Download Kinetics of Oral Dosing

LEARNING OBJECTIVES









Understand the plasma concentration-time profiles of single-dose orally administered drugs
Estimate relevant kinetic parameters of oral drug alone or in conjunction with IV kinetics
Know the major differences in the kinetics of oral drugs and IV bolus injections
Review the factors influencing the drug accumulation or disappearance rate in the body after
the oral administration
Appreciate the relative changes in the absorption and elimination rates after oral
administration
Know the major kinetic parameters that can be calculated from the oral data
Know the equations for
 Plasma concentration-time profiles after oral administration
 Plasma concentration-time curve when absorption is over
Explain the following concepts and methods
 Residual method
 Lag and onset time
 Flip-flop phenomenon
Calculate the following kinetic parameters for oral drugs:
 Maximum plasma concentration (𝐶𝑚𝑎𝑥 ) and time to reach 𝐶𝑚𝑎𝑥 (𝑡𝑚𝑎𝑥 )
 Elimination half-life
 Absorption and elimination rate-constants
 Clearance
 Distribution-volume
 Fraction-dose un-excreted
DIFFERENCES BETWEEN ORAL AND IV
ADMINISTRATIONS
 Oral dosing is one of the extravascular methods of administration
 Other extravascular routes:
 Intramuscular
 Subcutaneous
 Transdermal
 Inhalation
 Drugs administered via the extra-vascular routes are first absorbed before
entering the systemic circulation
 Dosage forms must disintegrate and drugs must dissolve for absorption to
occur
 The absorbed drugs pass through the liver before reaching the
systemic circulation
 The fraction-dose that survives the first-pass loss enters the systemic
circulation
 Once in the blood, our body treats all drugs equally regardless of their entry
into the system
KINETIC MODEL FOR ORAL DOSING
We will only focus on drugs
that are not subject to active
efflux
In case of one-compartment
model for an oral drug
without active efflux
 The absorption process
is either zero or firstorder
 Drug enters the systemic
circulation after
absorption
 Rapidly distributes in the
body
 Undergoes first-order
elimination
 A typical plasma
concentration-time curve
consists of rise and fall
of drug levels (the plot
on the right)
ABSORPTION AND ELIMINATION OF ORAL
DRUGS
After oral administration, the drug amount changes as a
function of absorption (input) and elimination (output)
processes:
 𝑅𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑏𝑜𝑑𝑦 =

𝑑𝐴𝐵
𝑑𝑡
𝑑𝐴𝐵
𝑑𝑡
= 𝑖𝑛𝑝𝑢𝑡 − 𝑜𝑢𝑡𝑝𝑢𝑡
= 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛 − 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑒𝑙𝑖𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛
When both absorption and elimination processes are firstorder:
 The absorption-rate depends on the drug amount in the GIT (𝐴𝐺𝐼 )
 The elimination-rate depends on the drug amount in the body (𝐴𝐵 )

