Question

We discussed in class the effect of constriction of the afferent and efferent arterioles on Renal Plasma Flow (RPF) and Glomerular Flow Rate (GFR). Assuming that GFR can be approximated by GFR = q \cdot RPF \cdot P_{GC} where $P_{GC}$ is the Hydrostatic Pressure in the Glomerulus and q is a conversion factor with units of 1/pressure, derive with equations and show that GFR first increases and then decreases as the resistance of the efferent arteriole $R_e$ is increased. Pa PGC Pe RPF Glomerulus Va VGC Ve Ra Re Electrical Model Flow Model A) To develop the equations, use the electrical model on the right which is analogous to the kidney system of interest. In an electrical analogue, voltages are representative of pressures and currents are representative of flow. B) Derive an expression for I and another for $V_{GC}$. Show the final equation for the electrical analogue giving $I \cdot V_{GC}$ which is equal to the analogue of GFR. C) Substitute back in for the pressure/flow variables, solve numerically, and plot RPF, $P_{GC}$, and GFR for $R_e$ = (0.0 - 0.3) (ranging from 0.0 to 0.3, with 0.01 as interval). Use the following values: Parameter Value $P_a$ 100 mmHg $P_e$ 20 mmHg $R_a$ 0.1 mmHg*min / ml q 0.005 1/mmHg

          We discussed in class the effect of constriction of the afferent and efferent arterioles
on Renal Plasma Flow (RPF) and Glomerular Flow Rate (GFR). Assuming that GFR can
be approximated by GFR = q \cdot RPF \cdot P_{GC} where $P_{GC}$ is the Hydrostatic Pressure in the
Glomerulus and q is a conversion factor with units of 1/pressure, derive with equations
and show that GFR first increases and then decreases as the resistance of the efferent
arteriole $R_e$ is increased.

Pa
PGC
Pe
RPF
Glomerulus
Va
VGC
Ve
Ra
Re
Electrical Model
Flow Model
A) To develop the equations, use the electrical model on the right which is analogous to the
kidney system of interest. In an electrical analogue, voltages are representative of
pressures and currents are representative of flow.
B) Derive an expression for I and another for $V_{GC}$. Show the final equation for the electrical
analogue giving $I \cdot V_{GC}$ which is equal to the analogue of GFR.
C) Substitute back in for the pressure/flow variables, solve numerically, and plot RPF, $P_{GC}$,
and GFR for $R_e$ = (0.0 - 0.3) (ranging from 0.0 to 0.3, with 0.01 as interval). Use the
following values:
Parameter Value
$P_a$ 100 mmHg
$P_e$ 20 mmHg
$R_a$ 0.1 mmHg*min / ml
q 0.005 1/mmHg

We discussed in class the effect of constriction of the afferent and efferent arterioles
on Renal Plasma Flow (RPF) and Glomerular Flow Rate (GFR). Assuming that GFR can
be approximated by GFR = q ·RPF ·PGC where PGC is the Hydrostatic Pressure in the
Glomerulus and q is a conversion factor with units of 1/pressure, derive with equations
and show that GFR first increases and then decreases as the resistance of the efferent
arteriole Re is increased.

Pa
PGC
Pe
RPF
Glomerulus
Va
VGC
Ve
Ra
Re
Electrical Model
Flow Model
A) To develop the equations, use the electrical model on the right which is analogous to the
kidney system of interest. In an electrical analogue, voltages are representative of
pressures and currents are representative of flow.
B) Derive an expression for I and another for VGC. Show the final equation for the electrical
analogue giving I · VGC which is equal to the analogue of GFR.
C) Substitute back in for the pressure/flow variables, solve numerically, and plot RPF, PGC,
and GFR for Re = (0.0 - 0.3) (ranging from 0.0 to 0.3, with 0.01 as interval). Use the
following values:
Parameter Value
Pa 100 mmHg
Pe 20 mmHg
Ra 0.1 mmHg*min / ml
q 0.005 1/mmHg

Added by Angela D.

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