DRUG KINETICS-NON COMPARTMENT METHODS

NON COMPARTMENT PHARMACOKINETICS

These methods involves comparison of the area under curves (AUC) in a graph plotted by taking the plasma concentration on the y-axis against the time t on the x-axis.The pharmacokinetic parameters for absorption,distribution and elimination are estimated with non compartment methods.

1.Mean Residence Time (MRT):-

The MRT is the mean average time for the drug molecules to reside inside the body.The synonyms are Mean Transit Time or Mean Sojourn Time.

The MRT depends on the route of administration with the assumption that the elimination of the drug molecules are drived from a central compartment.

The MRT is calculated by dividing the total transit or resident time for all drug molecules by the total number of drug molecules.

MRT For IV Bolus Injection

This can be calculated as follows.

                MRTIV =AUMC/AUC0-infinity

where AUMC is the area under the first moment verses time curve from t=0 to t=infinity,and AUC0-infinity is the plasma drug concentration versus time curve from t=0 to t=infinity,which is otherwise known as zero moment curve.

The MRTIV is related to the elimination half life by the following expression,

                     MRTIV =1/k

During MRTIV 62.3% intravenous bolus dose is eliminated.

The MRT for a drug given by a noninstantaneous input is longer than the MRTIV

Mean Absorption Time (MAT)

MAT is described as the difference between MRT and MRTIV after an extra vascular route is used.

                     MAT = MRTPO -MRTIV

when first order absorption occurs 

                     MAT = 1/ka

Steady State Volume Of Distribution

The steady state volume of distribution is the amount of drug in the body at steady state and the average steady state drug concentration.

After an I.V.bolus injection VSS is calculated as follows,

                      VSS = DoseIV (AUMC)/(AUC)squired         

 

DRUG KINETICS-PART-14-HEPATIC CLEARANCE

HEPATIC CLEARANCE

Liver plays a major role of deforming,modifying,detoxyfying and eliminating the drugs administered orally.Any drug taken by oral route should have to first pass through the liver and there it may or may not get modified according to its pharmacological and chemical nature.

Hepatic clearance is the volume of blood plasma containing the drug cleared by the liver per unit time.

Measurement of Hepatic Clearance

It is mathematically calculated by total body clearance substracted by renal clearance as follows,

                 ClH =ClT -ClR 

where ClH is the hepatic clearance.

In the above method the net clearance resulted from the above formula may be a rough hepatic clearance as it can be exactly defined as Nonrenal Clearance ClNR.

The exact hepatic clearance can be observed by the product of liver blood flow  (Q) and the Extraction Ratio (ER) as follows,

           ClH =QER.

The Extraction Ratio can be defined as the fraction of the drug that is irreversibly removed by the tissue of an organ when a portion of the plasma containing the drug perfuses through that organ tissue.

The ER is calculated by measuring the drug concentration of the plasma entering the liver and that concentration of the plasma exiting the liver.

                        ER = (Ca - Cv)/Ca

Values of the ER is usually ranges from 0 to 1.

For example if ER is 0.85, then 85% of the drug is removed by the liver as the plasma perfuses through the liver.If the ER is 0 then no drug is removed by the liver.

Systemic Elimination by Liver 

a)By Blood Flow

Blood flow to the liver is approximately 1.5 L/Min and may be altered by exercise,food,disease or drugs.

Drugs enter the liver through the hepatic portal vein and hepatic artery and leaves through hepatic vein.

After the oral administration the drug is absorbed by the intestine into the mesenteric vessels pass into the hepatic portal vein and into the liver.From there it goes into the general circulation.

b)By Intrinsic Clearance 

Intrinsic clearance states about the capacity of the liver to remove the drug independent of the blood flow.

Intrinsic clearance majorly occur due to the inherent ability of the biotransformation enzymes (mixed function oxidases) to metabolize the drug as it enters the liver.

Generally basal level mixed function oxidase enzymes biotransform drugs.

Drugs such as phenobarbital and nicotine may increase the activities of these enzymes.

On contrary drugs such as cimetidine and lead may decrease their activities.

c)By Protein Binding

Drugs bound by proteins are not cleared by liver or kidney as they cannot easily perfuse the the tissues of the organs.

