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Kinetics, Modeling Oct 15, 2006 Casarett and Doull,

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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


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