Team:IISER-Tirupati India/Engineering

Ovi-Cloak

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INDEX

Introduction
Module-1
Module-2
Module-3A
Module-3B
References

Introduction

The engineering cycle is a learning process with properly defined steps to develop a suitable method for improving the biological system. The process starts with identifying the problem one is dealing with and the questions that need to be addressed to solve the problem. Next, it is necessary to perform background research on the topic and to come up with a draft design suitable to solve the problem. This design is then constructed and tested using various methods depending on the problem and the results are interpreted. After analysing the results, if the solution doesn't seem to be satisfactory then redesigning is done based on the shortcomings in the previous solution and the next solution is tested again. This process continues until one finds a solution that best fits the problem.

All modules of our project went through iterations. This page tries to explain these iterations in the most convenient way.

Starting with the delivery system, the first idea was to modify an Intrauterine Device (IUD) and deliver the Genetically Modified Organisms (GMO) through the ostia. Its calculations were done, but many drawbacks came up for which an alternative solution of hysteroscopic delivery method was chosen.
Post-delivery, the bacteria colonizes the region that we studied through a growth model.
After reaching the stationary phase, the bacteria should produce ovastacin during the right period of time i.e. during ovulation and the fertile window, and genetic circuit needs to be designed for the same.
Similarly, for reversal of contraception and biosafety, the kill switches had to be designed and improved upon.

Module 1. Delivery System

Summary

In our idea, the GMO needs to be introduced into the fallopian tube up to the ampulla which is the desired location. The simplest way that one could think of introducing the GMO is to inject a GMO containing solution directly into the fallopian tube. Nevertheless, this gives rise to some problems and drawbacks. The next method utilizes a long, thin catheter that can reach up to the ampulla and comes with a camera, this was a simplified description of a hysteroscope that helped us overcome those obstacles.

The dimensions of the fallopian tube showing intramural ,isthmus and ampulla — Fig 1.1 The dimensions of the fallopian tube based on [35].

An ovum takes about 4-5 days to travel from the ovary to the uterus [1]. During the course of its journey, it spends about 3 days in the ampulla and gets degraded if it is not fertilized by the sperm. In order to prevent fertilization of ovum by the sperm we need to ensure that the ovum gets hardened even before a single sperm can reach it and penetrate it’s membranes. Thus we want to get as close to the ovum as possible.
Ampulla would thus be the intended location to introduce the GMO because the ovum would more or less be stationary. The commensal of oviduct Lactobacillus acidophilus is genetically modified to produce a protease called ovastacin that hardens the ovum to prevent sperm penetration. The aim of our first module is the idea of delivery of our GMO into the fallopian tube at the appropriate location.

Aim: To find the most feasible delivery mode

Iteration 1:

1.1 Design:

The fallopian tube can be approximated to be a cylindrical tube of diameter 7.5 mm. The fluid containing our bacteria must be of significant density difference from the oviductal fluid (1260 kg/m³) [36].

Fig 1.2 Low fluid density injected in a confined channel containing relatively denser fluid. Source: [2]

The fluid is then injected from the ostia or into the uterus at a volumetric flow rate of Q.

$q\rightarrow$ Volumetric flow rate
$g \rightarrow$ Acceleration due to gravity (g=9.8 m s^-1)
$h_0 \rightarrow$ Diameter of cylindrical tube (h₀ = 7.5 mm)
$\mu_1 \rightarrow$ Dynamic Viscosity of injected fluid (Water = 6.913 × 10^{− 4} Pa $\cdot$ s)
$\mu_2 \rightarrow$ Dynamic viscosity of oviductal fluid (Oviductal Fluid = 0.799 Pa $\cdot$ s)
$\rho_1 \rightarrow$ Density of injected fluid (Water= 1 g cm ³)
$\rho_2 \rightarrow$ Density of oviductal fluid (Oviductal fluid 1.26 g cm ³)
$u_2 \rightarrow$ Velocity of denser fluid [37] (V_fluid= 0.07 s^{− 1} [38])

1.2 Build:

Refering to [2]. The injection of fluid is done either with the help of a modified IUD or a catheter. An IUD was known to reach or get closer to both the ends of the ostia, and it was considered that bacterial fluid could then be delivered to both the fallopian tubes at once. The concern was to check how long the bacteria would take to reach the desired site i.e. ampulla and also ensure minimum invasion.

