Patent Application
20180251717
A weak direct-current electric field (dcEF) exists at the tissue level due to the transepithelial potential difference established by the tissue polarity (NPL No. 1). Cells demonstrate directional migration (electrotaxis) or orientation-change (electro-alignment) in response to a physiological dcEF in both in vitro and in vivo settings. The electrotaxis and dcEF stimulation have played pivotal roles in physiological processes such as embryonic development, neurogenesis, morphogenesis, and wound healing (NPL Nos. 1-5).
Numerous cellular signaling pathways have been regulated under electric field (EF) stimulation. Various membrane receptors (NPL Nos. 6-10) or ion channels (NPL Nos. 11-15) have been suggested to act as EF sensors and initiate many intracellular signaling cascades in different cell types (NPL Nos. 8, 13, and 16-21). Further investigations are required to clarify the functional roles of EF sensory proteins and signaling networks in regulating the electrotaxis phenomena.
Gaining a better understanding of signaling pathways demands a reliable and convenient electrical stimulation platform for microscopy imaging and cell product recovery with subsequent biochemical analysis. Even though an electrical cue can direct cell migration comparable to that of chemical cues (NPL No. 22) and synergistically promote directional migration with other physical factors such as shear stresses (NPL No. 23), electrotaxis is less well studied than chemotaxis, possibly due to the lack of experimental tools for convenient EF stimulation comparable to a boyden chamber (transwell chamber) that is routinely used for chemotaxis (NPL No. 24).
Conventional in vitro electrical stimulations were commonly performed either by direct stimulation using electrodes, or stimulation in a microfluidic chamber with salt bridges. The EF created through direct electrode stimulation is not uniform and cells are often exposed to toxic electrolysis products. Thus conventional electrotaxis studies usually employ a confined microfluidic chip in which cells are cultured in the bottom of the culture chamber (NPL Nos. 25-30). The small cross-section of the chamber limits the applicable electrical current and reduces the Joule heating that could be harmful to the cells.
Despite the success of using microfluidic chips for electrical stimulation in recent studies, these microfluidic chips often require special fabrication procedures on cell culture dishes days prior to the actual experiment, thereby limiting the adaptivity with common laboratory settings. Further, a simple rectangular shaped cell culture microchamber is usually placed on a circular shaped tissue-culture polystyrene (TCPS) petri dish to generate the uniform EF. As a result, a large portion of the cell culture area on the dish is unused, leading to a low cell yield and poor cell product recovery. Even though larger cell yields have been recently achieved by scaling up the rectangular shaped microchamber with increased cell culture area (NPL Nos. 29 and 30), a large fraction of the circular shaped TCPS dish is still unutilized. In a circular-shaped area, a uniform EF cannot be intuitively created by two electric potentials due to different electrical resistances originated from the length difference between the diameter of the circle and the length of any parallel chord of the bottom circular chamber where cells are cultured. For example, Marotta et al. electrically stimulated muscle cells to pace contraction by using a 6-well plate (NPL No. 31). A computer simulation indicates that the cells used in Marrotta et al. were subjected to non-uniform EF as well as electrolysis products. Furthermore, a computer simulation indicates that tissue pacing studies with a commercial electrical stimulation system suffered similar drawbacks (C-dishes, IonOptix, MA, USA) (NPL Nos. 32-35). Lin et al. used a modified transwell assay to study cell electrotaxis by applying EF through the transwell insert coupled with platinum electrodes (NPL No. 36). Alternatively, Garcia-Sanchez et al. used patterned electrodes to stimulate cells in multi-well plates (NPL No. 37). Their systems require sophisticated microfabrication procedures, and small EF-null gaps between electrodes also decrease the EF homogeneity. Recently, Ahirwar et al. used electromagnetic induction method with a boyden chamber to demonstrate non-contact directing electrotaxis, but non-uniform EF persisted (NPL No. 38).
