Techniques that model microvascular hemodynamics have been developed for decades. While the physiological significance of pressure pulsatility is acknowledged, most of the microcirculatory models use steady flow approaches. To theoretically study the extent and transmission of pulsatility in microcirculation, dynamic models need to be developed. In this paper, we present a one-dimensional model to describe the dynamic behavior of microvascular blood flow. The model is applied to a microvascular network from a rat mesentery. Intravital microscopy was used to record the morphology and flow velocities in individual vessel segments, and boundaries are defined according to the experimental data. The system of governing equations constituting the model is solved numerically using the discontinuous Galerkin method. An implicit integration scheme is adopted to increase computing efficiency. The model allows the simulation of the dynamic properties of blood flow in microcirculatory networks, including the pressure pulsatility (quantified by a pulsatility index) and pulse wave velocity (PWV). From the main input arteriole to the main output venule, the pulsatility index decreases by 66.7%. PWV obtained along arterioles declines with decreasing diameters, with mean values of 77.16, 25.31, and 8.30 cm/s for diameters of 26.84, 17.46, and 13.33 μm, respectively. These results suggest that the 1D model developed is able to simulate the characteristics of pressure pulsatility and wave propagation in complex microvascular networks.

References

References
1.
Gaehtgens
,
P.
,
1970
, “
Pulsatile Pressure and Flow in the Mesenteric Vascular Bed of the Cat
,”
Pfluegers Arch. Eur. J. Physiol.
,
316
(
2
), pp.
140
151
.10.1007/BF00586482
2.
Seki
,
J.
,
1994
, “
Flow Pulsation and Network Structure in Mesenteric Microvasculature of Rats
,”
Am. J. Physiol. Heart Circ. Physiol.
,
266
(
2
), pp.
H811
H821
.
3.
Wiederhielm
,
C. A.
,
Woodbury
,
J. W.
,
Kirk
,
S.
, and
Rushmer
,
R. F.
,
1964
, “
Pulsatile Pressures in the Microcirculation of Frog's Mesentery
,”
Am. J. Physiol.
,
207
(
1
), pp.
173
176
.
4.
Huang
,
W.
,
Tian
,
Y.
,
Gao
,
J.
, and
Yen
,
M. R. T.
,
1998
, “
Comparison of Theory and Experiment in Pulsatile Flow in Cat Lung
,”
Ann. Biomed. Eng.
,
26
(
5
), pp.
812
820
.10.1114/1.107
5.
Mahler
,
F.
,
Muheim
,
M. H.
,
Intaglietta
,
M.
,
Bollinger
,
A.
, and
Anliker
,
M.
,
1979
, “
Blood Pressure Fluctuations in Human Nailfold Capillaries
,”
Am. J. Physiol. Heart Circ. Physiol.
,
236
(
6
), pp.
H888
H893
.
6.
Nakano
,
T.
,
Tominaga
,
R.
,
Nagano
,
I.
,
Okabe
,
H.
, and
Yasui
,
H.
,
2000
, “
Pulsatile Flow Enhances Endothelium-Derived Nitric Oxide Release in the Peripheral Vasculature
,”
Am. J. Physiol. Heart Circ. Physiol.
,
278
(
4
), pp.
H1098
H1104
.
7.
Li
,
Y.
,
Zheng
,
J.
,
Bird
,
I. M.
, and
Magness
,
R. R.
,
2003
, “
Effects of Pulsatile Shear Stress on Nitric Oxide Production and Endothelial Cell Nitric Oxide Synthase Expression by Ovine Fetoplacental Artery Endothelial Cells
,”
Biol. Reprod.
,
69
(
3
), pp.
1053
1059
.10.1095/biolreprod.102.013474
8.
Uryash
,
A.
,
Wu
,
H.
,
Bassuk
,
J.
,
Kurlansky
,
P.
,
Sackner
,
M. A.
, and
Adams
,
J. A.
,
2009
, “
Low-Amplitude Pulses to the Circulation Through Periodic Acceleration Induces Endothelial-Dependent Vasodilatation
,”
J. Appl. Physiol.
,
106
(
6
), pp.
1840
1847
.10.1152/japplphysiol.91612.2008
9.
Sezai
,
A.
,
Shiono
,
M.
,
Orime
,
Y.
,
Nakata
,
K.
,
Hata
,
M.
,
Yamada
,
H.
,
Iida
,
M.
,
Kashiwazaki
,
S.
,
Kinishita
,
J.
,
Nemoto
,
M.
