電気通信大学
脳科学ライフサポート研究センター特別講演会
平成25年5月14日

脳血流のバイオメカニクス

谷下一夫
早稲田大学ナノ理工学研究機構

血管は単なるパイ
プではない→物理現象である血流との整合性は？

Observed distributionof atherosclerotic
plaques (grey shading)in the vasculatures ofmice fed a high-fat diet

8. Left subcravian artery
9. Thoracic aorta
10. Renal artery
11. Abdominal aorta
12.Iliac artery

1. Aortic sinus
2. Ascending aorta
3. Inner curvature ofaortic arch
4. Outer curvature ofaortic arch
5. Innominate artery
6. Right common
carotid artery
7. Left common
carotid artery(VanderLaan et al.)

動脈硬化病変の局在性脳動脈瘤発生も好発部位が存在：血流の影響？
Schematic diagram of thefrequent appearance of
intracranial aneurysms within
the circle of Willis.
(A.G. Osborn, 1995)*Anterior cerebral artery:
40%*Internal carotid artery: 30%*Middle cerebral artery:20%*Basilar artery: 10%

Internal carotid artery

Flow
separation
Complexhelical flow
patterns
occupy theseparated flow
regionHydrogen bubble visualization of flow in molds of carotid
bifurcation. A. flow is rapid, laminar. Large area of flow
separation is formed along the outer wall of the sinus
Zarins et al.

Blood flow

physics

Pathophysiologicalevents in the bloodvesselbiology

The interface between the physics and biology is theinner surface of blood vessels: endothelial cells

The generation of shear stress by blood flow andgeneration of normal stress and circumferential stretch
due to the action of pressure(Shu Chien)

The plaque-prone hemodynamic flow patterns impair
endothelial function in carotid arteries.
We should elucidate the role of disturbed flow pattern inendothelial function and dysfinction to get insights intomechanisms of pathophysiological processes for theprevention and management of vascular diseases resulting
from atherosclrosis and thrombosis.
What is “disturbed flow”?

動脈硬化病変が生じる場所：disturbed flowが生じている？

Gradient of wall shear stress

EC proliferative rate is increased in regions of disturbed flow.
The proliferation of cultured bovine aortic ECs assayed by
BrdU incorporation assays is markedly elevated in the
disturbed flow region near the reattachment point in the step
flow channel. (Chien)Effects of different flow patterns and associated shear
stresses on endothelial and vascular biology. (Shu Chien)
血管は流れの状態を感知している

血行力学説(hemodynamic hypothesis)→血流からの流体力とアテロームの発生とを結び付ける考え方The formation of atheroma is strongly associatedwith the blood flow. This is referred to as thehemodynamic hypothesis.

Molecular Hypothesis of
Atherosclerotic lesion formation (Ross)
Lymphocyte
Monocyte
Selectin

Adhesive molecule

βLDL
LDL

Platelet

Receptor
Macrophages Endothelial cell

βLDL
Oxidized LDL

Foam cell

IntimaMedia SMC
Media

Ross, R., Nature (1993)

Real time O2- production at 4h with oscillatory flow
Mahsa Rouhanizadeh et al. (2008)
振動流において、活性酸素が生じている事を蛍光で同定。
核が白く見える部分が活性酸素が生じている場所。

The disturbed flow is the condition of•Low shear stress•Oscillating shear
which is prone to initiate thevasculardisease.

