Question

A drug (CL = 7 L/h, V_d= 140 L) is to be administered as an IV infusion. A steady-state plasma concentration of 1.1 mg/L is desired. Calculate the following:

- infusion rate (R_inf)

- assuming it would take 4 half-lives to achieve the steady-state, how long would it take to achieve this steady-state, t_ss.

Answer 1

ANS:

Given:

C_L= 7 L/h

V_d = 140 L

steady state plasma concentration, C_ss = 1.1 mg/ L

Infusion rate, K₀ =?

At steady state, infusion rate can be calculated using the following formula:

           C_ss = K₀ / C_L

Therefore, K₀ = C_ss * C_L

                 K₀     = 1.1 * 7 = 7.7 mg/h

Now coming to the second part, the time to reach the steady state is defined by the elimination half life of the drug.

C_ss = K₀ / C_L

and K_el = elimination constant= C_L/ V_d = 7/ 140 = 0.05 hr^-1

Plasma concentration C_{p =} C_ss /2 = C_ss [ 1- e ^{-kel . t half}]

calcelling c_ss from both sides, we get

1/2 = [1- e ^{-kel . t half} ]

1/2 -1 = - e ^{-kel . t half}]

2 = e^{kel . t half}

kel . t half = ln 2 = 0.693

thus, t_1/2 = 0.693 / kel

Halfway 50%	to steady state in 1 half life
75 %	to steady state in 2 half life
87.5 %	to steady state in 3 half life
94 %	to steady state in 4 half life

Thus, putting all the values we can calculate the t_1/2

t_1/2 = 0.693 / 0.05 =13.86 hr

so the time required to achieve this steady state = 4 half lives = 4 * 13.86 hrs

                                                                             = 55.44 hrs = 2.31 days