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Kinetics, Modeling

Kinetics, Modeling. Oct 19, 2009. 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 - Dose. 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 19, 2009 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 - Dose • External exposure – ambient air, water • Dose received by body • Dose at target organ • Dose at target tissue • Dose at target molecule • Molecular dose

  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. 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

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

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

  7. 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

  8. 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

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

  10. Steady-state kinetics k1 k2 E + S ES E + P [ES] is constant, i.e. ES/t = 0 k-1

  11. Saturated metabolism • Saturated activation • Saturated detoxication

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

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

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

  15. 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

  16. 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

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

  18. One compartment system

  19. First-order decay of plasma concentration

  20. Area under the curve (AUC)

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

  22. 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

  23. A more complex time-course

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

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

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

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

  28. 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

  29. 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

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

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

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