MEDICATION CONCENTRATION IN THE BLOODSTREAM A lot of medication is taken on a da
ID: 93394 • Letter: M
Question
MEDICATION CONCENTRATION IN THE BLOODSTREAM
A lot of medication is taken on a daily basis. Why is it, if taken as prescribed correctly, that oral medication does not rise to a dangerous level in our bloodstream? It is because only part of the medication remains in your system from one day to the next. But still part of the medication does remain in your system. The following lab will help to understand part of the mathematical representations of medication concentration in the bloodstream.
Learning outcomes:
Upon completion student will be able to:
Use growth rates to analyze quantitative data in various contexts including real world data, student generated data or data found in current media.
Represent linear and exponential models as equations, tables, graphs and verbal descriptions.
Use interpolation and extrapolation of real world data describe when each is appropriately used.
Scoring/Grading rubric: Each section is individually detailed concerning scoring.
Directions: Working in groups of 3, answer the questions. Each student should complete the handout, but only one will be collected from each group. At the end of the activity, pick one paper to hand-in. All group members will sign to indicate that they agree with all the answers. Do not sign unless you are happy with the group product. After completing lab, you should have a better mathematical understanding on how some medications are sustained in the body through formulas and through graphing.
Based on the experiences of members in your group, when taking medication over a prolonged period of time, what orders will the doctor give you when a medication is prescribed? Scoring: Each question is worth 2 points each.
How do you take the medication?
For how long do you usually take the medication?
What are you usually told to do if you miss a dose?
You take your medicine as instructed:
Perhaps you’ve wondered this before: Why can I take oral medication day after day and not build up a dangerous level in your system? We will seek to answer this question now.
Injected drugs, shots, and patches are carried in the blood and absorbed directly into the body but those taken orally move through the digestive tract to the liver. After the medication is in the liver, the liver will process part of that medicine out of the body. Scoring: This section is worth 12 points.
Let's suppose that a particular medication experiences a 25% reduction in bodily presence per day, and that you have been prescribed one pill each day.
On Day 1, you take one pill. What percentage is left on Day 2 from Day 1? _____
So, as a decimal, how much of the one pill you took on Day 1 do you have left on Day 2? _____
Indicate the addition required after you add the pill you take on day 2: _____
What is the total concentration on day 2? _____
From this, continue to proceed from day to day to see what happens to the concentration of the medication as successive days go by, making sure to keep 4 decimal places.
The Calculator Process:
The construction of this chart would be easier on a calculator, especially if we wanted to go much further. Start with taking a single pill on day 1:
Now, retain 75% of that pill and take a new pill (important to use the Ans capability). This shows you day 2's status.
If you continue to hit enter the next few days will be shown, as the Ans answer value is repeatedly captured from the status of the previous day. This display now also shows the status on days 3, 4 and 5. Now, keep pressing ENTER and count out the days as you go. If your calculator does not allow you to simply press ENTER, then either use the previous entry button (scroll up on most calculators) or continue to use the Ans feature of the calculator.
Complete the following table using your calculator:
What is the concentration of the drug in your system by day 5? ______
What is the concentration of the drug in your system by day 21? ______
What concentration do you get close to but don’t ever seem to reach? _______
Oh no! You forgot!
Life gets in the way sometimes and oh no! You forgot to take your medicine one day. What happens if you skip a day, and then go back to your regular routine? Scoring: This section is worth 10 points.
Start with what you found on Day 21: ______
This will start Day 22 but DO NOT add a pill only take 75% of it: ______
This will begin day Day 23. On Day 23 you remember to take your pill. Hooray!
Now, complete the following chart:
Now continue with the following table using the calculator trick described before:
How long does it take for your body to regain the level you were on before you forgot your medicine?
You double up
Let’s go back to Day 21 when you were being so good at taking your medication, and on Day 22 you thought you forgot, but you did NOT forget, and you took your medication TWICE! But on Day 22 you regain your senses and only take one pill. Let’s see what happens. Scoring: This section is worth 10 points.
