Estimating Uncertain Flow and Transport Parameters Using a ...
Biophysics - Flow Basic Parameters
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Transcript of Biophysics - Flow Basic Parameters
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8/17/2019 Biophysics - Flow Basic Parameters
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Prof. dr hab. Zbigniew Dunajski
English Division
Zakład Biofizyki i Fizjol. Cz. Warsaw
Medial !niversi"y
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Press#rePress#re
0 p
h
h p p ρ 0
h
2m
Newton Pascal
area
force
S
F p
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Ci$nienieCi$nienie
0 p
h
h p p ρ 0
h
2m
Newton Pascal
przekrój
sila
S
F p
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%ydros"a"i &ress#re%ydros"a"i &ress#re
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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 $bigniew %una&s'i
( fl#id) any 'edi#' "ha" an flow) inl#ding gases) and li*#idss#h as wa"er.
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+he flow of a fl#id "hro#gh a &i&e is desribed by
Berno#lli,s e*#a"ion, whih is an a&&lia"ion of"he law of conservation of mechanical energy "o a
'oving fl#id-
Berno#lli,s law
here P is the pressure of the uid, ρ its density, h its
height and v its velocity, g= *acceleration
const v
gh P =⋅
++2
2 ρ
ρ
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Berno#lli,s law
22
2
2
2
2
*
*v P v P ρ ρ
)(2
)(222
2
*
2
2*
2
2
2
**
2
2
2
*
*2
vv P vv P vv
P P ρ ρ ρ ρ
*2 vv > *2 P P <
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Berno#lli,s law
const v p =
2
2
ρ
2
22
2
**
22
v pv p ρ ρ
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e/eli zaniedba0 z'ian1 wysoko$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
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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
@
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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
)(∆=
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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.
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Prze&ływ la'inarnyPrze&ływ la'inarny
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%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.
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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
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%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.
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%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
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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