Latest revision as of 03:34, 28 October 2020

Model

Surfactant between Experimental Data and Theories

Overview

There are three critical parts in our project that crucially affect our final design of Eye kNOw: IOP-elevation induced contact lens deformation, NO diffusion efficiency in ocular system, and seeking for higher effectiveness. Experiment alone is not enough to provide the answers. To build a bridge between experimental data and scientific theories, we built three models that fully describe the whole working process of Eye kNOw:

Contact Lens Deformation Model: Provide quantitative result of contact lens deformation caused by IOP elevation.
NO Ocular Diffusion Model: Obtain the initial parameters needed for Eye kNOw design, and describe NO ocular diffusion with quantitative simulation.
NO Ocular Diffusion Model: Utilize model 1, model 2 and experimental data to precisely calculate the effectiveness of Eye kNOw.

Background

This year, We aim to provide a real-time treatment that can release ocular hypotensive agents (nitric oxide) according to patients’ IOP in a contact lens system—Eye kNOw. Eye kNOw contains a designed chamber filled with L-arginine, IPTG, and our engineered bacteria. Here are the three main principles we used to design Eye kNOw:

NOS produced by our engineered bacteria turns L-arginine into NO.
Different concentrations of IPTG induces different production rates of NOS.
IOP elevation causes corneal radius of curvature to change, leading to deformation of Eye kNOw.

Below are the workflows of Eye kNOw:

IOP elevates, causing the cornea's radius of curvature to change.
Chamber’s volume decreased due to the deformation of the cornea.
The semipermeable chamber only allows water and gas to pass. Therefore, the concentration of IPTG inside the chamber elevates.
Elevated IPTG leads to higher production rate of NOS by engineered bacteria.
The more NOS produced, the more L-arginine turned into NO.
More NO is released into the eyes, relaxing trabecular meshwork.
Finally, IOP will be lowered to normal level.

We establish three models to simulate the whole process above: contact lens deformation model and NO ocular diffusion model. Model 3 combines model 1, model 2 and experimental data, which precisely calculate the effectiveness of Eye kNOw.

Our goals

To build a model that describes the deformation of contact lens quantitatively.
To establish a model that simulates nitric oxide ocular diffusion system.
To precisely calculate the effectiveness of Eye kNOw by taking both experimental data and model theories into consideration.

Model 1: Deformation of Contact Lens

This model is used to describe the deformation of the contact lens under varying intraocular pressure (IOP) with quantitative estimation. Research suggested that the radius of cornea curvature increases linearly with the increment of IOP^[1]. However, the pressure exerted on the contact lens while being worn is not fully studied, not to mention the volume difference of contact lens with respect to different IOP. Therefore, to build this model from scratch, we first made the following assumptions:

The contact lens fits on the cornea perfectly no matter it deforms or not.
The contact lens remains in the shape of a sphere during the whole process of deformation.
Deformation of the contact lens is not changing with time, which is a static model.

Fig. 1A. Cross-section diagram of pressure balance.

Table 1A shows the parameters of cornea that will be used in our model.

	Description	Value
E_Cornea	Elastic modulus of the cornea	15.3 mPa
t_Cornea	Thickness of the cornea	0.666 mm
R_{Cornea_0}	Corneal radius of curvature	8.45 mm

Table 1A. Parameters of cornea used in model 1^[2][3].

First, we need to obtain the relationship between IOP and radius Eye kNOw. Considering the force equilibrium equation between the pressure of fluid and the membrane (cornea) in the section, we obtain Equation 1.1:

According to Hooke’s Law, we have Equation 1.2:

Under proportional limit, the radius difference (ΔR), is given by Equation 1.3:

From the equations listed above, we obtain Equation 1.4:

For a thick membrane, which means the thickness of the membrane is too large to be neglected in comparison to the radius. Thus, we have a constant term that is related to the poisson ratio, ν, in the Equation 1.5^[1][4].

Notice that the p in Equation 1.4 and Equation 1.5 represents the pressure difference with respect to the initial pressure instead of the pressure itself. We assumed the initial IOP to be 10 mmHg. By Equation 1.5, we predict the relation between IOP and the radius difference, or the strain, is linear, which fits the results of digital image correlation experiment. (See Proof of concept: step 1 )

Second, we calculate the relationship between IOP and volume difference of the chamber in Eye kNOw. Table 1B lists all the parameters of Eye kNOw used in the following calculation.

	Description	Value
R_{Eye_kNOw_0}	Inner radius of curvature	8.2 mm
E_{Eye_kNOw}	Elastic modulus of Eye kNOw	3．10⁶ dyne/mm²
d	Diameter of Eye kNOw	14 mm
d₁	Inner diameters of the chamber	10 mm
d₂	Outer diameters of the chamber	12 mm
t_{Eye_kNOw}	Thickness of Eye kNOw	2．10^-4 mm

Table 1B. Parameters of Eye kNOw used in model 1.

The volume of the chamber in Eye kNOw , which is a ring-like compartment, is calculated by the same method of the volume of revolution in calculus. After calculation, the volume of the chamber equals 4.4 cubic millimeters initially.

The volume difference is given by the elongation of the part above the compartment in meridional direction, which is given by the formula list below:

while

The ratio of volume difference is given by Equation 1.9:

After calculation with the parameters listed above, the result is approximately 1% when the IOP has an increment of 1 mmHg.

Model 2: Nitric Oxide Diffusion Model

Overview

Eye is a complicated organ consisting of various tissues with different physical properties. In most of the ocular delivery models, they consider the whole eye as one compartment since their drugs are stable and large enough that the difference of tissue characteristics can be ignored. However, we use NO as our drug, which is small and unstable. Thus, we need to set up a new model to simulate NO ocular delivery system.

This model divides the eye system into three different compartment according to the tissues differences, and provide quantitative NO concentration profiles dynamically. This model can be applied on ocular drug delivery system of other small and unstable drugs.

Background

Eye structure can be divided into three main compartments: cornea, anterior chamber, and posterior chamber. Target site of NO is trabecular meshwork, which is located at the posterior angle of anterior chamber. We simplify the eye structures into one dimension as below:

Since the tissue characteristics of the three compartments varies a lot, we need to simulate the behavior of NO in them separately, by different partial differential equations (PDEs).

Model

First, we establish the initial state of NO distribution in the eye before Eye kNOw being triggered. Second, we build the dynamic NO concentration profile according to time and distance after Eye kNOw activation. We use several partial differential equations(PDEs) to describe the behavior of NO. Table 2A lists all the abbreviations used in PDEs.

	Full Name	Unit
C	Concentration of NO	M
x	distance (from outside of the eye to inside)	cm
t	time (t=0 resembles the time when Eye kNOw start to produce NO)	s
D	Diffusion coefficient	cm²/s
R	Flow rate of liquid	L/s
k	Degradation coefficient of NO	M^-2/s
Pro	Production rate of NO in the compartment	mol/s
V	Volume of the compartment	L

Table 2A. Abbreviations and variables used in PDEs.

1. Setting up PDEs:

PDEs take the factors that may affect the concentration of NO into consideration to describe the behavior of NO. Factors are listed below:

(1) Degradation

The two main factors that will cause degradation of nitric oxide in the human body are hemoglobin and oxygen. Hemoglobin doesn’t exist in the eye system, thus we only need to consider oxygen as the factor causing NO degradation.

According to current studies, the formula can be written as below:

(2) Diffusion

By Fick's second law, the diffusion of chemicals can be described as below:

(3) Endogenous production

Glaucoma patients’ aqueous humor has an initial average concentration of NO around 53.4uM^[7], which is maintained by endogenous NO produced by NO synthase (NOS). There are three different types of NOS in human eyes: e-NOS, n-NOS, and i-NOS^[7].

e-NOS and n-NOS work constantly, which are expressed on iris, cornea, vascular endothelium, etc. i-NOS only works when ocular inflammation happens, which is not a common symptom for glaucoma, thus we can ignore it. We assume that these NOS produce NO in a constant rate, so the formula can be written as below:

(4) Convection

There’s a flow of aqueous humor in the anterior chamber, which is 2.4 uL/min^[8]. Convection will affect the distribution of nitric oxide, which can be written as below:

Combining the factors listed above, the PDE for describing the distribution of NO can be written as below:

Equation 2.5 is a heterogeneous PDE, which is very hard to solve. We need to simplify Equation 2.5 into homogeneous form for further calculation.

First, since the concentration of oxygen can be maintained by oxygen in the air( oxygen in the air can dissolve and penetrate into our eyes), we can set k[Oxygen] as a constant.

Second, we want to simplify the C² term into C. In order to prevent over-estimation of nitric oxide concentration, we change C² into C_max．C, where C_max is the max concentration of nitric oxide in the compartment. Since C_max．C is always larger than (or same as) C², we can make sure that we won’t over-estimate the concentration of nitric oxide. Since C_max is a constant, we can consider constant B = k[Oxygen]C_max.

Therefore, the modified form of PDE will be:

2. Obtaining parameters from current studies:

Parameters used are listed in table 2B. We collected them from current studies.

	Contact Lens	Cornea	Aqueous Humor	Unit
D	1.8．10^-6^[9]	2.81．10^-5^[10]	3．10^-5^[11]	cm²/s
B	?	?	?	1/s
R	0	0	4．10^-8^[8]	L/s
V	2.77．10^-5	1.6．10^-5^[12]	2.5．10^-4^[13]	L
Pro	?	?	?	mol/s
Initial Average [NO]	?	?	5.34．10^-5^[6]	M
Maximum Distance	0.02	0.055^[14]	1.122^[15]^[16]	cm

Table 2B. Parameters of Eye kNOw used in model 2.

We're still lacking some of the parameters. We can estimate them by solving the steady state of NO distribution.

3. Calculating steady state:

We start from the contact lens compartment. When in steady state, NO concentration won't change by time. Thus, Equation 2.6 can be written as below:

Where subscript 1 stands for the parameters and variables of the contact lens compartment. By solving Equation 2.7, we can get the solution of C₁ in steady state:

We use the approximation:

Thus turning Equation 2.8 into linear form:

Since C₁(0)=0 (one of the boundary conditions), the final form of C₁ in steady state can be written as below:

By the same method, we can simplify the concentration of NO in cornea and aqueous humor compartments as a linear formula of x. To simplify the formulas, we set the outer surface of every compartment as the starting position of that compartment. For example, for cornea compartment, the interface of cornea and contact lens is considered the starting position, namely x=0.

As for the boundary conditions, the interfaces should have only one concentration. For example, the formula of C₁ at x=0.02 should have the same value as C₂ at x=0. Combining these conditions, we can get the function of C₂ and C₃:

Now we need to solve the slope of NO concentration, namely a₁, a₂, a₃. Here, we use Fick’s first law as boundary conditions, that is at the interfaces, input of NO from one compartment should be the same as output of another compartment. For example, at the interface of cornea and contact lens, input of NO to contact lens should be the same as output of NO from cornea.

The input of NO to contact lens can be written as below, according to Fick’s first law:

The output of NO from cornea can be written as below:

Applying the solution we’d obtained, we can get the relationship of slopes of each compartment:

Therefore, we can draw the steady-state-graph of NO distribution in the eye:

Fig. 2C. NO Concentration Profile in Steady State. A stands for contact lens compartment, B stands for cornea comparment, C stands for aqueous humor compartment.

Now, there are just B and Pro not determined yet. Recall that B = k[Oxygen]C_max, we can calculate them. As for Pro, we can calculate each compartment’s total input and output, they should be the same since we’re dealing with steady state. After calculations, Table 2B can be filled completely as Table 2C.

