1. Kinetics, Modeling Oct 15, 2006 Casarett and Doull,
6th Edn, Chapter 7, pp
7th Edn, Chapter 7, pp
Timbrell, Chapter 3, pp (3rd Edn)

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

3. 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?

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

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

6. 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

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

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

9. Saturated metabolism
Saturated activation
Saturated detoxication

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

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

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

13. 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

14. 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

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

16. One compartment system

17. First-order decay of plasma concentration

18. Area under the curve (AUC)

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

20. 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

21. A more complex time-course

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

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

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

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

26. Physiologically-Based Pharmacokinetic Modeling
Each relevant organ or tissue is a compartment
Material flows into compartment, partitionnns 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

27. 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

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

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