Blood flow (Q) and intrinsic clearance (Clint) and free plasma concentration (f) can be related as follows,

               ClH = Q*(fClint)/(Q+Clint)

Factors Affecting Hepatic Clearance

1.Changes in blood flow and inhibitors of the drug metabolism enzymes which affects the hepatic clearance of the drugs(Propranolol) that have high extraction ratios and high Clint values 

2.The hepatic clearance of the drugs that have low extraction ratios and low Clint is only affected by changes in hepatic blood flow.

3.Only drugs that are highly plasma protein -bound and have a low intrinsic clearance (Phenytoin) are affected by a sudden shift in protein binding.This shift causes an increase in free-drug plasma concentration.

Biliary Drug Excretion

Biliary excretion is an active transport process in which some drugs are excreted by liver.

There are separate active systems exist for weak acids and weak bases.

1.Drugs that are generally excreted through bile are high molecular weight drugs (>500),polar drugs,such as reserpine,digoxine,and various glucuronide conjugates.

2.Recycling of drugs by enterohepatic circulation

Some drugs are absorbed from GI tract through the mesenteric and hepatic portal veins proceeds to the liver,the liver may secrete actively some drugs changed as glucuronide complexes or unchanged into the bile.

From the bile the drug may be secreted into the GI tract through the bile duct  for excretion. 

If the drug is a glucuronide complex the bacterial flora in the GI tract may hydrolyze the glucuronide moeity allowing the released drug to be reabsorbed.

Presystemic Elimination by First Pass

Usually most of oral drugs undergo first pass.A portion of the drug is eliminated before it enter into the systemic circulation.

1.First pass effects generally result from rapid biotransformation of the drug by liver enzymes.Other mechanism include metabolism by GI mucosal cells,intestinal flora,or biiary secretion.

2.First pass effects are usually observed by measuring the absolute bioavailability (F) of the drug.If F is < 1 that means some of the drug is eliminated before systemic absorption.

3.Drugs that have high liver extraction ratio such as propranolol shows first pass effects.

If the first pass effect is high (>90%) then either

The drug dose could be increased (Propranolol,penicillin)

The drug could be given by an alternate route.(nitroglycerin,insulin)

The dosage form could be modified (Mesalamine)

  

 

 

  

DRUG KINETICS-PART-13-RENAL CLEARANCE

RENAL CLEARANCE

Renal clearance is one of the major routes of excretion for hydrophilic polar drugs which means all water soluble substances are excreted through kidneys.

Kidneys are excreting the drug by glomerular filtration and active tubular secretion.

Glomerular filtration is a passive filter process in which smaller molecules are filtered through the fine meshwork in the glomerulus of the nephron.

Albumin like plasma proteins are large molecules and cannot pass through the glomerular mesh work and hence drugs bound up with this proteins escapes from filtration.

Endogenous renal excretory substances such as creatinine and insulin are not actively secreted or reabsorbed but filtered through glomerulus.Hence they are used as a marker to measure the glomerular filter rate (GFR)

Tubular Reabsorption is a passive process in which the Fick's Law Of Diffusion is applicable.

The Fick's Law states that a solute from the region of higher concentration moves to the region of lower concentration across a concentration gradient with an assumption that all the regions are in a steady state level.

1.Fat soluble substances are reabsorbed from the interstitial cells of the lumen of the nephron back to the blood stream.

2.For weak electrolytes urine pH affects the ratio of non ionized and ionized drug.If the drug is primarily non ionized lipophilic form then it is reabsorbed by the lumen of the nephron back to the blood.On contrary if the drug is primarily in a polar,ionized hydrophilic form then it is excreted through the urine.

In more acidic urine excretion of weak acids are retarded.If the urine pH is increased by alkalinization of the urine for example by the administration of sodium bicarbonate,weak acids like salicylic acids are excreted more easily.

Administration of diuretics induce diuresis which causes increased urine flow and decrease in the time for reabsorption and the result is more drugs are excreted.

Active Tubular Secretion (ATS) which involves carrier mediated active transport system that require energy.

Two types of ATS systems are available in the kidneys.One for weak acids and another for weak bases.