1.3 Test:

Defining,

\begin{equation}\tag{1.1.1} x_c=\frac{\Delta \rho g h_0^4}{\mu_1 q} \end{equation} \begin{equation}\tag{1.1.2} t_c=\frac{\Delta \rho g h_0^5}{\mu_1 q^2} \end{equation} \begin{equation}\tag{1.1.3} H=\frac{h_1}{h_0} \end{equation} \begin{equation}\tag{1.1.4} X=\frac{x}{x_c} \end{equation} \begin{equation}\tag{1.1.5} T=\frac{t}{t_c} \end{equation} \begin{equation}\tag{1.1.6} X_f=\frac{x_f}{x_c} \end{equation} \begin{equation}\tag{1.1.7} \lambda=\frac{\mu_1}{\mu_2} \end{equation} \begin{equation}\tag{1.1.8} \Delta \rho=\rho_2-\rho_1 \end{equation}

calculating,

$\lambda=$ 1.156 × 10³ Pa $\cdot$ s
$\Delta \rho=$ 0.26 g cm ³)
$x_c=\frac{1.1674\times10^{-6}}{q}$ m
$t_c=\frac{8.7555\times10^{-10}}{q^2}$ s

Early Time (T << 1)

In the early time period, i.e., T << 1, the horizontal length of the current x << x_c, or equivalently, X << 1.

So, the advective term is negligible compared with the diffusive term. In addition, in the early time period, both H <<1 and |($\lambda$ −1)H| << 1 hold such that the current is effectively unconfined. Then, the advection-diffusion equation is reduced to a nonlinear diffusion equation, which describes the spreading of a viscous gravity current on an impermeable horizontal substrate,

\begin{equation}\tag{1.1.9} H(X,T) \approx 1.6679 \left(1-\frac{X}{0.8 T^{\frac{4}{5}}}\right)^{\frac{1}{3}}T^{\frac{1}{5}} \end{equation}

Setting H=0, we get

\begin{equation}\tag{1.1.10} X(T) \approx 0.8 T^{\frac{4}{5}} \end{equation}

Late Time

At longer times, the convective term can no longer be neglected. In the late time period, by neglecting the diffusive term, the full governing equation is approximated by the nonlinear hyperbolic equation. Under the series expansion

\begin{equation}\tag{1.1.11} \lim\limits_{H \rightarrow 1^-}\frac{dF}{dH}=\frac{X}{T}=\frac{6}{\lambda}(1-H)+\frac{6(5\lambda-6)}{\lambda^2}(1-H)^2+O((1-H)^3) \end{equation}

Knowing that $\lambda$ is a large number we choose only the first term.

\begin{equation}\tag{1.1.12} H \approx 1-\frac{\lambda}{6}\frac{X}{T} \;,\; H \rightarrow 1^{-} \end{equation}

Setting H=0, we get

\begin{equation}\tag{1.1.13} X_f=\frac{6}{\lambda}T \end{equation}

For higher order terms

\begin{equation}\tag{1.1.14} \frac{d^2 H(\xi)}{d\xi^2}=10\left(\frac{dH(\xi)}{d\xi}\right)^2 \end{equation}

where,

\begin{equation}\tag{1.1.15} \xi=\frac{X}{T} \end{equation}

The plot for the injected fluid length vs. time for different time regions is given below.

Graphical representation of liquid front distance with respect to time. — Fig 1.3 Liquid front distance with respect to time.

From the above equations, using q=20 mL s^{− 1} we get

By early time, it can take anywhere from 1.259 or 1.804 seconds for the injected fluid to reach the ampulla.

By the later time, it can take anywhere from 216.711 to 288.948 seconds for the injected fluid to reach the ampulla.

Since, x_f < x _c we take the early time approximation

1.4 Learn:

As suggested by Gynecologist Dr Prameela Menon and Prof Debjani Paul during our iHP meetings, modifying an existing device like an IUD can get complicated and if there exists a method for a similar goal it would be easier to work with. Also, more the modifications in a device, more would be the rise in price of the process and hence not suitable for mass consumption. Another disadvantage of using a modified IUD was that depending on different sizes of the uterus, the ends of the device may or may not reach the fallopian tube entrances on both sides, and the vagina can also get colonised by the GMO.

Other disadvantages:

The fluid contains the GMO which is in contact with all of the oviduct contaminating the undesirable regions
The cross-section is too small that surface tension comes into play which isn’t taken into account
More GMO are needed to account for undesirable colonisation in other regions

A catheter can do fluid injection into the uterine cavity or it can go up to the ostia or even into the fallopian tube itself. The cost goes up as the injection site is closer to the destination (ampulla) but it minimizes unwanted colonization in other regions.

Iteration 2:

2.1 Design:

In this iteration we wanted to explore a design using a catheter with an idea of its prevailing use in the delivery of gametes or zygote during in-vitro fertilization treatments. We wanted to check if we could build upon the idea to improve this method of delivery for our purposes. The catheter goes inside the oviduct up to the ampulla. Due to peristalsis and other involuntary actions, the procedure is done under the guidance of a medical practitioner and it involves the application of anaesthesia.

2.2 Build:

After some literature mining during the design phase, we found that the procedure best suited for our purpose is hysteroscopy under ultrasound sonography (USG) guidance. We built upon this to find out its working technique. It consists of a catheter of various possible gauges with a camera attached to it for observing the uterine cavity and the ostia of the fallopian tube. Hence we solve the issue of delivering our GMO into different sizes of uteruses using the same device.

