kinetics of single and multple idoses of drugs

7/28/2019 Kinetics of Single and Multple idoses of drugs

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KINETICS FOLLOWINGSINGLE AND MULTIPLE

DOSAGE OF DRUG


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The speed of onset, intensity, and duration of a

pharmacological effect depend on the concentration of drug at itssite(s) of action

As it is difficult to collect tissue samples, the time course of drug concentration at its site of action is approximated bymeasuring drug concentration in plasma, which can be measuredwith accuracy

The plasma drug concentration-time curve is obtained by

measuring the concentration of drug in plasma samples taken atvarious intervals of time after administration of a dosage form and

plotting the concentration of drug in plasma (Y-axis) versus thecorresponding time at which the plasma samples were

collected (X-axis)

Plasma Drug Concentration-Time Profile


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If a drug is administered by oral or extravascular(IM, SC, IP, etc.) route, it slowly enters the systemiccirculation and plasma drug concentration graduallyrises to a maximum (peak level)

As the drug is being absorbed into blood, it is

distributed to body tissues and may also simultaneously being eliminated

The ascending portion of curve to the left of peak

represents the absorption phase because in this phase rateof absorption is greater than rate of distribution andelimination


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Generally, the distribution phase of non-intravenous

doses is masked by the absorption phase

The descending section of curve to the right of peak generally represents the elimination phase because in this phase rate of elimination exceeds rateof absorption

The rate or velocity with which absorption andelimination processes occur is given by respectiveslopes of the curve and are expressed by absorptionrate constant (K a) and elimination rate constant

(), respectively


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2. Maximum safe concentration (MSC) orMinimum toxic concentration (MTC):

It is the concentration of drug in plasma above which toxiceffects are produced. Concentration of drug above MSC is said to

be in toxic level. The drug concentration between MEC andMSC represents the therapeutic range

3. Maximum plasma concentration/Peak plasmaconcentration (C max or C Pmax) : It is the point of maximum concentration of drug in plasma

The maximum plasma concentration depends on administereddose and rates of absorption (absorption rate constant, K a) andelimination (elimination rate constant, ) The peak represents the point of time when absorption rateequals elimination rate of the drug ( g/ml)


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3. Area under curve (AUC): It is the total integrated area under the plasma

drug concentration -time curve. It expresses thetotal amount of drug that comes into systemiccirculation after administration of the drug

4. Peak effect: It is the maximal or peak pharmacological effect

produced by the drug. It is generally observed at peak plasma concentration.


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5.Time of maximum concentration/Time of peak concentration (t max )

It is the time required for a drug to reach peak concentrationin plasma. The faster the absorption rate, the lower is the t max

It is also useful in assessing the efficacy of drugs used to treatacute conditions (e.g., pain) that can be treated by a singledose. It is expressed in hr

6. Onset of action

It is the beginning of pharmacological response produced bythe drug. It occurs when the plasma drug concentration justexceeds the MEC


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Temporal characteristics of drug effect and relationship to the therapeutic window(e.g.,singledose,oral administration).


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A lag period is present before the plasmadrug concentration (Cp) exceeds theminimum effective concentration (MEC) forthe desired effect.

Following onset of the response, theintensity of the effect increases as the drugcontinues to be absorbed and distributed.

This reaches a peak, after which drugelimination results in a decline in Cp and inthe effects intensity.

Effect disappears when the drugconcentration falls below the MEC.

Accordingly, the duration of a drugs action isdetermined by the time period over whichconcentrations exceed the MEC. An MEC

exists for each adverse response, and if drugconcentration exceeds this, toxicity willresult.


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The therapeutic goal is to obtainand maintain concentrationswithin the therapeutic windowfor the desired response with aminimum of toxicity .

Drug response below the MEC forthe desired effect will besubtherapeutic ; above the MECfor an adverse effect , theprobability of toxicity willincrease.

Increasing or decreasing drugdosage shifts the response curveup or down

Increasing the dose also prolongsa drugs duration of action, at therisk of increasing the likelihood of adverse effects.

AUC can be used to calculate theclearance, Bioavailability

Thus, the therapeutic goal is tomaintain steady-state druglevels within the therapeutic

window.


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Orders of Pharmacokinetic Processes

The rate at which various pharmacokinetic processes(ADME) occur is affected by the amount of drug in body

The manner in which concentration of drug influences

the rate of a process is called the order of process

The three commonly encountered rate processes in pharmacokinetics are

Zero order processFirst order process

Mixed order process .


