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 Pharmacokinetics: General Principles-Lecture II, slide 1

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  • Absorption

    • Fick's Law

  • Routes of Administration

  • First-Pass Effect

  • Pulmonary Effects

  • Pharmacokinetics

    • Volume of distribution

    • Clearance

      • Renal clearance: clearance of unchanged drug and metabolites

        • Other Factors Affecting Renal Clearance

      • Factors Affecting Hepatic Clearance

      • Capacity-Limited Elimination

      • Half-life

      • Drug Accumulation

    • Bioavailablity

      • Extent of Absorption

      • First-Pass Elimination

      • Rate of Aborption

    • Some Pharmacokinetic Equations

    • Placental Transfer

    • Redistribution

    • Drug-Plasma Protein Binding

    • Renal Clearance

  • Drug Metabolism

    • Introduction

    • Phase I and Phase II Reaction Overview:

    • Phase I characteristics

    • Phase II characteristics

    • Conjugates

    • Principal organs for biotransformation

      • Sequence I

      • Sequence II

    • Bioavailability

    • Microsomal Mixed Function Oxidase System and Phase I Reactions

      • The Reaction

      • flavoprotein--NADPH cytochrome P450 reductase

      • Cytochrome P450: -- terminal oxidase

      • P450 Enzyme Induction

      • P450 Enzyme Inhibition

      • Human Cytochrome P450

    • Phase II Reactions

      • Toxicities

  • Individual Variation in Drug Responses

  • Genetic Factors in Biotransformation

  • Effects of Age on Drug Responses

  • Drug-Drug Interactions

Pharmacokinetics and some IV Anesthetics Agents

  • Barbiturates

    • Thiopental

  • Benzodiazepines

  • Ketamine and Etomidate

  • Propofol

  • Opioids

    • Membrane Bilayer Structure






Some Pharmacokinetic Equations


Elimination Rate Constant

  • kel = km + kex

    • where kel = drug elimination rate constant

    • km = elimination rate constant due to metabolism

    • kex = elimination rate constant due to excretion



  • t1/2 = ln 2 /kel = 0.693/kel

    • where t1/2 is the elimination half-life (units=time)

  • Derivation: The time it takes to shift from one concentration to another, for example to 1/2 the initial concentration is described by:

    • f = 1 - e-ket where f is the fractional shift, ke is the elimination rate constant and t is time.

    • To get to 50% of the initial concentration, let's set f = 0.5 and rearrange the equation to give:

      • 0.5 = 1- e-ket or

      • 0.5 = e-ket ; now taking the natural ln of both sides,

      • ln 0.5 = -ket which is 0.693 = -ket

      • Therefore the time it takes to reduce the concentration by 50%, in other words the half-time, t1/2 = 0.693/ke.


Amount of Drug in Body

  • Xb = Vd · C

    • Xb: amount of drug in the body (units, e.g. mg)

    • Vd: apparent volume of distribution (units, e.g. mL)

    • C: plasma drug concentration (units, e.g. mg/mL)



Volume of Distribution Calculation (one compartment, i.v. infusion)

  • Vd = Div / Co

    • Vd: apparent volume of distribution (units, e.g. ml/kg)

    • Div: i.v dose (units, e.g. mg/kg)

    • Co: plasma drug concentration (units, e.g. mg/ml)




  • CL = rate of elimination/C, where C is the concentration of drug in blood or plasma

  • rate of elimination = CL· C

  • CL = Vd x kel where Vd = volume of distribution and kel is the elimination rate constant

  • CL = Vd · (0.693/t1/2) where 0.693 = ln 2 and t1/2 is the drug elimination half-life

  • note that plasma clearance CLp include renal (CLr) and metabolic (CLm) components

Renal Clearance

  • CLr = (U · Cur) / Cp ; where U is urine flow (ml/min); Cur is urinary drug concentration and Cp is plasma drug concentration.



Steady-State Drug Plasma Concentration (Css)

  • The calculation required to determine being steady-state drug plasma concentration illustrates the sensitivity of the plasma concentration to number of factors, in this case for a drug taken orally.

