Difference between revisions of "Team:SUSTech Shenzhen/Model"

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url=wiki/images/1/17/T--SUSTech_Shenzhen--Model.svg|size=100px|title=Model|subtitle=}}
 
url=wiki/images/1/17/T--SUSTech_Shenzhen--Model.svg|size=100px|title=Model|subtitle=}}
 
{{:Team:SUSTech_Shenzhen/main-content-begin}}
 
{{:Team:SUSTech_Shenzhen/main-content-begin}}
 +
 +
= Overview =
 +
 +
When we were discovering audio-genetics, to find correspondences between our mechanosensitive(MS) channels and different sound wavelengths, we needed the support of modeling and logical result ascription besides constructing a huge mutagenesis library and testing them in vitro continuously, although it is already very hard to do. We designed the experiment based on the discovery of the mechanism of MS channel and applying it on the regulation of downstream gene expression. Modeling has been our guide throughout the project and we finally got the result we initially expected.
 +
 +
In one part, we employed microfluidics to realize the stable force field controlled by fluidic velocity. In-vitro experiments were operated on the designed chips. On the other hand, we used various devices to generate sound field and tested cell response in different conditions.
 +
 +
Finite Element Analysis (FEA) was applied to modeling of the field generated by the microfluidic devices and the acoustic stimulators. COMSOL Multiphysics® acted as both the modeling tool and the data analysis tool. Modeling reliability has been tested and confirmed by comparing the calculated result with raw results from the experiments.
  
 
= Microfluidics =
 
= Microfluidics =
  
To quantitively measure the response of MS channel on the cell membrane, we designed our experiment manipulated on microfluidic chip. CHO-K1 cells were cultured adherent on the bottom of PDMS tunnel. Stable and flexible force field could be formed surrounding cell, which directly controlled by the pumped-inflow rate. Each time when we applied a constant pumped inflow, cells in 3 different observation tunnel could receive corresponding small, middle, large, 3 level of force magnitude(1: 9: 81). By changing the pumped flow rate, we could measure MS channel response under a series of force.
+
To quantitatively measure the response of MS channel on the cell membrane, we designed our experiment manipulated on microfluidic chip. CHO-K1 cells were cultured adherent on the bottom of PDMS tunnel. Stable and flexible force field could be formed surrounding cell, which directly controlled by the pumped-inflow rate. Each time when we applied a constant pumped inflow, cells in 3 different observation tunnel could receive corresponding small, middle, large, 3 level of force magnitude(1: 9: 81). By changing the pumped flow rate, we could measure MS channel response under a series of forces with different magnitude order.
  
 
{{SUSTech_Image | filename=T--SUSTech_Shenzhen--rendered-device.png|width=800px|caption=}}
 
{{SUSTech_Image | filename=T--SUSTech_Shenzhen--rendered-device.png|width=800px|caption=}}
Line 14: Line 22:
 
== Mathematical Demonstration ==
 
== Mathematical Demonstration ==
  
In experiment, when fluid(culture medium F-12K) flowed through the tunnel, the shear force was applied on the wall. Seeing the culture medium as a Newtonian flow, it has a constant viscosity μ,0.012dyn·s/cm2.<ref>Booth, R., & Kim, H. (2012). Characterization of a microfluidic in vitro model of the blood-brain barrier (μBBB). Lab on a Chip, 12(10), 1784-1792.</ref> The shear stress that medium generated on wall is proportional to strain rate. As a result, we could relate the magnitude of stress to the  the velocity gradient along the transversal surface of each tunnel.  
+
In experiment, when fluid(culture medium x flowed through the tunnel, the shear force was applied on the wall. Seeing the culture medium as a Newtonian flow, it has a constant viscosity μ,0.012dyn·s/cm<sup>2</sup><ref>Booth, R., &amp; Kim, H. (2012). Characterization of a microfluidic in vitro model of the blood-brain barrier (μBBB). Lab on a Chip, 12(10), 1784-1792.</ref>. The shear stress that medium generated on the wall is proportional to strain rate. As a result, we could relate the magnitude of stress to the velocity gradient along the transversal surface of each tunnel.
Due to the extremely small scale of microfluidic tunnel (only 0.285mm of width), fluid in it observes the Laminar flow. We could assume there is no turbulence when inflow applied constantly, even at the corners. The modeling of flow between 2 parallel plates applies to such stable state, in which the magnitude of shear stress on the bottom is proportional to the maximum velocity( at the cutline).  
+
 