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Zero-order kinetics


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1. Zero-order process/Zero-order kinetics

Zero-order process (constant-rate kinetics ) may be defined asa pharmacokinetic process whose rate is independent of theconcentration of drug

The rate of pharmacokinetic process remains constant andcannot be increased further by increasing the concentration of

drug. In other words, in the zero-order kinetics a fixed amount/

quantity of drug is processed per unit time. Examples of zero-order kinetics include metabolism and

absorption, distribution, and excretion of drugs by carrier mediated transport under saturated conditions

Administration of drugs by a constant rate IV infusion or bycontrolled delivery system (e.g., implants) also tends to follow

zero-order kinetics.


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Examples of drugs that follow zero-order kinetics are alcohol, phenytoin, salicylates, etc

In the zero order kinetics as a constant/ fixed amount of drugis eliminated per unit of time, the half-life of a drug undergoingzero-order elimination is not constant but is proportional to theconcentration of drug in the plasmaTherefore, the zero-order half-life rises with increase in drugconcentration and declines with decrease in drug concentration

Applications of zero-order processes include administration of adrug as an intravenous infusion, formulation and administrationof a drug through controlled release dosage forms andadministration of drugs through transdermal drug deliverysystems.

Special care is needed while increasing dose of drugs whichfollow zero-order kinetics to avoid adverse drug effects


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2.First-order process/First-order kinetics:

First-order process (first-order kinetics or linear kinetics) may bedefined as a pharmacokinetic process whose rate is directlyproportional to the concentration of drug

Greater the concentration, faster is the process. In contrastto the zero-order kinetics, in first-order kinetics a fixed fractionof drug is processed per unit time

It is because of such a proportionality between the rate of process and the concentration of drug that the first-order processis said to follow linear kinetics i.e. log-plasma concentration-time curve is linear.


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First-order kinetics


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The first-order pharmacokinetic processes are

nonsaturable over a wide range of plasma concentration First-order elimination is extremely important in

pharmacokinetics since the majority of therapeutic drugsare eliminated by this process.

Most drugs follow first-order kinetics in absorption,distribution, and elimination

In the first-order kinetics as a constant fraction of drug is

eliminated per unit time, the half-life of a drugundergoing first-order elimination remains constant andindependent of drug concentration in plasma


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Conc. Vs. time plots


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3.Mixed-order process/Mixed-order kinetics

Mixed-order process (mixed order kinetics , non-linear kinetics or dose-dependent kinetics ) maybe defined as a

process whose rate is a mixture of both zero-order andfirst-order processes

The mixed order process follows zero-order kinetics athigh concentration and first order kinetics at lower concentration of the drug

This type of kinetics is usually observed at increased or multiple doses of some drugs


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The phenomenon is mainly seen when a particular pharmacokinetic process that involves presence of

carriers or enzymes , which are substrate specific andhave definite capacities, and get saturated at high drugconcentration

Since deviations from an originally linear pharmacokinetic profile are observed, the rate process of such a drug is called non-linear kinetics

Mixed-order kinetics has been observed in absorption(e.g.,vitamin C), distribution (e.g., naproxen), andelimination (e.g., riboflavin) of some drugs.


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Dosage Calculations:

Loading dose- dose to establish a rapid therapeutic [drug] plasma = V d x desired [drug] plasma

In the case of toxic drugs (digitalis) Loading dose is dividedinto several portions and given over a long time

Maintenance dose = dose required to maintain a desired steady-state

Rate of el imination (i n hour s) x dosage interval i n hour s

At steady state: rate of elimination=rate of administration (absorption) Rate of el imination = Cl x avg [Drug] steady-state plasma


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What is Steady State (SS) ?

Rate in = Rate Out

Reached in 4 5 half-lives (linear kinetics)

Important when interpreting drugconcentrations in time-dependentmanner or assessing clinical response


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Steady-State

Steady-state occurs after a drug has been given for approximately five elimination half-lives.

At steady-state the rate of drug administration equals therate of elimination and plasma concentration - timecurves found after each dose should be approximatelysuperimposable.