𝑑𝐴𝐵
𝑑𝑡
= 𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 − 𝑒𝑙𝑖𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 = 𝑘𝑎 𝐴𝐺𝐼 − 𝑘𝐴𝐵
ORAL PLASMA CONCENTRATION-TIME CURVE
 After oral administration, the drugamount in the GIT and the
absorption rate (𝑘𝑎 𝐴𝐺𝐼 ) are
maximum
 With the increase in drug-amount,
plasma-concentration increases
 With the fall in the drug-amount,
absorption-rate falls
 The drug-amount continues to rise
until the absorption-rate equals the  The drug absorption
continues after 𝑡𝑚𝑎𝑥 but at a
elimination-rate
rate slower than the
 The time-point when absorptionelimination-rate
rate equals the elimination-rate is
 The 𝐶𝑚𝑎𝑥 of oral drugs is
called 𝒕𝒎𝒂𝒙
smaller than the 𝐶𝑚𝑎𝑥 of IV
 After 𝑡𝑚𝑎𝑥 , the elimination-rate
drugs administered at the
surpasses the absorption-rate, the
same dose
plasma-concentration starts falling
EQUATION FOR ORAL PLASMA CONCENTRATIONTIME DATA
The plasma-concentration of orally
administered drug at any time is
expressed by:
𝐶 =
𝐹𝐷𝑜𝑠𝑒𝑘
𝑉 𝑘𝑎 −𝑘
(𝑒 −𝑘𝑡 − 𝑒 −𝑘𝑎 𝑡 )
 F=fraction-dose in the
systemic circulation
 V= distribution-volume
 𝑒 −𝑘𝑎 𝑡 =absorption process
 𝑒 −𝑘𝑡 =elimination process
The plasma concentration-time on loggraphs exhibits a terminal linear relation
or a linear-segment
The linear-segment represents the
presence of one-exponential term: The
end of absorption and start of elimination
EQUATION FOR THE ELIMINATION PHASE OF
ORAL ABSORPTION
The equation below describe the elimination phase
𝐶=
𝐹𝐷𝑜𝑠𝑒𝑘𝑎 −𝑘𝑡
𝑒
𝑉 𝑘𝑎 −𝑘
This equation is a complex version of the equation for
IV bolus plasma-concentration data: 𝐶 = 𝐶0 𝑒 −𝑘𝑡
Taking log converts the equation into a straight-line
equation
 𝑙𝑛𝐶 = ln
𝐹𝐷𝑜𝑠𝑒𝑘𝑎
𝑉 𝑘𝑎 −𝑘
− 𝑘𝑡
 The intercept of the line is ln
𝐹𝐷𝑜𝑠𝑒𝑘𝑎
𝑉 𝑘𝑎 −𝑘
and slope is -k
The slope of the terminal phase of the oral plasma
concentration-time data is the same as the slope of the
straight-line for IV plasma concentration-time data
ELIMINATION RATE CONSTANT CALCULATION
For most drugs, the absorptionrate is faster than eliminationrate
 𝑘𝑎 >>k
When the absorption process
stops, the plasma concentration
is defined by the single
exponential term related to the
elimination with a slope of –k and
a half-life.
You can calculate the elimination
rate-constant and half-life from
the terminal linear segment of
the oral plasma concentrationtime curve
LAG AND ONSET TIMES
 Lag time
 Some drugs do not exhibit absorption phase immediately after
administration
 This delay in absorption is called lag time
 Drug formulation and physiologic factors such as gastric emptying
time may be responsible for lag-time
 The lag-time can be a few minutes to hours.
 Long lag- times are observed for enteric-coated tablets
 Onset Time
 The time required for the pharmacologic effects to start
 Depends on how fast the plasma concentrations reach the minimum
effective concentration
GENERAL ASSUMPTIONS FOR ORAL
ABSORPTION
 Majority of the orally administered
drugs and drug formulations meet
the following assumptions:
 The absorption rate-constant
(𝑘𝑎 ) is much larger than the
elimination rate-constant (𝑘𝑎
>>k)
 The terminal rate-constant and
half-life represent elimination
rate-constant and half-life,
respectively
 The half-life calculated from the
terminal linear-segment of the
oral data is equal to the half-life
for the IV data
 Both lines (terminal segment of
oral data and IV data) represent
elimination and produce the
same slope
FLIP-FLOP PHENOMENON
 Some orally administered drugs’ absorption is
very slow or the elimination is very fast
 For these drugs, the absorption rate constant is
smaller than elimination rate constant (k>> 𝑘𝑎 )
 When absorption rate constant is smaller than that
of elimination, the terminal phase of plasma
concentration-time profile represents the
absorption process instead of the elimination
process, a phenomenon called flip-flop, or
reversal of the assumption that ka >> k
 Flip-flop (ka<<k) occurs when
 Drug absorption is inherently slow
 Drug formulation is controlled or sustained
release type
 Drug elimination half-life is short
 Flip-flop causes the following changes
 The half-life (elimination 𝑡1/2 ) for IV data does
not match the half-life from the terminal
linear-segment of oral plasma-concentrationtime data (absorption 𝑡1/2 )
 Drugs exhibits absorption-rate limited
elimination
IDENTIFICATION OF THE FLIP-FLOP
PHENOMENON
Flip-flop phenomenon can be identified by
 Using IV data
 Using data from different dosage forms administered via
the same route
 Using data from different routes administration
USING IV DATA
When the half-lives for oral and IV data are very similar
(IV-𝑡1/2 ≅ Oral-𝑡1/2 ), then the terminal oral half-life is
related to the elimination
If the IV half-life is shorter than that of oral (IV-𝑡1/2 <
Oral-𝑡1/2 ), then the terminal oral half-life is related to the
absorption process
DIFFERENT DOSAGE FORMS
ADMINISTERED VIA THE SAME ROUTE
In the absence of IV data, different dosage forms of a drug
with different absorption profiles can be used to determine
whether the terminal half-life is related to elimination or
absorption
A drug may have different absorption profiles when
administered in the solution or tablet form
Solutions exhibit faster absorption and shorter half-lives but
tablets show slower absorption, or longer absorption halflives
When tablets and solutions are administered at different
occasions to a subject, we may observe two scenarios:
Case I and Case II
In both cases, the absorption of the solution is faster than
tablet, resulting in higher 𝐶𝑚𝑎𝑥 and earlier 𝑡𝑚𝑎𝑥 values for
the solution
CASE I: SAME HALF-LIVES FOR
SOLUTION AND TABLET
Both the solution and
tablet exhibit the same
terminal half-lives

