Lessons · Medicine foundations · the loading dose
The loading dose: fill the space first
A loading dose is the volume of distribution multiplied by the target concentration, both of them given by the problem.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
It is the neatest piece of arithmetic in pharmacokinetics and the units are what make it click: litres times milligrams per litre leaves milligrams, and the litres cancel in front of you. Once you have seen that cancel, the formula stops being a thing to memorise.
How to think about it
If the volume of distribution comes in litres per kilogram, multiply by the weight first to get litres for this person, on its own line. Then multiply by the target concentration in milligrams per litre. Watch the units cancel; if they do not, a figure is in the wrong form.
Worked example
Loading dose = volume of distribution × target concentrationThe formula.
Volume of distribution given as 0.5 L/kg, weight 70 kgPer kilogram, so it is not yet a volume.
0.5 × 70 = 35 L, the volume for this personNow it is litres.
Target concentration 20 mg/L: 35 × 20 = 700 mgLitres times milligrams per litre. The litres cancel and milligrams are left.
Your turn
The volume of distribution is 0.7 L/kg, the weight is 60 kg and the target concentration is 10 mg/L. Write the line that gives the loading dose.
0.7 × 60 × 10 = mg
Solve one, graded on the server
The trap
Leaving the volume of distribution in litres per kilogram and multiplying straight by the concentration. The answer comes out in milligrams per kilogram, which is a different quantity entirely, and it is out by a factor of the person's whole weight.