Pharmacokinetics of an IV and EV dose

 The knowledge about kinetics helps us to modify the dosing parameters pertaining to patient's specific needs.

In the last post we saw the how clearance parameter was derived using various factors , here we'll see the rest of  parameter

Clearance

Clearance is the volume of fluid presented to the eliminating organ that is effectively cleared of drug per unit time

DRUG ELIMINATION  is defined as the sum total of  metabolic inactivition and excretion.

k = Rate of elimination / Amount in the reservoir

   = Cl . C / A

   = Cl . C / V.C

Fractional rate of elimination (k) = Cl/v (aka first order elimination rate constant)

fig. 1: Compartment model for distribution and elimination

FIRST ORDER KINETICS

The rate of elimination is directly proportional to the drug concentration , Cl remains constant 

fig.2: As the concentration of the beaker increases the rate of elimination also increases. The water being removed demonstrates the rate of elimination and the water in the beaker refers to the drug
concentration. source: http://www.NonstopNeuron.youtube.com

ZERO ORDER KINETICS

The rate of elimination remains constant irrespective of drug concentration , Cl decreases with increase in concentration.

fig.3: The cars irrespective of their number only couple of cars can pass through the checking here cars referring to the drug concentration and couple of cars passing through refers to the constant rate of elimination. source: http://www.NonstopNeuron.youtube.com  

Half-life 

Half - life in the context of medical science typically refers to the elimination half-life. The definition of elimination half - life is the length of time required for the concentration of a particular substance typically a drug to decrease to half of its starting dose in the body 

Since First order kinetics is an exponential process , mathematically , the elimination  half-life can be given by,

T_{1/2 = ln 2 / k}

_{where ln 2 is the natural logarithm of 2 ( or 0.693) , k is the elimination rate constant of the drug}

_{k = CL / V} 

_therefore    T_1/2 = 0.693  . V / CL

HALF LIFE OF SOME REPRESENTATIVE DRUGS
Aspirin	4 hrs
Digoxin	40 hrs
Digitoxin	7 days

Area under the curve

fig.4: Concentration-time graph for an EV dose

In pharmacology, the area under the plot of plasma concentration of drug versus time after dosage 

( called "area under the curve" or AUC) gives an insight into the extent of exposure to a drug and its clearance rate from the body

Dose = Cl . AUC

V      =  CL / k         = Dose / AUC .k

fig.5: Plasma concentration - time curves for a drug given by IV injection and 2 oral dosage forms Source:https://basicmedicalkey.com/drug-absorption-and-bioavailability/

Interplay between distribution and elimination for Intravenous administration

Following drug injection , distribution occurs within the central compartment (blood) and to the peripheral compartments (tissues). Transfer of the drug between the central and peripheral compartments can be described by appropriate rate constants. Elimination occurs from the central compartment and can be described by elimination rate constant. By measuring the plasma concentration over a period of time from the injection of the drug, it is possible to describe the concentration vs time profile for the drug. 

fig.6: Plasma (log) concentration-vs-time curve for a hypothetical drug after a single IV dose
(sr: https://aneskey.com/pharmacologic-principles/)

The curve (A+B) is the sum of the contributions from the rapid distribution (A) phase and the slow elimination phase (B) phase to the logarithmic decline in concentration after a bolus dose. 

In the first-order kinetics, a plot of the logarithm of serum concentration after initial distribution vs time is a straight line. The IV injection of the drug results in an initially high serum drug concentration, followed by a rapid decrease because of drug distribution. After the distribution ( or alpha) phase, the serum concentration further decreases because of the drug elimination or the beta phase. At any  point of time, the serum drug concentration (Cs) can be calculated from the bi exponential disappearance function :

C_s= Ae ^–αt + Be ^-βt

where  α and β are the first order rate constants for the alpha and beta phases respectively.

KINETICS FOR AN EXTRAVASCULAR DOSE

fig.7: Compartment model for an EV dose (cr: http://dx.doi.org/10.1021/acsomega.9b03735)

For a dose present in Extravascular compartment, there is a lag time due to absorption of the drug . 

Considering fig. 4 and 5, the following elements come in: 

• LAG TIME : time from administration to appearance in blood 
• ONSET OF ACTIVITY : time from administration to blood level reaching minimal effective concentration (MEC).
• TIME TO PEAK : time from administration to C max.