Shear stimulus affects the cell functions
Albumin uptake intothe cells depends on the shear stress stimulus
The amount of albumin uptake isdetermined by the fluorescentintensity in the images(a) without flow(b) Shear stress ＝ 1 Pa(c) Shear stress ＝6 Pa
Bar = 20 µm

Shear dependency of albumin uptake into thecellsNormalized Albumin Uptake
into Endothelial Cells

*

*

*
*
*

*

Shear Stress (dyn/cm2)* P < 0.05 vs. control

Normalized albumin uptake as a function of imposed shear stress(Kudo, Tanishita et al. Trans. JSME, 1998)

Shear stress effect on mitochondrial membranepotential
JC-1
Low membrane potential: green fluorescence emission
High membrane potential: red fluorescence emission
Fluorescence was detectedby Confocal laser scanningmicroscope.
MP: Mitochodrial membrane potential
AH: Area of higher membrane potential
AT: Total area of mitochondria
AR: AH/AT
Kudo et al. BBRC (2000)

Endogeneous ATP depends on the imposed shear
stress stimulus

The favorite sites of cerebral aneurysm
Schematic diagram of thefrequent appearance of
intracranial aneurysms within
the circle of Willis.
(A.G. Osborn, 1995)*Anterior cerebral artery:40%
脳動脈瘤は局所的に特*Internal carotid artery: 30%
定な部位に発生している。
何故？
*Middle cerebral artery:20%
もしかしたら血流のせ*Basilar artery: 10%
い？
UCLA Prof.

Possibility of rupture of cerebral aneurysm
Cerebral aneurysm
Rupture（0.05-1%）

Unrupture (more than 99 %)Observation

Neurosurgical intervention

Endovascular embolization

High morbidity & mortality

No long-term efficacy

Aneurysms without possibility of rupture should not
be treated.
What is a predictor (risk factor) for rupture?
N.Engl J Medicine (1998)

The patterns of intra-aneurysmal flow
The intra-aneurysmal flow consists of*inflow: position and size of the neckand flow ratio into the distal branches*circulating flow: aspect ratio (depth /neck width)*outflow: usually nonpulsatile and low
velocity
Ujiie et al. recognizes that the intrraaneurysmal flow is determined by the
aspect ratio, rather than theaneurysmal size.
Ujiie et al. Neurosurgery (1999)

Necessity of prospective study basedon the anatomically realistic models

The knowledge of intra-aneurysmal flow inthe realistic models are required to ensure
the hemodynamic hypothesis

Tateshima et al., J. Neurosurg. (2001)
This study received the award of MAGNA CUM LAUDECITATION from the American Society of Neuroradiology in 2001.

Reconstruction of Cerebral Aneurysm
bleb

CT images

3D Surface Model•Abstraction of the vessel wall
•Piling up•Smoothing

Epoxy Resin Model•Photoforming method•Magnification (×2.6)

Features of the morphology•Asymmetrical shape of the aneurysm•Presence of a bleb (daughter aneurysm)

Realistic models of cerebral aneurysm cases
・Unruptured
・Middle cerebral
bifurcation aneurysm
・Aneurysm size = 6.3mm･Neck size = 5.7mm
・With a bleb

Model 1Case ２
Case 2Model 2・Ruptured・Middle cerebral
bifurcation aneurysm
・Aneurysm size
= 4.7 – 7.7mm
・Neck size = 4.3mm
・With a bleb(from Dept. of Radiological Science, UCLA)

Vector diagrams in the middle cerebral
artery (unruptured case)Flow

0.1m/sMinimum phase (t = 0 s)

Acceleration phase (t = 1.0 s)

Maximum phase ( t = 1.8 s)

Deceleration phase (t = 3.0 s)

Fig.5-2 Velocity profiles of profile b measured with PIV

Speed
0.048
0.045
0.042
0.039
0.036
0.033
0.029
0.026
0.023
0.020
0.017
0.014
0.011
0.008
0.005
0.002

[m/s]

Vector diagrams in the middle cerebral
artery aneurysm (ruptured case)
Minimalphase
Minimalphase

Acceleration phase

flow
bleb

Flow separation

Spee
0.043
0.040
0.037
0.034
0.032
0.029
0.026
0.023
0.021
0.018
0.015
0.012
0.010
0.007
0.004
0.001

[m/s]
Maximum phase

Recirculation

Deceleration phase

Distribution of vorticity in aneurysma) Unruptured MCBAb) Ruptured MCBA

Wall shear stress profiles obtained by LDV
5Minimal phase
Acceleration phase
Maximum phase
Deceleration phase

