### Description

A first-order process will increase or decrease exponentially based on the initial value and the time since starting. The time it takes to reach a given value can be predicted if certain data is available.

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.