Compartmental analysis is an analytical method developed to assume the kinetics ( absorption, distribution, metabolism, half life, excretion, etc.) of a drug, where a live organ is considered as one or more compartments. Observed result helps a researcher to predict how the drug or formulation may act inside body, for how long, if the formulation is suitable to produce maximum deliberation of drugs in body as well as compatibility of drug or drug toxicity study. Among numerous models, in non cmpartmental model it is considerd that the formulation kinetics depend on other variables instead of compartment itself. This slide is an short overview of pharmaceutical compartmental models with a slightly elaborate discussions about different non compartmental analytical methods.

1. NON COMPARTMENTAL
ANALYSIS
GROUPA
BKH1703001F, MUH1703005F, BKH1703006F,
MUH1703028F, BKH1703029F.

2. OUTLINE
• PHARMACOKINETIC MODELS
• CATEGORIZATION
• ALLOMETRIC SCALING
• INTERSPECIES SCALING
• MECHANISTIC MODELS
• COMPARTMENTAL MODEL
• INDIVIDUALANALYSIS
• POPULATION ANALYSIS
• PHYSIOLOGICAL PHARMACOKINETIC
MODELS (PBPK)
• PHYSIOLOGIC PHARMACOKINETIC
MODEL WITH BINDING

3. PHARMACOKINETIC MODELS
• Assumption on parameters like tissue blood flow, plasma or tissue volume etc.
• Predicts and obtains parameters (e.g. Cmax, tmax, t1/2, AUC, clearance, etc.) to predict
drug dosing outcomes, pharmacodynamics, and toxicity.
• Useful in:
- describing time course of drug action;
- improving drug therapy by enhancing drug efficacy;
- minimizing adverse reactions through more accurate dosing regimens.
• Used routinely within the development process of new molecules or drug delivery
systems.

4. CATEGORIZATION
.
EMPIRICAL MODELS
• Focused on describing the data with the
specification of very few assumptions about
the data being analyzed.
• Example: allometric scaling model.
MECHANISTIC MODELS
• Specify assumptions and attempt to
incorporate known factors about the systems
surrounding the data into the model, while
describing the model with equations and
underlying assumptions.
• Example: physiological modeling
and compartmental modeling.

5. ALLOMETRIC SCALING: An empirical model
• Allometry – change of organism’s
characteristics according to size.
• Gives an empirical relationship that
allows for approximate interspecies
scaling based on the size of the species.

6. INTERSPECIES SCALING
• An approach to compare and predict the pharmacokinetics of a drug among different species.
• Used in toxicokinetics and for the extrapolation of therapeutic drug doses in humans from
nonclinical animal drug studies.
• Assumptions:
-Physiologic variables (e.g. Clearance, heart rate, organ weight, and biochemical processes) are
related to the weight or body surface area of the animal species;
- All mammals use the same energy source (oxygen) and energy transport systems across
animal species.

7. INTERSPECIES SCALING
Considered factors:
• Aging rate, &
• Life span of the species (MLP).
Maximum life-span potential (MLP)
- Characteristic & genetically controlled,
- Many energy-consuming biochemical processes,
including drug metabolism, vary inversely with the aging
rate or life span of the animal,
-Used for drugs eliminated mainly by hepatic intrinsic
clearance.
Not considered interspecies differences:
• Gender,
• Nutrition,
• Pathophysiology,
• Route of drug administration,
• Polymorphisms.

8. • The general allometric equation obtained by Interspecies scaling method:
y = bW ^a
where , y = pharmacokinetic or physiologic property of interest, b = allometric coefficient,
W = weight or surface area of the animal species, and a = allometric exponent.
Both a and b vary with the drug.
• Relationship between biperiden intrinsic clearance with body weight and MLP:
where, MLP = maximum life-span potential of the species, B = body weight of the species,
clint = hepatic intrinsic clearance of the free drug.

9. MECHANISTIC MODELS
• To create a mathematical and statistical model defined by integrated, matrix, and/or partial differential
equations (equations having derivatives with respect to more than one variable).
• Describe the Pharmacokinetic or Pharmacodynamic behavior of a drug.
• Obtained data “fitted” to suitable techniques to estimating mean parameter along with their variability
in an individual or population.

10. COMPARTMENTAL MODEL
• Different body compartments.
• Aims to develop a model that is associated with predicted concentration values (or whatever
observation is being studied) that are as close as possible to the observed values.
One
compartmental
model
(Central)
Two
compartmental
model
(Central+
Peripheral)
Three
compartmental model
(Central+
Tissue+
Deep tissue)

11. INDIVIDUAL ANALYSIS
• Involves the development of a model using data from one source (such as one human or one animal).
• Can never perfectly predict the observed data as the error is always inherent in data, whether related
to the collection procedures themselves or to analytical assays.
• The relationship between observed and predicted concentration values:
Xi = a vector of known values (such as dose and sampling times), ci= the vector of observed concentrations, εi =
measurement errors, φj= vector of model parameters (i.e. Pharmacokinetic parameters), fi= function that relates ci,
φj and xi.= total number of observations or values.

12. POPULATION ANALYSIS
• An extension of individual analyses, to predicts concentration data associated with different
individuals or animals.
• Similar concept as individual analysis, except takes into consideration of interindividual variability.
• Predicts concentration values and describes the behavior for each individual within the population,
also provides an “overall” (mean or population) set of predictions.
• Unlike individual analysis always use the same structural model to fit all individuals’ data for a
specific drug under study.
Xij = vector of known values (represented by i) for the jth subject, cij= vector of
observed concentrations for the jth subject, εij= measurement errors for the jth
subject, φj= vector of model parameters for the jth subject, and , fij= is the
function that relates cij to φj and xij , i= pharmacokinetic parameter , j= animal

13. PHYSIOLOGICAL PHARMACOKINETIC
MODELS (PBPK)
• Mathematical models describing drug movement and disposition based on organ blood flow and
the organ spaces penetrated by the drug.
• Aims to consider as much as possible all process of drug uptake, distribution and elimination,
• Considers the drug to be blood flow limited.
 Drugs carried by blood flow to organs → rapid drug uptake into tissue and a quickly established
constant ratio of drug tissue/ blood partition co efficient, P) → Rapid drug transmembrane
movement, no permeation resistance by capillary membrane → rapidly equilibrates with the
interstitial water.

14. Rate of blood flow to tissue (Qt ) and rate of change in drug concentration with respect to time within a
given tissue organ is expressed as-
C art = arterial blood drug concentration
C vein = venous blood drug
concentration
Q t = blood flowing throw a typical
tissue organ per unit of time.
Clearance (Cl) : The rate of drug elimination is the product of the drug concentration in the
organ and the organ clearance.

15. PHYSIOLOGIC PHARMACOKINETIC
MODEL WITH BINDING
• Unlike PBPK, considers drugs binding to plasma
or tissues.
Assumptions:
• bound and free drug in both tissue and plasma are
in equilibrium,
• Free drug in plasma and in the tissue equilibrates
rapidly,