 +
Due to the extremely small scale of microfluidic tunnel (only 0.285mm of width), fluid in it observes the Laminar flow. We could assume there is no turbulence when inflow applied constantly, even at the corners. The modeling of flow between 2 parallel plates applies to such stable state, in which the magnitude of shear stress on the bottom is proportional to the maximum velocity( at the longitudinal central line).
 +
 
 +
As the shear stress is proved proportional to the flow rate in the tunnel, we designed the chip to achieve that each of 3 tunnels in observation area has the same transversal surface but the gradient (81: 9: 1 from up to bottom) flow rate, also the average speed.<br />
 +
The lengths of straight tunnels between AB and AC (L<sub>AB</sub>, L<sub>AC</sub>)are 14.3mm and 12.0mm, and the curved tunnels between AB and BC(R<sub>AB</sub>, R<sub>BC</sub>) are 108.0 mm and 105.0mm.
  
 
{{SUSTech_Image | filename=T--SUSTech_Shenzhen--35011F22BF6BCC10C3DF1F593E43DCF1.jpg|caption=}}
 
{{SUSTech_Image | filename=T--SUSTech_Shenzhen--35011F22BF6BCC10C3DF1F593E43DCF1.jpg|caption=}}
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For a constant flow rate within the tunnel, the average velocity remains same
 
For a constant flow rate within the tunnel, the average velocity remains same
 
{{SUSTech_Shenzhen/bmath|equ=<nowiki>\bar V=\frac{Q}{A}=\frac{\int_A udA}{A}=\frac{1}{2}V</nowiki>}}
 
{{SUSTech_Shenzhen/bmath|equ=<nowiki>\bar V=\frac{Q}{A}=\frac{\int_A udA}{A}=\frac{1}{2}V</nowiki>}}
 
As the shear stress is proved proportional to the flow rate in the tunnel, we designed the chip to achieve that each of 3 tunnels in observation area has the same transversal surface but the gradient (81: 9: 1 from up to bottom) flow rate, also the average speed.
The lengths of straight tunnels between AB and AC (LAB, LAC)are 14.3mm and 12.0mm, and the curved tunnels between AB and BC(RAB, RBC) are 108.0 mm and 105.0mm.
 
  
 
{{SUSTech_Image | filename=T--SUSTech_Shenzhen--annotated-device.png|width=800px|caption=}}
 
{{SUSTech_Image | filename=T--SUSTech_Shenzhen--annotated-device.png|width=800px|caption=}}
  
Based on the integral form of continuity equation for a incompressible fluid, during a given time, the sum of flow volume in each branch is equal to the total volume pumped in the whole chamber. According to Kirchhoff's law, the accumulation of flow speed at the joint point must be zero. It is easy to get the equation that  
+
Based on the integral form of the continuity equation for an incompressible fluid, during a given time, the sum of flow volume in each branch is equal to the total volume pumped in the whole chamber. According to the Kirchhoff's law, the accumulation of flow speed at the joint point must be zero. It is easy to get the equation that{{SUSTech_Shenzhen/bmath|equ=<nowiki>\begin{matrix} L_{AC}V_1=L_{AB}V_2+R_{AB} V_3 \\
{{SUSTech_Shenzhen/bmath|equ=<nowiki>\begin{matrix} L_{AC}V_1=L_{AB}V_2+R_{AB} V_3 \\
+
 
