PHARMACOKINETIC

PARAMETERS

WHAT ARE THE IMPORTANT PHARMACOKINETIC PARAMETERS:

1. volume of distribution (Vd)

2. Half life 3. Clearance

VOLUME OF DISTRIBUTION

Also referred to as APPARENT VOLUME OF DISTRIBUTION

As a general rule, V does not represent a physiological volume (real volume) but an apparent volume intowhich the drug would have to distribute to achievethe measured concentration.

The volume of body fluid in which the drug distributes itself at a concentration which is in equilibrium with the plasma concentration of the drug it is not necessary that the volume in which the drug distributes itself contain equal conc. Of the drug and it is possible that the drug is present in different concentration through out its distributed volume the total body water is called as the REAL VOLUME OF DISTRAIBUTION

drugs which binds selectively to plasma protein e.g. WARFARIN have

Vapp < V real

And lie between blood volume and total body water that is between 6 to 42 liters drugs which bind selectively to extra vascular tissue e.g., CHLOROQUINE

Vapp > V real And always more than 42 liters .

Drugs Vd lit/70 kg heparin 5digioxin 420

Mathematical formula :

1. Vd = amount of drug in body amount of drug in plasma

Case 1 : 120mg in body 20 mg/ml in plasma= 6 liter

Case 2: 120 mg in body 1 mg/ml in plasma=120 liter

Low Vd High drug in plasma

high VdLow drug in plasma

The principle of volume of distribution. With Drug A, the measured concentration in the sampling compartment is 10 mg/l,therefore the volume is estimated at 10 litre (100 mg/10 mg/l). Drug B is highly bound to plasma proteins, therefore the measured concentration of 100 mg/l results in an estimated volume of 1 litre. Drug C is extensively distributed into the tissues and the measuredconcentration of 1mg/l gives an apparent volume of 100 litre.

The volume of distribution is therefore mainlydetermined by the ratio of plasma to tissue bindingand by how much of the total amount of drug inthe body is outside the sampling compartment (i.e.the blood). Other factors, such as lipid and watersolubility, may also be important. For example, thevolume of distribution of chloroquine, whichaccumulates in several tissues, is 204 litre/kg7,while gentamicin, which is water soluble, has avolume of distribution that approximates to theextracellular fluid volume.

Volume of distribution (V) can be defined as a proportionality constant that links the amount ofdrug in the body to the measured plasma concentration2 . As the con of the drug in the body is equal to the given dose so

Vd = dose Cp3. if we want to calculate the volume of distribution at the elimination phase then we consider the following graph.

So now the concentarattion in the body is Co hencee

Vd = Co Cp

CLEARANCE

volume of body fluid that is completely cleared of drug per unit time CLEARANCE =volume = ml time minVoloume of the blood which is cleared of the drug which is irreversibly removed from the body w.r.t time

Nothing about the amount of drug but it is volume of body fluid cleared of drug When we talk about the amount it is the rate of elimination It is the proportionality factor used to determine the

rate of elimination

So ;Rate of elimination = clearance * concentration mass / time volume / time mass/volume

Zero order kinetics

clearance

clearance = Vd * Kel ( 1st order elimination rate constant ) volume /time volume 1/ time

K el = cl/Vd

Total clearance Cl tatal = renal clearance + hepatic clearanc + other routes

most important clinically Rate of eliminatin =Cl tot * Cp

Organ clearance

The volume of blood that is completely cleared of drug per unit of time by the patient 'organ.this is the measure of efficiency of the organ in the elimination of drug from the blood reaching the organ .

is the product of extraction ratio and blood (or serum) flow rate clearance = extraction ratio * flow rate volume/time volume 1/time

the units of clearance are therefore volume/time (e.g. litre/h or ml/min).

Extraction ratio describes the efficiency with which an organ of elimination (e.g. liver, kidney, etc) removes a drug from the blood.It can be determined by measuring the concentration entering (Cin) and leaving (Cout) the organ.

If Cout = 0, the drug will be totally removed and the extraction ratio will be 1.However, if Cout = Cin, there is no drug removaland the extraction ratio will be 0.The extraction ratio generally lies somewhere between these two values

Flow rate determines the rate of drug delivery tothe eliminating organClearance represents the irreversible removal of adrug from the body and determines the averagesteady state concentration achieved with a regularmaintenance dose

now,

Organ clearance = rate of drug entering organ – rate of drug leaving organ conc of drug enetring organ

Where as the rate of drug entering the organ = blood flow in artery* conc of drug in plasmaThe rate of drug leaving the organ = blood flow in vein* cinc of drug in plasma

For every drug, each organ of elimination has its own clearance (e.g. hepatic clearance, renal clearance). The total body clearance results from the addition of these clearances: CL= Renal CL+ Hepatic CL+ other CL

Renal clearance ClrClearance of the drug from the body w.r.t time via kidney is called as renal clearance Renal excretory process takes place via 1. glomerular filtration 2. Active tubular secretion3. Tubular reabsorobtion Usually, a drug's renal clearance is proportional to the patient's renal function. Whether a drug's dosing rate needs to be modified in patients with renal dysfunction depends on whether the drug is primarily excreted through the kidneys and whether increased drug levels are associated with adverse effects.