A l i S d S


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100

187.5194

175

150

75

87.5 9497

50

200

100

Accumulation to Steady State100 mg given every half-life


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C

t

Cp a

Four half lives to reach steady state


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Acute vs Steady State


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Drug Metabolism and pK


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Steady-State Concentration (Css)

Steady-state (ss) is defined as the time during whichconcentrations remain stable or consistent when drugis given repeatedly or continuously (IV infusion)The time to reach steady state is a function of

elimination half-life (t 1/2) and is achieved when therate of drug entering systemic circulation equals therate of eliminationFor most drugs, the steady state concentration isreached in approximately 5 half-livesThe time to reach steady state is independent of dosesize, dosing interval and number of doses

C ti d lti l d ki ti


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Steady-State Principle:for drugs exhibiting first-order pharmacokinetics

Rate of administration or absorption Rate of elimination rate

[Drug] [Drug] plasma [Drug] Urinerate= [Drug] x k a rate =[Drug] Plasma x k e

Initially rate of admin. or absorption greater than rate of elimination because initially [Drug] is low

-rate of elimination gradually increases as [Drug] plasma increases

and reaches a plateau. This is termed the steady-state concentration

Continuous and multiple dose kinetics


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Multiple Dosing

When a drug is administered in a fixed dose at fixedintervals, the plasma concentration rises exponentiallyto a plateau or steady state with a half time of increasethat is equal to the elimination half-life of the drug

Thus 50% of the steady state level is achieved in oneelimination half time, 75% (50 + 25) in two, 87.5% (50+ 25+12.5) in three, 93.75% (50 + 25 + 12.5 + 6.25) infour, 96.88% (50 + 25 + 12.5 + 6.25 + 3.13) in five


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It takes 5 half-lives to complete a 1 St order process:(1/2 n)=1/ 2x2x2x2x2= 1/32= 0.03 or 3% remains or 97% produced

after 5 half-lives


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And so forth [when the first dose D 0 is

administered at time 0, the amount of drug in bodywill be D = D 0

At the next dosing interval (equal to on t 1/2) whenD = 1/2 D0, the amount remaining in the body,administration of next dose (D 0) raises bodyconcentration to D = D 0 + 1/2 D 0, and so forth]

During the initial period, the intake is more than theelimination, so there is continuous rise in plasmaconcentration.


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Subsequently, when the intake equals the elimination,

a steady state is reached

In practice, a useful estimate of time to reach a

steady state is obtained by the equationTime to 95% steady state = 4.3 x t 1/2

Therefore, the shorter the half-life , the more rapidlysteady state is reached, and vice-versa

A l ti


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Accumulation

Accumulation is the ratio of maximum plasmaconcentration following the dose at steady state comparedwith that following the first dose (i.e: C ss, max / C 1 max )The extent to which a drug accumulates in body during

multiple dosing is a function of dosing interval andelimination half-life , but is independent of dose sizeIf the elimination half-life is equal to the dosing interval

(T = t 1/2) then at steady state level, the drug will

accumulate two folds (C ss, max / C 1 max = 2)When T< t 1/2 , the degree of accumulation will be greater,and drug may show toxic responses


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Fl t ti


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Fluctuation

Fluctuation is defined as the ratio of the maximum

concentration to the minimum concentration of drug in plasmaat steady state (i.e., C max /Cmin). Greater the ratio, greater will

be the fluctuationFluctuation primarily depends on dosing interval and half-life

of drug, but is also affected by dose sizeFor a given dose, if dosing interval is increased, C maxand C min will decrease (drug efficacy will decrease), but the fluctuationswill increase

The opposite is observed when dosing interval is reduced;toxicity of drug in such cases may increase due to greater drugaccumulation .


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On the other hand, for a given dose interval, if dose size isincreased, C max and C min will increase with greater fluctuationsduring each dosing interval; toxicity of drug in such cases alsoincrease due to higher drug concentrations

The greatest fluctuation is observed when the drug is given as IV bolus. Fluctuations are small when the drug is given

extravascularly because of continuous absorption of the drug

Administration of smaller doses in less frequency results in smallfluctuations

Administration of drugs by intravenous infusion maintains aconstant steady state or plateau level without fluctuations (IVinfusion is the only method which does not produce fluctuations)


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I. Single-dose kinetics Plasma [Drug] curve

Upon administration[drug] plasmareaches a max Then begins to decline as the

Drug is eliminated Cp max : max plasma [drug] t max : time to reach Cp max AUC : area under the curve These measures are useful for

comparing the bioavailabilityof different pharmaceuticalformulation


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kinetics of single and multple idoses of drugs

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