V_2:V_3=R_{AB}:L_{AB}
 
V_2:V_3=R_{AB}:L_{AB}
 
\end{matrix}</nowiki>}}
 
\end{matrix}</nowiki>}}
Consequently, we could reach the conclusion that the maximum velocity, average flow rate and the shear force on the bottom of each tunnel is at a ratio of 81:9:1.
+
Consequently, we could reach the conclusion that the maximum velocity, average flow rate and the shear force on the bottom of each tunnel is at a ratio of 81:9:1. To confirm the modeling result, we made calibration in real microfluidics chip, and the testing result is very close to designing value (about 80:10:1) (See the [[Measurement|Team:SUSTech_Shenzhen/Measurement]] page)
 
+
'''Overview'''
+
 
+
When we were discovering audio-genetics, to find correspondences between our mechanosensitive(MS) channels and different sound wavelengths, we needed the support of modeling and logical result ascription besides constructing a huge mutagenesis library and testing them in vitro continuously, although it is already very hard to do. We designed the experiment based on the discovery of the mechanism of MS channel and applying it on the regulation of downstream gene expression. Modeling has been our guide throughout the project and we finally got the result we initially expected.
+
 
+
In one part, we employed microfluidics to realize the stable force field controlled by fluidic velocity. In-vitro experiments were operated on the designed chips. On the other hand, we used various devices to generate sound field and tested cell response in different conditions.
+
 
+
Finite Element Analysis (FEA) was applied to modeling of the field generated by the microfluidic devices and the acoustic stimulators. COMSOL Multiphysics® acted as both the modeling tool and the data analysis tool. Modeling reliability has been tested and confirmed by comparing the calculated result with raw results from the experiments.
+
 
+
'''Microfluidics'''
+
 
+
To quantitatively measure the response of MS channel on the cell membrane, we designed our experiment manipulated on microfluidic chip. CHO-K1 cells were cultured adherent on the bottom of PDMS tunnel. Stable and flexible force field could be formed surrounding cell, which directly controlled by the pumped-inflow rate. Each time when we applied a constant pumped inflow, cells in 3 different observation tunnel could receive corresponding small, middle, large, 3 level of force magnitude(1: 9: 81). By changing the pumped flow rate, we could measure MS channel response under a series of forces with different magnitude order.
+
 
+
(design draft)
+
 
+
'''Mathematic Demonstation'''
+
 
+
In experiment, when fluid(culture medium x flowed through the tunnel, the shear force was applied on the wall. Seeing the culture medium as a Newtonian flow, it has a constant viscosity μ,0.012dyn·s/cm<sup>2</sup><ref>Booth, R., &amp; Kim, H. (2012). Characterization of a microfluidic in vitro model of the blood-brain barrier (μBBB). Lab on a Chip, 12(10), 1784-1792.
+
</ref>. The shear stress that medium generated on the wall is proportional to strain rate. As a result, we could relate the magnitude of stress to the velocity gradient along the transversal surface of each tunnel.
+
 
+
Due to the extremely small scale of microfluidic tunnel (only 0.285mm of width), fluid in it observes the Laminar flow. We could assume there is no turbulence when inflow applied constantly, even at the corners. The modeling of flow between 2 parallel plates applies to such stable state, in which the magnitude of shear stress on the bottom is proportional to the maximum velocity( at the longitudinally central line).
+
 
+
As the shear stress is proved proportional to the flow rate in the tunnel, we designed the chip to achieve that each of 3 tunnels in observation area has the same transversal surface but the gradient (81: 9: 1 from up to bottom) flow rate, also the average speed.<br />
+
The lengths of straight tunnels between AB and AC (L<sub>AB</sub>, L<sub>AC</sub>)are 14.3mm and 12.0mm, and the curved tunnels between AB and BC(R<sub>AB</sub>, R<sub>BC</sub>) are 108.0 mm and 105.0mm.
+
 
