PHARMACOKINETIC MODELS
Drug movement within the body is a complex process. The major objective is therefore to develop a generalized and simple approach to describe, analyse and interpret the data obtained during in vivo drug disposition studies.
The two major approaches in the quantitative study of various kinetic processes of drug disposition in the body are
Model approach, and
Model-independent approach (also called as non-compartmental analysis).
The presentation concisely describes the different pharmacokinetic parameters and basics of compartment modelling. It will help undergraduate students to understand the basic concepts of Biopharmaceutics.
This presentation will give the students a basic knowledge about the pharmacokinetics of durgs. It will help them clear the basics before digging deep into the topic.
PHARMACOKINETIC MODELS
Drug movement within the body is a complex process. The major objective is therefore to develop a generalized and simple approach to describe, analyse and interpret the data obtained during in vivo drug disposition studies.
The two major approaches in the quantitative study of various kinetic processes of drug disposition in the body are
Model approach, and
Model-independent approach (also called as non-compartmental analysis).
The presentation concisely describes the different pharmacokinetic parameters and basics of compartment modelling. It will help undergraduate students to understand the basic concepts of Biopharmaceutics.
This presentation will give the students a basic knowledge about the pharmacokinetics of durgs. It will help them clear the basics before digging deep into the topic.
Strategies of linear feedback control and its classificationTELKOMNIKA JOURNAL
This paper is concerned with the control problem for a class of nonlinear dynamical
(hyperchaotic) systems based on linear feedback control strategies. Since the obtaining positive feedback
coefficients are required for these strategies. From this point of view, the available
ordinary/dislocated/enhancing and speed feedback control strategies can be classified into two main
aspects: control the dynamical systems or can't be control although it own a positive feedback coefficients.
So, we focused on these cases, and suggest a new method to recognize which system can be controller it
or not. In this method, we divided the positive feedback coefficient which obtain from these strategies in to
four categories according to possibility of suppression and show the reason for each case.
Finally, numerical simulations are given to illustrate and verify the results.
Plasma Drug Concentration Time Profile
Pharmacokinetic Parameter
Pharmacodynamic Parameter
Zero, First Order & Mixed Order Kinetic
Rates & Order Of Kinetics
Pharmacokinetic Models
Application Of Pharmacokinetic
Strategies of linear feedback control and its classificationTELKOMNIKA JOURNAL
This paper is concerned with the control problem for a class of nonlinear dynamical
(hyperchaotic) systems based on linear feedback control strategies. Since the obtaining positive feedback
coefficients are required for these strategies. From this point of view, the available
ordinary/dislocated/enhancing and speed feedback control strategies can be classified into two main
aspects: control the dynamical systems or can't be control although it own a positive feedback coefficients.
So, we focused on these cases, and suggest a new method to recognize which system can be controller it
or not. In this method, we divided the positive feedback coefficient which obtain from these strategies in to
four categories according to possibility of suppression and show the reason for each case.
Finally, numerical simulations are given to illustrate and verify the results.
Plasma Drug Concentration Time Profile
Pharmacokinetic Parameter
Pharmacodynamic Parameter
Zero, First Order & Mixed Order Kinetic
Rates & Order Of Kinetics
Pharmacokinetic Models
Application Of Pharmacokinetic
ESR spectroscopy in liquid food and beverages.pptxPRIYANKA PATEL
With increasing population, people need to rely on packaged food stuffs. Packaging of food materials requires the preservation of food. There are various methods for the treatment of food to preserve them and irradiation treatment of food is one of them. It is the most common and the most harmless method for the food preservation as it does not alter the necessary micronutrients of food materials. Although irradiated food doesn’t cause any harm to the human health but still the quality assessment of food is required to provide consumers with necessary information about the food. ESR spectroscopy is the most sophisticated way to investigate the quality of the food and the free radicals induced during the processing of the food. ESR spin trapping technique is useful for the detection of highly unstable radicals in the food. The antioxidant capability of liquid food and beverages in mainly performed by spin trapping technique.
hematic appreciation test is a psychological assessment tool used to measure an individual's appreciation and understanding of specific themes or topics. This test helps to evaluate an individual's ability to connect different ideas and concepts within a given theme, as well as their overall comprehension and interpretation skills. The results of the test can provide valuable insights into an individual's cognitive abilities, creativity, and critical thinking skills
The ability to recreate computational results with minimal effort and actionable metrics provides a solid foundation for scientific research and software development. When people can replicate an analysis at the touch of a button using open-source software, open data, and methods to assess and compare proposals, it significantly eases verification of results, engagement with a diverse range of contributors, and progress. However, we have yet to fully achieve this; there are still many sociotechnical frictions.