4.5
4x* = -1

Wall Shear Stress [Pa]

3.5
3
2.5
2
1.5

x* = 11
0.5

x* = 0

Unruptured MCBA

0
-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

x*

6
Minimal phase
Acceleration phase (t = 1.0s)
Acceleration phase (t = 1.6s)
Maximum phase
Deceleration phase5x * = -1

x* = 0Wall Shear Stress [Pa]x* = 1

4

3

2

1

Ruptured MCBA

0
-1

-0.8

-0.6

-0.4

-0.2

0
x*

0.2

0.4

0.6

0.8

1

What is the difference between ruptured
and unruptured cases?
MCBA (unruptured)
Vinflow = 80-90% of Vmax
Aspect ratio = 1.0
Area ratio = 2.0
Single circulation

MCBA (ruptured)
VInflow: = 70-80% of Vmax
Aspect ratio = 1.8
Area ratio = 2.1
Bleb:Recirculation
Peaked WSS

The internal elastic lamina is absent.

The pathology of intracranial arterial saccular aneurysms
indicates that the aneurysmal sac lacks normal layers.
Particularly the internal elastic lamina is usually absent
or reduced to fragments.
Weir and Macdonald, in Neurosurgery, 1996, McGraw-Hill

Treatment by intravascular surgery
Use of Intravascularstent
The thrombus formation
is induced by making theflow stagnant in theaneurysm.
Hademenos, G.J and
Mssoud, T.F., (1998)

Intravascular surgery is quite
promising and related technology
will be developing rapidly.

微小血管内の血流
実際の臓器における検証が重要

細動脈における血管のリモデリング

血流が減ると血管が細くなる

血流が増えると血管が太くなる血管の径が血流量の変化によって変わる⇒血流を感ずるセンサーがあるはずShape change of endothelial cell due to shear stress
Flow

StaticFlow Exposed(2 Pa, 48 h)

100 µm

ブタの内皮細胞を培養して、４８時間流れの刺激を与えたOxygen is delivered to brain by the blood
flow.
20μm
O2

Increase of oxygen consumption
due to the increased activity
Increase of oxygen delivery due tothe increased blood flow

Minimal reserves of oxygen and glucose are stored in the brain, so that
failure of delivery of either will quickly result in energy depletion.
That is why we need to know the oxygen transfer related to thehemodynamics in the brain.

Confocal image

Geometry of capillary

The bifurcating geometry and density of capillary
networkDensity of capillary network in the each layer
数100 μm

Ⅰ
Ⅱ

Ⅳ
Ⅴ

Ⅵ

血管数密度 (本/100 micron)Ⅲ

大脳皮質における血管数密度2Ⅳ1.8 Ⅰ-Ⅱ Ⅲ
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
10
20
30

Ⅴ

40

50
60
深さ (%)

Ⅵ

70

SC

80

K. Masamoto, K. Tanishita, et al. Brain Research

90

100

Estimate of module unit by 3D structurereconstructed by surface rendering.
Distance between
the arteriole isidentified.

Surface of cerebral cortex

Cross sectional view

150 micron

500 micron
300-400micron

Micro-CT image (Skyscan 1072, Toyo Technica)(3D-DOCTOR：Able Software Corp.)Depth profile of pO2 distribution in the somatosensory areas ofrat(without functional stimulation)

The layers from IV to VI depend on the area.

pO2 change after
the functional
stimulation

Puzzling results!