The ATS systems are competition based.For example probenecid a weak acid competes for the same system with penicillin which is some what stronger yet another weak acid and thereby decreasing the excretion of penicillin.

The renal clearance of drugs that are actively secreted such as p-aminohippurate (PAH) is used to measure Effective Renal Blood Flow(ERBF)

Renal Clearance is defined as the volume of the drug present in the plasma that is removed by the kidney per unit time.The units are available as ml/min or L/hr.

Renal clearance (ClR) can be calculated as follows,

     ClR  =Rate of drug excretion/Cp =(dDU/dt)/Cp

Where Cp plasma concentration,DU is the drug in the urine,and dDU/dt is the rate of drug excretion.

The renal clearance can also be expressed by another equation as follows,

              ClR  =keVD  where ke is the first order renal excretion rate constant and VD is volume of the drug distributed.

                ClR = DU power infinity/AUC

                   where DU to the power infinity or steady state is the total amount of unchanged parent compound excreted in the urine and AUC is the Area Under Curve.

Renal Clearance can also be measured with the mechanism of getting clearance ratio which relates drug clearance to insulin (GFR) as follows:-

1.If the clearance ratio is < 1 the mechanism for drug clearance may result from filtration and reabsorption.

2.If the ratio = 1 the mechanism is by filtration only

3.If the ratio is > 1 the mechanism may be by filtration and active tubular secretion.

DRUG KINETICS-PART-12-DRUG CLEARANCE

DRUG CLEARANCE

Clearance is the measurement of drug elimination from the body.

1.Total Body Clearance (Clr)

Total body clearance is the rate of drug clearance per plasma drug concentration.

The concept of clearance is a portion of the drug from the total apparent volume of distribution in the body in which the drug is dissolved,is eliminated in unit time.

The following equation express this concept of total body clearance.

a)    Clr = drug elimination/plasma concentration

        = (dDe/dt)/Cp

            Clr = VDk    -----***

       Clr = FD0/AUC 

b)For the drugs which follows linear(First Order) kinetics,total body clearance is the sum of the clearances in the body as follows.

          Clr  = ClR + ClNR
where ClR is the clearance by kidneys and ClNR is the non clearance.
The relation between Clr and t1/2  is well established by substituting 0.693/t1/2 for k in equation marked *** above as follows,
                 Clr  =  VD 0.693/Clr  where VD and Clr are considered as independent variables and t1/2 as a dependent variable.
As in renal desease clearance decreases t1/2 increases.Changes in VD also bring proportional changes in t1/2. 

 

 

DRUG KINETICS-PART-11-NONLINEAR DRUG KINETICSW

NONLINEAR OR EXPONENTIAL KINETICS

Non linear kinetics does not obey first order straight line kinetics on increase in dosages.It is the kinetics that follows after the drug is saturated in some enzymatic or carrier mediated system inside the body on increasing in dosage.In other words,the body will not move the drug immediately after administration until the drug is saturated in some system of the body.Hence this kinetics does not follow a straight line first order plot in a graph rather it follows a curved line in a graph plotted the plasma concentration values on y-axis against the time interval of the dosage on the x-axis.

1.The Area Under the Curve (AUC) does not follow the dose

2.The drug excreted does not proportional to the drug administered.

3.High doses may promote the elimination half life.

4.Increase in dosage may change the ratio of the metabolites formed.

These are the characteristics of the non linear drug kinetics.

The non linear drug kinetics are mathematically described by the following velocity reactions devised by Michalis-Menten Equation.

                     -dCp/dt  = VmaxCp/kM+Cp

where Vmax is the maximum velocity of the reaction,Cp is the sustrate or plasma drug concentration,and kM is the rate contant equals to the Cp at 0.5 Vmax.

At low C p values where kM >> Cp this equation becomes a first order kinetics because both kM and Vmax are constants.

              -dCp/dt = Vmax Cp/km =k'Cp 

At high Cp values where Cp >> kM the equation reduces to a zero order kinetic equation as follows.

                -dCp /dt   = Vmax

From the above illustration it is observed that drugs that follows non linear kinetics may show zero order elimination at high concentration ,a mix of zero-first order kinetics at intermediate concentration and a first order kinetics at low concentration.