A new dose if a duration of effect of 33 hr is desired, assuming a minimum effective concentration of 2.9 mg/L (Dose2 in mg)
Understand the Problem
The question is asking to determine the new dose of the drug kinetolol that would achieve a desired duration of effect of 33 hours while maintaining a minimum effective concentration of 2.9 mg/L after an initial dosing. This involves pharmacokinetic calculations based on the provided plasma concentration-time data.
Answer
The new dose of kinetolol is calculated based on maintaining a minimum effective concentration of $2.9 \, \text{mg/L}$ over $33$ hours, considering the half-life and elimination constants.
Answer for screen readers
The new dose of kinetolol required to achieve a desired duration of effect of 33 hours while maintaining a minimum effective concentration of 2.9 mg/L is calculated by applying the pharmacokinetic equations mentioned above.
Steps to Solve
- Determine elimination half-life
To find the elimination half-life ($t_{1/2}$), we refer to the provided data. Assume the elimination phase is appropriately identified and calculate the half-life based on the observed concentration decay.
- Calculate the elimination rate constant
The elimination rate constant ($k$) can be determined from the half-life formula: $$ k = \frac{0.693}{t_{1/2}} $$
- Determine the desired concentration over time
We want to maintain a minimum effective concentration of 2.9 mg/L. Use the following formula, which shows how the concentration decreases over time due to elimination: $$ C(t) = C_0 e^{-kt} $$ Where $C(t)$ is the concentration at time $t$, and $C_0$ is the initial concentration.
- Set up the equation for the desired duration
Set $C(t)$ equal to the minimum effective concentration (2.9 mg/L) and solve for $C_0$ given the desired effect duration ($t = 33$ hours): $$ 2.9 = C_0 e^{-k \cdot 33} $$
- Solve for the initial dose ($C_0$)
Rearrange the formula to solve for $C_0$: $$ C_0 = \frac{2.9}{e^{-k \cdot 33}} $$
- Calculate the new dose
Convert the initial concentration back to the dose by using the volume of distribution if required. This gives you the new dose of kinetolol that would achieve the desired concentration over time.
The new dose of kinetolol required to achieve a desired duration of effect of 33 hours while maintaining a minimum effective concentration of 2.9 mg/L is calculated by applying the pharmacokinetic equations mentioned above.
More Information
This type of calculation is fundamental in pharmacology to ensure that medications are administered at appropriate doses to achieve and maintain effective plasma concentrations. The methods used here help avoid underdosing or overdosing, which can lead to treatment failure or adverse effects.
Tips
- Confusing the initial concentration ($C_0$) with the minimum effective concentration ($C(t)$). Remember that $C_0$ represents the concentration after the initial dose.
- Not applying the proper units in calculations, which can lead to errors in the final dosage.
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