Start with what you found on Day 21: ______
This will start Day 22. Take 75%: ______
Add 2 pills: ______
This will begin day Day 23. On Day 23 you remember to take ONLY ONE pill. Hooray!
Now, continue with the following table using the calculator trick described before:
Even after 18 days your body is still not quite at the level it was before. Does this explain why patients are told to take medicine as prescribed? In both previous examples of forgetting and doubling up what could be the ramifications?
Predictions: This section is worth 31 points.
Could we have predicted the steady-state dosage level of the equivalent of 4 tablets per day without using the calculator to see it?
Hint: If you were at a steady level of medication, then the level from one day to the next is the same. Pick a variable and let it represent the level of medicine in your body:
How did you determine what the next level dosage was when you were taking your medication as prescribed?
If the goal is for the previous day total and the present day total to be the same, let the variable you picked previously represent both totals:
Then solve for the variable:
What if the level of metabolism is 40% per day?
What it if is 10% per day?
What absorption rate would lead to a steady-state level of 6 tablets? *Pick a different variable for absorption rate and hold the totals the same*
First-Order Kinetics. This section is worth 31 points.
What we have been examining is medicine that is considered first-order kinetics; i.e., medication that is taken on a regular basis that depletes from the body with a constant fraction. Every day, part but not all of the medication is depleted from your system. So, thinking about a graph of this medication where a constant fraction of the medication is metabolized per unit time, we might arrive at something like the following:
Let’s analyze the graph a little more closely. Begin by filling in the following table:
Note that there will be no medication from the 2nd dose at 2 hours because you have not taken it yet and is also true for the 3rd and 4th doses. Therefore, * represents this information in the table.
Now, graph using the information on the table with Time on the x-axis and Concentration as the y-axis. Ordered Pairs will follow with (Time since 2nd Dose, 2nd Dose Amount), (Time since 3rd Dose, 3rd Dose Amount) and (Time since 4th Dose, 4th Dose Amount). Therefore, you will have 9 points on your graph connecting with curved, not straight, lines.
For a single dose of medication in your body that depletes on a % or fractional basis, it will look like the above graph. But not all medication depletes fractionally.
Zero order kinetics...
With a few drugs, such as aspirin, ethanol, and phenytoin, the doses are very large. As the amount of drug rises in the plasma, certain processes that have limited capacity become saturated; i.e., the rate of the process reaches a maximum at which it remains constant degradation due to limited amount of enzymes even if the dose increases; so, it is not proportional to the dose. This is also called rate- limited.
What kind of function does this remind you of? ____________
For Further information you can look at the following website:
http://www.merckmanuals.com/professional/clinical_pharmacology/pharmacokinetics/drug_metabolism.html
Here is an excerpt from that website that applies to what we have done today:
Rate: For almost all drugs, the metabolism rate in any given pathway has an upper limit (capacity limitation). However, at therapeutic concentrations of most drugs, usually only a small fraction of the metabolizing enzyme's sites are occupied, and the metabolism rate increases with drug concentration. In such cases, called first-order elimination (or kinetics), the metabolism rate of the drug is a constant fraction of the drug remaining in the body (i.e., the drug has a specific half-life). For example, if 500 mg is present in the body at time zero, after metabolism, 250 mg may be present at 1 h and 125 mg at 2 h (illustrating a half-life of 1 h). However, when most of the enzyme sites are occupied, metabolism occurs at its maximal rate and does not change in proportion to drug concentration; instead, a fixed amount of drug is metabolized per unit time (zero-order kinetics). In this case, if 500 mg is present in the body at time zero, after metabolism, 450 mg may be present at 1 h and 400 mg at 2 h (illustrating a maximal clearance of 50 mg/h and no specific half-life). As drug concentration increases, metabolism shifts from first-order to zero-order kinetics.
Explanation / Answer
1) While prescribing medication, the doctor will give following information about how to take the drug,
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