1. Aim:
To
inves)gate
how
changes
in
renal
arterial
pressure
and
venous
pressure
separately
and
in
combina)on
affect
renal
hemodynamic
and
re-­‐absorp)ve
func)on,
in
simulated
states
of
normal,
elevated
and
strongly
elevated
levels
of
Angiotensin
II
(Ang
II).
Background:
Heart
failure
(HF)
is
associated
with
impaired
renal
func)on.
This
has
been
aCributed
to
systemic
hemodynamic
changes:
forward
failure
causing
decreased
renal
arterial
pressure
(RAP)
and
backward
failure
causing
venous
conges)on
and
increased
renal
venous
pressure
(RVP).
Aus)n
Baird1,
Branko
Braam2
and
Anita
Layton1
1
Dept.
Mathema)cs,
Duke
Univ.,
Durham,
NC,
USA
and
2
Div.
Nephrology,
Dept.
Medicine
and
Dept.
Physiology,
Univ.
of
Alberta,
Edmonton,
AB,
Canada
Conclusion:
Our
model
implicates
that
a
decrease
in
renal
arterial
pressure
leads
to
a
decrease
in
sodium
excre)on
under
normal
condi)ons,
which
becomes
more
pronounced
when
venous
pressure
is
increased.
Angiotensin
II
leads
to
a
depression
of
GFR,
and
to
a
strong
decrease
in
frac)onal
sodium
excre)on.
Further
studies
will
be
directed
to
inves)gate
the
role
of
the
myogenic
response
and
tubuloglomerular
feedback
on
renal
func)on
and
response
to
changes
in
renal
arterial
and
venous
pressures.
This
research
was
supported
in
part
by
NIH
grant
DK-­‐89066
and
by
NSF
grant
DMS1263995
Implica)ons
of
increased
renal
venous
pressure
for
renal
hemodynamic
and
reabsorp)ve
func)on
studied
by
a
mathema)cal
model
of
the
kidney
IM:
Inner
medulla;
CDs:
collec)ng
ducts;
MD:
macula
densa;
PCT:
proximal
convoluted
tubule;
DVR:
descending
vasa
recta;
AVR:
ascending
vasa
recta.
RVP (mmHg)
5 10 15 20
25
30
RAP (mmHg)
80
100
120
SNGFR(nl
min)
0
5
10
15
20
25
30
35
5 10 15 20 25 30
RVP (mmHg)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Sodiumexcretion(umol/min)
baseline
low
high
5 10 15 20 25 30
RVP (mmHg)
50
100
150
200
250
300
350
400
SNBF(nl/min)
baseline
low
high
5 10 15 20 25 30
RVP (mmHg)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
FractionalNaexcretion(%)
baseline
low
high
80 100 120 140 160 180 200
RAP (mmHg)
0
2
4
6
8
10
Sodiumexcretion(umol/min)
baseline
low
high
RVP (mmHg)
5 10 15 20
25
30
RAP (mmHg)
80
100
120
SNGFR(nl
min)
0
5
10
15
20
25
30
35
Inner
stripe
Inner
medulla
Outer
stripe
Renal
Venous
Pressure
(RVP)
Renal
Arterial
Pressure
(RAP)
RVP (mmHg)
5 10 15 20
25
30
RAP (mmHg)
80
100
120
FractionalNaexcretion%
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Cortex
RVP (mmHg)
5 10 15 20
25
30
RAP (mmHg)
80
100
120
FractionalNaexcretion%
0.0
0.2
0.4
0.6
0.8
1.0
1.2
RVP (mmHg)
5 10 15 20
25
30
RAP (mmHg)
80
100
120
FractionalNaexcretion%
0.0
0.2
0.4
0.6
0.8
1.0
1.2
High
Ang
II
Figure
2:
SNGFR
and
SNBF,
obtained
for
the
superficial
nephron,
whole
kidney
sodium
excre)on
and
frac)onal
sodium
excre)on
dependency
on
RVP
in
normal
(baseline),
elevated
(low)
and
strongly
(high)
elevated
Ang
II
states.
RAP
=
100
mmHg
for
all
simula)ons.
RVP (mmHg)
5 10 15 20
25
30
RAP (mmHg)
80
100
120
SNGFR(nl
min)
0
5
10
15
20
25
30
35
Figure
3:
Effects
on
SNGFR
and
frac)onal
whole
kidney
sodium
excre)on
upon
combined
changes
of
RAP
and
RVP
in
normal
(baseline),
elevated
(low)
and
very
elevated
(high)
Ang
II
states.
SNGFR
reported
for
the
superficial
nephron
simula)ons.
Baseline
Low
Ang
II
Renal
Venous
Pressure
(RVP)
80 100 120 140 160 180 200
RAP (mmHg)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
FractionalNaexcretion(%)
baseline
low
high
80 100 120 140 160 180 200
RAP (mmHg)
10
20
30
40
50
60
70
SNGFR(nl/min)
baseline
low
high
80 100 120 140 160 180 200
RAP (mmHg)
150
200
250
300
350
400
450
SNBF(nl/min)
baseline
low
high
5 10 15 20 25 30
RVP (mmHg)
0
10
20
30
40
50
60
SNGFR(nl/min)
baseline
low
high
References:
1.
R
Moss
and
AT
Layton,
AJP
Renal,
2014.
Methods:
We
used
a
published
and
well-­‐characterized
mathema)cal
kidney
model
incorpora)ng
superficial
and
deep
nephrons
and
renal
hemodynamics,
including
myogenic
response
(MR),
tubulo-­‐
glomerular
feedback
(TGF),
and
segmental
sodium
handling
[1].
Figure
1:
Single
nephron
GFR
(SNGFR)
blood
flow
(SNBF),
both
obtained
for
the
superficial
nephron,
and
whole
kidney
sodium
excre)on
and
frac)onal
sodium
excre)on
dependency
on
renal
artery
pressure
(RAP)
in
normal
(baseline),
elevated
(low)
and
strongly
(high)
elevated
Ang
II
states.
RVP
=
5
mmHg
for
all
simula)ons.