This terminal phase halflife cannot represent
absorption because
solution exhibits a
shorter absorption halflife
Thus, this half-life is the
elimination half-life
CASE II: DIFFERENT HALF-LIVES FOR
SOLUTION AND TABLETS
 A change in the half-life
reflects the terminal halflives
 The terminal half-life of
the tablet is related to
the absorption process
DATA FOR DIFFERENT ROUTES OF
ADMINISTRATION
For two different routes, the absorption half-life will be
different, but the elimination half-life will be the same
When a drug is administered via IM and oral routes, the
terminal half-lives are going to be the same
CALCULATION OF KINETIC PARAMETERS
USING ORAL PLASMA DATA
Cmax and tmax
Elimination half-life
Clearance
Distribution-volume
Oral bio-availability
CALCULATION OF 𝐶𝑚𝑎𝑥 and 𝑡𝑚𝑎𝑥
 𝒕𝒎𝒂𝒙
 If you know the absorption (𝑘𝑎 ) and elimination (k) rate
constants, use the following equation to calculate 𝑡𝑚𝑎𝑥
𝑘
 𝑡𝑚𝑎𝑥 =
ln( 𝑘𝑎 )
𝑘𝑎 −𝑘
 𝑪𝒎𝒂𝒙
 To calculate 𝐶𝑚𝑎𝑥 , use plasma concentration equation
and 𝑡𝑚𝑎𝑥 obtained using the above equation
 But the estimation of absorption rate-constant is not usually
accurate
 By taking enough samples around 𝑡𝑚𝑎𝑥 , both 𝐶𝑚𝑎𝑥 and 𝑡𝑚𝑎𝑥
can be estimated from the plasma concentration-time curve
 𝑘𝑎 and k can affect 𝑡𝑚𝑎𝑥 , a larger 𝑘𝑎 or k reduces 𝑡𝑚𝑎𝑥 and vice
versa.
 k a , k, F, dose and V influence Cmax
ELIMINATION HALF-LIFE
You can use the data points that fall on the linear section of
the curve to calculate the half-life and rate-constant of the
linear-segment of the plasma-concentration-time

But to confirm whether the data obtained from the linear
segment of the terminal phase belong to elimination phase,
you need additional information like IV data
CLEARANCE FROM ORAL DATA
The equation for the clearance after oral dosing
𝐹𝐷𝑜𝑠𝑒
 𝐶𝑙 =
𝐴𝑈𝐶
 You have to know F (oral bioavailability) to calculate Cl
after oral administration
 Calculate AUC using the trapezoidal rule
𝐶𝑙𝑎𝑠𝑡
 Calculate 𝐴𝑈𝐶𝑡𝑙𝑎𝑠𝑡−∞ using
𝑘𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑙
 You must calculate 𝐴𝑈𝐶𝑡𝑙𝑎𝑠𝑡−∞ regardless whether 𝑘𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑙
is related to absorption or elimination
 Oral clearance (𝐶𝑙0 )
 A clearance term obtained by dividing the oral dose with
the oral AUC, without considering F
 Oral clearance is defined by
 𝐶𝑙0 =
𝐷𝑜𝑠𝑒𝑝𝑜
𝐴𝑈𝐶𝑝𝑜
=
𝐶𝑙
𝐹
CALCULATION OF DISTRIBUTIONVOLUME
The equation for the distribution-volume
 𝑉=
𝐶𝑙
𝑘
Use this equation to calculate Cl and k
You need IV data to calculate Cl and k
In the above equation k is the elimination rate constant
If the drug-disposition is absorption-rate limited, the terminal
rate constant from oral-plasma concentration time cannot be
used to calculate V
Use the rate-constant from IV data
When only oral data is available and F is unknown, you can
calculate V/F, instead of V

𝑉
𝐹 =
𝐶𝑙𝑜
𝑘
ORAL BIOAVAILABILITY (F)
F is calculated from the AUC for oral and IV data at the
same dose:
𝐹=
𝐴𝑈𝐶𝑝𝑜
𝐴𝑈𝐶𝐼𝑉
In case of different doses, the AUC ratios are corrected for
the dose:
•𝐹=
𝐴𝑈𝐶𝑝𝑜
𝐴𝑈𝐶𝐼𝑉
×
𝐷𝑜𝑠𝑒𝐼𝑉
𝐷𝑜𝑠𝑒𝑝𝑜
CALCULATION OF KINETIC PARAMETERS USING
ORAL URINE DATA
Half-life
Fraction-excreted unchanged
Renal clearance
Oral bio-availability
HALF-LIFE FROM ORAL URINE DATA
The urinary drug excretion-rate is proportional to the amount
of drug in the body (AB), regardless of the route of drug
administration

𝑑𝐴𝑢
𝑑𝑡
= 𝑘𝑟 × 𝐴𝐵
 A plot of urinary drug excretion-rate against the midpoint of
sample collection interval would parallel the plot of the drugamount in the body or plasma drug concentration against
time
 The terminal half-life and rate-constant of the rate plot
would be similar to that of the plasma drug concentrationtime curve
 But the terminal rate constant or half-life may stem from
either absorption or elimination
FRACTION EXCRETED UNCHANGED ( 𝑓𝑒 )
To calculate 𝑓𝑒 for oral administration, use the fraction-dose
in the systemic circulation (F Dose) instead of Dose used to
calculate 𝑓𝑒 for IV bolus
 𝑓𝑒 =
𝐴∞
𝑢
𝐹∙𝑑𝑜𝑠𝑒
You must know F from a previous study to calculate 𝑓𝑒 for oral
administration
RENAL CLEARANCE
You need both plasma and urine data to calculate the renal
clearance for oral administration
The renal clearance can be calculated directly from oral data
without any IV data
 𝐶𝑙𝑟 =
𝐴∞
𝑢
𝐴𝑈𝐶0−∞