	Contact Lens	Cornea	Aqueous Humor	Unit
D	1.8．10^-6	2.81．10^-5	3．10^-5	cm²/s
B	2.84．10^-2	1.03．10^-2	1.566．10^-2	1/s
R	0	0	4．10^-8	L/s
V	2.77．10^-5	1.6．10^-5	2.5．10^-4	L
Pro	7．10^-6	1.52．10^-5	1.239．10^-3	mol/s
Initial Average [NO]	C₁ = 933.7x	C₂ = 59.818x + 18.674	C₃ = 56.063x + 21.964	uM
Maximum Distance	0.02	0.055	1.122	cm

Table 2C. Complete table of parameters used for model 2.

4. Calculating NO concentration after production of NO by Eye kNOw (non-steady state):

After confirming all the parameters, we continue to calculate the NO concentration of each compartment when Eye kNOw is activated by elevation of IPTG concentration. We assume that the production rate of Eye kNOw raised j% after activation compared with steady state. Table 2D. Shows the PDEs, initial conditions, and boundary conditions:

	PDE	Initial Condition	Boundary Condition
Contact Lens
Cornea
Aqueous Humor

Table 2D. PDEs, initial conditions, boundary conditions of each compartment.

However, we found the PDEs hard to solve by current methods, including Fourier transform and separation of variables. After lots of effort, we finally solved the PDEs by means of double Laplace transform and inverse double Laplace transform.

We developed two MATLAB programs, one of them functioning as PDE solver utilizes double Laplace transform, and another one working as Laplace transform estimator for functions which cannot be transformed by current method. These programs are available on the internet with clear documentation, see modeling software for more information.

The dynamic NO concentration profiles can be described by three formulas as follow:

Notice that there is an undefined parameter r in our solutions. Parameter r is correlated with the interfaces’ properties in our eyes, namely the interface of cornea and contact lens, and the interface of cornea and aqueous humor. Since we cannot do experiments on living animals, we cannot obtain the value of r. In fact, the value of r varies individually, so we just pick some of the r to demonstrate the result.

We use MATLAB to plot the dynamic NO concentration profile of each compartment according to time:

Video 1. NO Distribution. (r=0.0156 j=20)

Model 3: Effectiveness of Eye kNOw

As a new developing treatment of Glaucoma, it's important to show that the effectiveness of Eye kNOw is better than current treatment. Effectiveness reflects how a drug actually works in the patient's body, which can be evaluated by time and drug amount needed to cause therapeutic effect. Particularly, the minimum concentration of a drug that can cause therapeutic effect is called minimum effective concentration (MEC).

To prove that Eye kNOw can help treat glaucoma more effectively, this model combines model 1, model 2, and experimental data, aiming to precisely quantify Eye kNOw's MEC and the time needed to reach it. Noted that there's no MEC data of NO since current treatment utilizes NO donor instead of NO directly, but estimation can be made by adopting data from current NO prodrug. Here, we adopt data of Latanoprostene Bunod to estimate the MEC of NO, approximately 1.182．10^-8M.^[17]^[18]^[19]

We assume that contact lens deformation happens immediately after IOP elevation, and [IPTG] elevation happens immediately after contact lens deformation, too. Therefore, the only two steps we should concern are how fast will NOS be produced after [IPTG] elevates, and how fast will [NO] at trabecular meshwork reach MEC. We’ll discuss them one by one.

First, we calculate the speed of NOS production after [IPTG] elevation. By wet team’s results (NO kinetics experiment and IPTG induction experiment), we can calculate the NO production rate according to [IPTG] and time:

Notice that the unit of Equation 3.1 is nmol/hr, and the reaction volume of the experiments is 60uL. Since the volume of Eye kNOw’s chamber is 4.4uL, the production rate in Eye kNOw can be written as below:

Notice that the production rate depends on not only the efficiency of NOS, but also the concentration of NOS in the solution. We set IOP = 15mmHg, [IPTG] = 0.1mM as initial conditions. By model 2, the initial production rate should be 7．10^-6 mol/s to maintain steady state. Therefore, by elevating bacteria concentration in Eye kNOw, the initial production rate of NOS in Eye kNOw can be written as Equation 3.3:

Since in initial state, NOS has already been made, so we can neglect the time-related term in Equation 3.2. Assume that patient’s IOP raises i mmHg, the production rate of NOS can be written as below:

Second, we calculate the time needed for Eye kNOw to raise the [NO] at the trabecular meshwork to MEC once the IOP is elevated. We use MATLAB to plot out the concentration change of NO at trabecular meshwork according to time after induction. Below are the results:

Fig. 3A. NO concentration at trabecular meshwork in different volume change-large time scale.

Fig. 3B. NO concentration at trabecular meshwork in different volume change-small time scale.

We can obtain that time needed for Eye kNOw to raise trabecular meshwork’s NO concentration up to MEC is very short, which theoretically proves that Eye kNOw can treat glaucoma with high efficiency and accuracy.

References

Chen G-Z, Chan I-S, Leung LKK, Lam DCC. Soft wearable contact lens sensor for continuous intraocular pressure monitoring. Medical Engineering & Physics. 2014;36(9):1134-1139.
Berest P, Nguyen-Minh D. Response of a spherical cavity in an elastic viscoplastic medium under a variable internal pressure. International Journal of Solids and Structures.
Sanchez I, Martin R, Ussa F, Fernandez-Bueno I. The parameters of the porcine eyeball. Graefe’s Archive for Clinical and Experimental Ophthalmology. 2011;249(4):475-482.
Dupps WJ, Netto MV, Herekar S, Krueger RR. Surface wave elastometry of the cornea in porcine and human donor eyes. Journal of refractive surgery (Thorofare, NJ : 1995). 2007;23(1):66-75. Accessed October 24, 2020.
Ford PC, Wink DA, Stanbury DM. Autoxidation kinetics of aqueous nitric oxide. FEBS Letters. 1993;326(1-3):1-3.
Ghanem AA, Elewa AM, Arafa LF. Endothelin-1 and Nitric Oxide Levels in Patients with Glaucoma. Ophthalmic Research. 2011;46(2):98-102.
Forstermann U, Sessa WC. Nitric oxide synthases: regulation and function. European Heart Journal. 2011;33(7):829-837.
Goel M. Aqueous Humor Dynamics: A Review~!2010-03-03~!2010-06-17~!2010-09-02~! The Open Ophthalmology Journal. 2010;4(1):52-59. ‌
Pozuelo J, Compañ V, Gonzalez-Meijome JM, Mollá S. Oxygen and ionic transport in hydrogel and silicone-hydrogel contact lens materials: An experimental and... ResearchGate. Published February 2014. Accessed October 25, 2020.
Larrea X, Bu¨chler P. A Transient Diffusion Model of the Cornea for the Assessment of Oxygen Diffusivity and Consumption. Investigative Opthalmology & Visual Science. 2009;50(3):1076.
Borland C, Moggridge G, Patel R, Patel S, Zhu Q, Vuylsteke A. Permeability and diffusivity of nitric oxide in human plasma and red cells. Nitric Oxide. 2018;78:51-59.
Cerviño A, Gonzalez-Meijome JM, Ferrer-Blasco T, Garcia-Resua C, Montes-Mico R, Parafita M. Determination of corneal volume from anterior topography and topographic pachymetry: application to healthy and keratoconic eyes. Ophthalmic and Physiological Optics. 2009;29(6):652-660.
Cunanan C. Ophthalmologic Applications: Glaucoma Drains and Implants. Biomaterials Science. Published online 2013:940-946.
Classify corneas simply as average, thin or thick. Healio.com. Published 2020. Accessed October 25, 2020.
Mashige KP. A review of corneal diameter, curvature and thickness values and influencing factors*. African Vision and Eye Health. 2013;72(4).
Huang G. Anterior Chamber Depth, Iridocorneal Angle Width, and Intraocular Pressure Changes After Phacoemulsification. Archives of Ophthalmology. 2011;129(10):1283.
Vyzulta (Latanoprostene Bunod) Ophthalmic Solution. Fda.gov. Published 2017. Accessed October 27, 2020.
Addis VM, Miller E. Latanoprostene bunod ophthalmic solution 0.024% in the treatment of open-angle glaucoma: design, development, and place in therapy. Clinical Ophthalmology. 2018;Volume 12:2649-2657.
Karki R, Meena M, Prakash T, Rajeswari T, Goli D, Kumar S. Reduction in drop size of ophthalmic topical drop preparations and the impact of treatment. Journal of Advanced Pharmaceutical Technology & Research. 2011;2(3):192.

