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Pharmacology calculations

Pharmacology calculations. Application of mathematics in calculation of dosages and some pharmacokinetic parameters. T1/2 = Vd/CL X 0.693 (Vd = volume of distribution CL=Clearance) Plasma level (ss) x CL Dosage = ___________________ Bioavailability (F)

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Pharmacology calculations

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  1. Pharmacology calculations • Application of mathematics in calculation of dosages and some pharmacokinetic parameters.

  2. T1/2 = Vd/CL X 0.693 (Vd = volume of distribution CL=Clearance) Plasma level (ss) x CL Dosage = ___________________ Bioavailability (F) (ss=steady state) Dosage = Plasma level (ss) x CL for continuous intravenous infusion Loading dose = (Vd x target conc) /bioavailability

  3. Lidocaine is given to a patient of myocardial infarction for an arrhythmia. • A continuous iv infusion, 1.92 mg/min is started at 8 am. Its Vd is 77 L, CL is 640 ml/min, half life is 1.8 hrs. The expected steady state plasma concentration is how much?

  4. Plasma level(ss)(Cp) x CL • Dosage = ___________________ • Bioavailability (F) • 1.92 mg/min = Cp x 640 ml/min • Cp = 1.92 mg/min / 640 ml/min • Cp = 1.92 /640 mg/min / ml/min • Cp = 0.003 mg/min x min/ml • Cp = 0.003 mg/ml • Cp = 0.003 x 1000 mg/liter • Cp = 3 mg/liter

  5. A normal volunteer receives a drug in phase I trial. Clearance and Vd of this drug are 1.386 L/Hr and 80000 ml respectively. Half life of this drug is --

  6. T1/2 = Vd x 0.693 / CL • = 80 L x 0.693 / 1.386 L/hr • = 80 L x ½ L/hr • = 40 hours

  7. Tobramycin is ordered for a patient with gram negative pneumonia. CL and Vd of tobramycin is 80 ml/min and 40 L respectively. • What maintenance dose should be administered intravenously every 6 hours to eventually obtain average steady state plasma conc of 4 mg/L?

  8. Dosage = Plasma level(ss) x Clearance / F • = 4 mg/L x 0.08 L/min / 1 • = 0.32 mg / min • At 6 hourly interval, = 0.32 mg/min x 60 x 6 = 115.2 mg every 6 hours

  9. If we wish to give an intravenous loading dose to achieve therapeutic plasma concentration of 4 mg/L rapidly, how much should be given?

  10. Loading dose = Vd x desired conc / bioavaila • = 40 L x 4 mg/L / 1 • = 160 mg

  11. Passive diffusion • Aqueous diffusion: • Small, water soluble molecules pass through aqueous pores • Governed by: • FICK’S LAW OF DIFFUSION

  12. Rate of movement = (C1 – C2) x [ Permeability coefficient/Thickness of membrane] x [Area of permeation] C1=conc outside C2=conc inside

  13. Lipoid diffusion- weak acids and weak bases Henderson-Hasselbalch equation • Determines extent of ionization pKa = pH at which 50% of drug is ionized. • WEAK ACIDS: • log (ionized form/nonionized form)= pH – pKa • WEAK BASES: • log (nonionized form/ionized form)= pH – pKa

  14. WEAK ACIDS • log (ionized form/nonionized form)= pH – pKa • A drug is a weak acid. pKa is 3.5. If stomach pH is 1.5, what percentage of drug will be in absorbable form? pH – pKa = 1.5 – 3.5 = - 2 (see next slide)

  15. Remember – absorbable means nonionized ! • pH – pka = -2 • This -2 in the table for weak acid matches to 99%. • And this is supposed to be the nonionized form, which is same as “absorbable form” that is asked in this problem. • Hence the absorbable form is 99%.

  16. Weak bases log (nonionized form/ionized form)= (pH) – (pKa) A drug is a weak base. pKa is 8. If urine pH is 6, what percentage of drug will be in the ionized form? pH – pKa = 6 – 8 = - 2 (see next slide)

  17. Please remember – ionized means nonabsorbable ! • pH – pka has come as -2. • In the table for weak base, -2 matches with 1%. But this 1% is nonionized form. What is asked is – ionized. • So, ionized is 100 – 1 = 99%.

  18. Dose adjustments Young Formula Dose= {Age/ (age + 12)} x adult dose Clarke Formula Dose= (Weight in kg/70) x adult dose Dilling Formula Dose= (Age/20) x adult dose

  19. Practice these with your own examples – • By taking a body weight of a patient and adult dose for a drug • Or • By taking age for a patient (child) and adult dose for a particular drug.

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