2. Applied Pharmacokinetics Flashcards
- Have a basic understanding of nonlinear pharmacokinetics and how dosage changes can produce drug accumulation changes that are greater or less than expected (objective)
Answer later
- Know how to calculate maintenance dose, drug half-life, drug clearance, and the amount of drug present in the body at various times after it is administered (objective)
Answer later
- Know the effect of disease states (i.e changes in renal and hepatic function) on drug elimination, drug dosage and dosing schedule (objective)
Answer later
- Know how to calculate the concentration (or amount of drug) present during a constant intravenous administration (objective)
Answer later
- Understand what factors determine the drug plateau levels and the minimum and maximum plasma levels for a drug administered using a fixed dose and fixed dosing interval schedule (objective)
Answer later
Drug Metabolism
Occurs via enzyme-catalyzed reactions, and thus follows Michaelis Menten kinetics
Michaelis-Menten Equation
V=(Vmax[D]) / (Km+[D])
V= rate of metabolism of drug
Vmax=max rate in presence of infinite [drug]
[D]= concentration of drug in body
Km= dissociation constant of drug-enzyme complex
Plot the Rate of Change of Drug Metabolism with Drug Concentration
Rate of Metabolism of Drug (V) vs. Concentration of Drug (D)
Plateau observed
Slide 6
First Order Reaction Phase
V=(Vmax[D])/Km
Steep red-dotted incline
See slide 7
First Order Reaction
Relatively low substrate concentrations
Generally when V is less than or equal to Vmax
V is directly proportional to D (concentration of drug in body)
D in equation (when added to Km) can be treated like it is not there
Zero Order Reaction Phase
Graph of plateau (V=Vmax)
Zero Order Reaction
When concentration of drug is relatively high
V=Vmax
Change in Reaction Velocity as a Function of Drug Concentration
Velocity vs Drug Concentration graph
Zero order: high velocity but remains constant with drug concentration
First order: with increasing drug concentration the reaction speeds up linearly
Nonlinear Pharmacokinetics
Drugs whose absorption/distribution/metabolism/elimination follow first-order follow linear pharmacokinetics (plasma concentrations increase proportionally with dose)
Drugs with relationship between drug dose and plasma concentrations not linear follow nonlinear pharmacokinetics
Nonlinear pharmacokinetics: zero vs first order drug accumulation
Case where plasma concentration increases more than expected for a given increase in drug dose
(Plasma concentration vs Dose graph)
Nonlinear increases exponentially
Linear increases linearly (duh)
Nonlinear Pharmacokinetics: auto inhibition or nonlinear protein binding
Case where plasma concentration increases less than expected for a given increase in drug dose
(Plasma concentration vs Dose graph)
Linear continues going up consistently
Nonlinear starts to plateau
Drug Elimination
Elimination of many drugs is by first order (linear) models
Discussion of this is based on one compartment (one state) model, that drug is thought to exist in single, homogenous compartment.
But really should use multi compartment model (2 or 3 compartments_
First Order vs Zero Order (drug elimination)
Zero order: constant amount of drug is eliminated per unit of time
First order: constant fraction (or percent) of drug is eliminated per unit of time
Differential Equation Describing the Rate of Change in the Amount of Drug in the Body
(dD/dt)=-ke*D
(dD/dt)= instant rate of change in the amount of drug in the body D= total amount of drug that's in body ke= elimination rate constant (fraction of D that is being removed per unit time)
Integrated Rate Equation for the First Order Elimination of a Drug (integrated from differential equation)
D=Doe^(-ket)
Do=initial amount of drug (loading dose) D= amount of drug at time t after administration ke-elimination rate constant e= base of natural logarithms t= time since initial dose
Integrated rate equation (in terms of concentration)
C= Coe^-ket
C=(Do/Vd)(e^-ket)
Uses of Integrated Rate Equation
Calculate the amount of drug remaining in the body at time t after administration of the initial dose Do.