Computer aided design and computer aided manufacturing (CAD/CAM) use computer software to precisely design model structure and program manufacturing processes. Mathematically depicted 3D structures for workpieces can be easily created by CAD/CAM software, and are conveniently adopted for numerical simulations. Thus, time, material, and manpower are greatly reduced for prototyping effort. In recent years, additive manufacturing (3D printing) (NPL No. 39) takes the advantage of CAD/CAM to rapidly prototype workpieces through layer-by-layer stacking of raw materials, and this technology has been used to fabricate microfluidic chips (NPL Nos. 40-43).
The conventional techniques described above have not yet provided convenient and efficient means for creating reliable uniform electric field in circular culture plate/cultureware.
An object of the present invention is to provide an efficient and very effective way to establish a uniform electric field in circular culture plate/cultureware.
To achieve these and other advantages and in accordance with the purpose of the present invention, as embodied and broadly described, in one aspect, the present invention provides an insert to be inserted into a circular-shaped petri dish for generating a substantially uniform electric field across the petri dish filled with a fluid establishing a salt bridge, comprising: a circular-shaped bottom plate configured to be fitted into the circular-shaped petri dish, the bottom plate defining a circular-shaped space of a substantially uniform thickness together with a circular-shaped bottom surface of the petri dish as a channel accepting said fluid when the insert is inserted into the petri dish; a side channel vertically erecting from a circular periphery of said bottom plate, the side channel communicating with said circular shaped space defined by the bottom plate so as to accept said fluid; and a pair of current rectifying chambers each having a generally planar shape connecting to and communicating with the side channel, the current rectifying chambers being diagonally disposed to face each other along a diameter of the circular shaped bottom plate and being line-symmetric with each other with respect to said diameter, each of the current rectifying chambers extending inwardly from a respective portion of a top end of the side channel and having a salt bridge port to accept the fluid and provide the fluid to said circular-shaped space defined by the bottom plate through said side channel so as to establish the salt bridge, wherein portions of the side channel other than the portions thereof respectively connecting to the current rectifying chambers each have a generally concave top profile having a lowest point at a center between the pair of current rectifying chambers and are each shaped such that when the salt bridge is established, the circular-shaped space defined by the bottom plate exhibits a uniform electric field in a direction of said diameter in a substantially entire area thereof.
Here, the circular shaped petri dish may be a tissue-culture polystyrene (TCPS) petri dish. Said generally concave top profile of the side channel may outline a curve defined by an intersection of a paraboloid with a cylindrical column. Further, said generally concave top profile of the side channel may have a stair-like shape outlining said curve.
In another aspect, the present invention provides a device for establishing a uniform electric field in a planar circular-shaped space filled with a fluid having a prescribed resistivity, comprising a unitary or multipart member that defines: the planar circular-shaped space of a substantially uniform thickness; a side channel vertically erecting from a circular periphery of said planar circular-shaped space; and a pair of planar chambers each connecting to and communicating with the side channel, the planar chambers being diagonally disposed to face each other along a diameter of the planar circular-shaped space and being line-symmetric with each other with respect to said diameter, each of the planar chambers extending inwardly from a respective portion of a top end of the side channel and having a port to accept the fluid and provide the fluid to said planar circular-shaped space through said side channel, each port being configured to be applied with a prescribed voltage when the planar circular-shaped space, the side channel and the planar chambers are filled with the fluid, wherein portions of the side channel other than the portions thereof respectively connecting to the planar chambers each have a generally concave top profile having a lowest point at a center between the pair of planar chambers and are each shaped such that when filled with the fluid and said prescribed voltages are applied, the planar circular-shaped space exhibits a uniform electric field in a direction of said prescribed diameter in a substantially entire area thereof.
Here, said unitary or multipart member may comprise an insert and a circular-shaped petri dish to which the insert is inserted, together defining said planar circular-shaped space, said side channel, and said pair of planar chambers.
According to one or more aspects of the present invention, a uniform electric field can be established in circular culture plates/cultureware, which can be used in various research and development efforts in the biological and similar academic and industrial fields.
Additional or separate features and advantages of the invention will be set forth in the descriptions that follow and in part will be apparent from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims thereof as well as the appended drawings.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory, and are intended to provide further explanation of the invention as claimed.
