Final answer:
The rate of excretion of a drug administered intravenously is proportional to its plasma concentration and is calculated by multiplying the concentration by the elimination rate constant (κ). It varies as the concentration changes with time due to excretion and metabolism. Drug elimination is affected by the kidneys through processes including glomerular filtration, tubular secretion, and tubular reabsorption.
Step-by-step explanation:
The rate of excretion of a drug that is administered intravenously at a constant rate and is excreted at a rate proportional to the quantity present in the body can be described using the pharmacokinetics principles. Let's denote the constant of proportionality by κ, which represents the elimination rate constant. If the concentration of the drug in the plasma is denoted by 'C', then the rate of excretion, which is how much drug is being removed from the body per unit time, can be mathematically expressed as the product of κ and 'C' (Rate of excretion = κ * C).
For example, if the drug concentration in the plasma is 50 mg/L and the constant of proportionality (κ) is 0.1 per hour, the rate of excretion would be 0.1 * 50 = 5 mg per hour. It's important to note that this rate will change as the concentration of the drug in plasma changes due to continuous excretion and metabolism.
Factors such as glomerular filtration rate (GFR), tubular secretion, and tubular reabsorption play crucial roles in the elimination process of drugs from the body through urine. These factors ensure that water-soluble drugs are adequately filtered and secreted, or reabsorbed, maintaining homeostasis in the body's internal environment.