東北大学機関リポジトリTOUR

Numerical simulation of bacterial flora in the

intestine of zebrafish larvae

著者

楊 金有

学位授与機関

Tohoku University

学位授与番号

11301甲第18814号

（ゼブラフィッシュ稚魚の腸内フローラの

数値シミュレーション）

○ 1 2

A.veronii

t

h h

h h h h

t Qin Q0 δf c h Qin Q0 δf c h Qin(δf c h δf(Qin Q0 c h h Qin Q0 δf c t Qin Q0 δf c h Qin Q0 δf c h P a(z) Pt c Qin Q0 δf h Qin δf c δf(Qin Q0 c h h (Qin Q0 δf c

×10 7 nc/N t ϕmax ϕmax = 1.0× 10 11 2 ϕmax = 5.0× 10 11 2 ϕmax = 1.0× 10 10 2 nc/N ϕmax nc/N t ‒ ϕmax ϕ0 nc/N ϕ0 Qin(Db = 1× 10 11 2 Db Qin = Q0

ϕ0 Qin Db Qin(Db = 1× 10−11 2 Db Qin = Q0 t ϕmax ×10−11 2 _ϕ max ×10−11 2 _ϕ max ×10−10 2 nc/N Uϕ UQ UD Uϕ Uϕ UQ UD

108

P roteobacteria Lactobacillales

Aeromonas

Aeromonas V ibrio

̶ ̶

Wl(z, t) = W24(z) + g(z, t), g(z, t) = δgexp ! −t τg " exp # ln0.5 λ2 g (z− zg0)2 $ , Wl(z, t) g(z, t) δg τg λg zg0 W24(z) i.e. t t zf 0 f (z, t) W (z, h + t)

40 80 120 160 200 240 0 0.4 0.8 1.2 1.6 Diameter [ µ m] z [mm] a From paper From equation 40 80 120 160 200 240 0 0.4 0.8 1.2 1.6 Diameter [ µ m] z [mm] b From paper From equation 40 80 120 160 200 240 0 0.4 0.8 1.2 1.6 Diameter [ µ m] z [mm] c From paper From equation 40 80 120 160 200 240 0 0.4 0.8 1.2 1.6 Diameter [ µ m] z [mm] d From paper From equation 40 80 120 160 200 240 0 0.4 0.8 1.2 1.6 Diameter [ µ m] z [mm] e From paper From equation 40 80 120 160 200 240 0 0.4 0.8 1.2 1.6 Diameter [ µ m] z [mm] f From paper From equation h h h h h h

W (z, h + t) = Wl(z, h) + fan(z, t) + fre(z, t) + ct ∂g(z, t) ∂t |(t=h), fan(z, t) =−δfJ(z, dan)exp % ln0.5 λ2 f {z − H(t, ∆tan)Uc− zf 0}2 & , fre(z, t) =−δfJ(z, dre)exp % ln0.5 λ2 f {z − H(t, ∆tre)Uc − zf 0}2 & , h fan(z, t) fre(z, t) δf λf Uc J(z, d)   J(z, d) = ⎧ ⎨ ⎩ 1, when _{|z − z}f 0| ≤ d exp[₋(|z − zf 0| − d) l ], when |z − zf 0| > d . d l d H(t, ∆t) ∆t c c i.e. i.e. ρ µ = 10−3 · = ρW Uc/µ

t V0 1 I0 1 I24 sum V10 I24 sum I0 1 Q0 = ! V24 sum − V10× I24 sum I0 1 " / (24_{× 60 × 60) = 8.3×10}−17 3_{/ V}24 sum Q0

0

5

10

15

20

25

80

100 120 140 160 180 200 220 240 260

Velocity [

µ

m/s]

y [µm]

Front line 1

Mesh number 202,752

Mesh number 404,096

Mesh number 806,784

Mesh number 1,511,488

5

10

15

20

25

30

35

40

45

100

120

140

160

180

200

220

240

Velocity [

µ

m/s]

y [µm]