+
(formulas+picture)
+
 
+
Based on the integral form of the continuity equation for an incompressible fluid, during a given time, the sum of flow volume in each branch is equal to the total volume pumped in the whole chamber. According to the Kirchhoff's law, the accumulation of flow speed at the joint point must be zero. It is easy to get the equation that
+
 
+
L<sub>AC</sub>*V<sub>1</sub>=L<sub>AB</sub>*V<sub>2</sub>+R<sub>AB</sub>*V<sub>3</sub>
+
 
+
V<sub>2</sub>:V<sub>3</sub>=R<sub>AB</sub>:L<sub>AB </sub>
+
 
+
Consequently, we could reach the conclusion that the maximum velocity, average flow rate and the shear force on the bottom of each tunnel is at a ratio of 81:9:1. To confirm the modeling result, we made calibration in real microfluidics chip, and the testing result is very close to designing value (about 80:10:1) ''See the measurement page''
+
  
'''Experimental result Analysis'''
+
== Experimental result Analysis ==
  
On October 12th, we testify one of our MS channels, Piezo1, under the simulation of shear stress, with R-GECO fluorescent indicating its activation level. (results showed below)
+
On October 12th, we testify one of our MS channels, Piezo1, under the simulation of shear stress, with R-GECO fluorescent indicating its activation level. (results shown below)
  
'''Simulation'''
+
== Simulation ==
  
 
To make the analysis of experimental result is convincible, we also made the simulation using COMSOL Multiphysics® to define that the field in microfluidic channel confirmed to our expectation.
 
To make the analysis of experimental result is convincible, we also made the simulation using COMSOL Multiphysics® to define that the field in microfluidic channel confirmed to our expectation.
Line 81: Line 56:
 
We made the simulation with the following procedures, and the result of maximum velocity and shear force applied on the bottom wall match with the mathematics perfectly.
 
We made the simulation with the following procedures, and the result of maximum velocity and shear force applied on the bottom wall match with the mathematics perfectly.
  
'''a. geometry'''
+
=== a. Geometry ===
  
First we imported the designed pattern file created by solidworks®.
+
First we imported the designed pattern file created by Solidworks®.
  
 
Then we draw two circles which have the diameter equal to the inner diameter of the fluid pipes that we used (0.65mm). The circles were placed around the center of the two circles we reserved for the fluid pipes. Since we used our bear hands to control the position of the holes for the fluid pipes in chip fabrication, the circles were just placed around the center parts like real cases.
 
Then we draw two circles which have the diameter equal to the inner diameter of the fluid pipes that we used (0.65mm). The circles were placed around the center of the two circles we reserved for the fluid pipes. Since we used our bear hands to control the position of the holes for the fluid pipes in chip fabrication, the circles were just placed around the center parts like real cases.
Line 89: Line 64:
 
Then we extruded the pattern to 90μm, and deleted the undesired parts. The final geometry was shown below.
 
Then we extruded the pattern to 90μm, and deleted the undesired parts. The final geometry was shown below.
  
'''b.Parameters'''
+
=== b.Parameters ===
  
All geometry domains were applied with the build-in material “water” to represent the petro medium that we used in our experiment.
+
All geometry domains were applied with the build-in material "water" to represent the petro medium that we used in our experiment.
  
 
The material parameters can be seen from bellow.
 
The material parameters can be seen from bellow.
  
{|
+
{|class="table table-striped"
 
| '''Description'''
 
| '''Description'''
 
| '''Value'''
 
| '''Value'''
Line 121: Line 96:
 
|}
 
|}
  
'''Table 1 Material Properties of “water”'''
+
'''Table 1 Material Properties of "water"'''
  
 
The parameters that we actually used was the dynamic viscosity (eta), and the density (rho). Their values with respect to the change of the temperature (K) can be seen form below.
 
