Pharmacology calculations

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Pharmacology calculations

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

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

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• 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?

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• 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

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• 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 --

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

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• 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?

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• 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

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

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

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Passive diffusion

• Aqueous diffusion
• Small, water soluble molecules pass through
  aqueous pores
• Governed by
• FICKS LAW OF DIFFUSION

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• Rate of movement
• (C1 C2) x Permeability coefficient/Thickness
  of membrane x Area of permeation
• C1conc outside
• C2conc inside

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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

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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)

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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.

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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)

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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.

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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

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• 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.