biophysics - flow basic parameters

8/17/2019 Biophysics - Flow Basic Parameters

1/20

Prof. dr hab. Zbigniew Dunajski

English Division

Zakład Biofizyki i Fizjol. Cz. Warsaw

Medial !niversi"y


2/20

Press#rePress#re

0 p

h

h p p ρ 0

h

2m

Newton Pascal

area

force

S

F p


3/20

Ci$nienieCi$nienie

0 p

h

h p p ρ 0

h

2m

Newton Pascal

przekrój

sila

S

F p


4/20

%ydros"a"i &ress#re%ydros"a"i &ress#re


5/20

Basi fea"#res and &ara'e"ers of flow

Flow is volume/unit time (Flow = velocity x cross

sectional area of the vessel)

Flow is usually more important than velocity in thecardiovascular system because the amount of a material that is

brought to or carried away from an organ is determined by the

volume of blood passing through an organ each minute, not by

the velocity of the blood

!v" ⋅=

#rof dr hab $bigniew %una&s'i

( fl#id) any 'edi#' "ha" an flow) inl#ding gases) and li*#idss#h as wa"er.


6/20

+he flow of a fl#id "hro#gh a &i&e is desribed by

Berno#lli,s e*#a"ion, whih is an a&&lia"ion of"he law of conservation of mechanical energy "o a

'oving fl#id-

Berno#lli,s law

here P is the pressure of the uid, ρ its density, h its

height and v its velocity, g= *acceleration

const v

gh P =⋅

++2

2 ρ

ρ


7/20

Berno#lli,s law

22

2

2

2

2

*

*v P v P ρ ρ

)(2

)(222

2

*

2

2*

2

2

2

**

2

2

2

*

*2

vv P vv P vv

P P ρ ρ ρ ρ

*2 vv > *2 P P <


8/20

Berno#lli,s law

const v p =

2

2

ρ

2

22

2

**

22

v pv p ρ ρ


9/20


10/20

e/eli zaniedba0 z'ian1 wysoko$i odink+w r#ry) "o wz+r #&raszza si1 do-

W r#rze o 'niejszy' &rzekroj# iez &łynie szybiej 2v3 4v5 6) w zwi7zk# z "y' &an#je w niej 'niejsze i$nienieni/ w r#rze o wi1kszy' &rzekroj#.

Ciecz płynąc w rurze o zmieniającym się przekroju ma mniejsze ciśnienie na odcinku, gdzie przekr ó j jest

mniejszy.

Podana wy/ej własno$0 iezy była znana &rzed sfor'#łowanie' r +wnania &rzez Berno#lliego i nie &o"rafiono

jej wy"ł#'azy0) s"wierdzenie "o i obenie kł+i si1 ze 8zdrowy' rozs7dkie'8 wiel# l#dzi i dla"ego znane jes" &od

nazw7 parado's hydrodynamicny.

const v

gh P =⋅

++2

2 ρ

ρ

http://pl.wikipedia.org/wiki/Paradoks_hydrodynamicznyhttp://pl.wikipedia.org/wiki/Paradoks_hydrodynamicznyhttp://pl.wikipedia.org/wiki/Paradoks_hydrodynamicznyhttp://pl.wikipedia.org/wiki/Paradoks_hydrodynamiczny


11/20

Conserva"ion of flow

93

95

9:

93 ; 95 < 9:

s3 s5

v3v5

v3=s3 ; v5=s5

Flow ; >ol#'e?"i'e;veloi"y @ ross se"ional

area of "he vessel

9 ; >?" ; v="=s?" ; v=s

> ; @=s ; v="=s

s

@


12/20

A For a li*#id 'oving along a horizon"al "#be) "he flow (Q) is&ro&or"ional "o "he &ress#re differene ∆P be"ween "heends of "he "#be

where is "he resis"ane of "he "#be. o"e "he si'ilari"ywi"h h',s aw- G ; >?

A +here are "wo "y&es of flow) la'inar 2s"rea'line6 and

"#rb#len". Gn s"rea'line flow an individ#al li*#id 'ole#lere'ains a" "he sa'e dis"ane fro' "he walls of "he vesselas i" "ravels down i" and "he f#r"her "he 'ole#le is fro'"he wall) "he fas"er i" 'oves and "he flow is silen".

R

P Q

)(∆=


13/20

a'inar 2s"rea'line6 flow

A +#rb#len" flow o#rs when individ#al 'ole#les 'ove

irreg#larly. +#rb#len" flow is noisy. Mos" flow in "he

ardiovas#lar sys"e' is s"rea'line.


14/20

Prze&ływ la'inarnyPrze&ływ la'inarny


15/20


16/20

%agenPoise#ille law +he la'inar flow "hro#gh a &i&e is desribed by "he

%agenPoise#ille law) s"a"ing "ha" "he flow ra"e 29 ;vol#'e of fl#id flowing &er #ni" "i'e6 is &ro&or"ional "o

"he &ress#re differene P be"ween "he ends of "he &i&e

and "he fo#r"h &ower of i"s radi#s r.

η

π

l

P r Q

-

=

η - viscosity he internal friction that causes the velocity gradient

is called the viscosity

the vessel in consideration is a small artery or an arteriole.


17/20

FlowFlow is &ro&or"ional "o "he &ress#re differene Pis &ro&or"ional "o "he &ress#re differene Pbe"ween "he ends of "he &i&e and "he fo#r"h &owerbe"ween "he ends of "he &i&e and "he fo#r"h &ower

of i"s radi#s r.of i"s radi#s r.

H resis"ane of "he vessel H h'Is low G ; >?

R

P Q

)(∆=

η

π

l

P r

Q

-

=

-r l R

π η

resistance of the vessel decreases with r to 4 power

*.2-

% d i J" d C "id Bif "i% d i J" d C "id Bif "i


18/20

%e'odyna'is- J"enosed Caro"id Bif#ra"io%e'odyna'is- J"enosed Caro"id Bif#ra"iooal blood flow &a""erns &lay an i'&or"an" role in "he develo&'en")

diagnosis and "rea"'en" of vas#lar disease. een" advanes in 'edial

i'aging 'ake i" &ossible "o i'age :D vas#lar ana"o'y wi"h s#b'illi'e"er

resol#"ion. +his da"a for's "he basis for o'"er si'#la"ions of blood flow"hro#gh KrealL vas#lar geo'e"ries. Flow &a""erns downs"rea' of a s"enosis

&rovide ondi"ions for &la*#e and blood lo" for'a"ion) leading "o s"roke.


19/20

%e'odyna'is- Coronary By&ass raf"%e'odyna'is- Coronary By&ass raf"

hese two animations show the results of pulsatile computational fluid dynamics studies in

simplified models of the distal end of a coronary bypass graft n the animation on the left, the

presence of a graft downstream (ie to the right) of the stenosis (far left) and branch producesrelatively slow flow in the host between the graft and branch n the movie on the right, the

graft has been placed close to the stenosis, and upstream of the branch, producing much faster

and more uniform flow in the host

!nimation provided by %r %avid 1teinmans research group


20/20

Co'"er Modeling of "he Miroir#la"ionCo'"er Modeling of "he Miroir#la"ion

1ince the 3% nature of microvascular networ's is often difficult to portray on paper, new

image analysis tools for investigating microvascular oxygen transport using intravital videomicroscopy (445) are being developed 6ith a few simple computer imaging techni7ues,

and specialied freeware, the microvasculature can be modeled in all its dimensions

8virtually

Movie acquired throughIVVM

3D Computer model ofmicrovasculature based on IVVM

biophysics - flow basic parameters

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