For every iGEM team, modeling is a necessary part to link wet team experimental results and dry team theories together. In most of the cases, we need to simulate the behavior of chemicals or bacteria, such as distribution or concentration of them. Scientists often utilize partial differentiation equations (PDEs) to describe those target substances’ behavior. However, PDEs usually don’t have solutions due to the lack of strategies to deal with them since the governing equation, say the heat equation, is usually involved in the distance and the time passed by, which implies it to be a function that has 2 variables. Here, we introduce a method that might help future iGEM teams to deal with PDEs—double Laplace transform.

The definition of the single-variable Laplace transform, which is what we normally adopted, is listed below:

The definition of the double-variable Laplace transform (or, double Laplace transform) has a similar form, listed below:

Notice that for single variable Laplace transform, the x domain is defined: { x | x > 0 }, so analogously, the domain of double Laplace transform, (x, y), is defined to be in the first quadrant, namely { (x, y) | x, y > 0 }.

The general properties of double Laplace transform are listed below [1]:

We performed a solution to one example of a partial differential equation using double Laplace transform.

Problem :

Solve the equation

with

Solution :

Taking the double Laplace transform of both side of the equation.

with

taking the inverse Laplace transform with respect to q gives

taking the inverse Laplace transform with respect to p gives the solution

from the property of convolution, we obtained the solution.

In order to create a personalized IOP tracking system, we designed an app - Eye Cloud that works with Eye Screen. Eye Cloud not only displays the IOP value on the phone through the Bluetooth connection but also upload each measurement value to ThingSpeak’s personal account that is convenient for long-term tracking and observation. In addition, it can also be used as a tool for large-scale data collection to assist the development of Eye kNOw or other research related to intraocular pressure.

ThingSpeak is an IoT analytics platform service that allows us to aggregate, visualize, and analyze live data streams in the cloud. We can easily send data to ThingSpeak from Eye Screen, allowing users to upload and record IOP value through a URL (your personal API Keys)

1. Sign up for ThingSpeak.

2. Click Channels > My Channels. Create a new channel.

3. Check the boxes next to Fields 1–3. Enter these channel setting values:

Name: Eye Screen

Field 1: IOP (mV)

4. Click Save Channel at the bottom of the settings.

5. Click API Keys tab and copy the write URL.

1. This is the homepage of Eye Cloud, with our lovely logo. Click the “START” button to start.

2. Then the next screen will ask if you have applied for a ThingSpeak account.

Click “Yes! Ready to start” button to next page and wait for your IOP receiving.

Click “No, click to apply” button to link to ThingSpeak homepage.

Click “No,thanks” button to start directly

3. Click “Bluetooth ” button to connect with Eye Screen when reaching this page.

4. Bluetooth connection screen.

After the IOP value shows on the screen, click the “Record” button to upload data to your ThingSpeak’s personal account, monitoring daily or monthly measurement records.