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

SF

CLC

τ

D then ,kVCL

SF

kVC

τ

D

τkV

SFDC

Tav0DT

Dav0

D

0av

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 g/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/ז or the dose rate =34 mg/hr. To convert to oral theophylline, S

& F should be considered :

28.9mg/hr

1

3410.85

τ

SFDrate dose neTheophylli 0

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.:

• Where Do = dose, = dosing interval

τV

Ft1.44DC

D

210

av

Equations for Cssmax and Css

min

kτkτ

D

0min

kτD

0max

ee1

1

V

DC

e1

1

V

DC

Effect of changing dose and dosing interval on Css

max and Cssmin and Css

av

• Cssav is most often used for dosage calculation

• Cssav Cannot be measured directly but obtained

by AUC/ז during 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; Css

av = 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 Css

av. • Thus a dose of 250 mg every 3 hours

could be changed to 500 mg every 6 hours without affecting Css

av .• However, as the זget longer, the size of

dose to maintain Cssav gets

correspondingly larger

For narrow therapeutic window drugs

• When an excessively long ז is chosen, the large dose may results in Cp above MTC although the Css

av 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 problemsPenicillin 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:

kτmin

max

e

1

C

C

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 g/mL. Adverse toxicity for this drug is often observed at serum conc greater than 20 g/mL. Calculate a dosage regimen (multiple iv doses) that will maintain the therapeutic range.

Solution

-0.231 4.76 = ז, 1.10 = -ז hr

The dose was determine by eq:

Let VD= 20%BW = 200mL/kg

Then Do = 2 mg/kg

So, the dose should be

2 mg/kgBW every 4.76 hrs

The ז should be made as convenient as

Possible, let take 6 hrs, then we

Should calculate the Do again

kτD0

max e1

/VDC

kτmin

max

e

1

C

C

333.0

1

5

15

231.0

)3/693.0(

e

e

76)(0.231)(4.0

e1

/200D15

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 9 mg/kg

> 16 yrs 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)