Inspired by David Donoho's vision, this talk aims to revisit the three crucial pillars of frictionless reproducibility (data sharing, code sharing, and competitive challenges) with the perspective of deep software variability.
Our observation is that multiple layers — hardware, operating systems, third-party libraries, software versions, input data, compile-time options, and parameters — are subject to variability that exacerbates frictions but is also essential for achieving robust, generalizable results and fostering innovation. I will first review the literature, providing evidence of how the complex variability interactions across these layers affect qualitative and quantitative software properties, thereby complicating the reproduction and replication of scientific studies in various fields.
I will then present some software engineering and AI techniques that can support the strategic exploration of variability spaces. These include the use of abstractions and models (e.g., feature models), sampling strategies (e.g., uniform, random), cost-effective measurements (e.g., incremental build of software configurations), and dimensionality reduction methods (e.g., transfer learning, feature selection, software debloating).
I will finally argue that deep variability is both the problem and solution of frictionless reproducibility, calling the software science community to develop new methods and tools to manage variability and foster reproducibility in software systems.
Exposé invité Journées Nationales du GDR GPL 2024
What is greenhouse gasses and how many gasses are there to affect the Earth.moosaasad1975
What are greenhouse gasses how they affect the earth and its environment what is the future of the environment and earth how the weather and the climate effects.
Phenomics assisted breeding in crop improvementIshaGoswami9
As the population is increasing and will reach about 9 billion upto 2050. Also due to climate change, it is difficult to meet the food requirement of such a large population. Facing the challenges presented by resource shortages, climate
change, and increasing global population, crop yield and quality need to be improved in a sustainable way over the coming decades. Genetic improvement by breeding is the best way to increase crop productivity. With the rapid progression of functional
genomics, an increasing number of crop genomes have been sequenced and dozens of genes influencing key agronomic traits have been identified. However, current genome sequence information has not been adequately exploited for understanding
the complex characteristics of multiple gene, owing to a lack of crop phenotypic data. Efficient, automatic, and accurate technologies and platforms that can capture phenotypic data that can
be linked to genomics information for crop improvement at all growth stages have become as important as genotyping. Thus,
high-throughput phenotyping has become the major bottleneck restricting crop breeding. Plant phenomics has been defined as the high-throughput, accurate acquisition and analysis of multi-dimensional phenotypes
during crop growing stages at the organism level, including the cell, tissue, organ, individual plant, plot, and field levels. With the rapid development of novel sensors, imaging technology,
and analysis methods, numerous infrastructure platforms have been developed for phenotyping.
The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptxMAGOTI ERNEST
Although Artemia has been known to man for centuries, its use as a food for the culture of larval organisms apparently began only in the 1930s, when several investigators found that it made an excellent food for newly hatched fish larvae (Litvinenko et al., 2023). As aquaculture developed in the 1960s and ‘70s, the use of Artemia also became more widespread, due both to its convenience and to its nutritional value for larval organisms (Arenas-Pardo et al., 2024). The fact that Artemia dormant cysts can be stored for long periods in cans, and then used as an off-the-shelf food requiring only 24 h of incubation makes them the most convenient, least labor-intensive, live food available for aquaculture (Sorgeloos & Roubach, 2021). The nutritional value of Artemia, especially for marine organisms, is not constant, but varies both geographically and temporally. During the last decade, however, both the causes of Artemia nutritional variability and methods to improve poorquality Artemia have been identified (Loufi et al., 2024).