Front line 2

Mesh number 202,752

Mesh number 404,096

Mesh number 806,784

Mesh number 1,511,488

14

16

18

20

22

24

26

28

30

32

80

100 120 140 160 180 200 220 240 260

Velocity [

µ

m/s]

y [µm]

Front line 3

Mesh number 202,752

Mesh number 404,096

Mesh number 806,784

Mesh number 1,511,488

4

6

8

10

12

14

16

18

230 240 250 260 270 280 290 300 310 320

Velocity [

µ

m/s]

y [µm]

Back line 1

Mesh number 202,752

Mesh number 404,096

Mesh number 806,784

Mesh number 1,511,488

5

10

15

20

25

30

35

250

260

270

280

290

300

310

Velocity [

µ

m/s]

y [µm]

Back line 2

Mesh number 202,752

Mesh number 404,096

Mesh number 806,784

Mesh number 1,511,488

6

8

10

12

14

16

18

20

240

250

260

270

280

290

300

310

320

Velocity [

µ

m/s]

y [µm]

Back line 3

Mesh number 202,752

Mesh number 404,096

Mesh number 806,784

Mesh number 1,511,488

t

10−4 10−5 D(t) = 1 N N * i=1 [ i(t)− i(0)]2 6t i i i i(t2) = i(t1) + + t2 t1 idt D D δf

(Uc) (∆t) (dre) (dan) δf ‒ Qin ‒ Q0 c ‒ h ‒ δf ‒ ∆T ∆Tre ∆Tan dre dan λf δf zf 0 δg τg λg zg0 c Uc ρ 3 µ · Qin ‒ Q0 Q0 × −17 3

i.e. z < zf 0 t Qin Q0, δf = 0.3 c h Qin Q0, δf = 0.3 c h D D D 10−12 2_/ Qin Q0 Q0 Q0 δf δf D t δf h D h h

Qin

0

2

4

6

8

10

0

500

1000

1500

2000

2500

D

[10

-12

m

2

/s]

t [s]

Qin Q0 δf c h t Qin Q0, δf c h c

0 2 4 6 8 10 0 500 1000 1500 2000 2500 D [10 -12 m 2 /s] t [s]

A

0Q₀ 1Q₀ 2Q₀ 3Q₀ 4Q₀ 5Q₀ 0 2 4 6 8 10 0 500 1000 1500 2000 2500 D [10 -12 m 2 /s] t [s]

B

δf=0.1R δf=0.2R δf=0.3R δf=0.4R δf=0.5R 0 2 4 6 8 10 0 500 1000 1500 2000 2500 D [10 -12 m 2 /s] t [s]

C

0 h 3 h 6 h 12 h 24 h Qin(δf c h δf(Qin Q0 c h h Qin Q0 δf c

P a(z) Pt P a(z) c Pt c Pt c Qin Qin g(z, t) δf δf δf h h

t Qin Q0 δf

-0.01

0

0.01

0.02

0.03

0.04

0.05

0

0.5

1

1.5

Pressure [Pa]

z [mm]

A

Without anterograde peristalsis

With anterograde peristalsis

-0.01

0

0.01

0.02

0.03

0.04

0.05

0

0.5

1

1.5

P

a

(z)

[Pa]

z [mm]

B

Without anterograde peristalsis

With anterograde peristalsis

Qin Q0 δf c h

-0.01

0

0.02

0.04

0.06

0.08

0

10

20

30

40

P

t

[Pa]

c

A

Without anterograde peristalsis

With anterograde peristalsis

0.025

0.027

0.029

0.031

0.033

0.035

0

1

2

3

4

5

P

t

[Pa]

Q

_in

[Q

₀

]

B

Without anterograde peristalsis

With anterograde peristalsis

0.015

0.02

0.025

0.03

0.035

0.1

0.2

0.3

0.4

0.5

P

t

[Pa]

