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Harvard-MIT Division of Health Sciences and Technology HST.151: Principles of Pharmocology Instructors: Dr. Carl Rosow, Dr. David Standaert and Prof. Gary Strichartz Midterm review - February 26, 2004 Pharmacokinetics: (Walsh, Langer, et al.) 1. Volume of distribution: Vd (in mLs or liters) = D/C0 where D is drug dose (e.g. after bolus IV), C0 = its plasma concentration at time 0 2. First order Kinetics dX/dt = -kX where k is the elimination rate constant and X(t) represents the amount of drug in the plasma as a function of time X(t) = X0e-kt ⇒ C(t) = (X0/Vd)e-kt t1/2 = ln2/k = 0.693/k (note: k has units of 1/time) 3. Clearance Cl = Vd * k i.e. volume of plasma cleared of drug/unit time 4. Constant (IV) infusion kinetics Steady state is achieved when the infusion rate of a drug equals its rate of elimination: k0 = (CssVd) k where Css is the steady state concentration and k0 is the rate of infusion Css = k0 / (Vdk) = k0 / Cl Æ therefore Maintenance Dose (IV) = CssCl mathematically: dX/dt = k0 – kX ⇒ X(t) = (k0/k)(1-e-kt) or C(t) = Css(1-e-kt) The time needed to reach steady state concentration is strictly determined by the half life of elimination t1/2. To reach steady state more quickly, give a Loading dose: CssVd which if given IV will instantaneously achieve steady state levels that can be maintained by IV infusion at a rate of k0 (from above). 5. Multiple dosing kinetics You want to keep the concentration between Cmax and Cmin ⇒ Loading dose: Cmax Vd Maintenance dose: (Cmax - Cmin) Vd Dosing interval (comes directly from first order equation): t = (1/k)ln(Cmax/Cmin) Maximal dose = VD x Ctoxic Maximal bolus dose given a certain toxic concentration Minimum dose = VD x Cthreshold of therapeutic effect If you know the target concentration, Ctarget, and want to maintain it at that target concentration, to calculate loading & maintenance dose: Loading target dose = Ctarget (Vd) Maintenance dose = Ctarget(ClT)HST 151 Midterm Review Renal Failure case: Toxicities limit maximal concentrations (Cmax) of some drugs (digoxin, gentamicin). Requirements for minimum concentration (Cmin) for biological activity mean you have to keep levels above a threshold (gentamicin). Renal clearance declines in renal failure, and for renally excreted drugs a patient could accumulate toxic levels. Basic strategies in renal failure patient are to decrease frequency of dosing (i.e. increase time interval between dosing) or decrease the dose, or both. 6. Bioavailability Fraction of dose absorbed into systemic circulation is known as a drug’s bioavailability. AUC refers to the area under the plasma concentration vs. time curve: AUC = F*D/Cl where D is the dose, F is the bioavailability (fraction absorbed), and Cl is clearance F is usually measured by comparing AUC of a dosage form of drug given by one route divided by the AUC of the drug given IV (i.e. AUCoral : AUCiv) Factors that influence bioavailability: • First pass effects • Chemical instability • Nature of drug formation 7. Notes: Lipophilic drugs tend to have large volumes of distribution which means they tend to exert their effects quickly and then redistribute into fat (ie propofol). As a consequence, they stick around and slowly leach out of the fat into the plasma. This may or may not be significant enough to cause lingering effects. You can think of first order kinetics as the ability (e.g. of an enzyme) to increase its activity as a function of the concentration of the substrate. When the enzyme’s ability is maxed out (i.e. drug concentrations are too high), the enzyme operates at a fixed (maximum) rate known as the Æ Zero order kinetics A typical example of zero order kinetics is the metabolism of ethanol. (Also IV drips, aspirin metabolism, and phenytoin metabolism [mixed 0 and 1st order kinetics {Standaert lecture}]) A drug could be completely absorbed, but if the rate of absorption is insignificant compared to clearance, its effect could be severely diminished 8. Langer Pharmacokinetics Lecture: Review briefly some of the problems in drug delivery, proposed solutions, and some of the important equations describing drug release from certain structures (i.e. zero order kinetics, release from a cylindrical reservoir). Always consider the side effect of a traumatic release of large quantity of the drug from the reservoir!!! Page 2 of 25HST 151 Midterm Review Receptors: (Strichartz, et al.) 1. Basic principle D ↔ DR ↔ DR*(active) ↑ ↑ potency/affinity efficacy/coupling 2. Efficacy the maximum effect a drug can have – depends on the ration DR*/DR (which alone depends on reaction rates, i.e. efficacy depends on the specific drug for a single receptor 3. Drug binding fraction of receptor bounds by drug = DR/ Ro = D / (D+ KD) where [D] is drug concentration, Ro = concentration of total receptors (Ro = R + DR) 4. KD (Dissociation constant = 1/affinity constant): the concentration of drug at which half of the receptors are bound 5. EC50 (known also as KAP): the concentration of drug needed to produce half maximal effect) (see Katzung) – the apparent dissociation constant • not to be confused with ED50 – which is a dose that produces half-maximal effect or desired response in 50% of the recipients (see Katzung) Effect / Max effect = D / (D + KAP) where D, R, DR are instantaneous concentrations of drug, free receptor, and bound receptor, respectively 6. Antagonism: Com pet it vei ( Sur m ount able) Noncom pet it vei ( I nsur m ount able) A iA Response A + ant ago ns t Response A + ant agonist Log Agonist ( A) Log Agonist a. Competitive Antagonists: The antagonist competes for binding at the receptor thus effectively increasing the EC50 (and KD) Page 3 of 25HST 151 Midterm Review Dose ratio equation: [D’ (with antagonist)/ D] – 1 = A / KA ⎛ ] ⎞⎟⎟ A+ 1 [EC with antag EC = without antag⎜⎜⎝ × 50 50 KA⎠ A K [] EC with antag50− 1 = EC without antag50 A where D’ = concentration of agonist D needed to produce the same effect in the presence of antagonist concentration A as D in the absence of antagonist b. Noncompetitive Antagonists: Antagonist binds to a different site than the drug, eliminating the drug’s ability to bind receptor. So EC50 is unchanged, but the efficacy is reduced (except in the case of spare receptors – see below) Vmax w/ inhibitor = Vmax * (1 – y) where y = occupancy by antag = [A] / ([A] + KA) c.


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MIT HST 151 - Midterm review

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