A subject with a body weight of 60 kg was injected with 10 ml of a 1% (w/v) solution of Evans Blue. After 10 min, the blood was sampled and found to contain 0.035 mg ml^-1 of the dye. What is the subject’s plasma volume in litres?
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To calculate the subject's plasma volume, we can use the dilution principle. The amount of the dye in the blood sample can be used to determine how much dye was initially injected. We can then compare this to the concentration of the dye in the plasma to calculate the plasma volume.
Let's break down the calculation step-by-step:
Step 1: Calculate the amount of dye injected.
To find the amount of dye injected, we need to multiply the volume of the solution injected by the concentration of the dye in the solution.
Amount of dye injected = Volume of solution injected * Concentration of dye in the solution
Given:
Volume of solution injected = 10 ml
Concentration of dye in the solution = 1% (w/v)
Concentration is given in weight/volume (w/v). In this case, 1% (w/v) means that 1 g of dye is dissolved in 100 ml of the solution. Since we have 10 ml of the solution, we can calculate the amount of dye injected as follows:
Amount of dye injected = 10 ml * (1 g/100 ml)
Step 2: Calculate the plasma volume.
To calculate the plasma volume, we need to divide the amount of dye injected by the concentration of the dye in the plasma.
Plasma volume = Amount of dye injected / Concentration of dye in the plasma
Given:
Concentration of dye in the plasma = 0.035 mg ml^-1
The concentration is given in milligrams per milliliter (mg ml^-1). Since the amount of dye injected was calculated in grams, we need to convert the concentration to grams per milliliter:
0.035 mg ml^-1 = 0.035 * 0.001 g ml^-1 (since 1 mg = 0.001 g)
Now we can calculate the plasma volume:
Plasma volume = (Amount of dye injected in grams) / (Concentration of dye in grams per milliliter)
Remember that the dye concentration is given in milligrams per milliliter, so we'll need to convert the result back to liters.
Calculating the Solution:
Amount of dye injected = 10 ml * (1 g/100 ml) = 0.1 g
Concentration of dye in the plasma = 0.035 * 0.001 g ml^-1 = 0.000035 g ml^-1 (1 mg = 0.001 g)
Plasma volume = 0.1 g / 0.000035 g ml^-1 = 2857.14 ml
Converting to liters:
Plasma volume in liters = 2857.14 ml * (1 L/1000 ml) = 2.86 L
Therefore, the subject's plasma volume is approximately 2.86 liters.