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Chapter 12: Problem 6

If the urine concentration of a substance is \(7.5 \mathrm{mg} / \mathrm{mL}\) of urine, its plasma concentration is \(0.2 \mathrm{mg} / \mathrm{mL}\) of plasma, and the urine flow rate is \(2 \mathrm{~mL} / \mathrm{min}\), what is the clearance rate of the substance? Is the substance being reabsorbed or secreted by the kidneys?

Short Answer

Expert verified
The clearance rate is 75 mL/min. The substance is being reabsorbed by the kidneys.

Step by step solution

01

- Identify given values

Identify and list the given values from the problem: \[ \text{Urine concentration} (U) = 7.5 \mathrm{mg} / \mathrm{mL} \] \[ \text{Plasma concentration} (P) = 0.2 \mathrm{mg} / \mathrm{mL} \] \[ \text{Urine flow rate} (V) = 2 \mathrm{mL} / \mathrm{min} \]
02

- Recall the clearance formula

Recall the formula to calculate the clearance rate (C) of a substance: \[ C = \frac{U \times V}{P} \]
03

- Plug in the given values

Substitute the given values into the formula: \[ C = \frac{7.5 \mathrm{mg} / \mathrm{mL} \times 2 \mathrm{mL} / \mathrm{min}}{0.2 \mathrm{mg} / \mathrm{mL}} \]
04

- Simplify the equation

Simplify the right-hand side of the equation: \[ C = \frac{15 \mathrm{mg} / \mathrm{min}}{0.2 \mathrm{mg} / \mathrm{mL}} \] \[ C = 75 \mathrm{mL} / \mathrm{min} \]
05

- Determine reabsorption or secretion

Compare the calculated clearance rate to the Glomerular Filtration Rate (GFR), which is typically around 125 mL/min: \[ \text{Since } C = 75 \mathrm{mL} / \mathrm{min} \text{ and it is less than the GFR}, \text{ the substance is being reabsorbed by the kidneys.} \]

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Key Concepts

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

urine concentration
Urine concentration refers to the amount of a particular substance present in the urine. It is typically measured in milligrams per milliliter (mg/mL). This value is crucial for many calculations involving kidney function because it helps understand how much of a substance is being excreted. For instance, in the exercise you are working on, the given urine concentration is 7.5 mg/mL, which is used to determine the clearance rate.
plasma concentration
Plasma concentration measures the amount of a substance present in the blood plasma. Similar to urine concentration, it is expressed in mg/mL. This value is essential for calculating how effectively the kidneys are filtering substances from the blood. In the exercise, the plasma concentration provided is 0.2 mg/mL. Knowing both the urine and plasma concentrations allows us to use the clearance rate formula accurately.
urine flow rate
Urine flow rate indicates how much urine is produced by the body over a given period of time, usually measured in milliliters per minute (mL/min). It is a vital component in the clearance rate formula. In the given problem, the urine flow rate is 2 mL/min. This rate helps us to understand the volume through which the substance is being cleared by the kidneys over time.
clearance rate formula
The clearance rate of a substance from the body is calculated using the formula: \( C = \frac{U \times V}{P} \) where:
  • \( C \) = Clearance rate
  • \( U \) = Urine concentration
  • \( V \) = Urine flow rate
  • \( P \) = Plasma concentration
This formula helps in understanding how efficiently the kidneys are clearing a particular substance. For our exercise example, substituting the values: \( C = \frac{7.5 \, \mathrm{mg} / \mathrm{mL} \times 2 \, \mathrm{mL} / \mathrm{min}}{0.2 \, \mathrm{mg} / \mathrm{mL}} = 75 \, \mathrm{mL} / \mathrm{min} \).
glomerular filtration rate
Glomerular Filtration Rate (GFR) is a measure of how well the kidneys filter blood, typically measured in mL/min. An average GFR is about 125 mL/min for a healthy adult. The GFR is an important benchmark for comparing clearance rates. In our exercise, the calculated clearance rate is 75 mL/min. Since this is less than the average GFR, it indicates that the substance is being reabsorbed by the kidneys, rather than being fully excreted.
reabsorption
Reabsorption refers to the process by which the kidneys reclaim substances from the filtrate back into the bloodstream. It is an essential function that prevents the loss of necessary substances like glucose and electrolytes. In the problem you're solving, after calculating the clearance rate and comparing it to the GFR, it is concluded that the substance is being reabsorbed. This conclusion is drawn because the clearance rate of 75 mL/min is less than the typical GFR of 125 mL/min.
kidney function
Kidney function includes various processes such as filtration, reabsorption, secretion, and excretion. Together, these processes maintain the body's fluid, electrolyte balance, and waste removal. Understanding kidney function is essential for interpreting values such as urine concentration, plasma concentration, and the clearance rate. Through the exercise, we've touched on key aspects of kidney function, including how substances are filtered and either reabsorbed or secreted. By mastering these concepts, you can better understand how the kidneys work to maintain homeostasis.

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Most popular questions from this chapter

The Gulf toadfish Opsanus beto (p. 561) switches from ammonotely to ureotely when crowded or confined, releasing urea in pulses. Hypothesize why it might do this.

Compare and contrast insect Malpighian tubules and mammalian nephrons. In doing so, describe all tubular transport processes that are linked to the basolateral \(\mathrm{Na}^{+} / \mathrm{K}^{+}\)ATPase in nephrons and the V-ATPase in Malpighian tubules.

Conn's syndrome is an endocrine disorder in some older domestic cats brought about by excessive growth of the adrenal cortex (sometimes due to a tumor). The result is secretion of unregulated excessive aldosterone. Given what you know about the functions of aldosterone, describe what the most prominent features of this condition would be.

If the plasma concentration of substance \(X\) is \(200 \mathrm{mg} / 100 \mathrm{~mL}\) and the GFR is \(125 \mathrm{~mL} / \mathrm{min}\), what is the filtered load of this substance? If the \(T_{\mathrm{m}}\) for substance \(\mathrm{X}\) is \(200 \mathrm{mg} / \mathrm{min}\), how much of the substance will be reabsorbed at a plasma concentration of \(200 \mathrm{mg} / 100 \mathrm{~mL}\) and a GFR of \(125 \mathrm{~mL} / \mathrm{min}\) ? How much of substance \(X\) will be excreted?

Explain tubular maximum \(\left(T_{m}\right)\) and renal threshold. Compare two substances that display a \(T_{\mathrm{m}}\) : one substance that is and one that is not regulated by the kidneys.
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