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Kinetics, Modeling

Kinetics, Modeling. Oct 15, 2006. Casarett and Doull, 6 th Edn, Chapter 7, pp. 225-237 7 th Edn, Chapter 7, pp. 305-317 Timbrell, Chapter 3, pp 48-61 (3 rd Edn). Exposure. External exposure – ambient air, water Dose received by body Dose at target organ Dose at target tissue

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Kinetics, Modeling

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  1. Kinetics, Modeling Oct 15, 2006 Casarett and Doull, 6th Edn, Chapter 7, pp. 225-237 7th Edn, Chapter 7, pp. 305-317 Timbrell, Chapter 3, pp 48-61 (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 – DoseHow 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 k1 k2 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 Active transport Filtration Lower concentration

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

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

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

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

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

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