the following equation:
TEER = ρ
A λ
2C = ρ
πr
2λ
22πr (2.2)
with r the radius of the blood vessel. Simplification of the original three dimen-
sional (3D) phenomena to this one dimensional (1D) model is justified when several
assumptions hold true. These include amongst others a radially negligible poten-
tial difference and a well conducting electrolyte surrounding the capillary. Thus, the
leaky cable theory can be used for estimating TEER values of small diameter blood
vessels only. The latter assumption is experimentally corrected for by superfusing
the investigated capillaries with a highly conductive solution.
In summary, Crone et al. proved that TEER values determined using the leaky cable theory are an indicative for endothelial barrier tightness. However, since sim- plified BBB models are predominantly 2D and in vitro, a translation of this 3D in vivo measurement method towards a 2D in vitro measurement set-up was required.
2.3.2 In vitro TEER measurements
TEER measurements have already been widely implemented in in vitro BBB mod- els to assess the barrier tightness. In 2D semi-permeable membrane based systems, TEER measurements are performed based on Ohm’s law, where a voltage is applied between electrodes positioned on both sides of the membrane and the resulting cur- rent is measured. Subsequently, the resistance can be calculated using Equation 2.3:
R
tot= U
I (2.3)
where U is the applied voltage, I the resulting current and R
totthe total resistance of the system which is reflected by the endothelium and the semipermeable membrane:
R
endothelium= R
tot− R
membrane(2.4)
indicating that these TEER measurements require a reference measurement to deter- mine the resistance of the semipermeable membrane. Finally, from this data TEER values can be obtained, which scale linearly with the surface area (A) of the semiper- meable membrane and endothelium and are mostly reported in Ωcm
2:
TEER = R
endothelium· A (2.5)
However, since the electrical behaviour of a cell is frequency dependent, impedance
spectroscopy provides further insight in the endothelium under investigation. As
shown in Figure 2.3a, the applied current can pass paracellular through the tight
junctions and transcellular through the cell layer, of which the latter pathway offers a
parallel resistive and capacitive pathway as a result of the lipid bilayer. Additionally,
a capacitive and resistive component are resulting from the electrode double layer
and electrolyte resistivity, respectively. The impedance spectrum of such a system
is depicted in Figure 2.3b, from which the characteristic double layer capacitance
(C
dl), the TEER plateau, lipid bilayer capacitance (C
cl) and resistance of the medium
(R
medium) can be recognized.
F
IGURE2.3: A) Schematic representation of the electrical circuit com- ponents contributing to the impedance as measured across an en- dothelium, further specified in a paracellular and transcellular path- way. B) Simplified electrical circuit (2) with corresponding impedance spectrum (1). R
medium: resistance of the medium, R
membraneresistance of the medium, C
cl: capacitance cell layer, C
dl: capacitance double
layer electrodes. Adapted from [21].
Practical implementation of TEER measurements in Transwell
Rsystems involves manually inserting electrodes in both fluidic compartments, whereas microfluidic system often have integrated electrodes on either side of the semi-permeable mem- brane in the channels. For the latter application, the position of the electrodes in the microfluidic channels is of great importance, preferably, as close to the semi- permeable membrane as possible to reduce the total resistance of the system. The resistance of an electrolyte (R
electrolyte) in a microfluidic channels can be estimated by:
R
electrolyte= ρ
electrolytel
channelA
channel(2.6)
with ρ
electrolytethe electrolyte resistivity and l
channeland A
channelthe microfluidic
channel length and cross sectional area, respectively, which indicates that the small
cross sectional area result in high resistances.