,
Koujima
,
T.
,
Sezai
,
Y.
, and
Saitoh
,
T.
,
1997
, “
Renal Circulation and Cellular Metabolism During Left Ventricular Assisted Circulation: Comparison Study of Pulsatile and Nonpulsatile Assists
,”
Artif. Organs
,
21
(
7
), pp.
830
835
.10.1111/j.1525-1594.1997.tb03752.x
10.
Orime
,
Y.
,
Shiono
,
M.
,
Nakata
,
K.-I.
,
Hata
,
M.
,
Sezai
,
A.
,
Yamada
,
H.
,
Iida
,
M.
,
Kashiwazaki
,
S.
,
Nemoto
,
M.
,
Kinoshita
,
J.-I.
,
Kojima
,
T.
,
Saito
,
T.
, and
Sezai
,
Y.
,
1996
, “
The Role of Pulsatility in End-Organ Microcirculation After Cardiogenic Shock
,”
ASAIO J.
,
42
(
5
), pp.
M724
728
.10.1097/00002480-199609000-00083
11.
O'Neil
,
M. P.
,
Fleming
,
J. C.
,
Badhwar
,
A.
, and
Guo
,
L. R.
,
2012
, “
Pulsatile Versus Nonpulsatile Flow During Cardiopulmonary Bypass: Microcirculatory and Systemic Effects
,”
Ann. Thorac. Surg.
,
94
(
6
), pp.
2046
2053
.10.1016/j.athoracsur.2012.05.065
12.
Lee
,
J.
, and
Smith
,
N.
,
2008
, “
Theoretical Modeling in Hemodynamics of Microcirculation
,”
Microcirculation
,
15
(
8
), pp.
699
714
.10.1080/10739680802229589
13.
Secomb
,
T.
,
Beard
,
D. A.
,
Frisbee
,
J. C.
,
Smith
,
N. P.
, and
Pries
,
A. R.
,
2008
, “
The Role of Theoretical Modeling in Microcirculation Research
,”
Microcirculation
,
15
(
8
), pp.
693
698
.10.1080/10739680802349734
14.
Mittal
,
N.
,
Zhou
,
Y.
,
Linares
,
C.
,
Ung
,
S.
,
Kaimovitz
,
B.
,
Molloi
,
S.
, and
Kassab
,
G. S.
,
2005
, “
Analysis of Blood Flow in the Entire Coronary Arterial Tree
,”
Am. J. Physiol. Heart Circ. Physiol.
,
289
(
1
), pp.
H439
H446
.10.1152/ajpheart.00730.2004
15.
Lipowsky
,
H. H.
, and
Zweifach
,
B. W.
,
1974
, “
Network Analysis of Microcirculation of Cat Mesentery
,”
Microvasc. Res.
,
7
(
1
), pp.
73
83
.10.1016/0026-2862(74)90038-7
16.
Pries
,
A. R.
,
Secomb
,
T. W.
,
Gaehtgens
,
P.
, and
Gross
,
J. F.
,
1990
, “
Blood Flow in Microvascular Networks. Experiments and Simulation
,”
Circ. Res.
,
67
(
4
), pp.
826
834
.10.1161/01.RES.67.4.826
17.
Grinberg
,
L.
,
Cheever
,
E.
,
Anor
,
T.
,
Madsen
,
J. R.
, and
Karniadakis
,
G. E.
,
2011
, “
Modeling Blood Flow Circulation in Intracranial Arterial Networks: A Comparative 3D/1D Simulation Study
,”
Ann. Biomed. Eng.
,
39
(
1
), pp.
297
309
.10.1007/s10439-010-0132-1
18.
Shi
,
Y.
,
Lawford
,
P.
, and
Hose
,
R.
,
2011
, “
Review of Zero-D and 1-D Models of Blood Flow in the Cardiovascular System
,”
Biomed. Eng. Online
,
10
(
1
), Paper No. 33.10.1186/1475-925X-10-33
19.
Olufsen
,
M. S.
,
Peskin
,
C. S.
,
Kim
,
W. Y.
,
Pedersen
,
E. M.
,
Nadim
,
A.
, and
Larsen
,
J.
,
2000
, “
Numerical Simulation and Experimental Validation of Blood Flow in Arteries With Structured-Tree Outflow Conditions
,”
Ann. Biomed. Eng.
,
28
(
11
), pp.
1281
1299
.10.1114/1.1326031
20.
Alastruey
,
J.
,
Parker
,
K. H.
,
Peiro
,
J.
