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Modeling Renal Hemodynamics E. Bruce Pitman (Buffalo)

Modeling Renal Hemodynamics E. Bruce Pitman (Buffalo). Harold Layton (Duke) Leon Moore (Stony Brook). The Human Kidneys:. are two bean-shaped organs, one on each side of the backbone represent about 0.5% of the total weight of the body

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Modeling Renal Hemodynamics E. Bruce Pitman (Buffalo)

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  1. Modeling Renal HemodynamicsE. Bruce Pitman (Buffalo) Harold Layton (Duke) Leon Moore (Stony Brook)

  2. The Human Kidneys: • are two bean-shaped organs, one on each side of the backbone • represent about 0.5% of the total weight of the body • but receive 20-25% of the total arterial blood pumped by the heart • Each contains from one to two million nephrons

  3. In 24 hours the kidneys reclaim: • ~1,300 g of NaCl (~97% of Cl) • ~400 g NaHCO3 (100%) • ~180 g glucose (100%) • almost all of the180 liters of water that entered the tubules (excrete ~0.5 l)

  4. Anatomy (approximate)

  5. Water secretion • Release of ADH is regulated by osmotic pressure of the blood. • Dehydration increases the osmotic pressure of the blood, which turns on the ADH -> aquaporin pathway. • The concentration of salts in the urine can be as much as four times that of blood. • If the blood should become too dilute, ADH secretion is inhibited • A large volume of watery urine is formed, having a salt concentration ~ one-fourth of that of blood

  6. Experimentpressure from a normotensive rat

  7. Experimentpressure spectra from normotensive rats

  8. Anatomy (approximate)

  9. Basics of modeling In all tubules and interstitium, balance laws for • chloride • sodium • potassium • urea • water • others

  10. Basics of modeling II Simplifying assumptions • infinite interstitial bath • infinitely high permeabilities • chloride as principal solute driver

  11. Basics of modeling III • Macula Densa samples fluid as it passes • Feedback relation noted at steady-state • We assume the same form in a dynamic model

  12. Basics of modeling IV • Single PDE for chloride • Empirical velocity relationship: apply steady-state relation to dynamic setting Flow rate * [Cl]

  13. Basics of modeling V

  14. Basics of modeling VI

  15. Model • Steady-state solution exists • Idea: Linearize about this steady solution • Look for exponential solutions

  16. Aside on delay equations

  17. Basic Analysis

  18. Basic Analysis • If the real part of λ>0, perturbation grows in time. If Imaginary part of λ≠0, oscillations. [unstable] • If the real part of λ<0, perturbation decays in time. [stable]

  19. Bifurcation results

  20. Bifurcation results II

  21. Bifurcation results III

  22. To Be Done • Complex perhaps chaotic behavior at high gain • Have 2 coupled nephrons. Need full examination of bifurcation • Need many coupled nephrons (O(1000)) • Reduced model

  23. 2-nephron model • as many as 50% of the nephrons in the late CRA are pairs or triples • some evidence of whole organ signal at TGF frequency

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