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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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