As discussed above, applying uniform electric field (EF) in vitro in the physiological range has been achieved in rectangular shaped microchannels. However, in a circular-shaped device, it has been difficult to create uniform EF from two electric potentials due to different electrical resistances originated from the length difference between the diameter of the circle and the length of any parallel chord of the bottom circular chamber where cells are cultured. To address this challenge, the present disclosure provides a three-dimensional (3D) computer-aided designed (CAD) polymeric insert to create uniform EF in circular shaped multi-well culture plates/cultureware. In some embodiments, a uniform EF with a coefficient of variation (CV) of 1.2% in the 6-well plate can be generated with an effective stimulation area percentage of 69.5%. In particular, NIH/3T3 mouse embryonic fibroblast cells are used to validate the performance of the 3D designed Poly(methyl methacrylate) (PMMA) inserts in a circular-shaped 6-well plate. The CAD based inserts can be easily scaled up (i.e., 100 mm dishes) to further increase effective stimulation area percentages, and also be implemented in commercially available cultureware for a wide variety of EF-related research such as EF-cell interaction and tissue regeneration studies. In some embodiments, using Ohm's law, an optimized CAD structure is created to equalize the electrical resistance in the circular shaped bottom chamber to generate a uniform EF. As a result, a large area of contemporary cell culture dish can be stimulated with the uniform EF, and a higher cell yield can be obtained.
<Material and Methodology>
<Microfluidic Chip Composition and Assembly>
The schematic diagram of an electrical stimulation setup using an assembled microfluidic chip according to an embodiment of the present invention is shown in
<Design Principle>
As discussed above, a uniform EF cannot be simply created in a circular area due to different electrical resistances originated from the length difference between the diameter of the circle and the length of any parallel chord. Creating a uniform EF in a circular shaped chamber with the largest possible surface area for cells is therefore challenging. As illustrated in
,
with its centroid on the y-axis). The insert on top of the red region contains a thin liquid column (LC), residing on top of the bottom chamber. The assembled microdevice contains the bottom chamber, liquid column, and the current rectifying chambers (CRC, also termed as world-to-chip interface). See
To address this challenge, the present disclosure uses CAD to design a structure in which the electrical resistances through any arbitrary current paths that pass through the bottom circular chamber are substantially the same among each other. The resulting ideal structure is shown in
the
and the liquid column LC (
(white dashed curve,
must be equal to that through
(solid line connecting A, B, C and D). In other words, the electrical current passing along the parabolic curve
should hold the same strength to the electrical current passing through
The arc length of curve
can be determined by using multivariate calculus (NPL No. 46). See detailed derivation and the design principle explained in a section below, entitled “Detailed Design Procedure.” In short, the constant of the paraboloids describing the level of curvature in xz and yz planes and the height of the liquid column can be calculated and used for model design in a commercial CAD software package (Rhinoceros, USA). The resulting structure is illustrated in
Note that in
<Numerical EF Simulation>
The CAD model for a plain polymeric insert, created by the aforementioned principle, was imported into COMSOL Multiphysics software (COMSOL Inc., USA). The model used the culture medium (Dulbecco's minimum essential medium, DMEM) as the ionic fluid that is filing in the created fluidic channel (having a shaped shown in the figures mentioned above), and the electric potential between the salt bridges SB was numerically simulated by solving steady-state Maxwell's equations using the alternating current/direct current (AC/DC) module in COMSOL for the structures of the fluidic channels shown in
Due to the limitation of in-house fabrication tools, the assembled microfluidic chip based on the 3D CAD model with smooth paraboloid surface was not fabricated in this work. Instead, an approximated 6-layered model shown in