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                          Model
                          <!--<span class="text-primary">Taylor</span>-->
                      </h1>
                      <h3 class="subheading mb-5 pl-2">
-                         	In one word, Laplace transform
+                         	Surfactant between Experimental Data and Theories
                      </h3>
                  </div>
              </div>
          </section>
-        <hr class="hrmar" />
          <!-- Project Background-->
          <section class="resume-section">
-             <div class="resume-section-content" id="poverview">
+             <div class="resume-section-content" id="overview">
-                <h2 class="mb-3">Overview</h2>
+            <h2 class="mb-3">Overview</h2>
-                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+            <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                    <div class="flex-grow-1">
+                        <p>	There are three critical parts in our project that crucially affect our final design of Eye kNOw: <b>IOP-elevation induced contact lens deformation, NO diffusion efficiency in ocular system, and seeking for higher effectiveness.</b> Experiment alone is not enough to provide the answers. To build a bridge between experimental data and scientific theories, we built three models that fully describe the whole working process of Eye kNOw:</p>
+             </div>
+             </div>
+             <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                          <p>    In our mission to address glaucoma comprehensively, we decided to provide an even more effective treatment for the disease. Inspired by existing treatments using the nitric-oxide (NO) signaling pathway to target the trabecular meshwork and reduce intraocular pressure<sup>[<a href="#ref1" class="linklink">1</a>]</sup>, we came up with a novel treatment based on gaseous nitric oxide. However, since NO has a short half-life of 400 seconds, we are unable to use the gaseous form NO directly in our treatment.</p>
+                      <ol class="mb-4">
+                          <li><p><b>Contact Lens Deformation Model</b>: Provide quantitative result of contact lens deformation caused by IOP elevation.</p></li>
+                         <li><p><b>NO Ocular Diffusion Model</b>: Obtain the initial parameters needed for Eye kNOw design, and describe NO ocular diffusion with quantitative simulation.</p></li>
+                    	 <li><p><b>NO Ocular Diffusion Model</b>: Utilize model 1, model 2 and experimental data to precisely calculate the effectiveness of Eye kNOw.</p></li>
+                      </ol>
                      </div>
-                </div>
+               </div>
-            </div>
-        </section>
+             <h4 class="mb-3">Background</h4>
-        <hr class="hrmar" />
+             <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
-        <!-- Approaches-->
-        <section class="resume-section">
-            <div class="resume-section-content" id="pcontact">
-                <h2 class="mb-3">Contact lens</h2>
-                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                         <p>    Literature research stated that the increase in patients’ IOP will result in the deformation of cornea, further leading to a structural change in contact lens<sup>[<a href="#ref2" class="linklink">2</a>]</sup>. We utilized this phenomenon to design a pair of contact lenses that structurally change in response to fluctuations in intraocular pressure.</p>
+                         <p>	This year, We aim to provide a real-time treatment that can release ocular hypotensive agents (nitric oxide) according to patients’ IOP in a contact lens system—Eye kNOw. Eye kNOw contains a designed chamber filled with L-arginine, IPTG, and our engineered bacteria. Here are the three main principles we used to design Eye kNOw:</p>
-                    </div>
+             </div>
+             </div>
-                </div>
+             <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
-                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
-                    <div class="flex-grow-1">
-                        <p>    Our contact lens will be fitted with a tubular semipermeable chamber that is filled with our engineered bacteria, IPTG, NO precursor - L-arginine, and DAP. The volume change of the chamber will cause water to flow out thus increasing the IPTG concentration inside the chamber. The increase in IPTG will induce the bacteria to produce more Nitric Oxide Synthase, which can then convert L-arginine into nitric oxide to lower the intraocular pressure (IOP). This structural change is then able to induce dynamic drug delivery.</p>
-                    </div>
-                </div>
-                <h3 class="mb-0" style="margin-top: 1rem;">IOP simulation experiment</h3>
-                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                          <p>    To prove the concept of our contact lens and our device, we designed an IOP simulation experiment with porcine eye.By changing the drip bag’s height, water pressure will directly increase IOP in the porcine eye, enabling precise control of IOP for experiments<sup>[<a href="#ref3" class="linklink">3</a>]</sup><sup>[<a href="#ref4" class="linklink">4</a>]</sup>.</p>
+                    <ol class="mb-4">
+                          <li><p>NOS produced by our engineered bacteria turns L-arginine into NO.</p></li>
+                         <li><p>Different concentrations of IPTG induces different production rates of NOS.</p></li>
+                    	 <li><p>IOP elevation causes corneal radius of curvature to change, leading to deformation of Eye kNOw.</p></li>
+                      </ol>
                      </div>
-                </div>
+              </div>
-                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+              <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                    <div class="flex-grow-1">
+                      <p>	Below are the workflows of Eye kNOw:</p>
+              </div>
+              </div>
+              <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                          <p>    For more details, please visit <a href="https://2020.igem.org/Team:NCKU_Tainan/Proof_Of_Concept" class="linkinthetext">proof of concept</a> and <a href="https://2020.igem.org/Team:NCKU_Tainan/Hardware" class="linkinthetext">hardware.</a></p>
+                    <ol class="mb-4">
+                          <li><p>IOP elevates, causing the cornea's radius of curvature to change.</p></li>
+                         <li><p>Chamber’s volume decreased due to the deformation of the cornea.</p></li>
+                    	 <li><p>The semipermeable chamber only allows water and gas to pass. Therefore, the concentration of IPTG inside the chamber elevates.</p></li>
+                     	 <li><p>Elevated IPTG leads to higher production rate of NOS by engineered bacteria.</p></li>
+                         <li><p>The more NOS produced, the more L-arginine turned into NO.</p></li>
+                         <li><p>More NO is released into the eyes, relaxing trabecular meshwork.</p></li>
+                         <li><p>Finally, IOP will be lowered to normal level.</p></li>
+                      </ol>
                      </div>
-                </div>
+              </div>
-                <div class="container-fluid p-0">
+              <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                    <div class="flex-grow-1">
+                      <p>	We establish three models to simulate the whole process above: contact lens deformation model and NO ocular diffusion model. Model 3 combines model 1, model 2 and experimental data, which precisely calculate the effectiveness of Eye kNOw.</p>
+              </div>
+              </div>
+               <div class="container-fluid p-0">
                  <div class="row no-gutters">
                  <div class="col-lg ">
                  <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
-                 <a href="https://static.igem.org/mediawiki/2020/4/4e/T--NCKU_Tainan--design_contact_lens.png" target="_blank" style="width:60%"><img src="https://static.igem.org/mediawiki/2020/4/4e/T--NCKU_Tainan--design_contact_lens.png" alt="" title="" style="width:100%"></a>
+                 <a href="https://static.igem.org/mediawiki/2020/2/20/T--NCKU_Tainan--Model_IOP.png" target="_blank" style="width:60%"><img src="https://static.igem.org/mediawiki/2020/2/20/T--NCKU_Tainan--Model_IOP.png" alt="" title="" style="width:100%"></a>
-                 <figcaption class="caption-design">Fig. 1. The structure and design of contact lens.</figcaption>
+                 <figcaption class="caption-design">Fig. 0A. Eye kNOw workflow chart.</figcaption>
                  </figure>
                  </div>
                  </div>
                  </div>
+             <h4 class="mb-3">Our goals</h4>
+             <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                    <div class="flex-grow-1">
+                    <ol class="mb-4">
+                         <li><p>To build a model that describes the deformation of contact lens quantitatively.</p></li>
+                         <li><p>To establish a model that simulates nitric oxide ocular diffusion system.</p></li>
+                    	 <li><p>To precisely calculate the effectiveness of Eye kNOw by taking both experimental data and model theories into consideration.</p></li>
+                      </ol>
+                    </div>
+              </div>
              </div>
          </section>
          <hr class="hrmar" />
-         <!-- Inspiration-->
+         <!-- Approaches-->
-        <section class="resume-section" >
-             <div class="resume-section-content" id="pgene">
-                <h2 class="mb-3">Gene Design</h2>
-                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+      <section class="resume-section">
+             <div class="resume-section-content" id="mone">
+            <h2 class="mb-3">Model 1: Deformation of Contact Lens</h2>
+            <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                         <p>    In order for our bacteria to reduce intraocular pressure, we planned to engineer our bacteria to have the ability to produce Nitric Oxide Synthase (NOS)<sup>[<a href="#ref5" class="linklink">5</a>]</sup>, an enzyme that can convert L-arginine into NO.</p>
+                         <p>	This model is used to describe the <b>deformation of the contact lens under varying intraocular pressure (IOP) with quantitative estimation.</b> Research suggested that the radius of cornea curvature increases linearly with the increment of IOP<sup>[<a href = "#ref1" class = "linklink">1</a>]</sup>. However, the pressure exerted on the contact lens while being worn is not fully studied, not to mention the volume difference of contact lens with respect to different IOP. Therefore, to build this model from scratch, we first made the following assumptions:</p>
-                    </div>
+            </div>
-                </div>
+            </div>
-                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+            <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                          <p>    For biosafety, we engineered our bacteria to overexpress <i>csgD</i> and <i>csgA</i> for securing bacteria onto the contact lens by increasing binding affinity between bacteria and lens.</p>
+                    <ol class="mb-4">
+                          <li><p>The contact lens fits on the cornea perfectly no matter it deforms or not.</p></li>
+                         <li><p>The contact lens remains in the shape of a sphere during the whole process of deformation.</p></li>
+                        <li><p>Deformation of the contact lens is not changing with time, which is a static model.</p></li>
+                      </ol>
                      </div>
+                  </div>
+              <div class="container-fluid p-0">
+                <div class="row no-gutters">
+                <div class="col-lg ">
+                <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+                <a style="width:40%"><img src="https://static.igem.org/mediawiki/2020/5/57/T--NCKU_Tainan--model_pressure_0.png" alt="" title="" style="width:100%"></a>
+                <figcaption class="caption-design">Fig. 1A. Cross-section diagram of pressure balance.</figcaption>
+                </figure>
                  </div>
-               <h3 class="mb-0" style="margin-top: 1rem;"><i>Nitric Oxide Synthases</i> (<i>NOS</i>)</h3>
-                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
-                    <div class="flex-grow-1">
-                        <p>    During literature research, we found out that Bacillus subtilis carries <i>Nitric Oxide Synthases</i>(<i>NOS</i>) and has the ability to produce NO, which is responsive to oxidative stress. So we cloned this gene from Bacillus subtilis' genome and designed a new biobrick which we then incorporated into our chassis, WM3064, allowing it to produce NO.</p>
-                    </div>
                  </div>
-                 <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                 </div>
+              <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                         <p>    In order to dynamically express NOS as patients’ IOP fluctuate, we put <i>NOS</i> under the control of <i>T7</i> promoter and a <i>lacO</i> binding site, which can be controlled by IPTG-inducible <i>T7</i> RNA polymerase provided by another plasmid PDT7 (Plasmid Drive <i>T7</i> RNA polymerase). As previously mentioned, the IPTG concentration inside the ring-like compartment will fluctuate according to the patients’ IOP, leading to dynamic expression of <i>NOS</i>.</p>
+                         <p>	Table 1A shows the parameters of cornea that will be used in our model.</p>
-                    </div>
+            </div>
+            </div>
+              <table class="table table-Border">
+                          <thead>
+                            <tr style="border:3px solid #7E3B40;">
+                              <th scope="col" style="font-size:1.2rem; text-align: center;"></th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Description</th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Value</th>
+                            </tr>
+                          </thead>
+                          <tbody>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">E<sub>Cornea</sub></td>
+                              <td style="font-size:1.1rem; text-align: center;">Elastic modulus of the cornea</td>
+                              <td style="font-size:1.1rem; text-align: center;">15.3 mPa</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">t<sub>Cornea</sub></td>
+                              <td style="font-size:1.1rem; text-align: center;">Thickness of the cornea</td>