Brine shrimp (Artemia spp.) are used in marine aquaculture worldwide. Annually, more than 2,000 metric tons of dry cysts are used for cultivation of fish, crustacean, and shellfish larva. Brine shrimp are important to aquaculture because newly hatched brine shrimp nauplii (larvae) provide a food source for many fish fry (Mozanzadeh et al., 2021). Culture and harvesting of brine shrimp eggs represents another aspect of the aquaculture industry. Nauplii and metanauplii of Artemia, commonly known as brine shrimp, play a crucial role in aquaculture due to their nutritional value and suitability as live feed for many aquatic species, particularly in larval stages (Sorgeloos & Roubach, 2021).
ANAMOLOUS SECONDARY GROWTH IN DICOT ROOTS.pptxRASHMI M G
Abnormal or anomalous secondary growth in plants. It defines secondary growth as an increase in plant girth due to vascular cambium or cork cambium. Anomalous secondary growth does not follow the normal pattern of a single vascular cambium producing xylem internally and phloem externally.
BREEDING METHODS FOR DISEASE RESISTANCE.pptxRASHMI M G
Plant breeding for disease resistance is a strategy to reduce crop losses caused by disease. Plants have an innate immune system that allows them to recognize pathogens and provide resistance. However, breeding for long-lasting resistance often involves combining multiple resistance genes
3. Dr/Omnia Sarhan
3
Upon successful completion of this course the student should be able to;
• Describe the physicochemical and physiological factors that influence the
absorption of drugs
from extra and intravascular routs of administration, their distribution within the
body, and their
routes and mechanisms of elimination
• Explain how dose, bioavailability, rate of absorption, apparent volume of
distribution, total
clearance, and elimination half-life affect the plasma concentrations of a drug after
administration of single oral or single IV bolus dose
• Describe the factors which determine the time-course of systemic accumulation of
a drug
administered by multiple oral, multiple IV bolus and continuous infusion doses
• Differentiate between linear and non-linear pharmacokinetic models
4. Introduction
Dr/Omnia Sarhan 4
I- Logarithm
The logarithm of a number is the exponent or power to which a given base number must be raised to equal
that number. Thus, the logarithm of Y to the base, b, equals X, or log b (Y) = X. The logarithm of 0 and all
negative numbers is undefined or nonexistent. The logarithm of 1 is 0 and of numbers <1 is negative in all
systems.
The relationships between common and natural logarithms are the following:
a. log Y = ln Y/ln 10 = ln Y/2.303
b. ln Y = ln 10 × log Y = 2.303 × log Y
5. Introduction
Dr/Omnia Sarhan 5
II- Calculus
1- Differential Calculus
Pharmacokinetics is the study of the rate of drug absorption and disposition in the body. Thus differential calculus
is an important stepping stone in the development of many of the equations used.
Differential calculus is involved with the study of rates of processes. The calculus part comes in when we look at
these processes in detail, that is, during small time intervals. We may say that at time zero a patient has a concentration
of 25 mg/l of a drug in plasma and at time 24 hours the concentration is 5 mg/l. That may be interesting in itself, but it
doesn't give us any idea of the concentration between 0 and 24 hours, or after 24 hours. Using differential calculus we
are able to develop equations to look at the process during the small time intervals that make up the total time interval
of 0 to 24 hours.
6. Introduction
Dr/Omnia Sarhan 6
In many cases the rate of elimination of a drug can
be described as being dependent on or proportional to
the amount of drug remaining to be eliminated. That is,
the process obeys first order kinetics. This can illustrated
by the opposite Figure.
This can be described mathematically using equation:
Where:
k is a proportionality constant (rate constant)
X is the amount remaining to be eliminated.
7. Introduction
Dr/Omnia Sarhan 7
Note: the use of the symbol 'd' to represent a very small increment in X or t. Thus dX/dt represents the slope of the
line (or rate of change) over a small region of the curved line. When data are collected at discrete times such as 4 and 6
hours the larger change in X and t can be represented by ΔX/Δt
Integration of the above equation (and other differential equations) provides the following integrated equations:
2- Integral Calculus
Differentiation is the reverse of integration. With differentiation breaking a process down to look at the
instantaneous process, integration sums up the information from small time intervals to give a total result over a larger
time period.