<Device Fabrication and EF Measurements>
The 6-layered approximation model for both 6-well plates and 35 mm dishes was used for the fabrication of inserts. Patterns were designed in AutoCAD software (Autodesk, USA) and a 1 mm thick PMMA substrate (Comoglas, Kuraray, Japan) was cut based on the 3D design by using a CO2 laser cutter (VLS2.30, Universal Laser Systems, USA). The layers were aligned and joined by thermal bonding and polymeric tapes (
To measure the EF in the bottom chamber in the insert, an array of holes in 0.3 mm diameter were drilled on the 1 mm-thick PMMA substrate (NPL Nos. 25 and 28). The spacing between each hole was 3 mm. The holes were temporarily sealed with a Kapton tape. The insert was filled with Dulbecco's minimum essential medium (DMEM, 12800017, Gibco, USA). A 46 V electric potential was applied through Ag/AgCl electrodes (25 mm×100 mm) by a DC power supply (E3641A, Keysight technologies, USA). Preparation of Ag/AgCl electrodes described in NPL No. 30 was used. To measure the voltage differences, two Ag/AgCl wire based electrodes (0.3 mm diameter) were inserted into two adjacent holes after piercing the tape cover (NPL Nos. 30 and 44). The voltage differences between any two electrodes in the chamber were measured by a digital multimeter (2100, Keithley Instruments, USA) for 20 samples at every position by using the Excel add-in function provided by the manufacturer (KI-LINK, Keithley Instruments, USA). The EFSs can then be calculated by dividing the voltage differences by the distance between respective electrodes. The results of mean EFSs and standard deviations are calculated and exported using a custom MATLAB script (Mathworks, USA). See Table 1 below.
<Cell Culture and Maintenance>
A Swiss murine embryonic fibroblast cell line with 3-day transfer protocol, NIH/3T3 (American Type Culture Collection, ATCC, USA) was used to demonstrate the electrical stimulation functionality with the polymeric circular insert and the rectangular microchannel described above. The cells were cultured on TCPS dishes in DMEM supplemented with 10% fetal bovine serum (FBS, Sigma-Aldrich, USA) at 37 degrees Celsius in a 95% relative humidity atmosphere supplemented with 5% CO2. The cells were sub-cultured twice a week by the recommended split ratio with trypsin-EDTA (Life Technologies, USA). For long term storage, the cells supplemented with 10% dimethylsulfoxide were cryopreserved in liquid nitrogen.
<EF Stimulation and Microscopy Analysis>
Each six-layered PMMA insert was disinfected and then affixed to individual wells in a 6-well TCPS plate or to a 100 mm TCPS dish (see
To start the cell experiment, PBS pre-filled chamber was first replaced by serum-containing cell culture medium, and a suspension of 5×105 cells was subsequently loaded into the chamber through the salt bridge ports by gravity feeding. After overnight culture for cell adhesion and growth, fittings to supply culture medium and for salt bridges (containing 1.2% agarose (LE agarose, Lonza, USA) in PBS) were connected to the top of the inserts. A syringe pump (YSP-202, YMC, Japan) was used to exchange cell culture medium during the time lapse experiment at a flow rate of 100 μL/h for the circular insert and 20 μL/h for the rectangular channels to obtain similar shear stress acting on the cells. A DC voltage and the current was applied and measured by a high voltage source meter unit (2410, Keithley Instruments, USA) through Ag/AgCl electrodes in PBS. The required current for a 300 mV/mm EF in a chamber of 30 mm in diameter and 0.26 mm in thickness was 3.545 mA.
The time lapse electrotaxis experiments were carried out on an automated microscope (Ti-E, Nikon, Japan). The phase contrast cell images were taken at different positions across the devices at an interval of 5 minutes. The morphology and centroid of cells were tracked manually for the duration of 5 hour time lapse using ImageJ analysis software package. All data are represented as the mean 95% confidence interval, which is 1.96 of standard error of mean, from triplicate experiments. Kruskal-Wallis one-way analysis of variance on ranks test with Dunn's multiple comparison post-hoc test were performed when non-Gaussian distribution of sample data was obtained from Bartlett's test. The confidence level to reject a null hypothesis between two data sets was set at 95%. A p-value (the probability for a true null hypothesis) less than 0.05 represents a statistical significance at 95% confidence.