,
Byrd
,
S. M.
, and
Sherwin
,
S. J.
,
2007
, “
Modelling the Circle of Willis to Assess the Effects of Anatomical Variations and Occlusions on Cerebral Flows
,”
J. Biomech.
,
40
(
8
), pp.
1794
1805
.10.1016/j.jbiomech.2006.07.008
21.
Huo
,
Y. L.
, and
Kassab
,
G. S.
,
2006
, “
Pulsatile Blood Flow in the Entire Coronary Arterial Tree: Theory and Experiment
,”
Am. J. Physiol. Heart Circ. Physiol.
,
291
(
3
), pp.
H1074
H1087
.10.1152/ajpheart.00200.2006
22.
Huo
,
Y.
, and
Kassab
,
G. S.
,
2007
, “
A Hybrid One-Dimensional/Womersley Model of Pulsatile Blood Flow in the Entire Coronary Arterial Tree
,”
Am. J. Physiol. Heart Circ. Physiol.
,
292
(
6
), pp.
H2623
2633
.10.1152/ajpheart.00987.2006
23.
Alastruey
,
J.
,
Khir
,
A. W.
,
Matthys
,
K. S.
,
Segers
,
P.
,
Sherwin
,
S. J.
,
Verdonck
,
P. R.
,
Parker
,
K. H.
, and
Peiro
,
J.
,
2011
, “
Pulse Wave Propagation in a Model Human Arterial Network: Assessment of 1-D Visco-Elastic Simulations Against in vitro Measurements
,”
J. Biomech.
,
44
(
12
), pp.
2250
2258
.10.1016/j.jbiomech.2011.05.041
24.
Alastruey
,
J.
,
Moore
,
S. M.
,
Parker
,
K. H.
,
David
,
T.
,
Peiro
,
J.
, and
Sherwin
,
S. J.
,
2008
, “
Reduced Modelling of Blood Flow in the Cerebral Circulation: Coupling 1-D, 0-D and Cerebral Auto-Regulation Models
,”
Int. J. Numer. Methods Fluids
,
56
(
8
), pp.
1061
1067
.10.1002/fld.1606
25.
Formaggia
,
L.
,
Gerbeau
,
J. F.
,
Nobile
,
F.
, and
Quarteroni
,
A.
,
2001
, “
On the Coupling of 3D and 1D Navier-Stokes Equations for Flow Problems in Compliant Vessels
,”
Comput. Methods Appl. Mech. Eng.
,
191
(
6–7
), pp.
561
582
.10.1016/S0045-7825(01)00302-4
26.
Ganesan
,
P.
,
He
,
S.
, and
Xu
,
H.
,
2011
, “
Modelling of Pulsatile Blood Flow in Arterial Trees of Retinal Vasculature
,”
Med. Eng. Phys.
,
33
(
7
), pp.
810
823
.10.1016/j.medengphy.2010.10.004
27.
Lee
,
J.
, and
Smith
,
N.
,
2008
, “
Development and Application of a One-Dimensional Blood Flow Model for Microvascular Networks
,”
Proc. Inst. Mech. Eng., Part H: J Eng. Med.
,
222
(H
4
), pp.
487
511
.10.1243/09544119JEIM308
28.
Pries
,
A. R.
,
Ley
,
K.
, and
Gaehtgens
,
P.
,
1986
, “
Generalization of the Fahraeus Principle for Microvessel Networks
,”
Am. J. Physiol. Heart Circ. Physiol.
,
251
(
6
), pp.
H1324
1332
.
29.
Nakano
,
A.
,
Sugii
,
Y.
,
Minamiyama
,
M.
, and
Niimi
,
H.
,
2003
, “
Measurement of Red Cell Velocity in Microvessels Using Particle Image Velocimetry (PIV)
,”
Clin. Hemorheol. Microcirc.
,
29
(
3
), pp.
445
455
.
30.
Golub
,
A. S.
,
Barker
,
M. C.
, and
Pittman
,
R. N.
,
2008
, “
Microvascular Oxygen Tension in the Rat Mesentery
,”
Am. J. Physiol. Heart Circ. Physiol.
,
294
(
1
), pp.
H21
H28
.10.1152/ajpheart.00861.2007
31.
Pries
,
A. R.
, and
Secomb
,
T. W.
,
2009
, “
Origins of Heterogeneity in Tissue Perfusion and Metabolism
,”
Cardiovasc. Res.
,
81
(
2
), pp.