Mathematically

Renal excretion rate = renal clearance * drug plasma conc that is the rate of drug passing through the kidney is equal to the drug excreted by the kidney

Renal clearance = renal excretion rate = blood flow (Q) * E.R drug in plasma Cp Renal clearance = filtration rate +active secretion – tubular reabsorbt ion plasma drug conc

Hepatic clearance volume of the body fluid cleared of drug per unit of time via liver hepatic clearance depend upon 1. hepatic blood flow (e.g. congestive heart failure)2. plasma protein binding (e.g. hypoalbuminemia,

displacement by other drugs)3. hepatic enzymatic activity (e.g. liver failure, specific

inhibition or induction by drugs, genetic polymorphism) also reffered to as intrinsic activity of liver

Whlie taking about the hepatic clearance a term is INTRNISIC HEPATIC CLEARANCE , it is the ability of liver to remove the drug from the body fluid in the absence of other suppressing factors.(blodd flow and protein binding)

Mathematically CLH = Qcpa –Qcpv Cpa = Q (cpa –cpv)) cpa extraction ration (E.R) = cpa – cpv cpa

CLH = Q* E.R HENCE RATE OF DRUG ENTERING MINUS LEAVING THE ORGAN IS NOT EQUAL TO EXTRACTION RATIO

ORGAN CLEARANCE = RATE OF – RATTE OF DRUG DRUG ENTERING LEAVING

CONC OF DRUG ENETERING

HALF LIFE

INTRODUCTION :A drug half life is the time it takes for half of the given dose to b eliminated from the body or bloodstream there are two types of half lives 1. BIOLOGICAL OR ELIMINATION HALF LIFE is the time

it takes for the bioactivity of the drug to reduce by 50% of its initial value

2. PLASMA HALF LIFE is the takes it takes for the concentration of the drug in the blood stream to reduce by 50%

We at this point are more concerned with PLASMA HALF LIFE

Plasma half life is the time measurement which starts when the drug reaches equilibrium that is equal amount of the drug is at administration site and in the blood circulation or it is fully absorbed

There are furthur two tyes of plasma half life 1. DISTRIBUTION HALF LIFE =when plasma level fall to

half of what they were at equilibrium due to distribution in body tissues

2. ELIMINATION HALF LIFE =when plasma level fall to half of what they were at equilibrium due to drug being metabolized and eliminated

While both half lives contribute to the effects of the drug on behavior ,it is elimination half life that is used to determine dosing schedules , to decide when it is safe to put patient on a new drug, etc

RULE OF 5 HALF LIFE : 5 * elimination half life is equal to the time at which the

drug is completely (97%) eliminated from the body (assuming that the drug is given in a single orignal dose )

No of half life Drug removed %

Remaing drug%

1 x ½ life 50 502 x ½ life 75 253 x ½ life 87.5 12.54 x ½ life 93.75 6.255 x ½ life 96.87 3.13

Half life of 1st order kinetics : half life of first order kinetics is constant

elimination rate constant is not actually a constant and changes with a change in conc of drugThey enzymes do not have achieved their Vmax consider the following example

time (hr )

plasma conc ( mg/lit)

Elimination rate = chnge in Cp/change in time

1 8 8-4 /1 =42 4 4-2/1= 23 2 2-1/1= 14 1 1-

0.5/1=o.5

Half life of zero order kinetics : half life is not constant elimination rate constant is a constant value irrespective of the conc of the drugThe enzymes have achieved their Vmax consider the following example

Time (hr)

Plasma con (mg/ml)

Elimination rate = chnge in cp/chnge in time

1 8 22 6 23 4 24 2 2

Some time a drug may have dual order of kinetics that is as the time passes the enzymes which were not previously fully saturated during the 1st order kinetics become fully saturated and the increase in conc of drug do not cause an increase in the rate of elimination which become constant that is independent of conc of drug so it becomes zero order kinetics for example , salicylates , ethanol , phenytoin

Time

Cp1st order

Zero order

Mathematically

half life = 0.693 / KelThis reflects that the elimination half life is inversely poportional to rate of elimination More the rate of elimination lesser will be the stay of drug with in the body and thus shorter will be the half life and vice versa .

Interrelationship of the three parameters t ½ = o.693/ Kel

And ,

Kel = clearance /VdSo , t ½ = o.693 Vd / clearance

From the equation we can say : half life has inverse relation with the clearance , more is the clearance shorter will be the half life half life has direct relation with the Vd . More the Vd more time will be taken by the drud to elimate and thus more will be half life .