DRUG KINETICS-PART-10-TWO COMPATMENT MODELS(ORAL)

TWO COMPARTMENT MODELS(ORAL )

In oral administration a drug may not show two comparment models if it absorbed with a rapid distribution and elimination.As the drug is absorbed it is distributed and equibrates with the tissues so that the eliminaion half life of the drug equals to 0.693/b where b is the first order elimination rate constant.

A drug after oral administration shows two compartment models if it is rapidly absorbed and distributed and eliminated slowly.

In general the addition of each new compartment to the model requires an additional first order phase.

The addition of a third new phase indicates the drug has an additional slow distribution and equillibrating into some deep tissue portion.If the drug is given at intervals then it begins to accumulate in the third compartment.

The terminal linear phase in a graph plotted the values of the plasma concentration in the y-axis against time intervals in x-axis represents the elimination phase by the body after equilibration occurs as the last compartment.The rate constant from the elimination phase used to calculate the dosage regimen.

A clear description of multicompartment models is possible only if there are distinct pictures of plasma concentration values from absorption distribution and elimination are available.

DRUG KINETICS-PART-9-MULTI COMPARTMENT MODELS

MULTICOMPARMENT MODELS

In this when a drug is administered inside the body the entire body cannot act on the drug as a whole single compartment because of the nature of some drugs which distributes into the body in different rates.

The drug distributes more rapidly in the tissues of high blood flow than the tissue area with low blood flow.Drug concentration in various tissues depends on the physical and chemical characters of the drug and the nature of the tissues.

Highly lipid soluble drugs accumulates in fatty tissues.

Two Compartment Models (I.V.Bolus Inj.)

When a drug is given through I.V.Bolus Injection the drug get rapidly distributed in highly perfused tissues (central compartment) and more slowly into peripheral tissues(tissue compartment)

The initial rapid decline in the plasma concentration is due to distribution into the tissues(distrbution phase) followed by the slower rate of decline after the  distribution reaches the equillibrium is known as the elimination phase.

The apparent volume of distribution depends on the type of drug kinetics calculations

Volume of distribution is the some of volume of distribution in the central compartment(Vp),the volume of distribution at steady state(Vss),and the volume of distribution at the tissue compartment(Vt)

DRUG KINETICS-PART-8-MULTIPLE DOSES

MULTIPLE DOSES

In this post we deal with the action of our body on the drug administered in multiple doses.Multiple dosages are employed to treat chronic illnesses.When a drug is given more frequently before the previously administered dose of the drug is completely eliminated by the body then the drug is accumulated in the blood to reach a steady state level after which the body eliminates the extra drug available.

A steady state plasma drug concentration (C to the power of infinity) fluctuates between maximum (Cmax to the power of infinity) and a minimum (Cmin to the power of infinity)

When a multiple dose regimen is calculated according to the super position principle it is assumed that the previous dose given has no effect on the following dose.

Hence the precalculated plasma drug concentration is the the sum of plasma concentration obtained by adding all the residual concentrations present after each previous doses.

When a multiple-dose regimen is designed it is possible to adjust the dosing rate very easily.This can be calculated by the size of the dose (D0) per time intervals(T) 

          Dosing Rare = D0/T

Thus   Dosing Rate = Average drug concentration at steady state (Cave to the power of infinity)

(e.g)  :- If a 500mg dose (D0) is given every 10 (T) hours the dosing rate is = D0/T =500/10 =50mg per hour.

Similarly a 100 mg dose given every 2 hours and a 300 mg dose given every 6 hours also gives the same 50mg per hour to produce the required Cave to the power of infinity or the steady state.

A higher dose such as 1000 mg given with a longer interval of time such as every 20 hours will produce higher fluctuaions such as higher Cmax and lower Cmin where as a lower dose such as 100 mg given more frequently with a shorter duration of intervals such as every 2 hours will yield a minimised fluctuations.

Certain antibiotics are given by rapid multidose I.V.bolus injections.

          Cmax at steady state(to the power infinity) can be calculated by (D0/VD )/1-e to the power -kT

Similarly the Cmin is calculated by 

 Cmin at steady state(power infinity)  =  Cmax at infinity multiplied by e to the power -kT

Average drug concentration Cave at steady state or infinity can be calculated by 

                  Cave at steady state=FD0/kVDT

For I.V bolus injections, F=1

Drugs Administered by Oral Routes   

In this multiple dose regimen in which the drug is immediately released such as oral liquids,tablets and capsules the drug is rapidly absorbed and slowly eliminated.