The parameters that we actually used was the dynamic viscosity (eta), and the density (rho). Their values with respect to the change of the temperature (K) can be seen form below.
Line 157: Line 132:
 
The outlet circle was given the pressure of 0.
 
The outlet circle was given the pressure of 0.
  
'''c. Mesh'''
+
=== c. Mesh ===
  
 
We choose “fine” mash to simulate our model. The specifics of the mash are shown below.
 
We choose “fine” mash to simulate our model. The specifics of the mash are shown below.
  
{|
+
{|class="table table-striped"
 
| '''Description'''
 
| '''Description'''
 
| '''Value'''
 
| '''Value'''
Line 205: Line 180:
 
'''Fig. Mash details'''
 
'''Fig. Mash details'''
  
'''d. Solver Configuration'''
+
=== d. Solver Configuration ===
  
 
The solver was configured to compute for the stationary values under this specific model configuration. The relative tolerance was set to 0.000001, which means that the solver will only stop computing if the deviation of the result from the actual solution to the equations is under one in a million of the value of the actual solution.
 
The solver was configured to compute for the stationary values under this specific model configuration. The relative tolerance was set to 0.000001, which means that the solver will only stop computing if the deviation of the result from the actual solution to the equations is under one in a million of the value of the actual solution.
  
'''e.Results'''
+
=== e.Results ===
  
 
In the microfluidic channels the fluid will be applied a dragging force from the channel walls. So the fluid in the center line of the channel flows with the fastest speed.
 
In the microfluidic channels the fluid will be applied a dragging force from the channel walls. So the fluid in the center line of the channel flows with the fastest speed.
Line 239: Line 214:
 
The speed at the central line in all three channels at three different flow rate is listed below.
 
The speed at the central line in all three channels at three different flow rate is listed below.
  
{|
+
{|class="table table-striped"
 
|
 
|
 
Channel
 
Channel
Line 266: Line 241:
 
'''Table 3 Simulation Results of Central Line Speed'''
 
'''Table 3 Simulation Results of Central Line Speed'''
  
'''g. Discussion'''
+
=== g. Discussion ===
  
 
In this simulation, we consider all the channel walls are rigid, but in real cases, channel walls will deform when pressure applied. So the cross section area of the channel will be larger than what we have considered in this simulation.
 
In this simulation, we consider all the channel walls are rigid, but in real cases, channel walls will deform when pressure applied. So the cross section area of the channel will be larger than what we have considered in this simulation.
Line 314: Line 289:
 
The speed at the central line in all three channels at three different flow rate is listed below.
 
The speed at the central line in all three channels at three different flow rate is listed below.
  
{|
+
{|class="table table-striped"
 
|
 
|
 
Channel
 
Channel

Revision as of 11:15, 16 October 2016

Team SUSTC-Shenzhen

Model

Overview

When we were discovering audio-genetics, to find correspondences between our mechanosensitive(MS) channels and different sound wavelengths, we needed the support of modeling and logical result ascription besides constructing a huge mutagenesis library and testing them in vitro continuously, although it is already very hard to do. We designed the experiment based on the discovery of the mechanism of MS channel and applying it on the regulation of downstream gene expression. Modeling has been our guide throughout the project and we finally got the result we initially expected.

In one part, we employed microfluidics to realize the stable force field controlled by fluidic velocity. In-vitro experiments were operated on the designed chips. On the other hand, we used various devices to generate sound field and tested cell response in different conditions.

Finite Element Analysis (FEA) was applied to modeling of the field generated by the microfluidic devices and the acoustic stimulators. COMSOL Multiphysics® acted as both the modeling tool and the data analysis tool. Modeling reliability has been tested and confirmed by comparing the calculated result with raw results from the experiments.

