So a patient asked me this question - "Should I wait 6 months after treatment before trying to get pregnant or would 3 months do?"

Being a little on the Aspberger spectrum I thought that's interesting, let's calculate the answer:

Hello T,

Drugs exit body at a rate determined by what is known at their 1/2 life.

Sofosbuvir has half life of 0.4 hours but main metabolite GS-331007 has half life of 27 hours (call it 1 day)

Ledipasvir has a slower half life of 47 hours (call it 2 days) meaning that level will fall to 1/2 after 2 days.

Let's forget about Sofosbuvir for a moment and consider how long the Ledipasvir will take to fall

So over 1 month ledipasvir levels will fall

Original x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 0.00003 = 3e-5 = 0.003%

After 2 months 0.0000000009 (9e-10)

After 3 months 0.00000000000003 (3e-14)

After 4 months 9e-19

After 5 months 3e-23

After 6 months 8e-28

So very little Ledipasvir will be left after 3 months. For sofosbuvir GS-331007 metabolite the level will be about 8e-28 at the same time (because it exits twice as fast, so it's the same number that Ledipasvir reaches in twice the time).

Now The number 6 x 10^23 (6e23) is called Avogadro's number. It's an interesting number because if I have:

- 529g of Sofosbuvir I have what is known in chemistry as 1 mole and it contains Avogadro's number of single Sofosbuvir molecules
- 889g of Ledipasvir is also 1 mole

Now the significance of Avogadro's number and the half life decay is that when I exceed 6 x 10e-23 we are literally down to the last molecule (assuming we started with 1 mole).

Now we don't start with one mole of either Sofosbuvir (34/529 moles) or Ledipasvir (8/889 moles) because we have about 34g total Sof dose and 8 g total Led dose.

For Sofosbuvir there will be nothing left within 3 months. For Ledipasvir there will still be a little, but there will definitely be nothing at 6 months.

So for complete safety 6 months would be best.

In fact because we only start with 8/889 ~ 1/100 = 1e-2 at 5 months we will have 3e-23 x 1e-2 = 3e-25

2 days later we will have 1.5e-25

4 days later we will have 7.5e-26

6 days later we will have 3.75e-26 and less than Avogadro's number of molecules

So more precisely you should wait 5 months and 6 days

Given you ovulate 10-14 days after the start of your menstrual period you would be safe to wait 5 months and then start trying with the optimal time being that 10-14 day period.