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  1. Review Steven A. Jones BIEN 501 Friday, May 14, 2007 Louisiana Tech University Ruston, LA 71272

  2. Simple Flow Field What is the pathline? Louisiana Tech University Ruston, LA 71272

  3. Simple Flow Field Louisiana Tech University Ruston, LA 71272

  4. Simple Flow Field Pathline follows the particle Louisiana Tech University Ruston, LA 71272

  5. Simple Flow Field What is the streakline? Louisiana Tech University Ruston, LA 71272

  6. What is the Differential Equation that Describes a Streamline? Assume we know that: Answer: Since So Louisiana Tech University Ruston, LA 71272

  7. Continuity For a two-dimensional flow: Use the equation of continuity to determine v. Louisiana Tech University Ruston, LA 71272

  8. Answer Louisiana Tech University Ruston, LA 71272

  9. What is the equation for a pathline? A pathline follows a fluid particle. Assume that you know the entire velocity field: and that the particle passes through the point at time 0. Answer: Louisiana Tech University Ruston, LA 71272

  10. Example Assume that: Is continuity satisfied? Answer: Louisiana Tech University Ruston, LA 71272

  11. What is the equation for a pathline? Assume that: What is the equation for the pathline through (1,2)? Answer: Louisiana Tech University Ruston, LA 71272

  12. What is the equation for a pathline? Write: Louisiana Tech University Ruston, LA 71272

  13. What is the equation for a pathline? so Louisiana Tech University Ruston, LA 71272

  14. Answer (Continued) Louisiana Tech University Ruston, LA 71272

  15. Two Compartment Model Peripheral Compartment Central Compartment C2 C1 Clearance Conservation of Mass Louisiana Tech University Ruston, LA 71272

  16. Two Compartment Model In terms of the volume ratio Conservation of Mass Initial Conditions Solve the two ODEs for C1 Louisiana Tech University Ruston, LA 71272

  17. ICs in terms of C1 Louisiana Tech University Ruston, LA 71272

  18. Solution The solution to: With Is Where: Louisiana Tech University Ruston, LA 71272

  19. Two Compartment Model Slow Release Rapid Release One Compartment Louisiana Tech University Ruston, LA 71272

  20. Two Compartment Model The two-compartment model obeys the same differential equations as the simple RLC circuit. It is useful to compare the individual components to the RLC circuit: Damping Transfer from L to C Louisiana Tech University Ruston, LA 71272

  21. Two Compartment Model One might expect that overshoot (ringing) could happen. However, ringing will only happen for imaginary values of l. In our case: As you increase k2 or ke, you must also increase (k1+k2+k3). And for the RLC Circuit: Can make the square root imaginary with small R or large C. Louisiana Tech University Ruston, LA 71272

  22. Two Compartment Model To see if the square root can become imaginary, minimize it’s argument w.r.t. ke and see if it can be less than 0. Louisiana Tech University Ruston, LA 71272

  23. Two Compartment Model What value does the argument of the square root take on at the minimum? Since k2 and k1 cannot be negative, the argument of the square root can never be negative. I.e. no ringing. Louisiana Tech University Ruston, LA 71272

  24. Pharmacokinetic Models Vascular Interstitial Q: Plasma Flow L: Lymph Flow Js, q: Exchange rates Cellular PBPK: Physiologically-Based Pharmocokinetic Model Louisiana Tech University Ruston, LA 71272

  25. Pharmacokinetic Models Z: Equilibrium concentration ratio between interstitium and lymph. Louisiana Tech University Ruston, LA 71272

  26. More Complicated Models Plasma Liver G.I. Track Kidney Muscle Louisiana Tech University Ruston, LA 71272

  27. Note on Complexity • While the equations become more complicated as more components are added, the basic concepts remain the same, and the systems can be analyzed with the same tools you would use to analyze a linear system in electrical engineering (e.g. transfer functions, Laplace transforms, Mason’s rule). Louisiana Tech University Ruston, LA 71272

  28. Louisiana Tech University Ruston, LA 71272

  29. What is the Differential Equation that Describes a Streamline? Louisiana Tech University Ruston, LA 71272