1. Pharmacokinetics – a practical application of calculus
April 6, 2009
Elena Ho

2. Bayer Aspirin
In 1897, Felix Hoffman, a research chemist employed by the "Farbenfabrikin vorm. Freidr. Bayer and Co." synthesized acetylsalicylic acid. On February 1, 1899, Aspirin® was registered as a trademark. On March 6th of the same year, this drug was registered with the Imperial Patent Office in Berlin. Aspirin quickly become popular worldwide, and remains an important drug today.
(Interestingly, it was not until 1971 that Sir John Vane discovered the mechanism of action of aspirin, a feat that earned him the 1981 Nobel Prize for Medicine.)

3. The Bayer Group is a global enterprise with companies in almost every country. The map shows some of the principal sites.
The Bayer Group is a global enterprise with companies in almost every country. The map shows some of the principal sites.
The Bayer Group is a global enterprise with companies in almost every country. The map shows some of the principal sites.

4. Business operations :
Bayer HealthCare makes an important contribution to human and animal health with its innovative products and by researching new therapeutic approaches. The subgroup has four operating divisions: Bayer Schering Pharma* (prescription medicines), Consumer Care (over-the-counter medicines and nutritional supplements), Medical Care (blood glucose monitoring systems and contrast injection systems), Animal Health (veterinary medicines and grooming products)
Bayer CropScience is a world leader in the areas of crop protection, pest control, seeds and plant biotechnology. As a partner in the production of high- quality food, feed and fiber, the company offers comprehensive solutions for modern, sustainable agriculture and non-agricultural applications.
Bayer MaterialScience is one of the world’s leading manufacturers of polymers and high-quality plastics. Apart from its polycarbonates and polyurethanes, this company’s offering also includes innovative developments in the fields of coatings, adhesives, insulating materials and sealants. Principal customers are the automotive and construction industries, the electrical/electronics sector and manufacturers of sports and leisure articles, packaging and medical equipment.

5. Products
The Bayer Group markets some 5,000 products. Best-sellers include:
in the health care field: Yasmin®/YAZ®/Yasminelle®, Betaferon®/Betaseron®, Kogenate®, Adalat®, Avalox®/Avelox®
in the nutrition field: Confidor®/Gaucho®/Admire®/Merit®, Flint®/Stratego®/Sphere®
in the field of high-tech materials: Makrolon®, Baydur®, Bayflex® Footwear, Desmodur®/Desmophen®

6. Workforce
On December 31, 2007, the Bayer Group had 106,200 employees worldwide (2006: 106,000). North America accounted for 16,800 of these employees, while 18,900 were based in Asia-Pacific, 14,300 in Latin America/Africa/Middle East and 56,200 in Europe. In Germany we had 39,100 employees, who made up 36.8 percent of the Group workforce.
106,200 employees worldwide (as of December 31, 2007), including: 56,200 in Europe 16,800 in North America 18,900 in Asia-Pacific 14,300 in Latin America/Africa/Middle East

7. Bayer is seeking exceptional college students for summer internships at the Berkeley site. Help us spread the word.
Visit website for details...
Application deadline is March 15, 2009.

12. Oral bio- availability Volume of Distribution
Dosing Regimen
How much ?
How often ?
Oral bio- availability
Half-life
Absorption
Clearance
Volume of Distribution
Permea-bility
Efflux
Aqueous Solubility
Metabolic Stability
Renal Excretion
Biliary Excretion
CNS Penetration
Protein Binding
Tissue Binding

13. Typical Study Tools

14. Barriers between Dose and Target
Kerns & Li 2003, DDT 8:

15. Interesting facts about a human body
Absorbing surface area of skin: m2
Absorbing surface area of the lung: 70 m2
Absorbing surface area of GI tract: ~200m2 (1/2 basketball court)
Small intestine is ~2” around, 22’ long
Total length of capillaries is ~ 37,000 miles

16. Compartment models
A compartment is an entity which can be described by a definite volume and a concentration (of drug)
Concentration Dose V
Dose (mg) = C (ug/ml) x V (ml)
V = Dose/Concentration
One compartment model: the drug enters the body, distributes instantly
between blood and other body fluid or tissues.

17. __________________________
Model
One compartment
Two compartment
Three compartment
Hydrodynamic analogy
Drug in
Drug in
Drug out
__________________________
Drug out
Drug in
central
tissue
Drug out
____________________________
Drug in
Drug in
Tissue 1
central
Tissue 2
Tissue 1
central
Tissue 2
Drug out
Drug recycle
Drug out

18. The human body is a multimillion compartment
model considering drug concentration in
different organelles, cells, or tissues
We have access to only two types of body fluid –
blood and urine
We will begin with the simplest model

19. Then : dA/dt = - kel A where kel = ke + km
Single dose, IV, one compartment : dose of drug introduced rapidly and completely and
quickly distributes into its homogenous volume of distribution. Drug is then eliminated by metabolism and excretion.
Then : dA/dt = - kel A where kel = ke + km
rearrange to : dA/A = - kel dt
Integrate: ∫A0 dA/A = - kel ∫ t0 dt
Gives: ln A | A0= - kel t | t0
or ln A – ln A0 = - kel . t – t0 A t A t
This yields the familiar exponential or logarithmic expressions
A = A0 e – Kel t
C = C0 e – Kel t
log C = log C0 – kel . t /2.3
Kel = 2.3/t . log C/C0 C0
- Kel/2.3
log C
time

