Team:BostonU HW/Model

BostonU_HW

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Summary

iGEM has done an excellent job of defining modeling projects related to wet lab experiments, however since MARS is a hardware project this was our team’s method of modeling our work.

During the process of developing the MARS repository there were many questions that we found ourselves asking consistently:
  1. Why is my chip not working?
  2. Is this what my chip should be doing right now?
  3. What part of my chip is failing?

The common theme within these questions was our inability to explain why our microfluidics chips were not functioning correctly. When we had performed a literature review there were no papers published regarding a standardized method of evaluating microfluidic chips. With that problem in mind the team went on to create an evaluation system known as Fluid Functionality.

Fluid Functionality is based around analyzing the functionality of each primitive in a microfluidic chip (refer to Microfluidics 101 on our Wiki for more information regarding primitives.) These primitives can be thought of as the individual electrical components that are a part of a larger circuit. If one and/or more primitive malfunctions the entire system will not work. However, how do we go about analyzing each primitive? Primitive analysis can be broken up into two parts:
  1. Qualitative: Observations that provide any indication of failure.
  2. Quantitative:C alculations that show whether your primitive failed or not.

By inter-relating the qualitative failures we have observed and with a corresponding quantitative analysis method we can explain why a microfluidic chip is not working. If for example a primitive has a qualitative failure and fails its quantitative test, than there is something wrong with the primitives dimensions. But if a primitive has a qualitative failure and passes its quantitative test, than there is some other source of error such as poor assembly.

The sections below describe the qualitative and quantitative analyses we have developed to evaluate microfluidic chips.

Qualitative

Leak (Initial)

This qualitative failure is characterized by liquid leaking out of a channel and/or primitive into the space between the PDMS and flow layer. An initial leak occurs almost immediately after a liquid passes the area of the leak. Regardless of scale, these leaks are considered a failure mode.

Leak (Over Time)

This qualitative failure is characterized by liquid leaking out of a channel and/or primitive into the space between the PDMS and flow layer. A leak that occurs over time is not characterized by an initial leak growing over time but as a leak that appears a significant amount of time after liquid has passed the location of a leak. These leaks can be seen in situations where a seal degrades during incubation period, leading to a new leak forming minutes after liquid initially passed through a section. Regardless of scale, these leaks are considered a failure mode.

Air Bubble

This qualitative failure is characterized by an air bubble being present within a channel or primitive. Air bubbles can affect proper liquid flow and can reduce the accuracy of design features such as time-dependent mixers and metering. Regardless of scale, air bubbles are considered a failure mode.

Liquid does not cross an OPEN Valve

This qualitative failure is characterized by liquid not crossing over a valve that has been opened by actuating the corresponding syringe on the control layer. This failure can exist in many forms, such as liquid pausing after filling the first portion of the valve and never crossing into the second section or leakage around the first portion of a valve. This failure is often accompanied by leakage due to pressure buildup.

Liquid crosses a CLOSED Valve

This qualitative failure is characterized by a liquid crossing over a valve that is closed, meaning that it’s corresponding control syringe has not been actuated. This failure can exist in many forms, such as liquid leaking over a valve that has never been opened before or leaking over a valve that was previously opened by is not closed. This failure can lead to contamination of liquids as well as inaccuracies with features such as metering.

Mixer does not mix liquids sufficiently

This qualitative failure is characterized by the final output of a mixer not being sufficiently mixed. This failure can be dependent on the chip being tested, as certain procedures will have varying levels of tolerance regarding mixture homogeneity. In general, liquids exiting a mixer should be relatively homogenous; a quantitative calculation of mixing can be performed to calculate how homogeneous the final mixture is.

Quantitative

PSI Calculation

When a chip's internal pressure exceeds the maximum pressure that the sealing can withstand many complications such as leaks will ensue. In order to evaluate whether the chip will be able to function without these issues a PSI calculation is needed to be performed. This quantitative test is utilized to measure the internal pressure of a specific primitive inside your microfluidic chip. The MARS chips have all been manufactured using Makerfluidics, and have been evaluated to withstand an internal pressure of up to 5 PSI. To calculate the pressure in a given primitive the following three equations need to be used.
  1. \[10h < w\] or \[2h>w\]

  2. \[12\mu L/wh^{3} < R_{fluid} < 32\mu L/wh^{3}\]

  3. \[\Delta P=R_{fluid}Q\]
Equations a-c are used to describe the relationship of pressure within a channel of a given length, width, and height. Equation a is used to determine which formula in equation b will provide a better approximation of fluid resistance based on the primitive dimensions. After determining an approximate value of fluid resistance, PSI can be calculated using equation c. Equation c is analogous to Ohm’s law but is used for fluid dynamics. The PSI value is directly proportional to both the fluid resistance and the flow rate. These calculations were written as a C++ file which can be compiled and executed.