328
335
.10.1093/cvr/cvn318
32.
Pries
,
A. R.
,
Secomb
,
T. W.
,
Gessner
,
T.
,
Sperandio
,
M. B.
,
Gross
,
J. F.
, and
Gaehtgens
,
P.
,
1994
, “
Resistance to Blood Flow in Microvessels in vivo
,”
Circ. Res.
,
75
(
5
), pp.
904
915
.10.1161/01.RES.75.5.904
33.
Pries
,
A. R.
,
Secomb
,
T. W.
, and
Gaehtgens
,
P.
,
1998
, “
Structural Adaptation and Stability of Microvascular Networks: Theory and Simulations
,”
Am. J. Physiol. Heart Circ. Physiol.
,
275
(
2
), pp.
H349
360
.
34.
Pries
,
A. R.
,
Reglin
,
B.
, and
Secomb
,
T. W.
,
2001
, “
Structural Adaptation of Microvascular Networks: Functional Roles of Adaptive Responses
,”
Am. J. Physiol. Heart Circ. Physiol.
,
281
(
3
), pp.
H1015
1025
.
35.
Pries
,
A. R.
,
Reglin
,
B.
, and
Secomb
,
T. W.
,
2005
, “
Remodeling of Blood Vessels: Responses of Diameter and Wall Thickness to Hemodynamic and Metabolic Stimuli
,”
Hypertension
,
46
(
4
), pp.
725
731
.10.1161/01.HYP.0000184428.16429.be
36.
Rakusan
,
K.
, and
Wicker
,
P.
,
1990
, “
Morphometry of the Small Arteries and Arterioles in the Rat Heart: Effects of Chronic Hypertension and Exercise
,”
Cardiovasc. Res.
,
24
(
4
), pp.
278
284
.10.1093/cvr/24.4.278
37.
Goodman
,
A. H.
,
Guyton
,
A. C.
,
Drake
,
R.
, and
Loflin
,
J. H.
,
1974
, “
A Television Method for Measuring Capillary Red Cell Velocities
,”
J. Appl. Physiol.
,
37
(
1
), pp.
126
130
.
38.
Sherwin
,
S. J.
,
Franke
,
V.
,
Peiró
,
J.
, and
Parker
,
K.
,
2003
, “
One-Dimensional Modelling of a Vascular Network in Space-Time Variables
,”
J. Eng. Math.
,
47
(
3
), pp.
217
250
.10.1023/B:ENGI.0000007979.32871.e2
39.
Tuma
,
R. F.
,
Duran
,
W. N.
, and
Ley
,
K.
,
2008
,
Microcirculation
,
Academic Press
,
New York
.
40.
Fung
,
Y. C.
,
Zweifach
,
B. W.
, and
Intaglietta
,
M.
,
1966
, “
Elastic Environment of the Capillary Bed
,”
Circ. Res.
,
19
(
2
), pp.
441
461
.10.1161/01.RES.19.2.441
41.
Salotto
,
A. G.
,
Muscarella
,
L. F.
,
Melbin
,
J.
,
Li
,
J. K. J.
, and
Noordergraaf
,
A.
,
1986
, “
Pressure Pulse Transmission Into Vascular Beds
,”
Microvasc. Res.
,
32
(
2
), pp.
152
163
.10.1016/0026-2862(86)90051-8
42.
Gore
,
R. W.
,
1974
, “
Pressures in Cat Mesenteric Arterioles and Capillaries During Changes in Systemic Arterial Blood Pressure
,”
Circ. Res.
,
34
(
4
), pp.
581
591
.10.1161/01.RES.34.4.581
43.
Smaje
,
L. H.
,
Fraser
,
P. A.
, and
Clough
,
G.
,
1980
, “
The Distensibility of Single Capillaries and Venules in the Cat Mesentery
,”
Microvasc. Res.
,
20
(
3
), pp.
358
370
.10.1016/0026-2862(80)90064-3
44.
Pries
,
A. R.
,
Secomb
,
T. W.
, and
Gaehtgens
,
P.
,
1996
, “
Biophysical Aspects of Blood Flow in the Microvasculature
,”
Cardiovasc. Res.
,
32
(
4
), pp.
654
667
.
45.
Pries
,
A. R.
, and
Secomb
,
T. W.
,
2005
, “
Microvascular Blood Viscosity in vivo and the Endothelial Surface Layer
,”
Am. J. Physiol. Heart Circ. Physiol.
,
289
(
6
), pp.