The elimination constant k is very very smaller than the absorbing constant kA

                                                        k  <  < kA

               Cmax at steady state =(FD0/VD) multiplied by (1/1-e power -kT)

          Cmin  at steady state =[FD0kA/VD(kA-k)]multiplied by [1/(1-e power -kT)] multiplied by e power -kT

The calculation of Cave at steady state is similar to the calculation given under multiple I.V.bolus injections

The factor (1/1-e power -kT) is the accumulation rate.

The fraction of the drug f  remaining in the body after each dose is calculated as follows

                        f = e power -kT

An initial loading dose DL is given to obtain the required therapeutic steady state drug level quickly.

                         DL   = DM multiplied by (1/1-e power -kT) where DM is the maintenance dose.

If DM is given at a dose interval equals to the elimination half life then DL equals twice the maintenance dose.    

 

   

DRUG KINETICS-PART-7-INTERMITTENT INTRAVENOUS INFUSIONS

INTERMITTENT I.V.INFUSIONS

In this post we deal with the action of body on the drug infused through the vein intermittently,in short periods to prevent the accumulation of the drug to produce toxicity.

Generally aminoglycosides such as gentamycin is infused for one hour in every 12 hours.In this course a steady state plasma concentration CSS  is not commonly reached.CSS is avoided to prevent drug accumulation to produce toxixity.

The peak plasma concentration is calculated as follows:-

                CPn    =R(1-e power -kt)(1-e power -nkt)/Cl(1-e power -kT)

Cpn is peak drug concentration,R-is the rate of drug infusion,Cl-is the total body clearance,T-is the dosage interval,and t-is the time duration of infusion.  

 

DRUG KINETICS-PART-6

HOW THE BODY MOVES DRUGS

In this post we see how the body moves the drug administered by,

Intravenous Infusion:-

When a drug is administered through continous intravenous drip the body absorb it by a zero order process that means the absorption is constant at a given time independent of the initial concentration or the concentration available for absorption followed by the elimination in a first order process that means the elimination occurs with a direct proportion to the available concentration.

Similarly a few oral controlled release tablets also follows a zero order absorption and first order elimination by the body.

The plasma concentration Cp at any time after the start of the I.V. infusion can be calculated by the following equation,

                     Cp  = [R/VDk ](1-e to the power -kt)

R-the zero order rate of infusion given in units as milligrams per constant time.

If the infusion stopped then the Cp decreases with the first order elimination.

k-the elimination half life can be calculated from the slope by plotting the declining Cp value against time.

As the infusion is continued the Cp increases to a plateau which is known as the plasma steady state concentration abbreviated by Css.

At the steady state concentration the rate of absorption equals to the rate of elimination.

                 Css  = R/VDk

and the rate of infusion can be calculated by the rearrangement of the above equation by the desired known values of Css,VD and k as follows'

                     R = Css *VD k.

where Css is the target desired concentration and the product of VDk is equals to total clearance ClT.

A loading dose DL is the initial I.V.bolus injection to attain the Css as quicly as possible.Once the point of steady state is reached we can start the infusion.

The time to reach Css depends on the elimination half life of the drug.

To reach a 99% of Css without dosing a DL it takes a time of 6.65 half life.

Hence DL is necessary to reach the Css quickly.

The DL can be calculated as follows.

          DL =Css * VD   or  R/k

For a highly toxic drug with a narrow therapeutic window an I.V.drip provides a relatively constant plasma concentration which should not be more than the Minimum Toxic Concentration(MTC) and shold not be less than the Minimum Effective Concentration(MEC).    

  

    

DRUG KINETICS-PART-5

MOVEMENTS OF THE DRUG BY THE BODY

Movements after Single Oral Dose

Any drug which has been given by oral formulations such as tablet,syrup,elixir,capsules,or pills is rapidly absorbed by the intestine in a first order kinetics that means the higher the drug concentration the higher the absorption.Elimination also follows in a first order kinetics.

When the values are plotted on a graph by taking the plasma concentration on the y-axis and the time in the x-axis it shows the elevation of the absorption line to a peak plasma level at the given time followed by the declining line shows the rapid elimination of the drug in the post absorption period.