Microfluidics

To quantitatively measure the response of MS channel on the cell membrane, we designed our experiment manipulated on microfluidic chip. CHO-K1 cells were cultured adherent on the bottom of PDMS tunnel. Stable and flexible force field could be formed surrounding cell, which directly controlled by the pumped-inflow rate. Each time when we applied a constant pumped inflow, cells in 3 different observation tunnel could receive corresponding small, middle, large, 3 level of force magnitude(1: 9: 81). By changing the pumped flow rate, we could measure MS channel response under a series of forces with different magnitude order.

T--SUSTech Shenzhen--rendered-device.png

Mathematical Demonstration

In experiment, when fluid(culture medium x flowed through the tunnel, the shear force was applied on the wall. Seeing the culture medium as a Newtonian flow, it has a constant viscosity μ,0.012dyn·s/cm2[1]. The shear stress that medium generated on the wall is proportional to strain rate. As a result, we could relate the magnitude of stress to the velocity gradient along the transversal surface of each tunnel.

Due to the extremely small scale of microfluidic tunnel (only 0.285mm of width), fluid in it observes the Laminar flow. We could assume there is no turbulence when inflow applied constantly, even at the corners. The modeling of flow between 2 parallel plates applies to such stable state, in which the magnitude of shear stress on the bottom is proportional to the maximum velocity( at the longitudinal central line).

As the shear stress is proved proportional to the flow rate in the tunnel, we designed the chip to achieve that each of 3 tunnels in observation area has the same transversal surface but the gradient (81: 9: 1 from up to bottom) flow rate, also the average speed.
The lengths of straight tunnels between AB and AC (LAB, LAC)are 14.3mm and 12.0mm, and the curved tunnels between AB and BC(RAB, RBC) are 108.0 mm and 105.0mm.

T--SUSTech Shenzhen--35011F22BF6BCC10C3DF1F593E43DCF1.jpg
Newtonian fluid flows between two wide, parallel plates Flow driven by pressure difference Parabolic velocity profile given by u = V[1-(y/h)^2] where V is the maximum velocity (along channel centerline y=0) Along bottom wall, y=-h, shear stress \tau=\mu \frac{du}{dy}=\mu(-2V\frac{y}{h^2})=\frac{2\mu V}{h} For a constant flow rate within the tunnel, the average velocity remains same \bar V=\frac{Q}{A}=\frac{\int_A udA}{A}=\frac{1}{2}V

T--SUSTech Shenzhen--annotated-device.png

Based on the integral form of the continuity equation for an incompressible fluid, during a given time, the sum of flow volume in each branch is equal to the total volume pumped in the whole chamber. According to the Kirchhoff's law, the accumulation of flow speed at the joint point must be zero. It is easy to get the equation that\begin{matrix} L_{AC}V_1=L_{AB}V_2+R_{AB} V_3 \\ V_2:V_3=R_{AB}:L_{AB} \end{matrix} Consequently, we could reach the conclusion that the maximum velocity, average flow rate and the shear force on the bottom of each tunnel is at a ratio of 81:9:1. To confirm the modeling result, we made calibration in real microfluidics chip, and the testing result is very close to designing value (about 80:10:1) (See the Team:SUSTech_Shenzhen/Measurement page)

Experimental result Analysis

On October 12th, we testify one of our MS channels, Piezo1, under the simulation of shear stress, with R-GECO fluorescent indicating its activation level. (results shown below)

Simulation

To make the analysis of experimental result is convincible, we also made the simulation using COMSOL Multiphysics® to define that the field in microfluidic channel confirmed to our expectation.

COMSOL Multiphysics® is a general-purpose software platform, based on finite element analysis, for modeling and simulating physics-based problems. It divides a large problem into smaller elements, these smaller elements will be solved separately and then be assembled backed to the original model. A collection of smaller elements is called a “mesh”, the “mesh” is constructed by numerous elements, the smaller the size of the element is, the finer the “mesh” is, and the more accurate will the result be.

We made the simulation with the following procedures, and the result of maximum velocity and shear force applied on the bottom wall match with the mathematics perfectly.

a. Geometry

First we imported the designed pattern file created by Solidworks®.