H2657
H2664
.10.1152/ajpheart.00297.2005
46.
Lindert
,
J.
,
Werner
,
J.
,
Redlin
,
M.
,
Kuppe
,
H.
,
Habazettl
,
H.
, and
Pries
,
A. R.
,
2002
, “
OPS Imaging of Human Microcirculation: A Short Technical Report
,”
J. Vasc. Res.
,
39
(
4
), pp.
368
372
.10.1159/000065549
47.
Alastruey
,
J.
,
Parker
,
K. H.
,
Peiro
,
J.
, and
Sherwin
,
S. J.
,
2008
, “
Lumped Parameter Outflow Models for 1-D Blood Flow Simulations: Effect on Pulse Waves and Parameter Estimation
,”
Comm. Comp. Phys.
,
4
(
2
), pp.
317
336
.
48.
Karniadakis
,
G.
, and
Sherwin
,
S. J.
,
2005
,
Spectral/hp Element Methods for Computational Fluid Dynamics
,
Oxford University
,
New York
.
49.
Sherwin
,
S. J.
,
Formaggia
,
L.
,
Peiro
,
J.
, and
Franke
,
V.
,
2003
, “
Computational Modelling of 1D Blood Flow With Variable Mechanical Properties and its Application to the Simulation of Wave Propagation in the Human Arterial System
,”
Int. J. Numer. Methods Fluids
,
43
(
6–7
), pp.
673
700
.10.1002/fld.543
50.
Cockburn
,
B.
, and
Shu
,
C. W.
,
1989
, “
TVB Runge–Kutta Local Projection Discontinuous Galerkin Finite-Element Method for Conservation-Laws. II. General Framework
,”
Math. Comput.
,
52
(
186
), pp.
411
435
.
51.
Jackson
,
K. R.
, and
Sacks-Davis
,
R.
,
1980
, “
An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff ODEs
,”
ACM Trans. Math. Softw.
,
6
(
3
), pp.
295
318
.10.1145/355900.355903
52.
Davis
,
T. A.
,
2004
, “
A Column Pre-Ordering Strategy for the Unsymmetric-Pattern Multifrontal Method
,”
ACM Trans. Math. Softw.
,
30
(
2
), pp.
165
195
.10.1145/992200.992205
53.
Davis
,
T. A.
,
2004
, “
Algorithm 832: UMFPACK V4.3—An Unsymmetric-Pattern Multifrontal Method
,”
ACM Trans. Math. Softw.
,
30
(
2
), pp.
196
199
.10.1145/992200.992206
54.
Gosling
,
R.
, and
King
,
D.
,
1974
, “
Arterial Assessment by Doppler-Shift Ultrasound
,”
J. R. Soc. Med.
,
67
(
6
), pp.
447
449
.
55.
Zweifach
,
B. W.
,
1974
, “
Quantitative Studies of Microcirculatory Structure and Function
,”
Circ. Res.
,
34
(
6
), pp.
841
857
.10.1161/01.RES.34.6.841
56.
Zweifach
,
B. W.
, and
Lipowsky
,
H. H.
,
1977
, “
Quantitative Studies of Microcirculatory Structure and Function. III. Microvascular Hemodynamics of Cat Mesentery and Rabbit Omentum
,”
Circ. Res.
,
41
(
3
), pp.
380
390
.10.1161/01.RES.41.3.380
57.
Safar
,
M. E.
, and
Lacolley
,
P.
,
2007
, “
Disturbance of Macro- and Microcirculation: Relations With Pulse Pressure and Cardiac Organ Damage
,”
Am. J. Physiol. Heart Circ. Physiol.
,
293
(
1
), pp.
H1
H7
.10.1152/ajpheart.00063.2007
58.
Carlson
,
B. E.
,
Arciero
,
J. C.
, and
Secomb
,
T. W.
,
2008
, “
Theoretical Model of Blood Flow Autoregulation: Roles of Myogenic, Shear-Dependent, and Metabolic Responses
,”
Am. J. Physiol. Heart Circ. Physiol.
,
295
(
4
), pp.
H1572
H1579
.10.1152/ajpheart.00262.2008
59.
Li
,
J. K.-J.
,
2004
,
Dynamics of Vascular System
,
World Scientific Publishing
,
Singapore
.
60.
Falcone
,
J. C.
,
Davis
,
M. J.
, and
Meininger
,
G. A.
,
1991
, “
Endothelial Independence of Myogenic Response in Isolated Skeletal Muscle Arterioles
,”
Am. J. Physiol. Heart Circ. Physiol.
