Created by Susan Stagg-Williams, Dieter Andrew Schweiss, Gavin Sy, and H. Scott Fogler, 1994
Updated by Apeksha Bandi, Gustav Sandborgh, and Arthur Shih, 2013

Case 4: Oops! That was a little too much antivenom


Learning from your last encounter, you now have antivenom prepared in case a cobra were to bite you. After accidentally slipping while climbing a hill, you feel something strike your left leg. You haphazardly reach into your pocket and inject antivenom into your thigh. Right after the antivenom injection had been administered, you notice a smaller young cobra slither away. You had just accidentally injected approximately ten times too much antivenom! In this case, we will explore what happens when too much antivenom has been injected.

Receptor Sites Analysis

The equations we'll enter into Polymath are based on the additional information given in the problem statement and the equations derived earlier.

Polymath Code and Results

Our Polymath code for Case 4 can be downloaded using the link below.

Download the Code (.pol)

Let's take a look at the resulting plot of the fraction of free sites versus time:

From the graph, we see that when the amount of antivenom administered is increased by around 10 times, the fraction of free sites drop down to around 0.10 at around 30 minutes. This means more than 85% receptor sites get blocked which can disturb the respiration process in humans.

Twitch Height Analysis

We will now analyze how twitch height varies with time when an injection of antivenom is administered right when a cobra bites. To compute the values of twitch height, we will generate values of fsv and fsa from Polymath then copy the values to a spreadsheet. The twitch height is then computed using Equation E-40.

Code and Results

Our Polymath code for the Twitch Height Analysis for Case 4 can be downloaded using the link below.

Download the Code (.pol)

As we see in the graph, the twitch height remains close to one and the respiration system of the victim is expected to function normally throughout the duration.

The twitch height drops below 0.243 which was found to be the threshold limit in case 1. It reaches a minimum value of around 0.15 somewhere near 30 minutes. Since the twitch height drops down significantly below 0.243, we can conclude that if more antivenom is injected then what is required, it can end up leading to the death of the cobra bite victim.