1. Kinetics, Modeling Oct 19, 2009 Casarett and Doull,
6th Edn, Chapter 7, pp
7th Edn, Chapter 7, pp
Timbrell, Chapter 3, pp (3rd Edn)

2. Exposure - Dose External exposure – ambient air, water
Dose received by body
Dose at target organ
Dose at target tissue
Dose at target molecule
Molecular dose

4. Exposure – Dose How are they related. Can we measure them
Exposure – Dose How are they related ? Can we measure them ? How can we describe the crucial steps so that we can estimate what we can’t measure?

5. Modeling and Kinetics
Mathematical descriptors of movement of chemicals into and out of the body
Consider the kinetics of the important steps/processes
Diffusion
Enzyme-catalyzed
Carrier-mediated

6. Enzymes: Biological catalysts
Proteins
May have metals at active site
Act on “substrate”
May use/require co-factors

7. Kinetics of Enzyme-catalyzed Reactions
Michaelis-Menten Equation:
v = Vmax * [S]
Km + [S]
First-order where Km >> [S]
Zero-order where [S] >> Km

8. Zero-Order Processes Follow straight-line time course
Rate is independent of concentration
v = δ[A]/δt = k
Units of k are mass/time, e.g mg/h
Saturated carrier-mediated processes
Saturated enzyme-mediated processes

9. First-Order Processes
Follow exponential time course
Rate is concentration-dependent
v = [A]/t = k[A]
Units of k are 1/time, e.g. h-1
Unsaturated carrier-mediated processes
Unsaturated enzyme-mediated processes

10. Second-Order Processes
Follow exponential time course
Rate is dependent on concentration of two reactants
v = [A]/t = k[A]*[B]

11. Steady-state kinetics
E + S ES E + P
[ES] is constant, i.e. ES/t = 0
k-1

12. Saturated metabolism
Saturated activation
Saturated detoxication

13. Uptake Higher concentration Carrier Pore Diffusion Lipid bilayer
Facilitated
diffusion
Filtration
Active
transport
Lower concentration

14. Elimination - excretion
Absorption - uptake
Elimination - excretion
Passive diffusion
Filtration
Carrier-mediated

15. The single compartment (one compartment) model
kin
kout

16. Kinetics of absorption
Absorption is generally a first-order process
Absorption constant = ka
Concentration inside the compartment = C
C/t = ka * D where D = external dose

17. Kinetics of elimination
Elimination is also generally a first-order process
Removal rate constant k, the sum of all removal processes
C/t = -kC where C = concentration inside compartment
C = C0e-kt
Log10C = Log10C0 - kt/2.303

18. First-order elimination
Half-life, t1/2
Units: time
t1/2 = 0.693/k

19. One compartment system

20. First-order decay of plasma concentration

21. Area under the curve (AUC)

22. Total body burden Integration of internal concentration over time
Area under the curve

23. Volume of Distribution
Apparent volume in which a chemical is distributed in the body
Calculated from plasma concentration and dose:
Vd = Dose/C0
Physiological fluid space:
approximately 1L/kg

24. A more complex time-course

25. The two-compartment model
Tissues
Central
compartment
Peripheral
kin
kout
Plasma

26. The three-compartment model
Deep
depot
Peripheral
compartment
kin
kout
Central
Slow equilibrium
Rapid equilibrium

27. The four-compartment model
Mamillary model
Peripheral
compartment
kin
Central
compartment
Deep
depot
Kidney
kout

28. The four-compartment model
Catenary model A B C D
kout
kin

29. Physiologically-Based Pharmacokinetic Modeling
Each relevant organ or tissue is a compartment
Material flows into compartment, partitions into and distributes around compartment, flows out of compartment – usually in blood
If blood flow rates, volume of compartment and partition coefficient are known, can write an equation for each compartment
Assuming conservation of mass, solve equations simultaneously – can calculate concentration (mass) in each compartment at any time

30. Example of equation δkidney/δt = (Cak * Qa) – (Ck * Qvk) IN OUT
Rate of change of the amount in the kidney =
Concentration in (incoming) arterial blood X arterial blood flow
Minus
Concentration in (outgoing) venous blood X venous blood flow

31. Example of a model Air inhaled Lungs Venous blood Arterial blood
Rest of body
Liver
Metabolism
Kidneys
Urine

32. Casaret and Doull, 7th Edn, Chapter 7, pp 317-325