Transcript Calculation of Doses

Calculation of Doses
Prof. Dr. Henny Lucida, Apt
Conversion from iv infusion to oral
dosing
• After the patient’s condition is controlled by iv
infusion, it is often desirable to convert to the
oral route of same medication
• in patient
out patient
• to minimize fluctuation, when iv infusion stop
(the Cp decreases according to first order
elimination) then oral dosage regimen starts
directly
the exponential decline of Cp
from iv infusion should be matched by the
exponential increases in Cp from the oral
product
• A conversion from iv infusion to a
controlled release oral medication given
once or twice daily has become most
common, exp: theophylline & quinidine
• Two methods for the calculation of
appropriate oral dosage regimen for a
patient whose condition has been
stabilized by an iv infusion
Method 1
• Assume: Css after iv infusion = C∞av desired
after multiple oral doses of the drug
SFD 0

C av 
kVD τ
D 0 C av kVD

τ
SF
D 0 C av CL T
CL T  kVD , then

τ
SF
Example
An adult asthmatic patient (age 55,78 kg)
has been maintained on an iv infusion of
aminophylline at a rate of 34 mg/hr.The
steady-state theophylline drug
concentration was 12 mg/mL and total
body clearance was calculated as 3.0 L/hr.
Calculate an appropriate oral dosage
regimen of theophylline for this patient.
Solution
• S = 0.85 (cause aminophylline, a soluble salt which contains 85%
theophylline)
• F = 1 (theophylline is 100% bioavailable)
• Do/‫ ז‬or the dose rate =34 mg/hr. To convert to oral theophylline, S
& F should be considered :
SFD0 0.85134
Theophylli ne dose rate 

 28.9mg/hr
τ
1
Solution (contd)
To convert the theophylline oral dose rate (28.9 mg/hr) to
a reasonable schedule for the patient with a
consideration of the various commercially theophylline
drug products:
the total daily dose = 28.9 mg/hr x 24 hr = 693.6 mg/day
possible theophylline dosage schedule:
700 mg/day or 350 mg every 12 hrs or 175 mg every 6
hrs.
The dose of 350 mg every 12 hrs could be given in
sustained-release form to avoid fluctuations.
Method 2
• Assumes that the rate of iv infusion (mg/hr) is
the same desired rate of oral dosage
• Using the example in method 1, the solution:
iv infusion rate = 34 mg/hr
the total daily dose of aminophylline = 34 mg/hr
x 24 hr = 816 mg, which equivalent to 816 x 0.85
= 693.6 mg of theophylline.
Thus 700mg of theophylline per day or 350 mg
controlled-release theophylline every 12 hours
Determination of dose
• The drug dose is estimated to deliver a
desirable (target) therapeutic level of drug
to the body. The dose of a drug is
estimated with the objective of delivering a
desirable therapeutic level of the drug to
the body.
• For many drugs, the desirable therapeutic
levels and pharmacokinetic parameters
are available in the clinical literature.
• For a drug given in multiple doses for an
extended period of time, the dosage regimen is
usually calculated, so that the average Css
(C∞av) is within the therapeutic range.
• The dose can be calculated with eq.:
C

av

1.44D 0 t 1 F
2
VD τ
• Where Do = dose, t = dosing interval
Equations for Cssmax and Cssmin
C

max
C

min
 1 

 kτ 
1 e 
D 0  1   kτ

e


 kτ
VD  1  e 
D0

VD
Effect of changing dose and dosing interval on
Cssmax and Cssmin and Cssav
• Cssav is most often used for dosage calculation
• Cssav Cannot be measured directly but obtained
by AUC/‫ ז‬during multiple dosage regimen
• Cssav as an indicator for deciding therapeutic
blood level.
• When dosing interval is changed, the dose may
be proportionally increased to keep Cssav
constant
Examples;
• Diazepam is given either 10 mg tid or 15 mg bid,
the same is obtained as shown by equation;
Cssav = SFDo/kVD‫ז‬
• In fact: if the daily dose is the same, the Cssav
should be the same.
• The dosing interval must be set with the
elimination half-life of the drug
• drugs with narrow therapeutic window must be
monitored to ensure safety and efficacy
Determination of frequency of drug
administration
• The more frequently a drug is
administered, the smaller the dose must
be to obtain the same Cssav.
• Thus a dose of 250 mg every 3 hours
could be changed to 500 mg every 6 hours
without affecting Cssav .
• However, as the ‫ז‬get longer, the size of
dose to maintain Cssav gets
correspondingly larger
For narrow therapeutic window
drugs
• When an excessively long ‫ ז‬is chosen, the
large dose may results in Cp above MTC
although the Cssav will remain the same.
• Thus, must be given relatively frequently
to minimize excessive peak and trough
fluctuation in blood levels.
Look at the example
• Penicillins, have relatively low toxicity, may be
given at intervals much longer than their t½
without any toxicity problems
Penicillin G: 250 mg every 6 hrs ( 8x its t½, ie
0.75 hrs), the TC >>100 times its EC
• Digoxin: 0.25 mg/day (0.59 x its t½, ie 1.7 days),
the TC is only 1.5 times its EC
• Therefore, a drug with a large therapeutic index
(a large margin of safety) can be given in large
doses and at relatively long ‫ז‬.
Determination of both dose and
dosage interval
• For intravenous multiple dosage regimen:
C
C