  • First  look at the overall form of the equation:

equation 1: Css= 1/(ke*Vd) * (F*D)/T 

  • The drug elimination rate constant,ke is related to the drug half-life ( t1/2 = 0.693/ke) and thus can be calculated from knowledge of the drug half-life.  

  • The plasma steady-state drug levels also dependent on the dose, D, as well as a fraction of the drug that's actually absorbed following ingestion (F). 

  • "T" is the dosing interval, so the once-a-day dosing would be 1 day or to keep the units consistent, 24 hours.

  • The steady-state level will also be dependent on the apparent volume of distribution (Vd)

  • Now let's take an example using the drug phenytoin (Dilantin) which is used to manage epilepsy.

    • The once-a-day dose is 200 mg.

    • The drug half-life is 15 hours

    • For the once-a-day dose, the dosing interval (T) is 24 hours [to keep the units the same as the drug half-life will use "hours"]

    • Let's say that about 60% of the ingested does is in fact absorbed, giving us a value of 0.6 for  "F" in equation 1 above.

    • The volume of distribution for phenytoin (Dilantin) is 40,000 mls (40 liters)

    • ke = 0.693/15 hours = 0.0462/hr

  • Let's now compute the results:

equation 1: Css= 1/(ke*Vd) * (F*D)/T  or

Css= 1/(0.0462/hour*40000 ml) * 0.6 (200 mg)/24 hours    or

Css = 0.0027 mg/ml or 2.7 ug/ml


Time to Steady-State

  • Let's consider the above problem from a little different point of view, that is, How long would it take to reach 50% of the Css (no bolus).

  • Consider the dose is 300 mg/24h (dosing interval is 24 h or T; dose is  300 mg) but for convenience we'll represent it as 12.5 mg/hr, such that T is now 1 hr. The equation is:

  • f = 1 - e -keTN  or 0.5 = 1 - e -keTN where ke is the elimination half-time of 0.0462/hr, T = 1 and N is the number of doses needed to reach 50% of Css

  • Rearranging, 0.5 = e -0.0462/hr * 1 hr * N --(note time (hour) units cancel) so taking antilogs,

  • -0.693 = -0.0462 * N or N = -0.693/-0.0462 = 15

  • 15 doses at an interval of 1 hour/dose gives the time to 50% of  Css equal to 15 hours--a predictable time since drugs reach 50% of their steady-state value in 1 half-life



Constant Infusion Dosing

  • Next, let's consider the case by which drugs are administered by constant infusion.

  • The infusion rate is Q or in this example, 150 ug/min and for simplicity, the drug is again phenytoin with a ke of 0.0462/hr; t1/2 of 15 hrs and a Vd of 40000 mls

  • Css = Q/(ke*Vd ) or 150 ug/min / (0.0462/60min * 40000 ml) = 4.87 ug/ml; 

    • [note that we have been careful to use the same units for ke and Q, i.e. 0.0462/hr = 0.0462/60 min]



  • Holford, N. H.G. and Benet, L.Z. Pharmacokinetics and Pharmacodynamics: Dose Selection and the Time Course of Drug Action, in Basic and Clinical Pharmacology, (Katzung, B. G., ed) Appleton-Lange, 1998, pp 34-49.

  • Benet, Leslie Z, Kroetz, Deanna L. and Sheiner, Lewis B The Dynamics of Drug Absorption, Distribution and Elimination. In, Goodman and Gillman's The Pharmacologial Basis of Therapeutics,(Hardman, J.G, Limbird, L.E, Molinoff, P.B., Ruddon, R.W, and Gilman, A.G.,eds) TheMcGraw-Hill Companies, Inc.,1996, pp. 3-27

  • Pazdernik, T.L. General Principles of Pharmacology, in ACE the Boards, (Katzung, B. G., Gordon, M.A, and Pazdernik, T.L) Mosby, 1996, pp 22-28

  • Edward J. Flynn, Ph.D. Professor of Pharmacology, New Jersey School of Medicine and Dentistry, personal communication, 1980, 1999.


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