After multiple conversations with IVF specialist Dr Sidra Khot and cardiologist Dr Akbar UL Haque, we came to a conclusion that to test the working of hysteroscopy, gynecologists, IVF specialists, and other professionals in related fields are familiar and trained with equipment might conduct clinical trials of the whole process which could only be done as a part of the future aspect after developing our GMO. The modification that we would require for our purpose would be that the injected bacteria is light sensitive, hence light should be used only for guidance, and then the bacteria should be injected under no light.

2.3 Test

The fallopian tube is a system with multiple species: the number of each individual species and the total number of species will oscillate about a certain equilibrium position.

Graph showing average population with respect to time y-axis shows bacterial count and x-axis shows time. — Fig 1.4 The average population with respect to time doesn't change even with a small perturbation for long time scales

First, the final population required is figured out using the diffusion and production models of ovastacin. Then using the following assumptions, a system with multiple species is constructed and inoculum calculated.

Assuming

This system is at a stable equilibrium meaning any perturbation of the system will bring it back to the equilibrium. The equilibrium being the carrying capacity.
The GMO does not have a survival advantage or disadvantage against normal Lactobacillus.
The inner walls of the fallopian tube are smooth.

$M \rightarrow$ Carrying capacity of the system for all the commensals.
$N_0 \rightarrow$ Initial amount of Normal Lactobacillus acidophilus
$N_f \rightarrow$ Final amount of Lactobacillus acidophilus
$I \rightarrow$ Inoculated/introduced amount of GMO
$a \rightarrow$ Final amount of GMO which was calculated in Diffusion section in Model Page

The derivation is based on the steady state achieved by the population after a long time. Since the oviduct is highly competitive we assume that the average proportion of each species is constant. So the ratios are given below as

\begin{equation}\tag{1.2.1}\chi_1=\frac{N_0}{M}=\frac{N_f+a}{M}\end{equation} \begin{equation}\tag{1.2.2}\chi_2=\frac{I}{N_0}=\frac{a}{N_f}\end{equation}

Assuming the survival factors of GMO and Lactobacillus are the same we continue by cancelling ‘M’ on both sides and substituting for ‘N_f’, Isolating ‘I’ we get,

\begin{equation}\tag{1.2.3}I=\frac{aN_0}{N_0-a}\end{equation}

By, [33] the microbe count is 10⁸ CFU/mL of oviductal fluid.

In, [34] 1-5% is Lactobacillus acidophilus. which gives us 10 ⁶ to 5 × 10 ⁶ CFU/mL

Treating the ampulla as a truncated cone of radii 10 mm and 5 mm of length 5 cm to 8 cm [35]. The volume of the ampulla region of the oviduct is 9.16 to 14.66 mL which means there’s a minimum of 0.92 × 10 ⁷ to 7.3 × 10 ⁷ CFU of Lactobacillus acidophilus in the ampulla.

This gives us ‘I’ to be 6835 to 6830 CFU.

Let the radius of the droplet (r_drop) be 0.75 cm. Hence volume of the droplet is 1.76 mL.

Now calculating

\begin{equation}\tag{1.2.4}\mathrm{The \;number\; of \;transfers\; required\; for\; the\; whole\; ampulla\;}=\frac{L}{2r_{drop}}\end{equation}

where, L is the length of the ampulla (5 to 8 cm).

The number of such transfers is hence, 6 or 4.

\begin{equation}\tag{1.2.5} \mathrm{The\; concentration\; thus\; prepared\;} = \left(\frac{I}{\mathrm{Number\; of\; transfer\;\; \times\;\; Volume \;of\; droplet}}\right)\end{equation} 644.165 to 966.955 CFU/mL.

To prevent possible blockage saline solution can be used although it was assured to us by the IVF specialist that it’s not likely to happen

If it’s a 0.1 mL droplet ($r_{drop}=0.288 cm $) then 9 to 14 transfers would be required and 4882.14 to 7588.89 CFU/mL solution would be prepared.

2.4 Learn:

The hysteroscopy procedure inserts the catheter. Since the ostia of the fallopian tube is a dynamical structure, it’s under USG guidance.

Fig 1.5 Schematics of the hysteroscopy procedure. Refer to the Model page for more explanation.

A solution of GMO is prepared either in saline (for biosafety) or an oil sono-opaque transfer, which can help locate the injected fluid’s presence. 2.9 mm is the hysteroscope diameter, and injectable volume will be 2-3ml, using air as the pushing entity. Based on current assumptions, $\approx$ 10³ CFU/mL inoculum concentration of bacterial fluid is needed using air is used to push out the 1.76 mL of a droplet containing the bacteria under USG guidance multiple times (usually 4 to 6 times) as much as it’s desired.

Now that the delivery of GMO has a clear picture, we move on to focus on the design of the GMO i.e contraception. The modified bacteria must be able to express ovastacin at the right time, and there shouldn’t be excess production of the protease. The next iteration discusses how the genetic circuits were modified in order to attain a fairly accurate expression pattern.