Then we draw two circles which have the diameter equal to the inner diameter of the fluid pipes that we used (0.65mm). The circles were placed around the center of the two circles we reserved for the fluid pipes. Since we used our bear hands to control the position of the holes for the fluid pipes in chip fabrication, the circles were just placed around the center parts like real cases.

Then we extruded the pattern to 90μm, and deleted the undesired parts. The final geometry was shown below.

b.Parameters

All geometry domains were applied with the build-in material "water" to represent the petro medium that we used in our experiment.

The material parameters can be seen from bellow.

Description Value
Dynamic viscosity eta(T[1/K])[Pa*s]
Ratio of specific heats 1.0
Electrical conductivity {{5.5e-6[S/m], 0, 0}, {0, 5.5e-6[S/m], 0}, {0, 0, 5.5e-6[S/m]}}
Heat capacity at constant pressure Cp(T[1/K])[J/(kg*K)]
Density rho(T[1/K])[kg/m^3]
Thermal conductivity {{k(T[1/K])[W/(m*K)], 0, 0}, {0, k(T[1/K])[W/(m*K)], 0}, {0, 0, k(T[1/K])[W/(m*K)]}}
Speed of sound cs(T[1/K])[m/s]

Table 1 Material Properties of "water"

The parameters that we actually used was the dynamic viscosity (eta), and the density (rho). Their values with respect to the change of the temperature (K) can be seen form below.

553x415px

Fig. Plot of eta(T)

eta(T)=1.3799566804-0.021224019151*T^1+1.3604562827E-4*T^2-4.6454090319E-7*T^3+8.9042735735E-10*T^4-9.0790692686E-13*T^5+3.8457331488E-16*T^6 (273.15K≤T≤413.15K)

eta(T)= 0.00401235783-2.10746715E-5*T^1+3.85772275E-8*T^2-2.39730284E-11*T^3 (413.15 K≤T≤553.75K)

553x415px

Fig. Plot of rho(T)

rho(T)=838.466135+1.40050603*T^1-0.0030112376*T^2+3.71822313E-7*T^3 (273.15K≤T≤553.75K)

Since the temperature of our model is set to the reference temperature as 293.15K, the respect value of eta(T) and rho(T) are 0.00101 Pa*s and 999.61509 kg/m³.

We used incompressible laminar flow interface to simulate our experiment, and the equations that the interface used is shown below.

67x16px167x25px

68x16px

All boundaries except the inlet and the outlet circles were set to be no slipping walls.

553x415px

Fig. Boundaries Considered as No Slipping Walls

The inlet circle was given the velocity of 2.5113E-4 m/s, 7.534E-4 m/s and 0.0022602 m/s, which will give us the rate of flow values of 5μL/min, 15μL/min and 45μL/min.

The outlet circle was given the pressure of 0.

c. Mesh

We choose “fine” mash to simulate our model. The specifics of the mash are shown below.

Description Value
Minimum element quality 9.185E-4
Average element quality 0.4356
Tetrahedral elements 503702
Pyramid elements 260
Prism elements 363692
Triangular elements 182924
Quadrilateral elements 160
Edge elements 19326
Vertex elements 524

Table 2 Mash Specifics

553x415px

Fig. Mash Generated

By choosing this mash size, the mash generated was fine enough to give six solution points with in the width of a single channel.

553x221px

Fig. Mash details

d. Solver Configuration

The solver was configured to compute for the stationary values under this specific model configuration. The relative tolerance was set to 0.000001, which means that the solver will only stop computing if the deviation of the result from the actual solution to the equations is under one in a million of the value of the actual solution.

e.Results

In the microfluidic channels the fluid will be applied a dragging force from the channel walls. So the fluid in the center line of the channel flows with the fastest speed.

In order to show the speed distribution inside the microfluidic channels, speed diagrams of the cut plane in the middle of the bottom plane and the top plane is shown below.