max

min

1
e
 kτ
Practice problem
• The t½ elimination of an antibiotic is 3 hrs
with VDapp equivalent to 20% of BW. The
usual therapeutic range is between 5 and
15 mg/mL. Adverse toxicity for this drug is
often observed at serum conc greater than
20 mg/mL. Calculate a dosage regimen
(multiple iv doses) that will maintain the
therapeutic range.
Solution
C max
1
  kτ

C min e
15
1
 ( 0.693 / 3)t
5 e
e 0.231t  0.333
-0.231‫ = ז‬-1.10, ‫ = ז‬4.76 hr

The dose was determine by eq:
max
Let VD= 20%BW = 200mL/kg
Then Do = 2 mg/kg
So, the dose should be
2 mg/kgBW every 4.76 hrs
The ‫ ז‬should be made as convenient as
Possible, let take 6 hrs, then we
Should calculate the Do again
C
D 0 /VD

1  e kτ
D 0 /200
15 
(0.231)(4.76)
1 e
Using nomograms and tabulation in
designing dosage regimens
Exp: Maintenance dose of theophylline when the Cp is not measured
Age
Dose
Dose/12hrs
6-9 yrs
24 mg/kg/day
12 mg/kg
9-12 yrs
20 mg/kg/day
10 mg/kg
12-16 yrs 18 mg/kg/day
> 16 yrs
9 mg/kg
13 mg/kg/day or 900 mg 6.5 mg/kg
Dosing of drugs in infants and
children
Life stages:
• Neonates (newborn baby)
• Infants
• children
Altered pharmacokinetic of drugs
Newborn babies / neonates:
• Drug disposition, erratic: distrib from
placenta
exp: opiates (for maternal pain and relief)
benzodiazepines (for maternal
eclampsia/preeclampsia)
Neonates: Drug absorption
• Drug absorption, erratic & unavailable in
the ill body. An iv route is recommended,
im route is avoided
exp: paraldehyde & diazepam (neonatal
seizures) and paracetamol
suppos
Neonates: Drug distribution
• Absolute GFR increases logarithmically with
post-conceptional age irrespective of the length
of a baby’s gestation
• Extracelluler fluids is highest at birth & falls due
to the post-natal diuresis over the first 48 hrs of
post-natal life
• The amount of adipose tissue vary substantially
(diabetic mother)
• Protein binding in plasma is influenced by the
amount of albumin (2/3 of adult concentration)
Neonates: Drug metabolism
• Not quantitatively different but the
efficiency of the process
• Drug metabolism is affected by
physiological hyperbilirubinemia of the
new-born. Bilirubin competes both for
enzyme binding sites & for glucuronate
Neonates: Drug elimination
• Immaturity of hepatic and renal function:
slow elimination of most drugs (advantage:
don’t need a maintenance dose). Ex :
phenobarbitone, a loading dose of 20
mg/kgBW is adequate to maintain the
therapeutic level for days. Drugs with
narrow therapeutic window (gentamycin,
vancomycin) should be given less
frequently and plasma blood level must be
asssayed to avoid toxicity
A guide to administration of low therapeutic
index antibiotics for neonates
• Use narrow spectrum & short courses antibiotics
• Use cephalosporins (cefotaxime & ceftadizime)
for blind treatment (should be stopped after 48
hrs if cultures negative) rather than
aminoglycosides due to lower toxicity and no
TDM needed.
• A routine TDM is required for aminoglycosides
and vancomycin ( also theophylline and
aminophylline)