<Results and Considerations>
<3D CAD Optimization for Uniform EF Creation>
The current density at the bottom of the chamber was simulated for the plain polymeric insert illustrated in
The simulated EF results for the plain polymeric insert, the smooth 3D CAD insert, and layered 3D CAD inserts are shown in
The simulated results are summarized in Tablet. In the plain polymeric insert without the 3D designed structure, the EF is non-uniform and the mean EFS and the coefficient of variation (CV, defined as the ratio of the standard deviation to the mean) are 75.03 mV/mm and 7.91%. In the 6-well plate (or a 35 mm dish) with the smooth CAD designed insert, an EF with mean EFS of 96.1 mV/mm is established with a 1.22% CV. As shown in Table 1, due to the rough surface in the layered approximation PMMA insert, the EF is less uniform than that in the smooth 3D CAD insert, which has smooth paraboloid surfaces. However, the layered PMMA insert can still create a very good uniform and directional EF, with mean EFS of 89.1 mV/mm and a CV of 1.30%, which is acceptable.
The double sided tape used in this study is a pressure sensitive adhesive prone to deformation under pressure or stretching. Effect of slight deformation in the chamber thickness to the EF uniformity was examined by numerical simulations.
The 3D CAD approach can be easily adapted to further scale up the insert for larger petri dishes such as 100 mm TCPS dishes. Uniform EFs are established in both a theoretical smooth 3D insert and an approximated layered PMMA insert with a height of 10 mm for a 100 mm dish as shown in Table 1 above and
<Validation of EF Uniformity in the Chamber>
<High Performance Cell EF Stimulation>
While the conventional in-vitro
electrical stimulation devices either sacrifice the culture area to stimulate cells uniformly, or stimulate large areas of cells with non-uniform EF, the polymeric circular inserts developed in this disclosure can provide uniform EF stimulation to large area percentage of cells. The effective stimulation area is defined as the area of the bottom chamber subtracting the area of where the liquid column resides. The effective stimulation area percentage is the ratio of the effective stimulation area over the total surface area of the TCPS dish.
Table 2 below lists the effective
stimulation area percentages using the polymeric inserts of the present disclosure and those reported in other literatures. As shown in Table 2, most existing devices cannot achieve uniform EF stimulation in more than 50% of the total cell culture area. In contrast, polymeric inserts according to embodiment of the present invention can provide uniform EF stimulation in more than 69% of the total area in a 6-well plate (or a 35 mm dish), and up to 90% in a 100 mm petri dish. Thus, the cell yields are higher when using polymeric inserts of the present invention for electrical stimulation. The higher cell yields will greatly benefit biochemical and molecular biology analysis.
<Cell Migration and Alignment Under Uniform EF Stimulation>
NIH/3T3 fibroblast cells were used to further verify the performance of the inserts according to embodiments of the present invention because they are known to align perpendicular to the EF vector after stimulation and they have shown cathodal electrotaxis (NPL Nos. 49-51). The phase contrast microscopy images of the cells under 300 mV/mm EF stimulation over 5 hours were taken and analyzed.
To quantify the cell migration and alignment of these cells, two parameters-directedness and orientation—are used with the following definition. See
The directedness of cell electrotaxis is defined as the average of
where Φi is the angle between the Euclidean vector of each cell migration and the vector of applied EF (from anode to cathode), and n is the total number of analyzed cells (see
The orientation is defined as the average of
where θi is the angle between the vector of applied EF and the long axis of a given cell; n is the total number of cells analyzed. A group of cells aligned perpendicular to the EF holds an orientation of −1; and a group of cells aligned in parallel to the applied EF holds an orientation of +1. For a group of randomly shaped cells, the average orientation is zero.
The directedness and orientation of the cells with and without EF stimulation, evaluated by the definitions provided above, are shown in
Before EF stimulation, cells in both rectangular channels and circular inserts demonstrated random orientation (0.05 to 0.09). After 300 mV/mm EF stimulation, the orientation of cells in rectangular channels and circular insert decreased to −0.60±0.05 and −0.49±0.06, indicating perpendicular alignment (
Detailed cell migration and orientation data are shown in Table 3 below. These results validated the performance of the inserts according to embodiments of the present invention for electrotaxis experiments comparable to the performance of a rectangular channel. However, the circular inserts have at least two fold higher effective stimulation percentage in comparison to that of rectangular channels. Thus, a higher cell yield can be achieved by using our circular inserts of the present invention.