+                              <td style="font-size:1.1rem; text-align: center;">0.666 mm</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">R<sub>Cornea_0</sub></td>
+                              <td style="font-size:1.1rem; text-align: center;">Corneal radius of curvature</td>
+                              <td style="font-size:1.1rem; text-align: center;">8.45 mm</td>
+                            </tr>
+                          </tbody>
+                        </table>
+                        <figcaption class="caption-design" style="margin-bottom:1rem; text-align: center">Table 1A. Parameters of cornea used in model 1<sup>[<a href = "#ref2" class = "linklink">2</a>][<a href = "#ref3" class = "linklink">3</a>]</sup>.</figcaption>
+             <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                    <div class="flex-grow-1">
+                        <p>	First, we need to obtain the relationship between IOP and radius Eye kNOw. Considering the force equilibrium equation between the pressure of fluid and the membrane (cornea) in the section, we obtain Equation 1.1:</p>
+              </div>
+              </div>
+               <div class="container-fluid p-0">
+                <div class="row no-gutters">
+                <div class="col-lg ">
+                <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+                <a style="width:30%"><img src="https://static.igem.org/mediawiki/2020/b/b5/T--NCKU_Tainan--model1.png" alt="" title="" style="width:100%"></a>
+                <figcaption class="caption-design">Equation 1.1</figcaption>
+                </figure>
                  </div>
+                </div>
+                </div>
+              <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                    <div class="flex-grow-1">
+                      <p>	According to Hooke’s Law, we have Equation 1.2:</p>
+              </div>
+              </div>
                  <div class="container-fluid p-0">
                  <div class="row no-gutters">
                  <div class="col-lg ">
                  <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
-                 <a href="https://static.igem.org/mediawiki/2020/3/3b/T--NCKU_Tainan--design_NOS.gif" target="_blank" style="width:60%"><img src="https://static.igem.org/mediawiki/2020/3/3b/T--NCKU_Tainan--design_NOS.gif" alt="" title="" style="width:100%"></a>
+                 <a style="width:35%"><img src="https://static.igem.org/mediawiki/2020/c/c7/T--NCKU_Tainan--model2.png" alt="" title="" style="width:100%"></a>
-                 <figcaption class="caption-design">Fig. 2. Plasmid design for <i>NOS</i>.</figcaption>
+                 <figcaption class="caption-design">Equation 1.2</figcaption>
                  </figure>
                  </div>
                  </div>
                  </div>
-                <h4 class="mb-0">Functional Test</h4>
+              <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
-                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                         <p>    We tested the kinetics of the enzyme using a NOS assay kit, which utilizes Griess reagents to react with NO and generate colorimetric readouts by measuring O.D.540 value. For the purpose of controlling the production of NOS, we induced bacteria with different concentrations of IPTG and cultured them for different period times.</p>
+                         <p>	Under proportional limit, the radius difference (ΔR), is given by Equation 1.3:</p>
-                    </div>
+              </div>
+              </div>
+               <div class="container-fluid p-0">
+                <div class="row no-gutters">
+                <div class="col-lg ">
+                <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+                <a style="width:30%"><img src="https://static.igem.org/mediawiki/2020/e/ec/T--NCKU_Tainan--model3.png" alt="" title="" style="width:100%"></a>
+                <figcaption class="caption-design">Equation 1.3</figcaption>
+                </figure>
                  </div>
-                <h3 class="mb-0" style="margin-top: 1rem;">Biosafety</h3>
-                <h4 class="mb-0">DAP-deficient strain</h4>
-                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
-                    <div class="flex-grow-1">
-                        <p>    We chose <i>E. coli</i> WM3064 as our chassis, which lacks the essential gene <i>dapA</i>. This gene encodes for 4-hydroxy-tetrahydrodipicolinate synthase that is critical to the production of lysine through the DAP pathway<sup>[<a href="#ref6" class="linklink">6</a>]</sup>. Lysine is an essential amino acid in animals, including humans, but can be synthesised de novo in bacteria, lower eukaryotes and plants for utilisation in protein and peptidoglycan cell wall synthesis<sup>[<a href="#ref1" class="linklink">7</a>]</sup>. Without this gene, the bacteria will have to depend on exogenous diaminopimelate (DAP) to survive.</p>
-                    </div>
                  </div>
-                 <div class="container-fluid p-0">
+                 </div>
+              <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                    <div class="flex-grow-1">
+                      <p>	From the equations listed above, we obtain Equation 1.4:</p>
+              </div>
+              </div>
+               <div class="container-fluid p-0">
                  <div class="row no-gutters">
                  <div class="col-lg ">
                  <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
-                 <a href="https://static.igem.org/mediawiki/2020/3/3c/T--NCKU_Tainan--design_DAP.gif" target="_blank" style="width:60%"><img src="https://static.igem.org/mediawiki/2020/3/3c/T--NCKU_Tainan--design_DAP.gif" alt="" title="" style="width:100%"></a>
+                 <a style="width:30%"><img src="https://static.igem.org/mediawiki/2020/0/03/T--NCKU_Tainan--model4.png" alt="" title="" style="width:100%"></a>
-                 <figcaption class="caption-design">Fig. 3. Design of biosafety chassis.</figcaption>
+                 <figcaption class="caption-design">Equation 1.4</figcaption>
                  </figure>
                  </div>
                  </div>
                  </div>
-                <h4 class="mb-0">Functional Test</h4>
-                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+              <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                         <p>    To test whether the bacteria will survive without exogenous DAP, we made plates with and without DAP. After streaking our engineered bacteria onto these plates, we can demonstrate the result by checking its phenotype. Furthermore, we ran a SDS-PAGE to confirm the function of the <i>T7</i> expression system in our engineered WM3064.</p>
+                         <p>	For a thick membrane, which means the thickness of the membrane is too large to be neglected in comparison to the radius. Thus, we have a constant term that is related to the poisson ratio, ν, in the Equation 1.5<sup>[<a href = "#ref1" class = "linklink">1</a>][<a href = "#ref4" class = "linklink">4</a>]</sup>.</p>
-                    </div>
+              </div>
+              </div>
+               <div class="container-fluid p-0">
+                <div class="row no-gutters">
+                <div class="col-lg ">
+                <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+                <a style="width:30%"><img src="https://static.igem.org/mediawiki/2020/2/27/T--NCKU_Tainan--model5.png" alt="" title="" style="width:100%"></a>
+                <figcaption class="caption-design">Equation 1.5</figcaption>
+                </figure>
                  </div>
-                <h4 class="mb-0">Overexpression <i>csgD</i> and <i>csgA</i></h4>
-                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
-                    <div class="flex-grow-1">
-                        <p>    Bacteria biofilm has been shown to exhibit extraordinary ability to help bacteria bind to biotic and abiotic surfaces[measurement reference]. We exploited this property to design one of the biosafety measures.</p>
-                    </div>
                  </div>
-                 <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                 </div>
+               <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                      <p>    We engineered our bacteria to overexpress <i>CsgD</i>, a master transcription regulator of biofilm formation, and <i>CsgA</i>, the major subunit of curli fibers. Overexpression of these two proteins have been reported to increase biofilm formation[measurement reference], which we anticipated to help the bacteria bind to the contact lenses more securely, thus preventing the leakage of bacteria if the contact lens encounters any damage.</p>
+                        <p>	Notice that the p in Equation 1.4 and Equation 1.5  represents the pressure difference with respect to the initial pressure instead of the pressure itself. We assumed the initial IOP to be 10 mmHg. By Equation 1.5, <b>we predict the relation between IOP and the radius difference, or the strain, is linear, which fits the results of digital image correlation experiment. </b>(See <a href="https://2020.igem.org/Team:NCKU_Tainan/Proof_Of_Concept" alt="" target="_blank">Proof of concept</a>: step 1 )</p>
-                    </div>
+              </div>
+              </div>
+              <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                    <div class="flex-grow-1">
+                        <p>	Second, we calculate the relationship between IOP and volume difference of the chamber in Eye kNOw. Table 1B lists all the parameters of Eye kNOw used in the following calculation.</p>
+              </div>
+              </div>
+              <table class="table table-Border">
+                          <thead>
+                            <tr style="border:3px solid #7E3B40;">
+                              <th scope="col" style="font-size:1.2rem; text-align: center;"></th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Description</th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Value</th>
+                            </tr>
+                          </thead>
+                          <tbody>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">R<sub>Eye_kNOw_0</sub></td>
+                              <td style="font-size:1.1rem; text-align: center;">Inner radius of curvature</td>
+                              <td style="font-size:1.1rem; text-align: center;">8.2 mm</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">E<sub>Eye_kNOw</sub></td>
+                              <td style="font-size:1.1rem; text-align: center;">Elastic modulus of Eye kNOw</td>
+                              <td style="font-size:1.1rem; text-align: center;">3．10<sup>6</sup> dyne/mm<sup>2</sup></td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">d</td>
+                              <td style="font-size:1.1rem; text-align: center;">Diameter of Eye kNOw</td>
+                              <td style="font-size:1.1rem; text-align: center;">14 mm</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">d<sub>1</sub></td>
+                              <td style="font-size:1.1rem; text-align: center;">Inner diameters of the chamber</td>
+                              <td style="font-size:1.1rem; text-align: center;">10 mm</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">d<sub>2</sub></td>
+                              <td style="font-size:1.1rem; text-align: center;">Outer diameters of the chamber</td>
+                              <td style="font-size:1.1rem; text-align: center;">12 mm</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">t<sub>Eye_kNOw</sub></td>
+                              <td style="font-size:1.1rem; text-align: center;">Thickness of Eye kNOw</td>
+                              <td style="font-size:1.1rem; text-align: center;">2．10<sup>-4</sup> mm</td>
+                            </tr>
+                          </tbody>
+                        </table>
+              <figcaption class="caption-design" style="margin-bottom:1rem; text-align: center">Table 1B. Parameters of Eye kNOw used in model 1.</figcaption>
+              <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                    <div class="flex-grow-1">
+                        <p>	The volume of the chamber in Eye kNOw , which is a ring-like compartment, is calculated by the same method of the volume of revolution in calculus. After calculation, the volume of the chamber  equals 4.4 cubic millimeters initially.</p>
+              </div>
+              </div>
+               <div class="container-fluid p-0">
+                <div class="row no-gutters">
+                <div class="col-lg ">
+                <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+                <a style="width:40%"><img src="https://static.igem.org/mediawiki/2020/a/a7/T--NCKU_Tainan--Model_chamber.png" alt="" title="" style="width:100%"></a>
+                <figcaption class="caption-design">Fig. 1B. Structure design of Eye kNOw.</figcaption>
+                </figure>
                  </div>
-                 <h4 class="mb-0">Functional Test</h4>
+                 </div>
-                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                </div>
+              <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                         <p>    We first characterized the biofilm formation using conventional congo red staining, then we developed a simple method to assess the binding ability of our engineered bacteria. For more information, please visit our <a href="https://2020.igem.org/Team:NCKU_Tainan/Measurement" class="linkinthetext">measurement page</a>.</p>
+                         <p>	The volume difference is given by the elongation of the part above the compartment in meridional direction, which is given by the formula list below:</p>
-                    </div>
+              </div>
+              </div>
+               <div class="container-fluid p-0">
+                <div class="row no-gutters">
+                <div class="col-lg ">
+                <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+                <a style="width:35%"><img src="https://static.igem.org/mediawiki/2020/0/0b/T--NCKU_Tainan--model6.png" alt="" title="" style="width:100%"></a>
+                  <figcaption class="caption-design">Equation 1.6</figcaption>
+                </figure>
                  </div>
-                 <h3 class="mb-0" style="margin-top: 1rem;">Growth switch</h3>
+                 </div>
-                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                </div>
