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Chapter 2: Problem 4

What dose of a drug should be injected intravenously every 8 hours to obtain an average steady-state plasma drug concentration of \(5 \mathrm{mg} / \mathrm{L}\) if the drug's volume of distribution is \(30 \mathrm{~L}\) and its clearance is \(8 \mathrm{~L} / \mathrm{hr}\) ? (A) \(40 \mathrm{mg}\) (B) \(80 \mathrm{mg}\) (C) \(160 \mathrm{mg}\) (D) \(320 \mathrm{mg}\) (E) \(400 \mathrm{mg}\)

Short Answer

Expert verified
The required dose is 320 mg; the correct answer is (D).

Step by step solution

01

Understand Key Terms

To solve the problem, it's important to understand key terms such as volume of distribution, clearance, dose, and steady-state concentration. Volume of distribution (Vd) is the distribution of the drug in the body, clearance (Cl) is the volume of plasma from which the drug is removed per unit time, dose is the amount of drug administered, and steady-state concentration is the concentration where the overall intake of a drug is fairly in dynamic equilibrium with its elimination.
02

Identify Necessary Formula

The formula to calculate the dose for achieving a steady-state concentration with multiple dosing is: \( \text{Dose} = ( \text{Cl} \times \text{Css} \times \text{dosing interval} ) \) where Css is the desired steady-state concentration, Cl is the clearance rate, and dosing interval is the time between doses.
03

Plug in the Given Values

Now, substitute the given values into the formula:- \( \text{Clearance} (\text{Cl}) = 8 \text{ L/hr}\)- \( \text{Steady-state concentration} (\text{Css}) = 5 \text{ mg/L}\)- \( \text{Dosing interval} = 8 \text{ hours}\)Thus, we have:\[ \text{Dose} = (8 \text{ L/hr} \times 5 \text{ mg/L} \times 8 \text{ hours}) \]
04

Calculate the Dose

Perform the calculations:\[ \text{Dose} = 8 \times 5 \times 8 = 320 \text{ mg} \]Thus, the dose required is 320 mg.
05

Choose the Correct Answer

Refer to the provided options and select the dose closest to our calculation: - (A) 40 mg - (B) 80 mg - (C) 160 mg - (D) 320 mg - (E) 400 mg The correct answer based on the calculation is (D) 320 mg.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Volume of Distribution
The volume of distribution (Vd) is a very important concept in pharmacokinetics. It describes how a drug disperses throughout the body's compartments. Imagine your body as a container filled with different compartments like blood, tissues, and organs. The volume of distribution gives you an idea of how well a drug spreads out in this container. It is expressed in liters (L) and helps in understanding where the drug goes after it enters the body.
  • A larger Vd suggests the drug extensively enters tissues and may not stay primarily in the blood plasma.
  • A smaller Vd indicates the drug stays mostly in the blood stream.
Knowing the volume of distribution helps doctors and pharmacists tailor drug dosages to individual needs, as it affects how much of a drug is available in the bloodstream to exert its effects.
Drug Clearance
Drug clearance (Cl) refers to the body's ability to remove a drug from the bloodstream. It is the rate at which the drug is eliminated and is usually expressed in liters per hour (L/hr). When a drug is cleared, its concentration in the blood decreases. Understanding clearance is key to maintaining the right amount of medication in the system.
Some factors that affect drug clearance include:
  • Kidney and liver function: These organs are crucial for metabolizing and excreting drugs.
  • Drug interactions: Other drugs can enhance or decrease clearance by affecting liver enzymes.
Proper dosing considers the drug's clearance rate to ensure a steady and effective concentration is maintained in the body. The higher the clearance rate, the more frequently a drug needs to be administered or a higher dose may be required.
Steady-State Concentration
Reaching a steady-state concentration means the amount of drug being administered matches the amount being eliminated. This balance is significant for long-term drug therapy. Once the steady-state is achieved, the drug's effects become predictable and consistent, helping to manage chronic conditions effectively.
Here鈥檚 what you need to know:
  • Achieving steady state: This depends on the drug's half-life and dosage schedule. It usually takes about 4-5 half-lives for a drug to reach a steady state.
  • Importance: At steady-state, monitoring and adjusting the dose becomes easier, ensuring therapeutic effectiveness while minimizing side effects.
Using the right dosing strategies keeps the drug concentration balanced within a desirable range, enhancing treatment outcomes.
Intravenous Dosing
Intravenous dosing, or IV dosing, involves administering medication directly into the bloodstream. This method offers immediate drug availability and is useful for drugs that require rigorous control over their concentrations.
Consider these benefits of intravenous dosing:
  • Rapid action: Drugs act quickly as they bypass absorption barriers found in other routes.
  • Precise control: IV dosing allows for exact control over the drug's concentration levels in the blood, crucial for drugs with narrow therapeutic windows.
This makes intravenous administration essential for emergency situations, critical care, or when precise dosing is mandatory, ensuring the patient receives the optimum therapeutic effect without delay.

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Most popular questions from this chapter

If a drug exhibits first-order elimination, then (A) the elimination half-life is proportional to the plasma drug concentration (B) the drug is eliminated at a constant rate (C) hepatic drug metabolizing enzymes are saturated (D) drug clearance will increase if the plasma drug concentration increases (E) the rate of drug elimination \((\mathrm{mg} / \mathrm{min})\) is proportional to the plasma drug concentration

After a person ingests an overdose of an opioid analgesic, the plasma drug concentration is found to be \(32 \mathrm{mg} / \mathrm{L}\). How long will it take to reach a safe plasma concentration of \(2 \mathrm{mg} / \mathrm{L}\) if the drug's half-life is 6 hours? (A) 12 hours (B) 24 hours (C) 48 hours (D) 72 hours (E) 1 week

If food decreases the rate but not the extent of the absorption of a particular drug from the gastrointestinal tract, then taking the drug with food will result in a smaller (A) area under the plasma drug concentration time curve (B) maximal plasma drug concentration (C) time at which the maximal plasma drug concentration occurs (D) fractional bioavailability (E) total clearance

The volume of distribution of a drug will be greater if the drug (A) is more ionized inside cells than in plasma (B) is administered very rapidly (C) is highly ionized in plasma (D) has poor lipid solubility (E) has a high molecular weight
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