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Модели квазиодномерной гемодинамики PowerPoint PPT Presentation


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Факультет вычислительной математики и кибернетики МГУ. Модели квазиодномерной гемодинамики. М.В.Абакумов, А.Я.Буничева, В.Б.Кошелев, С.И.Мухин, Н.В.Соснин, А.П.Фаворский, А.Б.Хруленко. Основные направления математического моделирования гемодинамики.

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Модели квазиодномерной гемодинамики

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6952933

.., .., .., ..,

.., .., ..


6952933

2D 3D ( -)

( , , ( ), , , , , ..)

2D 3D () .

  • (2D 3D )

  • ( , ) .

  • -

  • -

  • :

    • -

    • -

    • -

    • -

    • -

    • -

    • -

    • -

    • -


6952933

-

S

Kidney

p

Renal outflow qkid

Q

t

1. ( )

+ +

2. , - ( )

3.


6952933

-

g

4. .

5.

-

6.

-

. . .


6952933

Kidney

Q

t

- .

+

+

Renal outflow qkid

CVSS , - ,


6952933

u(t,x)

x

L

D(t,x), S=D2/4


6952933

S(x2)

S(x1)

X

X2

X1

, . .

x- , t- , S(x,t) - , u(x,t) - ( ), p(x,t) - , =const - , L- , F(x,t) .

( ).

S=S(p) .


6952933

S=const

Sconst

S=S(p)

S=S(p,u,Q, )

Q(S,p,u)=const

, , , .. . , .


6952933

S

Smax

Smin

pmax

pmin

p

S

Smax

Smin

P

Pmax

Pmin

S(p)


6952933

S

Smax

Smin

pmax

pmin

p

S

Smax

Smin

p

pmax

pmin

.

, ., Smin , Smax, Pmin, Pmax t x. , , , .


6952933

Q

Qconst

pmin

p1

pmax

p

-

p0

, .


6952933

,

, , , , ,

1. ( - ) - .

-

2. :

- ;

- ;

- .

  • . .

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6952933

, , , . , .

, (, , .).

() ( ), , .

.

( , , ..), .


6952933

p mm Hg

ptop

pbot

tsystdias t,

QA

QV

3.

.

- . . : , , .. .

.

,

,


6952933

Q

0 tS tD t

(VK )

QV

QA

VK

QV, , . , .

VKD : Vsurg=Kf VKD

: Vsurg=const


6952933

v

i,j , , zi=1

Kd-

1.

2. , , .

3. , , .

S(t,x)

u(t, x) -

p(t,x) -

t -

x -

- ( = const).

FT

FT


6952933

s = s ( p )

( )

( ) , dS/dp>0. , , .

, ( ).


6952933

4. . , , .

( Q(t) )

( p(t) )

5. , .


6952933

C (D=const- )

<<1 ,

l,k l- k , f , - .

- .

Cl . .

t , t . a . .


6952933

i

( )

, i=1,2,3,4 -

aS ,au

i , I , 2 =


6952933

j


6952933

, :

  • ;

  • , , ;

  • ;

  • ;

  • , , ;

  • , ;

  • , ;

  • ;

  • .


6952933

1

2

CVSS (CardioVascular Simulating System)

CVSS

Pre-processor

Solver

Post-processor


6952933

1. .

2. .

3. - .

4. ( ).

5. .


6952933

()

:

:

.


6952933

i arch

i- , (|u|<):

, ,


6952933

- .

.

:

j i

j

i

i

i


6952933

. ,

,

, ,

.


6952933

( ),

,

, .


6952933

- .

, .

,

, , , , , P1,P2,P3, A1,A2,A3,M1,M2,M3,

. .

.


6952933

First column is the flow without occlusions.

. 70% 90% . (, , ..) . () ( 2-9 ).

: ?

20%

?

. .


6952933

1

+ :

-

-

- , ,

-

2

.

1,8 , 1 .


6952933

Q

0 tS tD t

  • .

  • (, , , ..) .

  • ( ) .

  • - .

85 ml,

ts=0.3 s, td=0.5 s.

Ventrical

VK

QV

QA

aurical


6952933

85 , ts=0.3 , - td=0.5 . ( 5 - 10 ) - , ().

( )


6952933

.

(* . . .. , .. , 1998)

, :

;

;

;

;

;

;

.


6952933


6952933

.

.

.

:

, ,

, .


6952933

()

() () , . ()

() () tprd.


6952933

.

.

, B ,


6952933

<p>

Kidney

Renal normal outflow

Renal outflow qkid

q, 3/

q*

<p>, ..

50

100

150

200

: <p> , p*, ( q* )

Renal outflow

Volume of CVS

Renal pressure


6952933

-

- i-

1 - H=0%, 2 - H=25%, 3 - H=50%

4 - H=75%, 5 - H=90%

1 - R=1, 2 - R=0.5, 3 - R=0.1

4 - R=0.01

.


6952933

.

,


6952933

g

.

( + ) , , .

.

.


6952933

. .


6952933


6952933

.

  • .., .., .., .., .., .., .., .., ... - . . 1997. .33, 7, .892-898.

  • .., .., .., .., .., .., .., .., ... - . . 2000. .12, 2, .106-117.

  • .., .., .., .., ... . . 2000. .36, 7, .919-924.

  • .., .., .., ... . . 2001. .37, 7, .905-912.

  • .., .., .., .., .., .., .., ... CVSS. : . 2001. .,, .194-218.

  • .., .., .., ... . . 2004. .40, 1, .87-97.

  • .., .., .., ... . . 2004. .40, 7, .920-935.

  • .., .., .., .., .., ... . : . 2005. .,, .39-99.

  • .., .., ... . . 2006. .42, 7, .979-993.

  • .., .., .., ... . . 2007. .43, 7, .987-992.

  • .., .., .., .., ... - . . 2007. .19, 3, .15-28.


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