A. Hindlimb stim.

B. Trunk stim.

Caudal (mm)
0

0.5

1.0

1.5

2.0

2.5

Caudal (mm)
3.0

3.5

4.0

0

1.0

HL

1.5

2.0

2.5

3.0

3.5

4.0

2.0

1.5

Lateral (mm)Lateral (mm)

1.0

1.0

1.5

*a
Tr *c

2.5

FL
*b

3.0
3.5

2.0

*a

HL
* c Tr

2.5

FL

3.0

*b

3.5

130

a

120

a

120

b
c

110

b
c

ΔpO2 (%)

ΔpO2 (%)

0.5

110
100

100
90

Stimulus to Hindlimb

Stimulus to Trunk

90

80
-3

0

3

6

Time (sec)

9

12

-3

0

3

6

Time (sec)912

Dual response of tissue pO2 depending on the corticalareas.

K. Masamoto, K.
Tanishita, et al.
“Brain Research.
(2003)(N=6)

pO2 for HL and FL increases after the stimulation, on thecontrary pO2 for Tr decreases after the stimulation. ??

Simultaneous measurements of pO2 and local cerebral
blood flow in rat somatosensory cortex(Masamoto et al. J Appl Physiol 2007)

160

LCBF (%)

140
120
100
80
20
∆pO2 (torr)

15
10
5
0
-5
-20

0

20
Time (sec)40

We should note thepresence of initial dip ofK.
Masamoto, K. Tanishita,pO2.
et al. Journal of Cerebral
Blood Flow and Metabolism.
(2003)

ΔpO2 (torr)

In the activated region,
tissue pO2 initiallydecreased during the 3seconds after the onset of
acoustic stimuli, and thenincreased during the next
seconds.

**

Time (sec)
B. Initial decrease in tissue pO2

ΔpO2 (torr)

Biphasic changes of pO2

A. Average pO2 response
Stimulus
onset ****
* **
*
*****
*
*

1 torr3 sec

1 torr1 sec
Time (sec)Oxygen conservation equation for thecylindrical model∂p  1  ∂
 ∂
 ∂p
( r )  ∂p( z ) ∂p O 2(1 + m) O 2 + v z O 2  =  DB  r O 2   + DB∂z∂z  r  ∂r ∂t
 ∂r   ∂z

(0 < r < R1 )∂pO 2 1  ∂ ∂( r )  ∂p( z ) ∂p O 2+ RO 2 K=  DT  r O 2   + DTr  ∂r∂z∂t ∂r   ∂z

( R1 < r < R2 )dc HbO 2m=dcO 2Upper equation represents the oxygen conservation in the vessel.
Lower equation represents the conservation in the tissue.

Oxygen transfer model by Secomb (2000)
They calculated the pO2 profile in the cerebral tissue based on
the SEM imaging for three-dimensional vessel network.

Their result indicates thathypoxic damage is avoided bydecreasing the oxygen
consumption rate by 31 % for
the blood flow decrease by75%.
The oxygen transfer model contributes the prediction andavoidance of localized brain damage due to the cerebral
47
ischaemia and hypoxia.

Model for superficial and middle layers
38μｍSuperficial layer: 0-300 micron depth

400 micron

300 micron

300 micron

15μｍ

中間層/表層の比1500 μｍ

arteriole surface
2.01

Middle layer
477-777 micron depth

capillary networks surface
1.63
total vessels’ surface

Arteriolegeometry

1.69
Mesh size
arteriole tissue- 5 micron
capillary- 2 micron

Governing equations

Capillary

Arteriole

Plug profile
Parabolic profile

Y = rcNavier-Stokes equation∂U1+ (gradU ) U = − gradP + µ∇ 2 U
ρ∂t

L
Plasma
layer
Core

Y=0

Z

ρ

: density of blood ; 1.05g/ml

Y = rhμ: viscosity of blood ; 4mPa/s

Y

Re = 10-2

Core

Plasma layer∆ Prc
1− γ 22µ p L
2

Uh =

(

)

∆ Prc
U (Y ) =1− χ 22µ p L2(

γ＝ｒｈ/ rc
χ＝Y / rc,
Re = 10-3)