+              <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                        <p>    There are several things that need to be considered before selling Eye kNOw as a product. Since Eye kNOw won’t be used by the patient immediately after being manufactured, we designed a growth switch in order to control bacteria growth in different stages of our product lifetime. We were inspired by the work of <a href="https://2019.igem.org/Team:NUS_Singapore" class="linkinthetext">iGEM NUS 2019</a> who used a toxin-antitoxin system, <i>hicA</i>-<i>hicB</i>, to control the growth of bacteria. By manipulating the toxin-antitoxin ratio in a bacteria, we can determine when the bacteria should hibernate or grow.</p>
+                      <p>	while</p>
-                    </div>
+              </div>
+              </div>
+               <div class="container-fluid p-0">
+                <div class="row no-gutters">
+                <div class="col-lg ">
+                <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+                <a style="width:12%"><img src="https://static.igem.org/mediawiki/2020/f/f0/T--NCKU_Tainan--Thick_Epsilon.png" alt="" title="" style="width:100%"></a>
+                  <figcaption class="caption-design">Equation 1.7</figcaption>
+                </figure>
                  </div>
+                </div>
+                </div>
+              <div class="container-fluid p-0">
+                <div class="row no-gutters">
+                <div class="col-lg ">
+                <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+                <a style="width:12%"><img src="https://static.igem.org/mediawiki/2020/a/a8/T--NCKU_Tainan--Thick_VE.png" alt="" title="" style="width:100%"></a>
+                  <figcaption class="caption-design">Equation 1.8</figcaption>
+                </figure>
+                </div>
+                </div>
+                </div>
+              <p>	The ratio of volume difference is given by Equation 1.9:</p>
+               <div class="container-fluid p-0">
+                <div class="row no-gutters">
+                <div class="col-lg ">
+                <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+                <a style="width:55%"><img src="https://static.igem.org/mediawiki/2020/8/8d/T--NCKU_Tainan--Final1_9.png" alt="" title="" style="width:100%"></a>
+                <figcaption class="caption-design">Equation 1.9</figcaption>
+                </figure>
+                </div>
+                </div>
+                </div>
+               <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                    <div class="flex-grow-1">
+                        <p>	After calculation with the parameters listed above, <b>the result is approximately 1% when the IOP has an increment of 1 mmHg.</b></p>
+              </div>
+              </div>
+            </div>
+        </section>
+        <hr class="hrmar" />
+        <!-- Approaches-->
+        <section class="resume-section">
+            <div class="resume-section-content" id="mtwo">
+                <h2 class="mb-3">Model 2: Nitric Oxide Diffusion Model</h2>
+                <h4 class="mb-3">Overview</h4>
                  <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                         <p>    In our design, the <i>hicB</i> antitoxin is constitutively expressed at a basal level, while the <i>hicA</i> toxin is controlled by arabinose inducible promoter. The entire <i>hicA</i> cassette is flanked with <i>FRT</i> sites, which can later be deleted by the FLP recombinase. We also added a heat-activated <i>FRT</i>-FLP recombinase system from pCP20 as an inducible switch. This design enables us to control the bacteria growth in three stages - production, storage and medication.</p>
+                         <p>	Eye is a complicated organ consisting of various tissues with different physical properties. In most of the ocular delivery models, they consider the whole eye as one compartment since their drugs are stable and large enough that the difference of tissue characteristics can be ignored. However, we use NO as our drug, which is small and unstable. Thus, we need to set up a new model to simulate NO ocular delivery system.</p>
-                    </div>
                  </div>
-                 <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                 </div>
+              	<div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                         <p>    The production stage is when we are culturing our bacteria, so we need the bacteria to be able to grow normally. After the production process, the bacteria needs to be stored in the contact lens until it can be used. During the storage stage, <i>hicA</i> will be induced to hibernate the bacteria. The last stage is the medication stage, during which the contact lens will be used. When the contact lens is placed on the patient’s eye, the body temperature will activate the recombinase system and delete the hicA cassette, which will cause the bacteria to resuscitate and start producing the therapeutic agent.</p>
+                         <p>	This model <b>divides the eye system into three different compartment</b> according to the tissues differences, and provide <b>quantitative NO concentration profiles dynamically.</b> This model can be applied on ocular drug delivery system of other small and unstable drugs.</p>
-                    </div>
                  </div>
+                </div>
+                <h4 class="mb-3">Background</h4>
                  <div class="container-fluid p-0">
                  <div class="row no-gutters">
                  <div class="col-lg ">
                  <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
-                 <a href="https://static.igem.org/mediawiki/2020/9/9a/T--NCKU_Tainan--design_HicAB.gif" target="_blank" style="width:60%"><img src="https://static.igem.org/mediawiki/2020/9/9a/T--NCKU_Tainan--design_HicAB.gif" alt="" title="" style="width:100%"></a>
+                 <a href="https://static.igem.org/mediawiki/2020/8/89/T--NCKU_Tainan--model_eye.png" target="_blank" style="width:60%"><img src="https://static.igem.org/mediawiki/2020/8/89/T--NCKU_Tainan--model_eye.png" alt="" title="" style="width:100%"></a>
-                 <figcaption class="caption-design">Fig. 4. Plasmid design for grow switch</figcaption>
+                 <figcaption class="caption-design">Fig. 2A. Eye structure of human.</figcaption>
                  </figure>
                  </div>
                  </div>
                  </div>
-                <h4 class="mb-0">Functional Test</h4>
                  <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                         <p>    To verify the function of the FLP-<i>FRT</i> system, we will culture the bacteria with three plasmids, containing <i>hicA</i>, <i>hicB</i>, and <i>CI857</i> and <i>FLP</i> genes respectively. As the temperature rises to 42<sup>o</sup>C, <i>CI857</i> gene will be degraded, activating the <i>FLP</i> gene and deleting the <i>hicA</i> gene. If the <i>hicA</i> gene is present, the O.D.600 value will not increase since HicA protein represses the growth of bacteria. Hence, we can verify the function of the growth switch by measuring O.D. 600 value.</p>
+                         <p>	Eye structure can be divided into three main compartments: cornea, anterior chamber, and posterior chamber. <b>Target site of NO is trabecular meshwork</b>, which is located at the posterior angle of anterior chamber. We simplify the eye structures into one dimension as below:</p>
-                    </div>
+                </div>
                  </div>
-            </div>
+              <div class="container-fluid p-0">
-        </section>
+                <div class="row no-gutters">
-        <hr class="hrmar" />
+                <div class="col-lg ">
-        <section class="resume-section">
+                <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
-            <div class="resume-section-content" id="pdevice">
+                <a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/4/47/T--NCKU_Tainan--SchematicNew.png" alt="" title="" style="width:100%"></a>
-                <h2 class="mb-3">Device</h2>
+                 <figcaption class="caption-design">Fig. 2B. One dimensional schematic graph for NO ocular delivery model.</figcaption>
-                 <h3 class="mb-0" style="margin-top: 1rem;">IOP Detector</h3>
+                </figure>
+                </div>
+                </div>
+                </div>
                  <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
                      <div class="flex-grow-1">
-                        <p>    Since there are no early symptoms of glaucoma, the public is left unaware of its presence. Therefore, early detection is needed, so we developed a brand-new IOP detector - Eye Screen. By transmitting ultrasonic waves to the patient’s cornea and analyzing the reflected signal, we can get IOP readings immediately. With Eye Screen, we can quickly find people at high risk of glaucoma, without direct contact with the eyes.</p>
+                      <p>	Since the tissue characteristics of the three compartments varies a lot, we need to simulate the behavior of NO in them separately, by different partial differential equations (PDEs).</p>
+                </div>
+             	</div>
+          	    <h4 class="mb-3">Model</h4>
+          	    <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                    <div class="flex-grow-1">
+                      <p>	First, <b>we establish the initial state of NO distribution in the eye</b> before Eye kNOw being triggered. Second, we build the <b>dynamic NO concentration profile according to time and distance</b> after Eye kNOw activation. We use several partial differential equations(PDEs) to describe the behavior of NO. Table 2A lists all the abbreviations used in PDEs.</p>
+				</div>
+             	</div>
+              	<table class="table table-Border">
+                          <thead>
+                            <tr style="border:3px solid #7E3B40;">
+                              <th scope="col" style="font-size:1.2rem; text-align: center;"></th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Full Name</th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Unit</th>
+                            </tr>
+                          </thead>
+                          <tbody>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">C</td>
+                              <td style="font-size:1.1rem; text-align: center;">Concentration of NO</td>
+                              <td style="font-size:1.1rem; text-align: center;">M</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">x</td>
+                              <td style="font-size:1.1rem; text-align: center;">distance (from outside of the eye to inside)</td>
+                              <td style="font-size:1.1rem; text-align: center;">cm</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">t</td>
+                              <td style="font-size:1.1rem; text-align: center;">time (t=0 resembles the time when Eye kNOw start to produce NO)</td>
+                              <td style="font-size:1.1rem; text-align: center;">s</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">D</td>
+                              <td style="font-size:1.1rem; text-align: center;">Diffusion coefficient</td>
+                              <td style="font-size:1.1rem; text-align: center;">cm<sup>2</sup>/s</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">R</td>
+                              <td style="font-size:1.1rem; text-align: center;">Flow rate of liquid</td>
+                              <td style="font-size:1.1rem; text-align: center;">L/s</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">k</td>
+                              <td style="font-size:1.1rem; text-align: center;">Degradation coefficient of NO</td>
+                              <td style="font-size:1.1rem; text-align: center;">M<sup>-2</sup>/s</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">Pro</td>
+                              <td style="font-size:1.1rem; text-align: center;">Production rate of NO in the compartment</td>
+                              <td style="font-size:1.1rem; text-align: center;">mol/s</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">V</td>
+                              <td style="font-size:1.1rem; text-align: center;">Volume of the compartment</td>
+                              <td style="font-size:1.1rem; text-align: center;">L</td>
+                            </tr>
+                          </tbody>
+                        </table>
+              <figcaption class="caption-design" style="margin-bottom:1rem; text-align: center">Table 2A. Abbreviations and variables used in PDEs.</figcaption>
+                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                  <div class="flex-grow-1">
+                    <p>1. Setting up PDEs:</p>
+                    <p style="position: relative;left: 2rem;">	PDEs take the factors that may affect the concentration of NO into consideration to describe the behavior of NO. Factors are listed below:</p>
+                    <p style="position: relative;left: 2rem;"><b>(1) Degradation</b></p>
+                         <p style="position: relative;left: 4rem;">	The two main factors that will cause degradation of nitric oxide in the human body are hemoglobin and oxygen. Hemoglobin doesn’t exist in the eye system, thus we only need to consider oxygen as the factor causing NO degradation.</p>
+                         <p style="position: relative;left: 4rem;">	According to current studies, the formula can be written as below:</p>
+                       		<div class="container-fluid p-0">
+                			<div class="row no-gutters">
+              	  			<div class="col-lg ">
+               			     <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    <a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/3/30/T--NCKU_Tainan--model_1_1.png" alt="" title="" style="width:100%"></a>
+               				<figcaption class="caption-design">Equation 2.1</figcaption>
+             				</figure>
+                			</div>
+                			</div>
+               			    </div>
+                    <p style="position: relative;left: 2rem;"><b>(2) Diffusion</b></p>
+                          <p style="position: relative;left: 4rem;">	By <b>Fick's second law</b>, the diffusion of chemicals can be described as below:</p>
+							<div class="container-fluid p-0">
+                			<div class="row no-gutters">
+              	  			<div class="col-lg ">
+               			     <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    <a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/a/a1/T--NCKU_Tainan--model_1_2.png" alt="" title="" style="width:100%"></a>
+               				<figcaption class="caption-design">Equation 2.2</figcaption>
+             				</figure>
+                			</div>
+                			</div>
+               			    </div>
+                    <p style="position: relative;left: 2rem;"><b>(3) Endogenous production</b></p>