The following equation express the the drug movement by the body in a first order absorption and elimination principle.

                   Cp  = [FD0kA/VD(kA-k)](e to the power -kAt minus e to the power -kt)

where D0 - is the drug given by oral route.

           VD -is the volume of distribution,

           k-is the first order elimination constant. 

           kA-is the first order absorption rate constant and      F- is the fraction of the drug's bioavailability.

From the above equation it can be observed that any change in any of the following factors F,D0,VD,kA,and k will affect the plasma concentration Cp.

The time for the maximum or peak absorption can be expressed by the following equation,

               Tmax   =  2.3 log (kA-k)/kA-k

It is observed from the above equation that Tmax is affected by the rate constants only and not by any other factors.

The maximum plasma concentration Cmax can be calculated as follows,

                Cmax=[FD0kA/VD(kA-k)](e to the power of -kAtmax minus e to the power of -ktmax)

Lag Time

Lag time is well defined as a delay in systemic absorption due to delayed stomach emptying or other factors.

     

  

DRUG KINETICS-PART-4

SINGLE COMPARTMENT MODELS

In this model the whole body behaves as a single compartment on whatever the mode of administration of the drug.

Intra Venous Bolus Injection

In an intravenous bolus injection the whole dosage of the drug enter into the blood directly without any medium of absorption.The drug once entered into he blood distribute and equillibrates into various tissues.The body eliminates the drug in first order kinetic.

The volume of the drug distributed(Vd) multiplied by The total amount of the drug in the body(Db)equals to he bolus dosage.

The intravenous dose divided by the Vd will yield the extrapolated initial drug concentration C0(p).When the first order elimination proceed the slope of the graph is represented by k/2.303 where as k-is the first order elimination constant.k-can be calculated by summing up the first order elimination rate constants by various means such as metabolism and renal excretions as follows,

                       k  =  km    + ke
where km-- the rate constant by metabolism
           ke -  the rate constant by excretion.
The elimination half life is calculated by
                         t1/2  = 0.693/k
The volume of distribution Vd is the imaginary volume of body fluid in which the drug is dissolved.
Vd is needed to estimate the amount of drug in the body relative to the concentration of the drug in plasma as follows,
                           Vd  * CP =Db 
where Vd is the apparent volume of distribution,Cp is the plasma concentration and Db is the amount of drug in the body.
The Vd  and Cp both are inversely proportional to each other.If more drug is distributed extravascularly in the tissues then the Vd is increased and the plasma concentration Cp is decreased and vice versa.
The above equation can be rearranged to find out the apparent volume of distribution (Vd) as follows,
            Vd  =  Db(0)/Cp(0)
Db(0) is the amount of drug given by intravenous bolus injection and Cp(0) is the initial plasma concentration of the drug assumed by extrapolating the slope at the y-axis at which x-axis is zero.  
        

DRUG KINETICS-PART-3

MOVEMENTS OF THE DRUG BY THE BODY

First Order Reaction

In this kind of order of reaction,the rate of the reaction or the changes in concentration(C) is  proportional to the initial concentration(C0) of the drug with respect to time.

Mathematically this can be written as,

                    C is directly proportional to C0

                                       or

                               dC/dt = -kC

The drug concentration changes with respect to time(dC/dt) equals to the product of the rate constant(-k)

and the remaining drug concentration(C).

In otherwords the rate of reaction is directly proportional to concentration of the reactants.This can be expressed as C=C0e-kt in which C is the concentration of the reactants,C0 is the initial concentration,k is the first order rate constant in units of reciprocal of time,and t is time.

                           
                              C=C0e-kt

                         Int C = -kt+Int C0

                         log C =-kt/2.303+log C0

On putting the above equation on a graph we can see a negative descending linear slope which equals to -kt/2.303.It shows the time increases exponentially as the initial concentration(C0) of the reactants decreases.

The half life (t1/2) of the reaction can be defined as the time required for the concentration of a drug(C0) of a drug to one half of its initial value(C1/2).

The half life of a drug which is moved by the body on a first order reaction basis can be expressed as follows.

                     t1/2    =  0.693/k

According to the above expression the half life of the first order reaction is a constant.

The half life of the drug is very important which says that by how much speed a drug is eliminated from the body.The higher value of half life the slower the drug is eliminated.