Oxygen transport
Within the tissue

Within the vessel∂[O 2]∂ 2 PO 2= D eff α
ui
∂x i
∂2xi

 ∂ 2 Po 2 ∂ 2 Po 2 ∂ 2 Po 2 Dα 2 + 2 + 2  − M = 0
 ∂ x
∂ y
∂ z 


Deff : O2 effective diffusion coefficient

M : O2 consumption

α : O2 solubility ; 3e-05 ml/ml/mmHg

D : O2 diffusion coefficient ; 1.5e-5 cm2/s

1.2E-04

α : O2 solubility ; 3e-05 ml/ml/mmHg

Deff (cm2/s)

1.0E-04
8.0E-05
6.0E-05
4.0E-05

Algorithm

2.0E-05

SIMPLE

0.0E+00
0

20

40
60
Po2 (mm Hg)

80

100

SolverFluent 5 : Fluent

Assumptions for the calculation•Matching flux at the vessel wall
•The oxygen gradient at the edge of module unit is zero
•The oxygen consumption rate is zero in the superficial layer up
to 100 µm depth.
Superficial layer
Middle layer
arteriole inlet Po2

100 mm Hg

85 mm Hg

capillary inlet Po2

50 mm Hg

50 mm Hg
normal condition

CBF （cm3/100g/min）

153

247
control flow

pO2 profile when the consumption matches with the delivery.
Superficial layer pO2 profile

50micron

150micron

250micron

600micron

700micronMiddle layer pO2 profile

Po２（mm Hg）

500micronComparison between the calculation and measured pO2
Calculated

Po2 (mm Hg)

Near arteriole
50
45
40
35
30
25
20
15
10

50
45
40
35
30
25
20
15
10

Avrage 22.34 mm Hg

0

50

100

150

200

250

300

Avrage 18.62 mm Hg

y

477

527

577

627

677

727

777

Po2 (mm Hg)

Measured
50
45
40
35
30
25
20
15
10

Avrage 24.61 mm Hg

0

50

100

150

200

250

Avrage 20.26 mm Hg

300

350

400

450

depth (micron)

500

550

600

650

700

750

8

The increase of oxygen delivery due to the increase ofblood flow
CBF parameter
Change of blood flow

CBF

CBF (cm3/100g/min)Middle中間層
表層(cm3/100g/min) Superficial

１

Control flow

Control flow2

Art_CBF 30% up

Art_CBF 30% up189

189
(24)

297
297 (20)

3

Art_CBF(a) 30% up,
200 (31)200
Art_CBF 30% up + cap_CBF 33% up
cap_CBF 33% up

318
318 (29)

4

up 30% up,
Art_CBF
Art_CBF 30% up + cap_CBF 100%
221 (45)221
cap_CBF 100% up

153

153

(0)

247
247

(0)

(b)

360
360 (45)

全体の増加率 (％)(a) David et al (1998)(b) Afonst et al (2000)

Scap / Sart

Ratio of the oxygen supply from capillary to that fromarteriole is affected by the blood flow rate.
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3

Superficial

4

Middle

3

１

1.0

2

1.1

1.2

1.3

1.4

1.5

relative change of total rCBF
Sart 10 % Up Scap 26 % UP (Sup)

Scap 71 % UP (Sup)

Scap 33 % UP (Mid)

Scap 76 % UP (Mid)The oxygen transfer plays an important role in the brain function.

Blood flow
activity

Oxygen delivery

Brain science

Neural

太い血管

微小血管

壁面せん
断応力

低い

内皮細胞
から血管
壁へ

血管病変の
進行

能動的な血流制
御によるリモデリ
ング、適合性

血管壁の機
能が問題

臓器機能が
問題

高い

Viewpoints from biology and physics

Importance of biology in the mechanics:
biomechanics

Importance of mechanics in the biology:
mechanobiology

バイオメカニクスでなくて、メカノバイオロジー？？
物理的な環境・刺激が、生物反応・機能・現象を制御するメカニズムの解明を目指す領域。

（朝倉書店にて発刊）

御清聴有難う御座いました。
Acknowledgements