δ

f

C

Without anterograde peristalsis

With anterograde peristalsis

0.026

0.028

0.03

0.032

0.034

0

6

12

18

24

P

t

[Pa]

h [hours]

D

Without anterograde peristalsis

With anterograde peristalsis

Pt

c Qin Q0 δf h Qin δf c

δf(Qin Q0 c h h (Qin Q0 δf

DB DB = kBT /(6µr) kB T µ r ◦ _{· D} B 10−12 / D 10−12 / · HAM = A0 + M0σS/σ0 A0 M0 σ0 σs σs 10 3 ·

Aeromonas V ibrio

zf 0 f (z, t) W (z, t) ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ W (z, h + t) = W0(z, h) + fan(z, t) + fre(z, t), fan(z, t) =−δfJ(z, dan)exp % ln0.5 λ2 f {z − H(t, ∆tan)Uc − zf 0}2 & , fre(z, t) = −δfJ(z, dre)exp % ln0.5 λ2 f {z − H(t, ∆tre)Uc− zf 0}2 & , W0(z) fan(z, t) fre(z, t) δf λf Uc J(z, d) J(z, d) = ⎧ ⎨ ⎩ 1, when |z − zf 0| ≤ d exp[−(|z − zf 0| − d) l ], when |z − zf 0| > d . d l d H(t, ∆t ∆t

⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ ∇ · = 0, ∂ ∂t + ( · ∇) = − 1 ρ∇p + µ ρ∇ 2 . ∇ ρ p µ ρ m3 _{µ 10}−3 _· ρW Uc µ Q0 Q0 8.3× 10−17 3_/

‒

∂b ∂t + ∇b = Db∇ 2_{n +} ! λg n KM + n − λ d " b b Db λg λd KM i.e. ∂n ∂t + ∇n = Dn∇ 2_{n + Y} n n KM + n b Dn Yn 3 5.3×10−7 1012 −3 _{i.e. ≤} 3

ϕ = ϕmax -−a (z − z0)2 . ϕmax Aeromonas z0 i.e. 5.66 × 106 ϕmax = b_∇ϕ b ϕ ϕ 2 _∇ϕ λg

∂b ∂t + ( +∇ϕ) ∇b = Db∇ 2_{b +}/_λ g− λd− ∇2ϕ)b λg = ⎧ ⎨ ⎩ 3.2_{× 10}−4_s−1_{, (b≤ 6.5 × 10}15_m−3₎ 0. (b≥ 6.5 × 1015_m−3₎ 6.5_{× 10}15 b 6.5× 1015 ‒ ‒ ‒ δf

Uc ∆t dre dan Db 10 12 ₁₀ 10 2 _Q in ‒ Q0 Aeromonas ‒ nc/N i.e.

δf ∆T ∆Tre ∆Tan dre dan λf δf zf 0 × 12 ‒ 10 2 g × 4 −1 d × 5 −1 KM 3 × 16 κ × 7 × 10 2 Uc ρ 3 µ · Qin ‒ Q0

N nc/N nc/N ‒ 5.3_{× 10} 7 t 1012 _n c/N nc/N ‒ 5.3 × 10 7 107 _n c/N nc/N nc/N ‒

0

0.2

0.4

0.6

0.8

1

0

2

4

6

8

10

n

c

/N

Time [h]

