For a first order process, plotting the drug concentration directly versus time gives a logarithmic curve. A semilog plot of the drug concentration versus time is linear.
amount of drug in body at time T =
= ((amount of drug in body at time 0) * EXP((-1)*(elimination rate constant)*(time T)) =
= ((fraction of dose absorbed) * (dose)) * EXP((-1)*(elimination rate constant)*(time T))
If the drug is administered as an intravenous bolus, then the entire dose is the amount of drug in the body and it is rapidly distributed through the intravascular space.
amount of dose left in body at time T =
= (dose infused at time=0) * (fraction of drug remaining in the body) =
= (dose infused at time=0) * EXP((-1) * (elimination rate constant) * (time since drug administered))
where:
• Time = 0 is immediately after bolus dosing
amount of dose left in the body at time T =
= ((plasma drug concentration at time T) * (volume of distribution))
fraction of drug remaining =
= EXP((-1) * (elimination rate constant) * (time interval since drug administration))
fraction of drug lost from the body =
= (1 - (fraction of drug remaining in the body)) =
= (1 - EXP((-1) * (elimination rate constant) * (time interval since drug administration)))