In some embodiments of the present invention, a removable polymeric insert can further aid cell recovery right after the EF stimulation, which can be accomplished by adding a perfluoropolymer-coated layer between the adhesive tape and the insert (NPL No. 30). Alternatively, the removable insert can be fabricated by using polydimethyl-siloxane as the insert material. The silicone rubber can reversibly bond to the TCPS dish with air-tight seal by the clip-on design, similar to those in a transwell insert.
Inserts for 15 mm diameter well with a 24-well plate were fabricated as embodiments of the present invention and tested. In this embodiment, cased on the calculation and use of evaluation by commercially available software Mathematica, the following paraboloids parameters, P1 were used to modify a 2.3 mm-high cylinder with a shell thickness of 0.1 mm. The bottom chamber thickness was set to 0.05 mm. The very thin bottom chamber enables high electric field strength with low electric current input:
The small size of this 3D structured insert in 15 mm diameter cultureware allows the use of two-photon polymerization technique in manufacturing the insert. Thus, a smooth structure, instead of a layer-by-layer approximated multi-layered structure, can be fabricated, which is advantageous.
Due to the small configuration of 24-well dishes, the insert was designed to have minimized two interfaces, where salt bridges share the same interface with the inlet and outlet ports. This design also allows more space for easier and higher quality imaging.
In
Various embodiments described above are summarized in Table 4 below.
<Detailed Design Procedure>
In contrast to the conventional in vitro EF stimulation systems using a rectangular chamber, establishing a uniform EF in a circular shaped chamber (e.g., tissue culture polystyrene petri dish) is extremely difficult. This section describes the design principle for a 3D CAD insert of the type illustrated in
To maximize the cellular products for biochemical analysis, one desires to use as much of culture area as possible to increase the amount of cells to be stimulated in the circular chamber with a given height (the circular bottom channel shown in
To create a uniform EF, the electrical resistance from one electrode to the other through any cross-section in the system must be the same. To address this challenge, a three dimensionally (3D) designed structure is devised to equalize the electrical resistances through any arbitrary current line that passes through the bottom circular chamber. Such structure can be approximated as the liquid column (LC) intersected by two identical circular paraboloids (P1 and P2) at the intersection of midpoint between the two potentials and the diameter of the liquid column (
where ρ is the resistivity, 1 is the length, and Across-section is the cross-sectional area of the conductor. The arc length of the curves needs to be identified in this system to calculate the electrical resistance. Using a polar coordinate system, the bottom chamber (
.
For paraboloid P1, its apex resides with the origin 0 in the liquid column and the yz plane. The paraboloid intersects with the liquid column at the curve
M′=
(white dashed line,
(
equivalently,
R
M′
=R
+R
+R
.
If we assume the resistivity is the same across the sample, then the following is satisfied.
Equation 2 shows that a uniform EF distribution can be enabled when the ratio of the rectification of the curve M′ over the cross-sectional area of the liquid column equals to the ratio of
over the cross-sectional area of the liquid column, in addition to
over the cross-sectional area of the bottom chamber. Assuming all electrical currents pass through sufficiently thin paths, then the following is satisfied.
Since
and
can be easily measured, the value of M′ can be subsequently extracted by using Equation 3. With the information of M′, the shape of the circular paraboloid P1 and P2 can be determined as follows.
The shape for the circular paraboloid P1 and P2 can be described as
where a2/b is the constant describing the level of curvature in xz and yz planes of the paraboloid, which defines the shape of the paraboloid.
The equation for the liquid column can be considered as
x
2+(y−r)2=r2, (5)
where r is the radius of the column (also the radius of the circular bottom chamber). The coordinates of points O, A, and D can be presented in parametric form
The rectification of curve M′ along the paraboloid P1 can be calculated by integrating parametric equations (NPL No. 61),
The constant of the paraboloid
can be solved by solving Equation 3. Equation 3 is difficult to solve explicitly due to elliptic integral of the second kind related to M′ along the paraboloid P1 (Equation 7). But Equation 3 can be evaluated using Mathematica using the following code (Listing 1) by denoting a constant
(r is the radius of the circular bottom chamber) to simplify the calculation.