8. Introduction
Dr/Omnia Sarhan 8
First: How writing differential equations?
Rate processes in the field of pharmacokinetics are usually limited to first order, zero order and occasionally
Michaelis-Menten kinetics. Linear pharmacokinetic systems consist of first order disposition processes and bolus
doses, first order or zero order absorption rate processes. These rate processes can be described mathematically.
First Order Equation
Each first order rate process is described by a first order rate constant (k1) and the amount or concentration
remaining to be transferred (X1).
Zero Order Equation
9. Introduction
Dr/Omnia Sarhan 9
Zero order rate processes are described by the rate constant alone.
Michaelis Menten Equation
The Michaelis Menten process is somewhat more complicated with a maximum rate (velocity, Vm) and a
Michaelis constant (Km) and the amount or concentration remaining.
The full differential equation for any component of a pharmacokinetic model can be constructed by adding an
equation segment for each arrow in the pharmacokinetic model.
The rules for each segment:
1- Direction of the arrow
*If the arrow goes into the component the equation segment is positive
*If the arrow leaves the component the equation segment is negative.
10. Introduction
Dr/Omnia Sarhan 10
2- Type of rate process
*If the rate process is first order multiply the (first order) rate constant by the amount or
concentration of drug in the component at the tail of the arrow.
*If the process is zero order just enter the rate constant.
11. Introduction
Dr/Omnia Sarhan 11
Component 1 There is one arrow leading out of component one so the rate process is negative.
This process is zero order so we just write the rate constant. The equation for this component is:
Component 2 This component is more of a challenge. There are three arrows connected with this
component. One arrow leads to the compartment so this equation segment is positive. The other
two arrows lead away from the component and these equation segments are negative. Starting
with the zero order process provides is a positive k0 to the differential equation. The first order
process is developed as the rate constant multiplied by the amount remaining in component 2.
This is negative and is -k1 X2. The final segment is the Michaelis Menten process from
component 2 to component 4. This is also negative and is described as -Vm x X2 / (Km + X2).
The total differential equation for this component is:
12. Introduction
Dr/Omnia Sarhan 12
Component 3 OK; downhill from here. Now we have one arrow going to this component from
component 2, thus the equation segment is positive. The rate process is first order so we multiply the
rate constant by the amount remaining in the component at the tail of the arrow, component 2. The
equation is:
Component 4 The fourth component is also described with one equation segment. The arrow leads to
this component so the segment is positive. The rate process is a Michaelis Menten process. The
equation for this component is:
13. Introduction
Dr/Omnia Sarhan 13
GRAPHS
Graphs are usually used to present the relationship between two or more variables. In pharmacokinetics, graphs
are commonly utilized to represent the drug concentration in the systemic circulation or drug pharmacological effect as
a function of time after drug administration. In the two-dimensional graphs that are commonly used in
pharmacokinetics, the drug concentration or drug effect (the dependent variable) is plotted on the y-axis, while time
(the independent variable) is plotted on the x-axis. There are two types of scales that are commonly utilized in
pharmacokinetics, the Cartesian scale and the semilog scale.
1- Cartesian Scale
In the Cartesian scale, both the y-axis and the x-axis are linear. Each point can be plotted on the Cartesian scale by
a pair of numerical coordinates that determine the perpendicular distance of the point from the x-axis and the y-axis.
14. Introduction
Dr/Omnia Sarhan 14
Although negative or positive values can be used for the coordinates in the
Cartesian scale, only positive coordinate values are used to present plasma
concentration versus time profile. The opposite Figure is an example of the
Cartesian scale.
2- Semilog Scale
The semilog scale has a logarithmic scale on the y-axis and a linear scale on
the x-axis, as in the next Figure. This type of graph is useful in plotting values
that are changing exponentially. On the semilog graph the spacing of the scale on
the y-axis is proportional to the logarithm of the number, not the number itself.
Plotting data on the semilog scale is equivalent of converting the dependent
variable values to their
15. Introduction
Dr/Omnia Sarhan 15
log values, and plotting the data on the
linear scale. The semilog graph paper
consists of repeated units called cycles.