Cell constant
Results from impedance spectroscopy measurements not solely reflect the capaci- tance and resistance of the material, but also the electrode configuration and geom- etry of the sensor. The influence of the latter is summarized in one term, namely the cell constant (K
cell), which is proportional to the measured resistance (R
measured) and the material’s conductivity (σ
material), assuming a homogeneous electrolyte and infinite thin electrodes:
R
measured= K
cellσ
material(2.7)
Electrode configurations integrated in microfluidic set-ups are mostly parallel or coplanar. For parallel electrodes of the same surface area (A) at a perpendicular distance (D), the cell constant can simply be described by:
K
cell= R
measuredρ
material= D
A (2.8)
However, the cell constant for two coplanar electrodes situated in a microfluidic channel in direct contact with medium can be described according to Equation 2.9 and 2.10. [22]
K
cell= 2 L
K ( k )
K ( k
0) (2.9)
K ( k ) =
Z
01
1
p ( 1 − t
2)( 1 − k
2t
2) dt (2.10) with L the length of the electrodes and k and k’ dependent on the spacing between the electrodes (s) and width of the electrodes (w) as expressed in Equation 2.11 and 2.12:
k = s
s + w (2.11)
k
0= p 1 − k
2(2.12)
It has to be noted that these equations are based on the assumption of a semi-infinite medium on top of the electrodes. However, this is not the case in most microfluidic channels, where the electrode widths and spacing are not negligible in comparison to the channel height. A more accurate approximation of the cell constant was pre- sented by Lindholm et al. which allowed compensation for the channel height. [23]
For this, two conformal mappings are performed prior to using the final Schwarz-
Christoffel transformation as already presented in Equation 2.10. First, the sensor
geometry is simplified to a two dimensional (2D) design in the Z-plane with real
and imaginary as illustrated in Figure 2.4a. Integration of the height of the chan-
nel is done by replacing the left part of the symmetric channel with a conductor at
the centre (Figure 2.4b). Subsequently, the first transformation is performed to map all coordinates onto the real axis of the first intermediate plane, the U-plane, by us- ing a sine function (Figure 2.4c). The Schwarz-Christoffel transformation requires electrodes to be of the same width and symmetric around the origin of its plane.
Since this is not the case for the geometry as mapped on the U-plane, an additional mapping is needed. The coordinates of the U-plane are transformed using a bilinear function to the second intermediate plane, the V-plane (Figure 2.4d). The constants A, B, C and D need to be determined such that the previously stated requirements are met. This results in an expression for v4, of which the reciprocal is the modulus for the Schwarz-Christoffel transformation from the V-plane.
F
IGURE2.4: An overview of conformal mapping transformations of the electrode geometry (A) required to determine the cell constant theoretically. Due to symmetry, the left part of the channel can re- placed by a conductor (B, z1 and z2) with the same height as the mi- crofluidic channel (h). Second, a sine transformation is done to map all coordinates on the real part of the intermediate U-plane (C). Bilin- earization is then required to bring back symmetry (D), to then allow for a final mapping procedure into a plane parallel conductor (E) us-
ing Schwarz Christoffel mapping. Adapted from [23].
v
4= ( u
4− u
2)( u
3− u
1)
u
4( u
3+ u
2− 2u
1) + 2 p
( u
4− u
3)( u
4− u
2)( u
3− u
1)( u
2− u
1) + u
2u
1+ u
3(− 2u
2+ u
1) (2.13)
k = 1
v
4(2.14)
and can be filled in in Equation 2.10. The final step to determine the cell constant
is multiplying Equation 2.9 by a factor 2 to compensate for the fact that these math- ematical expressions only describe half of the microfluidic channel, resulting in the cell constants that can be described by Equation 2.15 (per transversal length, elec- trode length L) or 2.16 (dimensionless), respectively.
K
cell= 4 L
K ( k )
K ( k
0) (2.15)
K
cell= 4 K ( k )
K ( k
0) (2.16)
Chapter 3
Design optimization
The project started with a conceptual design of a hydrogel-based microfluidic chip for mimicking blood vessels with expansion possibilities to perform TEER measure- ments. During this project, this concept was optimized resulting in the novel chip design discussed in this report. First, the optimization of the concept is elaborated on, structured in 1) initial concept, 2) observed limitations and 3) proposed adapta- tions. Second, the design of the electrode configuration for the TEER measurements is discussed. Finally, all proposed adaptations are integrated into the final design, which is presented at the end of this chapter.
