Question #1:
t_1/2 = ln 2 /k_el = 0.693/k_el
where t_1/2 is the elimination half-life (units=time)
ANSWER: k_el = 0.693/15 hours = 0.0462 / hour
Review:
k_el = k_m + k_ex
where k_el = drug elimination rate constant
k_m = elimination rate constant due to metabolism
k_ex = elimination rate constant due to excretion
Question #2:
C_ss = F · (D/t)/(k_el * V_d )
F = 0.7 (fraction absorbed)
D =300 mg
t= 24 h (dosing interval, i.e. once a day)
k_el = 0.0462 / hour (elimination rate constant)
V_d = 40 L (apparent volume of distribution)
C_ss = 0.7 · (300 mg/24 hours) / (0.0462/hour · 40,000 ml)
ANSWER: C_ss = 0.0047 mg/ml or 4.7 μg/ml at 24 hours
 
Question #3:
C_ss = F · (D/t)/(k_el  * V_d )
F = 0.7 (fraction absorbed)
D =300 mg
t= 6 h (dosing interval, i.e. 4 times a day)
k_el = 0.0462 / hour (elimination rate constant)
Vd = 40 L (apparent volume of distribution)
C_ss = 0.7 · (300 mg/6 hours) / (0.0462/hour · 40,000 ml)
ANSWER: Css = 0.019 mg/ml or 19 μg/ml at 6 hours
 
Question #4:
Css = F · (D/t)/(k_el  *V_d)
F = 0.7 (fraction absorbed)
D =300 mg
t= 12 h (dosing interval, i.e. 2 times a day)
k_el = 0.0462 / hour (elimination rate constant)
V_d = 40 L (apparent volume of distribution)
C_ss = 0.7 · (300 mg/12 hours) / (0.0462/hour · 40,000 ml)
ANSWER: C_ss = 0.0095 mg/ml or 9.5 μg/ml at 12 hours
 
Question #5:
Css = F · (D/t)/(k_el  * V_d )
F = 0.7 (fraction absorbed)
D =300 mg
t= 48 h (dosing interval, i.e. once every 2 days)
k_el = 0.0462 / hour (elimination rate constant)
V_d = 40 L (apparent volume of distribution)
C_ss = 0.7 · (300 mg/48 hours) / (0.0462/hour · 40,000 ml)
ANSWER: C_ss = 0.0024 mg/ml or 2.4μg/ml at 12 hours
Note what happens to C_ss as we shorten or lengthen the dosage interval (qualitative % quantitative effects)
Dose = 300 mg of Drug X
Time (hours)
Css (μg/ml)
6
19
12
9.5
24
4.7
48
2.4

Question #6:
Css = F · (D/t)/(kel . Vd )
F = 0.7 (fraction absorbed)
D =150 mg
t= 24 h (dosing interval, i.e. once a day)
k_el = 0.0462 / hour (elimination rate constant)
V_d = 40 L (apparent volume of distribution)
C_ss= 0.7 · (150 mg/24 hours) / (0.0462/hour · 40,000 ml)
ANSWER: C_ss = 0.0024 mg/ml or 2.4 μg/ml at 24 hours
 
Question #7:
Css = F · (D/t)/(kel . Vd )
F = 0.7 (fraction absorbed)
D =600 mg
t= 24 h (dosing interval, i.e. once a day)
k_el= 0.0462 / hour (elimination rate constant)
V_d = 40 L (apparent volume of distribution)
C_ss = 0.7 · (600 mg/24 hours) / (0.0462/hour · 40,000 ml)
ANSWER: C_ss = 0.0095 mg/ml or 9.5 μg/ml at 24 hours
T is constant (once every 24 hours)
Dosage (mg)
C_ss(μg/ml)
150
2.4
300
4.7
600
9.5
Questions and answers based on material presented by Dr. Edward Flynn, Department of Pharmacology, New Jersey School of Medicine and Dentistry used with permission