From Michael, Winter Pharm.D. at UCSF Medical Center

I don’t keep old emails.

Time to steady state is a function of T ½ and what % of steady state you would accept as “OK close enough”

The fraction of steady state is 1 – e-Kt for continuous input where t is the duration of the input or 1 – e_KNtau for intermittent dosing where n is the number of doses where tau is the dosing interval)

You are at SS when e-Kt or KNTau is zero you are at SS. Problem is that mathematically t and N has to be infinity to get to zero.

So what most do is say “how close is close enough” some say 90% is close enough (e-Kt or KNTau is 0.1 and that is when you have gone 3.3 T 1/2 ) So many use 3.3 T ½ as SS.

Others want to be closeser to SS to guard against assuming SS when not true so they use 4 to 5 T ½ rather than 3.3.

The dosing interval is not the issue. When Tau is many T ½ (e.g. once daily high dose aminoglycosides or even Q 8 or Q 12) the first dose peak and trough are very close to what it will be at SS (unless something changes and it can). Can assume SS (assume no big error) and no loading dose required and no significant accumulation will occur

Other drugs take many doses to SS e.g phenobarbital with a T ½ of 4 or 5 days and can be given once or twice or more times daily will take weeks to get close to SS regardless of the dosing interval .

The above is only for “linear” drugs where CL and V are constant and not concentration dependent. Phenytoin is capacity limited metabolism and is Non-Linear Cl changes with concentration and does not follow the above rules

Mike Winter