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RENAL PHYSIOLOGY Florida State University Advanced Topics in - - PowerPoint PPT Presentation
RENAL PHYSIOLOGY Florida State University Advanced Topics in - - PowerPoint PPT Presentation
RENAL PHYSIOLOGY Florida State University Advanced Topics in Biomedical Mathematics MAP5932, Spring 2007 03/16/07 Brinda Pamulapati Goal 1 Background of the kidney 2 Glomerulus 3 Mathematical model of Glomerulus 4 Co-current and
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Kidney
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Kidney and Nephron picture
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Glomerulus and Bowman's Capsule
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Mathematical model of the glomerular filter
There are 3 pressures that effect the rate of glomerular filtration: 1 the pressure inside the glomerular capillaries that promote filteration(p1) 2 the pressure inside the Bowman's capsule that opposes filtration(p2) 3 the colloidal osmotic pressure of the plasma proteins inside the capillaries that
- pposes filteration(pi)
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Schematic diagram of the glomerular filtration(one dimentional
q1 q2 Qi Qe x=0 x=L
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Mathematical model of the glomerular filter(cont.)
1 2 1
( )
f c
dq K P P dx
- =
- +
c
RTc =
where osmotic pressure is
1 2 c f
, hydrostatic pressure
- smotic pressure of the suspended protei ns and formed elements of the blood
K capillary filteration rate P P
- =
= =
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Conservation Equation
(
- smosis
)
c
from RTc =
1 1 1 i 1
/ (where )
i i c i i c i i i c i i
c Q cq c Q q RT RTc Q q Q RTc q
- =
= = = =
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Mathematical Model of the Glomerulus
1 2 1
( )
f c
dq K P P dx
- =
- +
i c i i
Q q
- =
................(20.1) .......................................................(20.4)
ln 1 1
e e i i f i i
Q Q Q K L Q Q
- +
=
- ..............(20.5)
i 1 2
=efflux through the efferent arterioles L=length of the filter = /( )
e
Q P P
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Cocurrent and Countercurrent Mechanism
What is Cocurrent and Countercurrent Mechanism Why Study about it ?
The human kidney use countercurrent exchange to remove water from urine so the body can retain water that was used to move the nitrogenous waste products.
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Mathematical Model of the Cocurrent and Countercurrent Mechanism
1 1 1 2 1 2 2 2 1 2
( ) ( ) C C q d C C t x C C q d C C t x
- +
=
- +
=
- .....................(20.15)
..................(20.16)
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Mathematical Problem
To Find: The outflow concentration Given : 1) The inflow concentration 2) The length of the exchange chamber 3) Flow velocities are known Assume: Flows are in steady state The input concentrations are
1 2
& C C
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( ) ( ) ( ) ( )
1 1 2 2 1 1 1 1 1 2 2 2 1 1 1 1
COCURRENT MECHANISM 1 1 1 1 1 , , 1 COUNTERCURRENT MECHANISM 1 1 , , 1
L L
L
C L e C C q d C q q C L e C e C L C q d C C q q
- +
- =
+ + +
- =
= = +
- +
- +
=
- =
= = =
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Conclusion
Total transfer of solute is always more efficient with a countercurrent than with a cocurrent.
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