Calculate the filtered load of a substance that is dissolved in plasma, given a plasma concentration of 0.055 mg/ml and a GFR of 120 ml/min. Consider that 55% of the substance is bound to plasma proteins. Round your answer to one decimal place (for example, a value of 8.55 becomes 8.6 whereas a value of 8.54 rounded to one decimal place is 8.5). Enter your answer in this box: Answer …..mg/min.
The Correct Answer and Explanation is:
To calculate the filtered load of a substance, we use the formula:Filtered Load=GFR×Plasma Concentration of Free (Unbound) Substance\text{Filtered Load} = \text{GFR} \times \text{Plasma Concentration of Free (Unbound) Substance}Filtered Load=GFR×Plasma Concentration of Free (Unbound) Substance
Step-by-Step Solution:
- Given:
- Plasma concentration = 0.055 mg/ml
- GFR (Glomerular Filtration Rate) = 120 ml/min
- 55% of the substance is bound to plasma proteins
- Free (unbound) fraction:
- Only the unbound fraction of a substance is filtered by the glomerulus.
- Unbound percentage = 100% – 55% = 45%
- So, the free concentration of the substance: Free concentration=0.055 mg/ml×0.45=0.02475 mg/ml\text{Free concentration} = 0.055 \, \text{mg/ml} \times 0.45 = 0.02475 \, \text{mg/ml}Free concentration=0.055mg/ml×0.45=0.02475mg/ml
- Filtered load: Filtered Load=120 ml/min×0.02475 mg/ml=2.97 mg/min\text{Filtered Load} = 120 \, \text{ml/min} \times 0.02475 \, \text{mg/ml} = 2.97 \, \text{mg/min}Filtered Load=120ml/min×0.02475mg/ml=2.97mg/min
- Rounded to one decimal place: 2.97→3.0 mg/min2.97 \to \boxed{3.0 \, \text{mg/min}}2.97→3.0mg/min
Final Answer: 3.0 mg/min
Explanation:
The filtered load reflects how much of a substance is filtered from the blood into the kidney tubules each minute. However, only the free (unbound) portion of a substance can pass through the glomerular membrane. Plasma proteins are too large to be filtered, and substances attached to them stay in the bloodstream.
In this case, the total concentration of the substance is 0.055 mg/ml, but since 55% is protein-bound, only 45% is free and available to be filtered. We multiply this free concentration by the GFR to calculate the filtered load. The final step involves rounding the result to one decimal place as instructed.
This concept is important in understanding kidney function and how substances are processed in the body. It helps in pharmacology, nephrology, and clinical diagnostics.