Each of these cycles covers a single log10
unit, or 10-fold increase in number. The
semilog graph paper is available in one,
two, three, or more cycles per sheet.
Example
Plot the following drug concentration–
time data on the semilog scale:
16. Introduction
Dr/Omnia Sarhan 16
Answer
• The scale on the x-axis is chosen to make the time
points cover the largest portion of the x-axis.
• The drug concentration values are used to determine the
number of cycles needed.
Three cycles are needed to plot these values.
17. Problems
Dr/Omnia Sarhan 17
1-The linear relationship that describes the change in the drug amount (A) in mg, as a
function of time (t) in h, can be described by the following equation: A = 120 mg − 2
(mg/h) t.
a. Calculate the amount of the drug remaining after 10 h.
b. What is the time required for the drug amount to decrease to zero?
18. Problems
Dr/Omnia Sarhan
18
2- In an experiment to study the chemical decomposition, a drug solution was prepared and an aliquot of the
drug solution was obtained at different time points. The drug concentrations in the samples and the results
were as follows:
a. Draw the drug concentration against time on the Cartesian scale and graphically estimate the slope and y-
intercept.
b. Write the equation that describes the change in drug concentration with time.
19. Introduction
19
Rates and order of reactions
Rates
Is the velocity within which the reaction occurs. Consider the following reaction:
Drug A drug B
The amount of drug A is decreasing with respect to time
So Rate = - dA / dt (forward reaction)
Or
since the amount of B increases with respect to time
Rate = + dB / dt
The order of a reaction
Refers to the actual manner in which the concentration of the drug tends to influence the rate of
reaction or process. If the drug A changed to B and the concentration of A is C, the rate of change of A
to B as a function of time will expressed as
Dr/Omnia Sarhan
20. a +ve rate means that the concen. is increasing with time
(product).
a -ve rate means that the concentration is falling with time
(reactant).
Dr/ Omnia Sarhan
21. Introduction
21
dC / dt = - K Cn
Where;
dC / dt = the rate of reaction
K = rate constant
n = the order of the reaction or process.
When n = zero, it is called zero order reaction, when n = 1, it is called first order reaction, and so on.
1- Zero order kinetics (constant rate process);
Constant rate change and the change is independent on the concentration of the drug. It is not
possible to increase the rate of process by increasing the concentration of the drug. An example is the
elimination of alcohol. Drugs that show this type of elimination will show accumulation of plasma
levels of the drug and hence nonlinear pharmacokinetics.
Dr/Omnia Sarhan
22. Introduction
22
The amount of the drug (A) is decreasing at a constant time interval (t)
A = - Ko t + Ao
Where Ao = the amount of the drug at time = zero
A = the amount of the drug at time = t
Dr/Omnia Sarhan
24. – Equation of straight line:
– y = ax + b
– (a: slope, b: intercept)
x
y
Intercept
= b
Slope = a
kt
C
Ct
0
24
Dr/Omnia Sarhan
25. Introduction
25
The half-life (t ½);
Expresses the period of time required for the amount or concentration of a drug to decrease by one
half. Or the time required for the plasma concentration to drop from its initial value to the half. i.e.,
when t = t ½ , A = Ao / 2 .
t ½ for zero order reaction;
A = - Ko t + Ao
When t = t ½, A = Ao / 2
t ½ = Ao / 2 Ko
e.g., for zero order delivery
1. Sustained release
2. I.V infusion
3. Trans-dermal preparations
Dr/Omnia Sarhan
26. Half-life of Zero-order Reactions
0
0
2
/
1
2k
C
t
t
k
C
Ct 0
0
When one half-life has elapsed, by definition
2
/
1
0
0
0
2
t
k
C
C
2
0
C
Ct
2
0
0
2
/
1
0
C
C
t
k
2
0
2
/
1
0
C
t
k
Dr/ Omnia Sarhan
27. 0
0
2
/
1
2k
C
t
– Half life of zero order reaction is directly proportional to
initial concentration.