Used to derive equation for the calculation of the maintenance dose of a drug (the amount of drug that needs to be administered in order to maintain drug levels in the body)
Alternative forms of the integrated first order rate equation
D/Do=e^-ket
Ln(D/Do)=-ket
LogD= (-ket/2.3)+logDo
Plot of First Order Elimination of a Drug with Time
D (drug remaining in body) vs Time Graph
D=Doe^-ket
Downward plateau
Log Plot (of first order elimination)
LogD=(-ket/2.3)+logDo
Slope is -ke/2.3
LogD vs Time Graph: straight downward slope
*Note initial shape (steeper initial then flatter downward trend)
Effect of renal or hepatic abnormalities on drug elimination (log D vs time graph)
Normal Function (straight downward line) Subnormal Hepatic/Rena Function (straight downward line, but elevated flat slope) Induced Hepatic Enzymes (steeper downward slope)
Log Plot of the Amount of Different Doses of the Same Drug Remaining in the Body with Time
Slide 27 (clarify after lecture)
Half-Life of Elimination (time required to reduce the amount of drug to one-half initial value)
- ln(D/Do)=-ket
- When one half drug metabolized (D/Do=50/100)
ln50/100=-ket - -0.693=-ket
- t1/2= 0.693/ke *****
Recall: Clearance
Hypothetical volume of body fluid from which a drug is removed per unit time
Determined by blood flow to the site of metabolism (liver) or elimination (kidney) of the drug, efficiency of organ in removing drug from circulation
CL=Vd*ke
Where CL is clearance
Vd is volume of distribution
ke is the elimination rate constant
Relationship between clearance and half life
Half life of a drug is inversely proportional to clearance
Half-life of drug is directly proportional to Vd/CL (if Vd decreases or CL increases, half life decreases)
T1/2= 0.693*(Vd/CL)
Maintenance Dose
In most case, drugs given continuous infusion or series of repetitive doses, goal is to maintain a relatively steady-state concentration of a drug.
Continuous IV infusion, the rate of drug administration (maintenance dose) is adjusted so it is equal to rate of drug elimination
Intermittent drug administration, maintenance dose is equal to amount of drug that has been eliminated from the body since the previous dose was administered.
Maintenance Dose (calculation)
Following loading dose LD, amount of drug eliminated is the difference between LD and the amount of drug remaining D: Maintenance dose= drug eliminated=LD-D D=Doe^-ket Substitute ***Maintenance Dose= LD-(LD)e^-ket
Maintenance Dose (clearance equation)
Drug administration=drug elimination=CLCss
Bioavailability:
Fadministered dose=CL*Css
**Maintenance dose=(CL*Css)/F
Constant Intravenous Infusion
dC/dt=-keC+(Q/Vd) -keC(drug out)+Q/Vd(drug in) dC/dt is instant rate of change of drug concentration in the bloodstream C= concentration of drug in bloodstream ke= elimination constant Q= rate of infusion of drug into body Vd= apparent volume of distribution
Infusion of Drug into Body is Governed by Same Processes as Adding Water to a Tank
Q/Vd is infusion
dC/dt is rate
-keC is elimination
Slide 36
More equations (Cmax)
Cmax=(Q)/(keVd)
Remember CL=Vd*ke
Therefore Cmax=Q/CL
C=[(Q)(1-e^-ket)]/[keVd]
1-e^-ket how quickly approaches plateau
Max concentration directly proportional to infusion rate, inversely proportional to elimination constant and volume of distribution
Plot of Concentration of Drug in Body with Time of Infusion
Drug Body Concentration vs Time
C=[(Q)(1-e^-ket)]/[keVd] is upward plateau
Accumulation of drug that depends on infusion and elimination, max plateau is steady state concentration
Administration of a fixed dose at a fixed interval of time
Blank slide
Plasma Concentration of Drug During Constant Dose, Constant Interval of Time Schedule
Downward then straight up, repeat (each time reaching a higher peak)
Fluctuations get smaller
On log scale-
Plateau (at drug peaks): attained after about 4 half lives. Time to plateau is independent of dosage. Plateau concentration is proportional to dose/dosage interval and proportional to half-life.
Fluctuations: proportional to interval/half-life
Plasma Concentration of Drug with Time when the Drug is Not Instantaneously Absorbed
Log scale plot
Up then down, repeats getting higher every time (smooth curves)
Extra Information: Equations describing administration of a fixed dose at a fixed interval of time
Slide 43
Extra Information
Slide 44
Extra Information
Slide 45
Extra Information
Slide 46
Medication Adherence (Compliance)
Compliance issues
Prescription filled, taking as prescribed (dose, dosing interval, for duration of therapy)
Example: elderly, patients with mental disorders, patients on antibiotic therapy, patients who can’t afford meds, patients on multiple drugs