Listing 1: Example Code to Find the Descriptor for the Paraboloid P1:
Plot[Evaluate[Integrate[Sqrt[225+ĉ2−ĉ2*Sin [x]̂2,{x,0,Pi}]/0.5−2*c/0.5−30/0.26],{c,−4.715,−4.71}]
To design an insert for 6-well plates, denote the thickness of the liquid column to be 0.5 mm, the diameter of the bottom chamber to be 30 mm, and the thickness of the bottom chamber to be 0.26 mm, the parameter
(containing the constant for the paraboloid P1) can be evaluated and used to create the 3D model (described below) in a commercial CAD software for further numerical simulation and device fabrications.
With this design principle, two extreme cases can be considered: electrical current passing through the shortest chord and the longest chord (i.e., diameter), which will yield the constant of the paraboloid and the height of the liquid column required to achieve uniform EF. To find the electrical resistance for all arbitrary current lines passing through each different paths (for example, path line curves M″, M**, M*, and M′ in
Listing 2: Examples Code for all M Paths:
Table[Evaluate[2*Integrate[Sqrt[225+4.713̂2−4.713̂2*Sin [x]̂2],{x,0,y}/0.5+2*(−4.713)*(1−Sin [y])/0.5+2*15*Sin [Pi/2−y]/0.26],{y,0,Pi/2,Pi/180}]
The calculated resistance range with
θ∈(0°,90°)
is plotted in
corresponds to θ=0 and that of
corresponding to θ=90. The results show that resistances of all path lines converge toward both extreme cases, and this model provides a good approximation to achieve uniform EF in a circular chamber. Quadratic surface integral should also be helpful to further improve this design procedure.
In sum, establishment of a uniform EF in a circular-shaped microdevice is extremely difficult so the majority of existing EF stimulation devices avoids this issue by using a simple rectangular shaped chamber. The rectangular configuration requires modification to fit with the commercial labware, and only a small portion of the cell culture dish is used for cell culture, thus limiting the cell yield. By adding a 3D CAD based insert according to embodiments of the present invention in a circular shaped cell culture chamber, the present disclosure demonstrated that a uniform EF can be created in a circular-shaped area by modulating the electrical resistance across the device.
In some aspects of the present invention, the following features can be noted, some of which have been described above.
(1) The effective stimulation area percentage using the insert is at least 2 fold higher than that of existing EF stimulation devices. The yield of cells and its products can be increased for further biochemical analysis.
(2) The same CAD design principle can be easily scaled up or down to tailor design inserts for different sized TCPS dishes. Mass production of the polymeric insert can be achieved by CNC fabrication, injection molding, or other similar technology. The polymeric insert is useful for adapting electrical stimulation studies in a common laboratory due to the high effective stimulation area percentage and the ease of use.
(3) The polymeric insert is applicable for various studies. For tissue engineering, EF stimulation has been reported to induce synchronously contracting cardiac tissue (NPL Nos. 52 and 54-57). Osteoblastic differentiation from mesenchymal stem cells can be promoted under EF stimulation (NPL No. 58). Uniform EF stimulation to circular shaped area could also be useful to stimulate an entire brain slice or tissue slice.
It will be apparent to those skilled in the art that various modification and variations can be made in the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention cover modifications and variations that come within the scope of the appended claims and their equivalents. In particular, it is explicitly contemplated that any part or whole of any two or more of the embodiments and their modifications described above can be combined and regarded within the scope of the present invention.
The present invention relates to circular culture plates for research and development in biological and similar fields. This application hereby incorporates by reference U.S. Provisional Application No. 62/220,841, filed Sep. 18, 2015, in its entirety.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/JP2016/004255 | 9/16/2016 | WO | 00 |
| Number | Date | Country | |
|---|---|---|---|
| 62220841 | Sep 2015 | US |
