The kidney filters potentially toxic substances in the blood, and thus “clears”

Question

The kidney filters potentially toxic substances in the blood, and thus “clears” the blood of those substances. This clearance function is dependent upon and proportional to the diffusion gradient of the substance across filtering capillaries, i.e. if the concentration of the substance is doubled, twice as much will be cleared from each ml of blood that is filtered. Suppose that the body produces a constant amount of a substance X per unit of time. The kidneys eliminate substance X at a rate directly proportional to the concentration of the substance and the volume of blood cleared each minute (C): elimination = C × [X], where [X] is the steady-state concentration of substance X. Imagine an individual with an initial concentration of X equal to [X]0 who develops kidney disease. Her baseline clearance C0drops to one half of the original (½C0). What is the new steady state concentration of X? (For simplicity, assume that substance X is 100% filtered by the kidney).

The kidney filters potentially toxic substances in the blood, and thus "clears" the blood of those substances. This clearance function is dependent upon and proportional to the diffusion gradient of the substance across filtering capillaries, i.e. if the concentration of the substance is doubled, twice as much will be cleared from each ml of blood that is filtered. Suppose that the body produces a constant amount of a substance X per unit of time. The kidneys eliminate substance X at a rate directly proportional to the concentration of the substance and the volume of blood cleared each minute (C): elimination-C x [X], where is the steady-state concentration of substance X. Imagine an individual with an initial concentration of X equal to [Xlo who develops kidney disease. Her baseline clearance Co drops to one half of the original (½CJ. What is the new steady state concentration of X? (For simplicity, assume that substance X is 100% filtered by the kidney. 1.50lo 2.00lo

Explanation / Answer

The relationship between elimination of substance by kidneys and their plasma concentration is given by the formula,

Elimination = Clearance of the substance x concentration of the substance

Therefore, if the baseline clearance becomes half, the steady state concentration should be doubled inorder to maintain constant elimination rate.

So, the answer for this question is 2.0(X)0

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