,
260
(
1
), pp.
H130
H135
.
61.
Van Bortel
,
L. M. A. B.
,
Struijker-Boudier
,
H. A. J.
, and
Safar
,
M. E.
,
2001
, “
Pulse Pressure, Arterial Stiffness, and Drug Treatment of Hypertension
,”
Hypertension
,
38
(
4
), pp.
914
921
.10.1161/hy1001.095773
62.
Fry
,
B. C.
,
Lee
,
J.
,
Smith
,
N. P.
, and
Secomb
,
T. W.
,
2012
, “
Estimation of Blood Flow Rates in Large Microvascular Networks
,”
Microcirculation
,
19
(
6
), pp.
530
538
.10.1111/j.1549-8719.2012.00184.x
63.
Hyde
,
E.
,
Michler
,
C.
,
Lee
,
J.
,
Cookson
,
A.
,
Chabiniok
,
R.
,
Nordsletten
,
D.
, and
Smith
,
N.
,
2013
, “
Parameterisation of Multi-Scale Continuum Perfusion Models from Discrete Vascular Networks
,”
Med. Biol. Eng. Comput.
,
51
(
5
), pp.
557
570
.10.1007/s11517-012-1025-2
64.
Kassab
,
G. S.
,
Rider
,
C. A.
,
Tang
,
N. J.
, and
Fung
,
Y. C.
,
1993
, “
Morphometry of Pig Coronary Arterial Trees
,”
Am. J. Physiol. Heart Circ. Physiol.
,
265
(
1
), pp.
H350
365
.
65.
Kassab
,
G. S.
, and
Fung
,
Y. C.
,
1994
, “
Topology and Dimensions of Pig Coronary Capillary Network
,”
Am. J. Physiol. Heart Circ. Physiol.
,
267
(
1
), pp.
H319
325
.
66.
Kassab
,
G. S.
,
Lin
,
D. H.
, and
Fung
,
Y. C.
,
1994
, “
Morphometry of Pig Coronary Venous System
,”
Am. J. Physiol. Heart Circ. Physiol.
,
267
(
6
), pp.
H2100
2113
.
67.
Huang
,
W.
,
Yen
,
R. T.
,
McLaurine
,
M.
, and
Bledsoe
,
G.
,
1996
, “
Morphometry of the Human Pulmonary Vasculature
,”
J. Appl. Physiol.
,
81
(
5
), pp.
2123
2133
.
68.
Ganesan
,
P.
,
He
,
S.
, and
Xu
,
H.
,
2010
, “
Development of an Image-Based Network Model of Retinal Vasculature
,”
Ann. Biomed. Eng.
,
38
(
4
), pp.
1566
1585
.10.1007/s10439-010-9942-4
69.
Levy
,
B. I.
,
Ambrosio
,
G.
,
Pries
,
A. R.
, and
Struijker-Boudier
,
H. A. J.
,
2001
, “
Microcirculation in Hypertension: A New Target for Treatment?
,”
Circulation
,
104
(
6
), pp.
735
740
.10.1161/hc3101.091158
70.
Kaimovitz
,
B.
,
Lanir
,
Y.
, and
Kassab
,
G. S.
,
2010
, “
A Full 3-D Reconstruction of the Entire Porcine Coronary Vasculature
,”
Am. J. Physiol. Heart Circ. Physiol.
,
299
(
4
), pp.
H1064
1076
.10.1152/ajpheart.00151.2010
71.
Lauwers
,
F.
,
Cassot
,
F.
,
Lauviers-Cances
,
V.
,
Puwanarajah
,
P.
, and
Duvernoy
,
H.
,
2008
, “
Morphometry of the Human Cerebral Cortex Microcirculation: General Characteristics and Space-Related Profiles
,”
Neuroimage
,
39
(
3
), pp.
936
948
.10.1016/j.neuroimage.2007.09.024
72.
Ando
,
J.
, and
Yamamoto
,
K.
,
2011
, “
Effects of Shear Stress and Stretch on Endothelial Function
,”
Antioxid. Redox. Signal.
,
15
(
5
), pp.
1389
1403
.10.1089/ars.2010.3361
73.
Busse
,
R.
, and
Fleming
,
I.
,
1998
, “
Pulsatile Stretch and Shear Stress: Physical Stimuli Determining the Production of Endothelium-Derived Relaxing Factors
,”
J. Vasc. Res.
,
35
(
2
), pp.
73
84
.10.1159/000025568
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