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

SN

GFR

(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

Sod

ium

excr

etio

n(u

mol

/min

)

baselinelowhigh

5 10 15 20 25 30

RVP (mmHg)

50

100

150

200

250

300

350

400S

NB

F(n

l/min

)

baselinelowhigh

5 10 15 20 25 30

RVP (mmHg)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Frac

tiona

lNa

excr

etio

n(%

)

baselinelowhigh

80 100 120 140 160 180 200

RAP (mmHg)

0

2

4

6

8

10

Sod

ium

excr

etio

n(u

mol

/min

)baselinelowhigh

RVP (mmHg)

5 10 15 20 25 30 RAP (mmHg)

80

100

120

SN

GFR

(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

Frac

tiona

l Na

excr

etio

n%

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

Frac

tiona

l Na

excr

etio

n%

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

Frac

tiona

l Na

excr

etio

n%

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

SN

GFR

(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

Frac

tiona

lNa

excr

etio

n(%

)

baselinelowhigh

80 100 120 140 160 180 200

RAP (mmHg)

10

20

30

40

50

60

70

SN

GF

R(n

l/min

)

baselinelowhigh

80 100 120 140 160 180 200

RAP (mmHg)

150

200

250

300

350

400

450

SN

BF

(nl/m

in)

baselinelowhigh

5 10 15 20 25 30

RVP (mmHg)

0

10

20

30

40

50

60

SN

GFR

(nl/m

in)

baselinelowhigh

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.