– Thus half life decrease as reaction proceed with time
(when C0 is reduced by a factor of 2, the half-life is also
decreased by a factor of 2 (in fact each successive half-
life is half the preceding one)
100%A
10 min
50%A 25%A 12.5%A
5 min 2.5 min
27
Dr/Omnia Sarhan
28. Expiration Date
It is the date at which 10% drug concentration is decomposed
(increase toxicity & decrease activity).
k
C
t
10
0
90
%
90
0
0
9
.
0 t
k
C
C
0
9
.
0 C
Ct
0
0
%
90 9
.
0 C
C
kt
0
90 1
.
0 C
t
k
Dr/ Omnia Sarhan
29. A drug product has an initial concentration of 125 mg/ml decays by
zero order kinetics, (k=0.5 mg/ml/hr). What is the concentration of the
intact drug remaining after 3 days? When the drug reaches zero
concentration?
Answer:
C = Co – Kt
C = 125 - 0.5 * (3 x 24)
C = 89 mg / ml
C = Co – Kt
0 = 125 – 0.5*t
t = 250 hour
Example 1
29
Dr/Omnia Sarhan
30. t
C
C
k t
o
1
.
/
00052
.
473
0.225
-
0.47
k
days
liter
mole
months
days
K
C
t o
15
452
00052
.
0
2
47
.
0
2
2
/
1
The decomposition of multi-sulfa compound was found to follow zero order
kinetics. If its concentration was 0.47 mole/liter, when freshly prepared, and
after 473 days its concentration reached 0.225 mole/liter, calculate the
degradation rate constant and t1/2 .
Answer:
Example 2
kt
C
Ct
0
30
Dr/Omnia Sarhan
31. 300 240
10
6
o t
C C
k
t
90%
0.1 0.1 300
3
10
o
C
t
K
The degradation of a drug product follows zero order process. If the
Concentration was 300 units/ml when freshly prepared & after 6
Months, its concentration reached 240 units/ml. Calculate the Constant
of reaction and the shelf life of the product.
Answer:
units/ml/month
months
Example 3
kt
C
Ct
0
Dr/ Omnia Sarhan
32. Introduction
32
2- First order kinetics (linear kinetics)
The rate of reaction is directly proportional to the concentration. i.e., the change depends on the
concentration.
ln A – ln Ao = - k t
ln (A/Ao) = - k t
A /Ao = e-Kt………….. (1)
Where e is the natural logarithm, the equation has one exponent and called monoexponential rate
process.
Since ln = 2.303 log, equation 1 can be written as;
Log A = log Ao – k t / 2.303 ............ (2)
A plot of log A versus time, a straight line is obtained whose
slope = k / 2.303
intercept = log Ao
Dr/Omnia Sarhan
39. ln ln o
c c kt
ln ln5 0.0005 120
ln 1.549 ln
4.71 /
C
C shift
C mg ml
90%
0.105 0.105
210
0.0005
t
k
Don’t forget to
check the units of
the problem
An ophthalmic solution dispensed at 5 mg/ml conc. exhibits a first order
reaction, with a rate constant of 0.0005 day-1. How much drug remaining
after 120 days? & how long will it take for the drug to degrade to 90% of its
initial concentration?
Answer:
A first order reaction
days
Example 1
39
Dr/Omnia Sarhan
40. The original concentration of one sample was 50 mg/ml. When assayed
20 months later the concentration was found to be 40 mg/ml, assuming
that the decomposition is first order, What is the half-life of this
product?
Ans.:
Co= 50mg/mL Ct= 40mg/mL t= 20 mon.
log Ct= log Co- Kt/2.303
log 40= log 50- 20K/2.303
K= 0.0111mon-1
T1/2= 0.693/K= 0.693/ 0.0111= 62.43 mon.
Example 2
40
Dr/Omnia Sarhan
41. 1/ 2
0.693 0.693
0.1215
5.7
k
t
At 25 °C, the half-life period for the decomposition of N205 is 5.7
hours and is independent of the initial pressure of N205,
calculate:
a- The time for the completion of the reaction.
b- The specific rate constant for the reaction.
Answer:
•t1/2 is independent on the initial conc. So, it is 1st order, hence the
reaction never goes to an end and the life time (time for completion
of the reaction) is infinity.
hr-1
Example 3
41
Dr/Omnia Sarhan