A patient given digoxin started having side effects like nausea and vomiting. The serum concentration of digoxin was 4 mg/dL. The plasma therapeutic range is 1 mg/dL. If the half-life of digoxin is 40 hours, how long should one wait before resuming the treatment?
40 hours
80 hours
120 hours
140-180 hours
The Correct Option is B
Solution and Explanation
To determine how long to wait before resuming digoxin treatment, we need to calculate the time required for the serum concentration to decrease from 4 mg/dL to within the therapeutic range of 1 mg/dL using the drug's half-life.
The formula for calculating the time for a drug concentration to reduce in half is given by:
\( C_t = C_0 \times \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}} \)
Where:
- \( C_t \) is the target concentration (1 mg/dL).
- \( C_0 \) is the initial concentration (4 mg/dL).
- \( t_{1/2} \) is the half-life (40 hours).
- \( t \) is the time in hours.
Rearranging the equation to solve for \( t \):
\( t = t_{1/2} \times \log_2\left(\frac{C_0}{C_t}\right) \)
Substitute the values:
\( t = 40 \times \log_2\left(\frac{4}{1}\right) \)
\( t = 40 \times \log_2(4) \)
Since \( \log_2(4) = 2 \):
\( t = 40 \times 2 = 80 \) hours
Therefore, one should wait for 80 hours before resuming the treatment to ensure that the concentration of digoxin decreases to the therapeutic range.
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