Without nutrient flux across the wall With nutrient flux across the wall

ϕmax ‒ ϕmax nc/N ϕmax nc/N ϕmax nc/N ϕmax 1.0× 10 10 2 ϕmax

D

b

Q

in nc/N nc/N ϕmax ϕ0 nc/N Qin ϕ0 Db × 11 2 Qin Qin Qin i.e. Qin Q0 ϕ0 Qin Q0 ϕ0 Qin

t ϕmax

ϕmax = 1.0× 10 11 2 ϕmax = 5.0× 10 11 2

0

0.2

0.4

0.6

0.8

1

0

2

4

6

8

10

ϕ_max=1×10-10[m2/s] 5×10-11[m2/s] 1×10-11[m2/s] 5×10-12[m2/s] 1×10-12[m2/s]

n

c

/N

Time [h]

nc/N ϕmax

0

0.2

0.4

0.6

0.8

1

10

-12

10

-11

ϕ

0

10

-10

10

-9

0.75

Maximum n

c

/N

ϕ

_max

[m

2

/s]

nc/N t ‒ ϕmax ϕ0 nc/N

10

-11

10

-10

10

-9

10

-2

10

-1

10

0

10

1

slope 1

ϕ

0

[m

2

/s]

Q

_in

/Q

₀

A

10

-11

10

-10

10

-9

10

-12

10

-11

10

-10

10

-9

slope 1

ϕ

0

[m

2

/s]

D

_b

[m

2

/s]

B

ϕ0 Qin(Db = 1× 10 11 2 Db Qin= Q0

ϕ0 Qin = Q0 Db 3 10 11 2 ϕ0 Db Db 1 10 11 2 ϕ0 Db nc/N nc/N ϕ0 nc/N ϕ0 Qin Db ϕ0 ϕ0

10

-11

10

-10

10

-9

0.1

1

10

ϕ

0

[m

2

/s]

Q

_in

/Q

₀

A

With peristalsis

Without peristalsis

10

-11

10

-10

10

-9

10

-12

10

-11

10

-10

ϕ

0

[m

2

/s]

D

_b

[m

2

/s]

B

With peristalsis

Without peristalsis

ϕ0 Qin Db Qin(Db = 1× 10−11 2 Db Qin= Q0

t

ϕmax ×10−11 2

0

0.2

0.4

0.6

0.8

1

0

2

4

6

8

10

ϕ_max=1×10-10[m2/s] 5×10-11[m2/s] 1×10-11[m2/s] 5×10-12[m2/s] 1×10-12[m2/s]

n

c

/N

Time [h]

nc/N

ϕ = ϕmax 2 L ! L 2 − |z − z0| " ϕmax z0 i.e. Uϕ i.e. Uϕ ∼ϕ0 UQ UD UQ i.e. UQ ∼ in Am Am z0 UD UD ∼ b Uϕ UQ UD Uϕ UQ UD Uϕ UQ UD Uϕ

Uϕ UQ UD

Uϕ

Uϕ UQ UD Uϕ UQ+ UD Uϕ UQ UD ϕ0 Qin Qin Qin UQ UQ Qin UD Qin Db UQ UQ UD Qin ϕ0 Qin Qin ϕ0 Db Db UQ Qin Am Db ϕ0 UD UD UD ∼ b Db UD ϕ0 ‒ ϕmax ϕ0 nc/N Qin Db ϕ0

Qin Db Qin Db ϕ0 Qin

Db ϕ0

10 12 _/ ‒ ϕmax ϕ0 nc/N Qin Db ϕ0 Qin Db Qin Db ϕ0 Qin Db

ϕ0

Uϕ

‒

‒

‒

‒

‒ ‒ ‒ ‒ ‒ ‒ ‒ ‒ ‒

‒ ‒ 楊金有 下權谷祐児 石川拓司 ゼブラフィッシュの腸内フローラシミュレ ーション 日本流体力学会年会 年度年次大会 講演論文集 大 阪 年 月 楊金有 下權谷祐児 石川拓司 ゼブラフィッシュ稚魚の腸内輸送現象の シミュレーション 日本流体力学会年会 年度年次大会 講演論文集 東京 年 月 楊金有 下權谷祐児 石川拓司 ゼブラフィッシュ稚魚の腸内流れのシミュ レーション 日本機械学会第 回バイオエンジニアリング講演会 講演論 文集 名古屋 年 月