553x415px

Fig. Velocity magnitude Distribution Under Input Flow Rate 5μL/min (log phase)

553x415px

Fig. Velocity magnitude Distribution Under Input Flow Rate 15μL/min (log phase)

553x415px

Fig. Velocity magnitude Distribution Under Input Flow Rate 45μL/min (log phase)

In order to further show the speed difference under three different parameters, we draw a line on the cut plane from (-16, -4) to (-16, -6.45) crossing through three microfluidic channels in the observation zone. and plot the flow speed on that line.

553x415px

Fig. Cut Line Drawn

553x415px

Fig. Velocity Magnitude Distribution on The Cut Line

The speed at the central line in all three channels at three different flow rate is listed below.

Channel

Flow Rate

fast middle slow
5μL/min 5413.994μm/s 548.52153μm/s 67.9229μm/s
15μL/min 16241.73779μm/s 1645.63652μm/s 203.79536μm/s
45μL/min 48723.94763μm/s 4937.93255μm/s 611.65866μm/s

Table 3 Simulation Results of Central Line Speed

g. Discussion

In this simulation, we consider all the channel walls are rigid, but in real cases, channel walls will deform when pressure applied. So the cross section area of the channel will be larger than what we have considered in this simulation.

In real cases, the microfluidic channels have a lot of defects at the edges of the channels. So the dragging force applied by these channels will be larger than what we have considered in this simulation, causing the fluid to have a lower speed. But due to the random distribution of the defects, at some points, the defects might accelerate the fluid flow by making the channel to be narrower than usual.

553x311px

553x303px

Fig. Topside View of Microfluidic Channels 5X(up) and 20X(bottom)

In this simulation, microfluidic channel width was set to 285μm as we designed, with channel walls exactly perpendicular to the bottom. While as in real cases, due to the low transmittance of SU-8 photoresist to the low-wavelength light, the photoresist at the top side of the channel will absorb higher energy than the photoresist at the bottom, causing a trapezoidal cross section profile. The flow speed change caused by this phenomenon is still unknown to us.

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Fig. Optical Transmittance of SU-8 Photoresist

In order to obtain the exact sheer force applied to the cells by the fluid flow. We input the experimentally used flow rate as a boundary condition in our model, which have already been tested before, to calculate the sheer stress on the bottom of the channel where the cells can adhere to.

The inlet circle was given the velocity of 0.0012557 m/s, 0.0025113 m/s and 0.0050226 m/s, which will give us the rate of flow values of 25μL/min, 50μL/min and 100μL/min. And the outlet circle was given the pressure of 0.

Sheer force of the sheer stress on the bottom plane is shown below.

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Fig. 1 Sheer Stress Distribution Under Input Flow Rate 25μL/min (log phase)

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Fig. 2 Sheer Stress Distribution Under Input Flow Rate 50μL/min (log phase)

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Fig. 3 Sheer Stress Distribution Under Input Flow Rate 100μL/min (log phase)

In order to further show the sheer stress difference under different parameters, we draw a line on the bottom plane from (-16, -4) to (-16, -6.45) crossing through three microfluidic channels in the observation zone. and plot the sheer stress on that line.

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Fig. 4 Cut Line Drawn

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Fig. 5 Sheer Stress Distribution on The Cut Line

The speed at the central line in all three channels at three different flow rate is listed below.

Channel

Flow Rate

fast middle slow
25μL/min 1.07519Pa 0.10819Pa 0.0132Pa
50μL/min 2.15057Pa 0.21642Pa 0.02641Pa
100μL/min 4.30273Pa 0.43314Pa 0.05288Pa

Table 1 Simulation Results of Central Line Sheer Stress

Audio-genetics

References

  1. Booth, R., & Kim, H. (2012). Characterization of a microfluidic in vitro model of the blood-brain barrier (μBBB). Lab on a Chip, 12(10), 1784-1792.

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