Flashcards in 2. Applied Pharmacokinetics Deck (45):

1

## 1. 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

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## 2. 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

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## 3. 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

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## 4. Know how to calculate the concentration (or amount of drug) present during a constant intravenous administration (objective)

### Answer later

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## 5. 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

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## Drug Metabolism

### Occurs via enzyme-catalyzed reactions, and thus follows Michaelis Menten kinetics

7

## 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

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## 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

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## First Order Reaction Phase

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V=(Vmax[D])/Km

Steep red-dotted incline

See slide 7

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## First Order Reaction

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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

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## Zero Order Reaction Phase

### Graph of plateau (V=Vmax)

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## Zero Order Reaction

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When concentration of drug is relatively high

V=Vmax

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## Change in Reaction Velocity as a Function of Drug Concentration

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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

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## Nonlinear Pharmacokinetics

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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

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## Nonlinear pharmacokinetics: zero vs first order drug accumulation

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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)

16

## 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

17

## 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_

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## 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

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## Differential Equation Describing the Rate of Change in the Amount of Drug in the Body

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(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)

20

## Integrated Rate Equation for the First Order Elimination of a Drug (integrated from differential equation)

###
D=Do*e^(-ke*t)

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

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## Integrated rate equation (in terms of concentration)

###
C= Coe^-ket

C=(Do/Vd)(e^-ket)

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## Uses of Integrated Rate Equation

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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)

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## Alternative forms of the integrated first order rate equation

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D/Do=e^-ket

Ln(D/Do)=-ket

LogD= (-ket/2.3)+logDo

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## Plot of First Order Elimination of a Drug with Time

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D (drug remaining in body) vs Time Graph

D=Doe^-ket

Downward plateau

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## Log Plot (of first order elimination)

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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)

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## 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)

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## Log Plot of the Amount of Different Doses of the Same Drug Remaining in the Body with Time

### Slide 27 (clarify after lecture)

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## Half-Life of Elimination (time required to reduce the amount of drug to one-half initial value)

###
1. ln(D/Do)=-ket

2. When one half drug metabolized (D/Do=50/100)

ln50/100=-ket

3. -0.693=-ket

4. t1/2= 0.693/ke *****

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## Recall: Clearance

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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

30

##
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)

31

## Maintenance Dose

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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.

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## 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

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## Maintenance Dose (clearance equation)

###
Drug administration=drug elimination=CL*Css

Bioavailability:

F*administered dose=CL*Css

****Maintenance dose=(CL*Css)/F

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## Constant Intravenous Infusion

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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

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## Infusion of Drug into Body is Governed by Same Processes as Adding Water to a Tank

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Q/Vd is infusion

dC/dt is rate

-keC is elimination

Slide 36

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## More equations (Cmax)

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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

37

## Plot of Concentration of Drug in Body with Time of Infusion

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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

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## Administration of a fixed dose at a fixed interval of time

### Blank slide

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## Plasma Concentration of Drug During Constant Dose, Constant Interval of Time Schedule

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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

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## Plasma Concentration of Drug with Time when the Drug is Not Instantaneously Absorbed

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Log scale plot

Up then down, repeats getting higher every time (smooth curves)

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## Extra Information: Equations describing administration of a fixed dose at a fixed interval of time

### Slide 43

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## Extra Information

### Slide 44

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## Extra Information

### Slide 45

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## Extra Information

### Slide 46

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