+              		<p style="position: relative;left: 4rem;"><b>	Glaucoma patients’ aqueous humor has an initial average concentration of NO around 53.4uM<sup>[<a href = "#ref7" class = "linklink">7</a>]</b>, which is maintained by endogenous NO produced by NO synthase (NOS). There are three different types of NOS in human eyes: e-NOS, n-NOS, and i-NOS<sup>[<a href = "#ref7" class = "linklink">7</a>]</sup>.</p>
+                    <p style="position: relative;left: 4rem;">	e-NOS and n-NOS work constantly, which are expressed on iris, cornea, vascular endothelium, etc. i-NOS only works when ocular inflammation happens, which is not a common symptom for glaucoma, thus we can ignore it. We assume that these NOS produce NO in a constant rate, so the formula can be written as below:</p>
+                    <div class="container-fluid p-0">
+                			<div class="row no-gutters">
+              	  			<div class="col-lg ">
+               			     <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    <a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/b/b1/T--NCKU_Tainan--model_1_3.png" alt="" title="" style="width:100%"></a>
+               				<figcaption class="caption-design">Equation 2.3</figcaption>
+             				</figure>
+                			</div>
+                			</div>
+               			    </div>
+                     <p style="position: relative;left: 2rem;"><b>(4) Convection</b></p>
+                     <p style="position: relative;left: 4rem;">	There’s a flow of aqueous humor in the anterior chamber, which is 2.4 uL/min<sup>[8]</sup>. Convection will affect the distribution of nitric oxide, which can be written as below:</p>
+                      <div class="container-fluid p-0">
+                			<div class="row no-gutters">
+              	  			<div class="col-lg ">
+               			     <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    <a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/6/66/T--NCKU_Tainan--model_1_4.png" alt="" title="" style="width:100%"></a>
+               				<figcaption class="caption-design">Equation 2.4</figcaption>
+             				</figure>
+                			</div>
+                			</div>
+               			    </div>
+                    	<p style="position: relative;left: 4rem;">	Combining the factors listed above, the PDE for describing the distribution of NO can be written as below:</p>
+                     	<div class="container-fluid p-0">
+                			<div class="row no-gutters">
+              	  			<div class="col-lg ">
+               			     <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    <a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/f/f6/T--NCKU_Tainan--model_1_5.png" alt="" title="" style="width:100%"></a>
+               				<figcaption class="caption-design">Equation 2.5</figcaption>
+             				</figure>
+                			</div>
+                			</div>
+               			</div>
+                    	<p style="position: relative;left: 4rem;">	Equation 2.5 is a heterogeneous PDE, which is very hard to solve. We need to <b>simplify Equation 2.5 into homogeneous form for further calculation.</b></p>
+                    	<p style="position: relative;left: 4rem;">	First, since the concentration of oxygen can be maintained by oxygen in the air( oxygen in the air can dissolve and penetrate into our eyes), <b>we can set k[Oxygen] as a constant.</b></p>
+                    	<p style="position: relative;left: 4rem;">	Second, we want to simplify the C<sup>2</sup> term into C. In order to prevent over-estimation of nitric oxide concentration, <b>we change C<sup>2</sup> into C<sub>max</sub>．C, where C<sub>max</sub> is the max concentration of nitric oxide in the compartment.</b> Since C<sub>max</sub>．C is always larger than (or same as) C<sup>2</sup>, we can make sure that we won’t over-estimate the concentration of nitric oxide. Since C<sub>max</sub> is a constant, we can consider <b>constant B = k[Oxygen]C<sub>max</sub>.</b></p>
+                    	<p style="position: relative;left: 4rem;">	Therefore, the modified form of PDE will be:</p>
+                    	<div class="container-fluid p-0">
+                			<div class="row no-gutters">
+              	  			<div class="col-lg ">
+               			     <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    <a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/f/f8/T--NCKU_Tainan--model_1_6.png" alt="" title="" style="width:100%"></a>
+               				<figcaption class="caption-design">Equation 2.6</figcaption>
+             				</figure>
+                			</div>
+                			</div>
+                  	</div>
+                  </div>
                      </div>
+                <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                  <div class="flex-grow-1">
+                    <p>2. Obtaining parameters from current studies: </p>
+                         <p style="position: relative;left: 2rem;">	Parameters used are listed in table 2B. We collected them from current studies.</p>
+                    	 <table class="table table-Border">
+                          <thead>
+                            <tr style="border:3px solid #7E3B40;">
+                              <th scope="col" style="font-size:1.2rem; text-align: center;"></th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Contact Lens</th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Cornea</th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Aqueous Humor</th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Unit</th>
+                            </tr>
+                          </thead>
+                          <tbody>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">D</td>
+                              <td style="font-size:1.1rem; text-align: center;">1.8．10<sup>-6</sup><sup>[<a href = "#ref9" class = "linklink">9</a>]</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">2.81．10<sup>-5</sup><sup>[<a href = "#ref10" class = "linklink">10</a>]</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">3．10<sup>-5</sup><sup>[<a href = "#ref11" class = "linklink">11</a>]</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">cm<sup>2</sup>/s</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">B</td>
+                              <td style="font-size:1.1rem; text-align: center;">?</td>
+                              <td style="font-size:1.1rem; text-align: center;">?</td>
+                              <td style="font-size:1.1rem; text-align: center;">?</td>
+                              <td style="font-size:1.1rem; text-align: center;">1/s</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">R</td>
+                              <td style="font-size:1.1rem; text-align: center;">0</td>
+                              <td style="font-size:1.1rem; text-align: center;">0</td>
+                              <td style="font-size:1.1rem; text-align: center;">4．10<sup>-8</sup><sup>[<a href = "#ref8" class = "linklink">8</a>]</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">L/s</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">V</td>
+                              <td style="font-size:1.1rem; text-align: center;">2.77．10<sup>-5</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">1.6．10<sup>-5</sup><sup>[<a href = "#ref12" class = "linklink">12</a>]</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">2.5．10<sup>-4</sup><sup>[<a href = "#ref13" class = "linklink">13</a>]</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">L</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">Pro</td>
+                              <td style="font-size:1.1rem; text-align: center;">?</td>
+                              <td style="font-size:1.1rem; text-align: center;">?</td>
+                              <td style="font-size:1.1rem; text-align: center;">?</td>
+                              <td style="font-size:1.1rem; text-align: center;">mol/s</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">Initial Average [NO]</td>
+                              <td style="font-size:1.1rem; text-align: center;">?</td>
+                              <td style="font-size:1.1rem; text-align: center;">?</td>
+                              <td style="font-size:1.1rem; text-align: center;">5.34．10<sup>-5</sup><sup>[<a href = "#ref6" class = "linklink">6</a>]</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">M</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">Maximum Distance</td>
+                              <td style="font-size:1.1rem; text-align: center;">0.02</td>
+                              <td style="font-size:1.1rem; text-align: center;">0.055<sup>[<a href = "#ref14" class = "linklink">14</a>]</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">1.122<sup>[<a href = "#ref15" class = "linklink">15</a>]</sup><sup>[<a href = "#ref16" class = "linklink">16</a>]</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">cm</td>
+                            </tr>
+                          </tbody>
+                        </table>
+              <figcaption class="caption-design" style="margin-bottom:1rem; text-align: center">Table 2B. Parameters of Eye kNOw used in model 2.</figcaption>
+                         <p style="position: relative;left: 2rem;">	We're still lacking some of the parameters. We can <b>estimate them by solving the steady state of NO distribution</b>.</p>
+                 </div>
                  </div>
-                <h4 class="mt-1">Functional Test</h4>
                  <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
-                    <div class="flex-grow-1">
+                  <div class="flex-grow-1">
-                        <p>    To validate the function of Eye Screen, we adopted a gravity model to control the IOP of porcine eyeballs using the trocar system via microincision vitrectomy surgery. By adjusting the height of the saline bag connected to the eyeball, we can measure the IOP by calculating the difference in height of the saline and the eyeball. We then tested whether the amplitude of reflected signals can be proportional to the IOP according to the change in IOP.</p>
+                    <p>3. Calculating steady state:</p>
-                    </div>
+                         <p style="position: relative;left: 2rem;">	We start from the contact lens compartment. When in steady state,  NO concentration won't change by time. Thus, Equation 2.6 can be written as below:<p>
+                         <div class="container-fluid p-0">
+                			<div class="row no-gutters">
+              	  			<div class="col-lg ">
+               			     <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    <a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/9/9b/T--NCKU_Tainan--model_1_7.png" alt="" title="" style="width:100%"></a>
+               				<figcaption class="caption-design">Equation 2.7</figcaption>
+             				</figure>
+                			</div>
+                			</div>
+               			    </div>
+                    	<p style="position: relative;left: 2rem;">	Where subscript 1 stands for the parameters and variables of the contact lens compartment. By solving Equation 2.7, we can get the solution of C<sub>1</sub> in steady state:</p>
+         				  <div class="container-fluid p-0">
+                			<div class="row no-gutters">
+              	  			<div class="col-lg ">
+               			     <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    <a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/b/b5/T--NCKU_Tainan--model_1_8.png" alt="" title="" style="width:100%"></a>
+               				<figcaption class="caption-design">Equation 2.8</figcaption>
+             				</figure>
+                			</div>
+                			</div>
+               			    </div>
+                    <p style="position: relative;left: 2rem;">	We use the approximation:</p>
+                     <div class="container-fluid p-0">
+                			<div class="row no-gutters">
+              	  			<div class="col-lg ">
+               			     <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    <a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/1/1e/T--NCKU_Tainan--model_1_9.png" alt="" title="" style="width:100%"></a>
+               				<figcaption class="caption-design">Equation 2.9</figcaption>
+             				</figure>
+                			</div>
+                			</div>
+               			    </div>
+                      <p style="position: relative;left: 2rem;">	Thus turning Equation 2.8 into linear form:</p>
+                      <div class="container-fluid p-0">
+                			<div class="row no-gutters">
+              	  			<div class="col-lg ">
+               			     <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    <a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/7/73/T--NCKU_Tainan--Revised_Formula_Kelvin.png" alt="" title="" style="width:100%"></a>
+               				<figcaption class="caption-design">Equation 2.10</figcaption>
+             				</figure>
+                			</div>
+                			</div>
+               			    </div>
+                        <p style="position: relative;left: 2rem;">	Since C<sub>1</sub>(0)=0 (one of the boundary conditions), the final form of C<sub>1</sub> in steady state can be written as below:</p>
+                         <div class="container-fluid p-0">
+                			<div class="row no-gutters">
+              	  			<div class="col-lg ">
+               			     <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    <a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/0/0e/T--NCKU_Tainan--model_1_11.png" alt="" title="" style="width:100%"></a>
+               				<figcaption class="caption-design">Equation 2.11</figcaption>
+             				</figure>
+                			</div>
+                			</div>
+               			    </div>
+                   		 <p style="position: relative;left: 2rem;">	By the same method, we can simplify the concentration of NO in cornea and aqueous humor compartments as a linear formula of x. To simplify the formulas, <b>we set the outer surface of every compartment as the starting position of that compartment.</b> For example, for cornea compartment, the interface of cornea and contact lens is considered the starting position, namely x=0.</p>
+                          <p style="position: relative;left: 2rem;">	As for the boundary conditions, the interfaces should have only one concentration. For example, the formula of C<sub>1</sub> at x=0.02 should have the same value as C<sub>2</sub> at x=0. Combining these conditions, we can get the function of C<sub>2</sub> and C<sub>3</sub>:</p>
+                            <div class="container-fluid p-0">
+                			<div class="row no-gutters">
+              	  			<div class="col-lg ">
+               			     <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    <a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/a/ac/T--NCKU_Tainan--model_1_12.png" alt="" title="" style="width:100%"></a>
+               				<figcaption class="caption-design">Equation 2.12</figcaption>
+             				</figure>
+                			</div>
+                			</div>
+               			    </div>
