Requirements:
(1) first order rise or decline in a value
(2) constant k not known for an individual patient
For a value that rises as a first order process:
value now =
= (initial value at time 0) * EXP(k * (time interval in days))
For a value that decreases as a first order process:
value now =
= (initial value at time 0) * EXP((-1) * k * (time interval in days))
Doubline Time
If the value doubles then
(value now) / (initial value at time 0) = 2 =
= EXP(k * (doubling time in days))
and
LN(2) = k * (doubling time in days)
and
doubling time = LN(2) / k = 0.6931 / k
k =
= (LN(final value) - LN(initial value)) / (time interval in months between the 2 values)
k =
= LN(2) / (doubling time in months)
If these 2 equations are combined:
doubling time in months =
= LN(2) * (time interval months) / (LN(final value) - LN(initial value))
Generalized Version
Parameters:
(1) initial value
(2) value after time t
(3) target value
time to reach target value =
= LN((target value) / (initial value)) * (time t) / (LN(value at time t) - LN(initial value)) =
= (LN(target value) - LN(initial value)) * (time t) / (LN(value at time t) - LN(initial value))
Limitations:
• This assumes that the release characteristics do not change.