Mixer Effiency

The mixing of two fluids is something that can often be qualitatively observed, however in order to properly perform an experiment certain amounts of mixing must be achieved. In order to evaluate the degree of which fluids are being mixed in a mixer primitive a mixer efficiency test is needed to be performed. This quantitative test is broken down into a two part process:
  1. Image Processing
    2. After running fluid through your mixer, pictures need to be taken at the regions prior to entering the primitive and after it exits the primitive. In order to obtain RGB data from these images, image processing software such as ImageJ need to be implemented. Using ImageJ a 1 pixel wide box is created that spans the length of the channel. The two important pieces of data that need to be obtained using this box are the average RGB value over that area, and the RGB value at the outer edge of the channel. After collecting this data we can move on to calculate the mixing efficiency.
  2. Efficiency Calculation
    3. The efficiency of the mixing itself can be measured using the following equation:
    \[\gamma = 1-2\left [ \frac{\int RGB-RGB_{avg}dL}{\int dL} \right ]\]

    Once this value is obtained the channel primitive is able to measured to see if it is suitable to perform the needed function.

Valve Actuation

Even though it can be easily observed that a fluid is not traveling over a valve, it is not easy to determine whether the PDMS is being properly actuated by the primitive. In order to evaluate each valve’s functionality a valve actuation test can be performed.

This quantitative test involves modeling the deflection of the PDMS as a beam fixed at both ends. This is would only be an approximation since the valve geometry would not directly align with the geometry of a beam. The maximum deflection of the beam would be equivalent to the PDMS deflecting into the circle valve.
\[\Delta Z = \left ( \frac{5}{358} \frac{Wl^{3}}{EI}\right )\]

We would substitute the value of length in the max deflection equation with the diameter value of the valve. We can than calculate the force needed in order to fully actuate the PDMS into the circle valve.
\[W = (\frac{358\Delta Z E I }{5D^{2}})\]

The next step is to convert that value of force into a value of pressure. Can use the formula:
\[P = FA\]

Lastly, since we know the volume within the chip and tubing the syringe is connected to we can use Boyle's law to calculate for the amount of volume we would need to pull the syringe back to actuate the valve.
\[P_{1}V_{1} = P_{2}V_{2}\]

Metering Accuracy

The metering primitive was developed to dispense relatively accurate volumes of liquid. However, for biological experiments a certain level of accuracy is required when it comes to volumes used. In order to ensure this primitive is dispensing relatively accurate volumes of liquid, a metering accuracy test must be performed. This quantitative test is broken down into a two part process:
  1. Image Processing
    2. After running the metering portion of your chip, pictures need to be taken before and after the oil has dispensed all the liquid from the metering section. An image processing software, such as ImageJ is then used to analyze how much liquid was metered and how much was actually pushed.

    To analyze the amount of metered liquid, first set the scale for ImageJ in units of microns. Then, using the Rectangle selection tool, draw a rectangle encapsulating the first metered liquid section. This can be seen below:
    METERING PICTURE
    Then, using the measurement tool calculate the area in microns of of the metered section. To find the volume of this metered section, use the following formula:
    \[Volume Metered =Area*Depth*10^{-9}\]

    Repeat this process for each individual metering sections, summing them together as follows to find the total metered volume:
    \[Total Volume Metered =\sum_{i}^{n}Area_{i}*Depth_{i}*10^{-9}\]

    To analyze the amount volume of liquid dispensed, perform the same analysis as before on the image taken after all of the liquid has been displaced by the mineral oil.
  2. Accuracy Calculation
    3. The metering accuracy can be calculated using the following formula:
    \[Percent Accuracy = \frac{Volume Metered}{Volume Dispensed} * 100\]

    The metering error can be calculated using the following formula:
    \[Error(uL) = Volume Metered - Volume Dispensed\]

    If there is a significant error in metering, this suggests that there was either a milling inaccuracy or a leak at a channel and/or valve during the pushing process.