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Modeling Renal Hemodynamics E. Bruce Pitman (Buffalo)PowerPoint Presentation

Modeling Renal Hemodynamics E. Bruce Pitman (Buffalo)

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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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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

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)

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

Experimentpressure from a normotensive rat

Experimentpressure spectra from normotensive rats

Basics of modeling

In all tubules and interstitium, balance laws for

- chloride
- sodium
- potassium
- urea
- water
- others

Basics of modeling II

Simplifying assumptions

- infinite interstitial bath
- infinitely high permeabilities
- chloride as principal solute driver

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

Basics of modeling IV

- Single PDE for chloride
- Empirical velocity relationship: apply steady-state relation to dynamic setting

Flow rate

*

[Cl]

Model

- Steady-state solution exists
- Idea: Linearize about this steady solution
- Look for exponential solutions

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]

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

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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