20. ∫ A dA/A = - kel ∫ t0 dt Biological half-life (T1/2)
Consider again the rearranged expression
dA/A = - kel dt
Integrate between limits A and A/2
∫ A dA/A = - kel ∫ t0 dt
Gives: ln A – ln (A/2) = kel t1/2
ln 2 = kel t1/2 = 0.693
Therefore: t1/2 = / kel
t/2
A/2

21. Area Under the Curve (AUC)
The integral of drug blood level over time from zero to infinity
and a measure of quantity of drug absorbed in the body
Area = A o  ∞
Sum of all concentration from t0 to t∞
Linear trapezoidal method: AUC t1t2 = Area of a trapezoid t1t2
= (t2 – t1). (C2+ C1)/2
ii) Log trapezoidal method: AUC t1t2 = (t2 – t1). (C2+ C1)/ln(C2/C1)
Lagrange method: cubic polynomial equation
Spline method: piecewise polynomials for curve-fitting

23. Linear and/or Log trapezoidal method
T1, T2, T3, T4, T5, T T7
Advantages: Easy to use. Reliable for slow declining or ascending curves
Disadvantages: error-prone for data points with a wide interval; over or under
estimate the true AUC; log 0 is not defined; not good for multiexponential curve

24. In vivo Pharmacokinetics in Rodents
Time
Plasma Concentration
Distribution
Elimination
AUC(inf)
kel
Disposition kinetics:
single iv administration
repeated blood sampling
plasma concentration-time profile
Volume of Distribution at steady-state:
Plasma Half-life:
Plasma Clearance:
kel T
ln 2
1/2 =
T1/2 = x Vd/CL
AUC
Dose CL =
kel CL V
dss =
The clearance of compounds is evaluated in relation to the liver blood flow which is
60 and 90 mL/min/kg in rat and mouse, respectively.
The volume of distribution should exceed that of total body water, i.e L/kg which indicates that the compound distributes freely into tissues.

25. Absorption GI Tract Stomach: Dissolution Stability at pH 1 Intestines:
Permeability
Metabolic stability
Compound properties controlling absorption:
size MW
aqueous solubility Sw
lipophilicity logP
polarity PSA
ionization pKa
...

26. Absorption
Deriving Models of the Gastrointestinal Tract

27. FA% F% Oral bioavailability: Barriers and In vitro Models
Fraction of dose absorbed:
Gut Lumen
FA%
Portal Vein
Gut Wall
Oral bioavailability:
Liver F%
Oral Absorption
limited by:
Stability
Solubility
Permeability
ATP-dependent Efflux
Drug Metabolism
Hepatocellular Uptake,
Drug Metabolism and
Biliary Excretion
Gastric and
Intestinal
Juice
Phys.-Chem. Descr.
Caco-2
Intest. Microsomes
Liver Microsomes
Hepatocytes
S9 mix, Cytosol
In Vitro Models:

28. In vivo Pharmacokinetics in Rodents
Oral kinetics:
Time
Plasma Concentration
Cmax
Tmax
Absorption
Distribution
Elimination
AUC(inf)
kel
single po administration
repeated blood sampling
plasma concentration-time profile
Max. plasma conc. and Time of max. pl. conc.
Oral Bioavailability:
Tmax
Cmax iv po D
AUC F / =
x 100%
There is no possibility to extrapolate the bioavailability in rodents to that in man. The sources of its limitation are often more important than the actual value as this information may allow to study the corresponding mechanism using human in vitro systems and to extrapolate the expected bioavailability .

29. Example of a pharmacokinetic study: single dose IV in the rat
Study design
Animal : Sprague-Dawley male rat, approximately 10 weeks old weighing ~250 g each (n=4)
Compound : BAY xxxxxx supplied by AABBCC. Dissolve 0.7 mg in 10 ul of DMSO, bring it up to 1 mL with PBS.
Dosing : each animal will receive a dose equivalent to 0.7 mg/kg.
Time points: pre dose, 5 min, 30 min, 1, 2, 4, 7, 24, 28, 31 hours post dose
Blood sample : collect 225 ul of blood in 25 ul of 5% Na Citrate at each time point. Centrifuge blood at 5000 g for 5 minutes. Separate the plasma and keep at -80ºC until analysis

30. SUMMARY OF RESULTS: Plasma concentration in ng/ml:

31. Rat plasma concentration was determined using ELISA immunoassay method:

32. Xxxxxx

33. Pharmacokinetic parameters:
This compound represents a 2-compartment model.
Elimination T1/2 = 6.8 hours
Total plasma clearance = 135 ml/h/kg
Vss = 1.03 L/kg
Summary
Remark
This profile suggests a slow clearance compound with a moderate elimination
half life. The volume of distribution at steady state is high, suggesting the
compound distribution is beyond the plasma volume compartment

34. Predicting Human PK
Direct Scaling of in vitro rate of metabolism to the CL in vivo
in vitro CL
in vivo c t
physiologically based
metabolic CL only
 first-pass effect
 oral bioavailability
Allometric Scaling of human PK based on animal data in vivo
body weight CL
Vdss
empirical
total CL and Vss
requires mech. to be scalable
 t1/2

35. Thank you Research and development at Bayer HealthCare focus
on identifying and developing new active substances
to treat diseases with a high unmet medical need.
Our job is to contribute to the understanding
of our drug’s behavior and
save lives one day
Thank you