+                    		<div class="container-fluid p-0">
+                			<div class="row no-gutters">
+              	  			<div class="col-lg ">
+               			     <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    <a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/a/ae/T--NCKU_Tainan--model_1_13.png" alt="" title="" style="width:100%"></a>
+               				<figcaption class="caption-design">Equation 2.13</figcaption>
+             				</figure>
+                			</div>
+                			</div>
+               			    </div>
+                   			 <p style="position: relative;left: 2rem;">	Now we need to solve the slope of NO concentration, namely a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub>. Here, we use Fick’s first law as boundary conditions, that is <b>at the interfaces, input of NO from one compartment should be the same as output of another compartment.</b> For example, at the interface of cornea and contact lens, input of NO to contact lens should be the same as output of NO from cornea.</p>
+                             <p style="position: relative;left: 2rem;">	The input of NO to contact lens can be written as below, according to Fick’s first law:</p>
+                             <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    	<a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/5/54/T--NCKU_Tainan--model_1_14.png" alt="" title="" style="width:100%"></a>
+               					<figcaption class="caption-design">Equation 2.14</figcaption>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+					         <p style="position: relative;left: 2rem;">	The output of NO from cornea can be written as below:</p>
+                             <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    	<a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/7/75/T--NCKU_Tainan--model_1_15.png" alt="" title="" style="width:100%"></a>
+               					<figcaption class="caption-design">Equation 2.15</figcaption>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                     		<p style="position: relative;left: 2rem;">	Applying the solution we’d obtained, we can get the relationship of slopes of each compartment:</p>
+                    		 <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    	<a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/d/d3/T--NCKU_Tainan--model_1_16.png" alt="" title="" style="width:100%"></a>
+               					<figcaption class="caption-design">Equation 2.16</figcaption>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                    		<p style="position: relative;left: 2rem;">	Therefore, we can draw the steady-state-graph of NO distribution in the eye:</p>
+<div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    	<a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/3/3e/T--NCKU_Tainan--Model_NOABCABC.png" alt="" title="" style="width:100%"></a>
+               					<figcaption class="caption-design">Fig. 2C. NO Concentration Profile in Steady State. A stands for contact lens compartment, B stands for cornea comparment, C stands for aqueous humor compartment.</figcaption>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                    		<p style="position: relative;left: 2rem;">	Now, there are just B and Pro not determined yet. Recall that <b>B = k[Oxygen]C<sub>max</sub></b>, we can calculate them. <b>As for Pro, we can calculate each compartment’s total input and output, they should be the same since we’re dealing with steady state.</b> After calculations, Table 2B can be filled completely as Table 2C.</p>
+                             <table class="table table-Border">
+                          <thead>
+                            <tr style="border:3px solid #7E3B40;">
+                              <th scope="col" style="font-size:1.2rem; text-align: center;"></th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Contact Lens</th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Cornea</th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Aqueous Humor</th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Unit</th>
+                            </tr>
+                          </thead>
+                          <tbody>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">D</td>
+                              <td style="font-size:1.1rem; text-align: center;">1.8．10<sup>-6</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">2.81．10<sup>-5</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">3．10<sup>-5</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">cm<sup>2</sup>/s</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">B</td>
+                              <td style="font-size:1.1rem; text-align: center;">2.84．10<sup>-2</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">1.03．10<sup>-2</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">1.566．10<sup>-2</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">1/s</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">R</td>
+                              <td style="font-size:1.1rem; text-align: center;">0</td>
+                              <td style="font-size:1.1rem; text-align: center;">0</td>
+                              <td style="font-size:1.1rem; text-align: center;">4．10<sup>-8</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">L/s</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">V</td>
+                              <td style="font-size:1.1rem; text-align: center;">2.77．10<sup>-5</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">1.6．10<sup>-5</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">2.5．10<sup>-4</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">L</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">Pro</td>
+                              <td style="font-size:1.1rem; text-align: center;">7．10<sup>-6</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">1.52．10<sup>-5</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">1.239．10<sup>-3</sup></td>
+                              <td style="font-size:1.1rem; text-align: center;">mol/s</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">Initial Average [NO]</td>
+                              <td style="font-size:1.1rem; text-align: center;">C<sub>1</sub> = 933.7x</td>
+                              <td style="font-size:1.1rem; text-align: center;">C<sub>2</sub> = 59.818x + 18.674</td>
+                              <td style="font-size:1.1rem; text-align: center;">C<sub>3</sub> = 56.063x + 21.964</td>
+                              <td style="font-size:1.1rem; text-align: center;">uM</td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">Maximum Distance</td>
+                              <td style="font-size:1.1rem; text-align: center;">0.02</td>
+                              <td style="font-size:1.1rem; text-align: center;">0.055</td>
+                              <td style="font-size:1.1rem; text-align: center;">1.122</td>
+                              <td style="font-size:1.1rem; text-align: center;">cm</td>
+                            </tr>
+                          </tbody>
+                        </table>
+              <figcaption class="caption-design" style="margin-bottom:1rem; text-align: center">Table 2C. Complete table of parameters used for model 2.</figcaption>
+                 </div>
                  </div>
+              	 <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                  <div class="flex-grow-1">
+                    <p>4. Calculating NO concentration after production of NO by Eye kNOw (non-steady state):</p>
+                    <p style="position: relative;left: 2rem;">	After confirming all the parameters, we continue to calculate the NO concentration of each compartment when Eye kNOw is activated by elevation of IPTG concentration. We assume that <b>the production rate of Eye kNOw raised j% after activation compared with steady state.</b> Table 2D. Shows the PDEs, initial conditions, and boundary conditions:</p>
+                    <table class="table table-Border">
+                          <thead>
+                            <tr style="border:3px solid #7E3B40;">
+                              <th scope="col" style="font-size:1.2rem; text-align: center;"></th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">PDE</th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Initial Condition</th>
+                              <th scope="col" style="font-size:1.2rem; text-align: center;">Boundary Condition</th>
+                            </tr>
+                          </thead>
+                          <tbody>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">Contact Lens</td>
+                              <td style="font-size:1.1rem; text-align: center;">
+                                <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3" style = "background:white; margin-bottom:0">
+               			    	<a style="width:70%"><img src="https://static.igem.org/mediawiki/2020/6/61/T--NCKU_Tainan--Gan1.png" alt="" title="" style="width:100%"></a>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                              </td>
+                              <td style="font-size:1.1rem; text-align: center;">
+                              <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3" style = "background:white; margin-bottom:0">
+               			    	<a style="width:55%"><img src="https://static.igem.org/mediawiki/2020/c/cf/T--NCKU_Tainan--Gan2.png" alt="" title="" style="width:100%"></a>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                              </td>
+                              <td style="font-size:1.1rem; text-align: center;">
+                              <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3" style = "background:white; margin-bottom:0">
+               			    	<a style="width:55%"><img src="https://static.igem.org/mediawiki/2020/e/e6/T--NCKU_Tainan--Gan3.png" alt="" title="" style="width:100%"></a>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                              </td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">Cornea</td>
+                              <td style="font-size:1.1rem; text-align: center;">
+                                <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3" style = "background:white; margin-bottom:0">
+               			    	<a style="width:70%"><img src="https://static.igem.org/mediawiki/2020/f/f6/T--NCKU_Tainan--Gan4.png" alt="" title="" style="width:100%"></a>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                              </td>
+                              <td style="font-size:1.1rem; text-align: center;">
+                              <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3" style = "background:white; margin-bottom:0">
+               			    	<a style="width:70%"><img src="https://static.igem.org/mediawiki/2020/5/59/T--NCKU_Tainan--Gan5.png" alt="" title="" style="width:100%"></a>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                              </td>
+                              <td style="font-size:1.1rem; text-align: center;">
+                              <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3" style = "background:white; margin-bottom:0">
+               			    	<a style="width:70%"><img src="https://static.igem.org/mediawiki/2020/e/e5/T--NCKU_Tainan--Gan6.png" alt="" title="" style="width:100%"></a>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                                <p>   </p>
+                                <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3" style = "background:white; margin-bottom:0">
+               			    	<a style="width:75%"><img src="https://static.igem.org/mediawiki/2020/9/92/T--NCKU_Tainan--Gan7.png" alt="" title="" style="width:100%"></a>
+                                  </figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                              </td>
+                            </tr>
+                            <tr>
+                              <td scope="row" style="font-size:1.1rem; text-align: center;">Aqueous Humor</td>
+                              <td style="font-size:1.1rem; text-align: center;">
+                                <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3" style = "background:white; margin-bottom:0">
+               			    	<a style="width:80%"><img src="https://static.igem.org/mediawiki/2020/9/97/T--NCKU_Tainan--Gan8.png" alt="" title="" style="width:100%"></a>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                              </td>
+                              <td style="font-size:1.1rem; text-align: center;">
+                              <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3" style = "background:white; margin-bottom:0">
+               			    	<a style="width:80%"><img src="https://static.igem.org/mediawiki/2020/e/e4/T--NCKU_Tainan--Gan9.png" alt="" title="" style="width:100%"></a>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                              </td>
+                              <td style="font-size:1.1rem; text-align: center;">
+                              <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3" style = "background:white; margin-bottom:0">
+               			    	<a style="width:70%"><img src="https://static.igem.org/mediawiki/2020/7/71/T--NCKU_Tainan--Gan10.png" alt="" title="" style="width:100%"></a>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                                <p>   </p>
+                                <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3" style = "background:white; margin-bottom:0">
+               			    	<a style="width:75%"><img src="https://static.igem.org/mediawiki/2020/f/f2/T--NCKU_Tainan--Gan11.png" alt="" title="" style="width:100%"></a>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                              </td>
+                            </tr>
+                          </tbody>
+                        </table>
+              <figcaption class="caption-design" style="margin-bottom:1rem; text-align: center">Table 2D. PDEs, initial conditions, boundary conditions of each compartment.</figcaption>
+                    <p style="position: relative;left: 2rem;">	However, we found the PDEs hard to solve by current methods, including Fourier transform and separation of variables. After lots of effort, we finally solved the PDEs by means of <b>double Laplace transform and inverse double Laplace transform.</b></p>
+                  	<p style="position: relative;left: 2rem;">	We developed two MATLAB programs, one of them functioning as PDE solver utilizes double Laplace transform, and another one working as Laplace transform estimator for functions which cannot be transformed by current method. These programs are available on the internet with clear documentation, see modeling <a href="https://2020.igem.org/Team:NCKU_Tainan/Software" alt="" target="_blank">software</a> for more information.</p>
