Solutions

Equation

Let $\alpha_n$ (in mmol/kg) be the readout from the osmometer. Let $\delta$ be the desired volume change. Equating the osmoles before and after the volume change, we have:

$$(V - \delta) \cdot \alpha_n = V \cdot \alpha \\\ \Rightarrow \delta = (\frac{\alpha_n - \alpha}{\alpha_n})V$$

However, since the osmometer's first reading may not be accurate, it is safer to add 50%-70% of the computed $\delta$. So the equation becomes:

$$\delta = (\frac{\alpha_n - \alpha}{\alpha_n})V \cdot 0.5$$

Examples

1. One reads 330 mmol/kg when making 500 mL of NMDG. With a calculator, compute:

   $$\delta = [(330 - 305) / 330] \cdot 500 \cdot 0.5 = 38 \cdot 0.5 = 19\ \text{mL}$$

   In this case, one would add 19 mL of water (dH₂O) to the solution and re-test.

2. One reads 330 mmol/kg when making 1000 mL of ACSF. With a calculator, compute:

   $$\delta = [(330 - 295) / 330] \cdot 1000 \cdot 0.5 = 106 \cdot 0.5 = 53\ \text{mL}$$

   In this case, one would add 53 mL of water (dH₂O) to the solution and re-test.