3.1 Hydrogel-based microfluidic chip
3.1.1 Initial concept
The design and fabrication process of the hydrogel-based chip as illustrated in Fig- ure 3.1 formed the starting point of this project. It is comprised of two separate com- ponents: 1) a 3D printed holder with a lowered plateau in which a silicon mould with channel features for imprinting channel structures in hydrogel is placed; 2) a polydimethylsiloxane (PDMS) mould obtained by replica moulding using a mi- cromilled poly-(methyl methacrylate) (PMMA) master, which snugly fits into the mould holder. The injection set-up is assembled by transferring the PDMS mould onto the chip holder, thereby creating a cavity which sets the boundaries for the hy- drogel that is injected with a needle through the PDMS (Figure 3.1a, b). After gela- tion, the PDMS mould containing hydrogel with imprinted channel features was lifted from the mould holder and transferred onto a glass slide. Glass was the mate- rial of choice since it enables imaging of the hydrogel channels as well as electrode incorporation.
3.1.2 Observed limitations
It proved difficult to fabricate reproducible hydrogels with imprinted channel fea-
tures and to subsequently seal these channels on glass using this method. Com-
plications in hydrogel injection were caused by the flexibility of the PDMS and the
entrapped air in the cavity that compromised the geometry of the hydrogel channel
F
IGURE3.1: A hydrogel mixture is injected into injection setup, com- prised of the silicon mould holder below and the gel support on top (B). The channel structure is imprinted into the hydrogel by soft- lithography using a silicon mould with positive channel features. Af- ter gelation, the top part is lifted-off, leaving open hydrogel channels (C). The hydrogel chip can be placed on a glass slide with or without
electrodes to seal the channels (D).
features. The negative effect of the flexibility was that an uneven pressure distribu- tion across the PDMS mould during manual injection would result in deformation of the mould. Consequently, the PDMS mould would release from the mould holder so that the cavity was not properly sealed and additional air could enter the cavity.
Moreover, air entrapped in the cavity upon assembling the injection set-up could not escape in this design. All compromised the geometry of the hydrogel channels.
Second, complications in sealing the hydrogel channels were caused by the mechan- ical instability of the hydrogel on glass and the lack of binding between glass and the hydrogel. Upon addressing the hydrogel channels with a pipette tip, the flexi- ble PDMS mould would deform the hydrogel, resulting in the hydrogel to release from the glass surface and leaking its content. The latter could not be prevented by chemical functionalization of the glass surface to promote gel adhesion. In addition to aforementioned limitations, a self-contained constraint is the fact that manually aligning the channel to the sensor would be inaccurate. Hence, successful integra- tion of a sensor requires electrode alignment with the hydrogel channel.
3.1.3 Proposed adaptations
Since avoiding air entrapment in the cavity appeared a prerequisite, the geometry
of the cavity was changed. The optimized geometry resembles a tunnel with inlet
for the hydrogel and a outlet for the air. This inlet for hydrogel injection is designed
to tightly fit a pipette tip to prevent backflow. To accommodate for the flexibility
of the gel support, PDMS was replaced by PMMA. To mechanically stabilize the in-
jection set up and prevent additional air from entering the cavity, the gel support
was completely encapsulated by the mould holder and firmly secured by screws to
prevent both horizontal and vertical movement. A similar solution was proposed
to mechanically stabilize the hydrogel on the glass slide, by designing an additional
glass holder which simultaneously would ensure alignment of the hydrogel channel
with the electrodes on the glass slide. Additional inlets were incorporated in the gel
support for addressing the hydrogel channels, which needed to be perfectly sealed to prevent backflow.
3.2 Electrode configuration
Initial concept theory
From experiments performed by Crone et al. it was learned that an optimal distance between the current injecting and most distant potential measuring electrode ap- proximates two length constants for the specific capillary, resulting in an intercapil- lary potential of 10% of the initial potential at the current injecting electrode. [24] The length constant as expected for a semi-circular hydrogel channel (r
channel= 30 μm) containing cell culture medium (ρ
medium