+                    <p style="position: relative;left: 2rem;">	The dynamic NO concentration profiles can be described by three formulas as follow:</p>
+                     <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    	<a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/9/9a/T--NCKU_Tainan--model_2_4.png" alt="" title="" style="width:100%"></a>
+               					<figcaption class="caption-design">Equation 2.17</figcaption>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                     <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    	<a style="width90%"><img src="https://static.igem.org/mediawiki/2020/7/7f/T--NCKU_Tainan--model_2_9.png" alt="" title="" style="width:100%"></a>
+               					<figcaption class="caption-design">Equation 2.18</figcaption>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                    <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    	<a style="width:100%"><img src="https://static.igem.org/mediawiki/2020/a/ae/T--NCKU_Tainan--RevisedAns3.png" alt="" title="" style="width:100%"></a>
+               					<figcaption class="caption-design">Equation 2.19</figcaption>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                    <p style="position: relative;left: 2rem;">	Notice that there is an undefined parameter r in our solutions. Parameter r is correlated with the interfaces’ properties in our eyes, namely the interface of cornea and contact lens, and the interface of cornea and aqueous humor. Since we cannot do experiments on living animals, we cannot obtain the value of r. In fact, the value of r varies individually, so we just pick some of the r to demonstrate the result.</p>
+                     <p style="position: relative;left: 2rem;">	We use MATLAB to plot the dynamic NO concentration profile of each compartment according to time:</p>
+                   </div>
+              </div>
+                  <div class="container-fluid p-0" style="margin-top: 2rem; margin-bottom: 1.5rem;">
+                <div class="row no-gutters">
+                <div class="col-lg" style="text-align: center;">
+                <video autoplay controls id="myvideo" class="d-flex flex-column justify-content-center align-items-center px-lg-3" style="width:80%;margin-left:auto;margin-right: auto;">
+                <source src="https://static.igem.org/mediawiki/2020/6/6a/T--NCKU_Tainan--Non_Steady_Movie_Final.mp4" type="video/mp4" style="width:100%" />
+                 Your browser doesn't support the video tag.
+                </video>
+                <figcaption class="caption-design">Video 1. NO Distribution. (r=0.0156 j=20)</figcaption>
+                </div>
+                </div>
+                </div>
+           </div>
+        </section>
+        <hr class="hrmar" />
+        <!-- Inspiration-->
+        <section class="resume-section" >
+            <div class="resume-section-content" id="mthree">
+                <h2 class="mb-3">Model 3: Effectiveness of Eye kNOw</h2>
+                 <div class="d-flex flex-column flex-md-row justify-content-between mb-2">
+                  <div class="flex-grow-1">
+                    <p>	As a new developing treatment of Glaucoma, it's important to show that the effectiveness of Eye kNOw is better than current treatment. Effectiveness reflects how a drug actually works in the patient's body, which can be evaluated by time and drug amount needed to cause therapeutic effect. Particularly, <b>the minimum concentration of a drug that can cause therapeutic effect is called minimum effective concentration (MEC).</b></p>
+                    <p>	To prove that Eye kNOw can help treat glaucoma more effectively, this model combines model 1, model 2, and experimental data, aiming to precisely quantify Eye kNOw's MEC and the time needed to reach it. Noted that <b>there's no MEC data of NO since current treatment utilizes NO donor instead of NO directly</b>, but estimation can be made by adopting data from current NO prodrug. Here, we adopt data of <b>Latanoprostene Bunod</b> to estimate the MEC of NO, approximately <b>1.182．10<sup>-8</sup>M.</b><sup>[<a href = "#ref17" class = "linklink">17</a>]</sup><sup>[<a href = "#ref18" class = "linklink">18</a>]</sup><sup>[<a href = "#ref19" class = "linklink">19</a>]</sup></p>
+                    <p>	We assume that contact lens deformation happens immediately after IOP elevation, and [IPTG] elevation happens immediately after contact lens deformation, too. Therefore, the only two steps we should concern are <b>how fast will NOS be produced after [IPTG] elevates, and how fast will [NO] at trabecular meshwork reach MEC</b>. We’ll discuss them one by one.</p>
+                    <p>	First, we calculate the speed of NOS production after [IPTG] elevation. By wet team’s results (<a href="https://2020.igem.org/Team:NCKU_Tainan/Results" alt="" target="_blank">NO kinetics experiment and IPTG induction experiment</a>), we can calculate the NO production rate according to [IPTG] and time:</p>
+                    <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    	<a style="width:90%"><img src="https://static.igem.org/mediawiki/2020/3/34/T--NCKU_Tainan--model_3_1.png" alt="" title="" style="width:100%"></a>
+               					<figcaption class="caption-design">Equation 3.1</figcaption>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                    <p>	Notice that the unit of Equation 3.1 is nmol/hr, and the reaction volume of the experiments is 60uL. Since the volume of Eye kNOw’s chamber is 4.4uL, the production rate in Eye kNOw can be written as below: </p>
+                     <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    	<a style="width:90%"><img src="https://static.igem.org/mediawiki/2020/d/d8/T--NCKU_Tainan--model_3_2.png" alt="" title="" style="width:100%"></a>
+               					<figcaption class="caption-design">Equation 3.2</figcaption>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                    <p>	Notice that the production rate depends on not only the efficiency of NOS, but also the concentration of NOS in the solution. <b>We set IOP = 15mmHg, [IPTG] = 0.1mM as initial conditions.</b> By model 2, the <b>initial production rate should be 7．10<sup>-6</sup> mol/s to maintain steady state.</b> Therefore, by <b>elevating bacteria concentration in Eye kNOw</b>, the initial production rate of NOS in Eye kNOw can be written as Equation 3.3:</p>
+                    <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    	<a style="width:90%"><img src="https://static.igem.org/mediawiki/2020/a/a1/T--NCKU_Tainan--model_3_3.png" alt="" title="" style="width:100%"></a>
+               					<figcaption class="caption-design">Equation 3.3</figcaption>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                     <p>	Since in initial state, NOS has already been made, so we can neglect the time-related term in Equation 3.2. <b>Assume that patient’s IOP raises i mmHg</b>, the production rate of NOS can be written as below:</p>
+                    <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    	<a style="width:90%"><img src="https://static.igem.org/mediawiki/2020/8/82/T--NCKU_Tainan--Final_Func_3_3.png" alt="" title="" style="width:100%"></a>
+               					<figcaption class="caption-design">Equation 3.4</figcaption>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                     <P>	Second, we calculate the time needed for Eye kNOw to raise the [NO] at the trabecular meshwork to MEC once the IOP is elevated. We use MATLAB to plot out the concentration change of NO at trabecular meshwork according to time after induction. Below are the results:</p>
+                     <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    	<a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/8/82/T--NCKU_Tainan--Model_NO_TM_big1.png" alt="" title="" style="width:100%"></a>
+               					<figcaption class="caption-design">Fig. 3A. NO concentration at trabecular meshwork in different volume change-large time scale.</figcaption>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                     <div class="container-fluid p-0">
+                				<div class="row no-gutters">
+              	  				<div class="col-lg ">
+               			    	 <figure class="d-flex flex-column justify-content-center align-items-center px-lg-3">
+               			    	<a style="width:60%"><img src="https://static.igem.org/mediawiki/2020/c/c9/T--NCKU_Tainan--Model_NO_TM.png" alt="" title="" style="width:100%"></a>
+               					<figcaption class="caption-design">Fig. 3B. NO concentration at trabecular meshwork in different volume change-small time scale.</figcaption>
+             					</figure>
+                				</div>
+                				</div>
+               			   	 	</div>
+                    <p>	We can obtain that <b>time needed for Eye kNOw to raise trabecular meshwork’s NO concentration up to MEC is very short</b>, which theoretically proves that Eye kNOw can treat glaucoma with high efficiency and accuracy.</p>
+                   </div>
+              </div>
              </div>
          </section>
+        <hr class="hrmar" />
          <hr class="hrmar" />
          <section class="resume-section" >
@@ Line 454: / Line 1,432: @@
              <h2>References</h2>
                <ol>
-                 <li id="ref1">Muenster S, Lieb WS, Fabry G, et al. The Ability of Nitric Oxide to Lower Intraocular Pressure Is Dependent on Guanylyl Cyclase. <i>Investigative Opthalmology & Visual Science.</i> 2017;58(11):4826.</li>
+                 <li id="ref1">Chen G-Z, Chan I-S, Leung LKK, Lam DCC. Soft wearable contact lens sensor for continuous intraocular pressure monitoring. <i>Medical Engineering & Physics.</i> 2014;36(9):1134-1139.</li>
-                 <li id="ref2">Lam A. The effect of an artificially elevated intraocular pressure on the central corneal curvature. <i>Ophthalmic and Physiological Optics.</i> 1997;17(1):18-24.</li>
+                 <li id="ref2">Berest P, Nguyen-Minh D. Response of a spherical cavity in an elastic viscoplastic medium under a variable internal pressure. <i>International Journal of Solids and Structures.</i></li>
-                 <li id="ref3">Chen G-Z, Chan I-S, Leung LKK, Lam DCC. Soft wearable contact lens sensor for continuous intraocular pressure monitoring. <i>Medical Engineering & Physics.</i> 2014;36(9):1134-1139.</li>
+                <li id="ref3">Sanchez I, Martin R, Ussa F, Fernandez-Bueno I. The parameters of the porcine eyeball. Graefe’s Archive for Clinical and Experimental Ophthalmology. 2011;249(4):475-482.</li>
-                 <li id="ref4">Zhang J, Zhang Y, Li Y, et al. Correlation of IOP with Corneal Acoustic Impedance in Porcine Eye Model. <i>BioMed Research International.</i> 2017;2017:1-6.</li>
+                 <li id="ref4">Dupps WJ, Netto MV, Herekar S, Krueger RR. Surface wave elastometry of the cornea in porcine and human donor eyes. <i>Journal of refractive surgery</i> (Thorofare, NJ : 1995). 2007;23(1):66-75. Accessed October 24, 2020.</li>
-                 <li id="ref5">BRENDA - Information on EC 1.14.13.39 - nitric-oxide synthase (NADPH). Brenda-enzymes.org. <a href="https://www.brenda-enzymes.org/enzyme.php?ecno=1.14.13.39#pH%20OPTIMUM." target="_blank" class="linklink">https://www.brenda-enzymes.org/enzyme.php?ecno=1.14.13.39#pH%20OPTIMUM.</a> Published 2020. Accessed September 9, 2020.</li>
-                 <li id="ref6">Dante RA, Neto GC, Leite A, Yunes JA, Arruda P. Plant <i>Molecular Biology.</i> 1999;41(4):551-561.</li>
+                 <li id="ref5">Ford PC, Wink DA, Stanbury DM. Autoxidation kinetics of aqueous nitric oxide. FEBS Letters. 1993;326(1-3):1-3.</li>
-                 <li id="ref7">McLennan N, Masters M. GroE is vital for cell-wall synthesis. <i>Nature.</i> 1998;392(6672):139-139.</li>
+                 <li id="ref6">Ghanem AA, Elewa AM, Arafa LF. Endothelin-1 and Nitric Oxide Levels in Patients with Glaucoma. Ophthalmic Research. 2011;46(2):98-102.</li>
-              </ol>
+                <li id="ref7">Forstermann U, Sessa WC. Nitric oxide synthases: regulation and function. European Heart Journal. 2011;33(7):829-837. </li>
+              	<li id="ref8"> Goel M. Aqueous Humor Dynamics: A Review~!2010-03-03~!2010-06-17~!2010-09-02~! The Open Ophthalmology Journal. 2010;4(1):52-59. ‌</li>
+                <li id="ref9">Pozuelo J, Compañ V, Gonzalez-Meijome JM, Mollá S. Oxygen and ionic transport in hydrogel and silicone-hydrogel contact lens materials: An experimental and... ResearchGate. Published February 2014. Accessed October 25, 2020. </li>
+            	<li id="ref10">Larrea X, Bu¨chler P. A Transient Diffusion Model of the Cornea for the Assessment of Oxygen Diffusivity and Consumption. Investigative Opthalmology & Visual Science. 2009;50(3):1076.</li>
+                <li id="ref11">Borland C, Moggridge G, Patel R, Patel S, Zhu Q, Vuylsteke A. Permeability and diffusivity of nitric oxide in human plasma and red cells. Nitric Oxide. 2018;78:51-59. </li>
+               <li id="ref12">Cerviño A, Gonzalez-Meijome JM, Ferrer-Blasco T, Garcia-Resua C, Montes-Mico R, Parafita M. Determination of corneal volume from anterior topography and topographic pachymetry: application to healthy and keratoconic eyes. Ophthalmic and Physiological Optics. 2009;29(6):652-660.</li>
+                <li id="ref13">Cunanan C. Ophthalmologic Applications: Glaucoma Drains and Implants. Biomaterials Science. Published online 2013:940-946.</li>
+                <li id="ref14">Classify corneas simply as average, thin or thick. Healio.com. Published 2020. Accessed October 25, 2020.</li>
+                 <li id="ref15">Mashige KP. A review of corneal diameter, curvature and  thickness values and influencing factors*. African Vision and Eye Health. 2013;72(4).</li>
+                <li id="ref16">Huang G. Anterior Chamber Depth, Iridocorneal Angle Width, and Intraocular Pressure Changes After Phacoemulsification. Archives of Ophthalmology. 2011;129(10):1283. </li>
+                 <li id="ref17">Vyzulta (Latanoprostene Bunod) Ophthalmic Solution. Fda.gov. Published 2017. Accessed October 27, 2020.</li>
+                <li id="ref18">Addis VM, Miller E. Latanoprostene bunod ophthalmic solution 0.024% in the treatment of open-angle glaucoma: design, development, and place in therapy. Clinical Ophthalmology. 2018;Volume 12:2649-2657.
+</li>
+                <li id="ref19">Karki R, Meena M, Prakash T, Rajeswari T, Goli D, Kumar S. Reduction in drop size of ophthalmic topical drop preparations and the impact of treatment. Journal of Advanced Pharmaceutical Technology & Research. 2011;2(3):192.</li>
+            </ol>
            </div>
          </section>
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Difference between revisions of "Team:NCKU Tainan/Model"

Latest revision as of 03:34, 28 October 2020

Model

Surfactant between Experimental Data and Theories

Overview

Background

Our goals

Model 1: Deformation of Contact Lens

Model 2: Nitric Oxide Diffusion Model

Overview

Background

Model

Model 3: Effectiveness of Eye kNOw

References