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Physics in Medicine
PH3708
Dr R.J. Stewart
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Scope of Module
ardio!"ascular syste#
$%luid flow in pipes& circulation syste#& pressure
Me#'ranes
$(s#osis and solute transport
)rans#ission of electrical si*nals
$+er"es& ,-
(ptical %i'res and ,ndoscopy
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Scope of Module
ltrasound
$/#a*in* and Doppler #easure#ents
Radioisotope i#a*in* and radiolo*y
!ray *eneration and i#a*in*
+MR i#a*in*
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Module Resources
1e' Pa*e2$ http2www.rd*.ac.u4physicsnetunits3ph3708ph3708.ht#
5oo4s2$ -ood *eneral 'oo4s2
6Physics of the 5ody& a#eron& S4ofronic4 and
-rant
6Medical Physics& J.. Pope$ (ther #ore specialised 'oo4s are *i"en in the unit
description and will 'e referred to where necessary
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ardio"ascular Syste#
Physics of the Body, Cameron, Skofronick
and Grant, Ch. 8
/n considerin* the circulation of 'lood& one
essentially considers the flow of a "iscous
fluid throu*h pipes of different dia#eters
Define2$9iscosity2 arises fro# frictional forces associated
with the flow of one layer of li:uid o"er another
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9iscosity
onsider a circular cross section pipe2
$%low throu*h pipe due to pressure difference
$ssu#e2 flow at walls of pipe ; 0& #a=rv
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9iscosity
)he slower #o"in* fluid outside the central =shaded> re*ion e
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9olu#e %low Rate
)he a"era*e flow fro# the heart is the
stro4e "olu#e =the "olu#e of 'lood eected
in each 'eat> < nu#'er of 'eats per second.)his is E F0 =#l'eat> < 80 ='eats#in> ;
G800 #l#in
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9olu#e %low Rate
Poiseulles ,:uation
$9olu#e flow rate& Q& related to pressure
difference P& len*th land radius a'y2
l
a
P1 P2
P P1! P2
Qa
lP=
G
8
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9olu#e %low Rate
(ften con"enient to define a resistance, "
to flow& such that PQ"
P1 P2 P#
"1 "2 "#
P P1$ P2$ P#Q"1$Q"2$Q"#Q"
""1$"2$"#
Series Parallel
"1,Q1
"2,Q2QQ1$Q2P%"1$P%"2P%"
1/"1%"1$1%"2
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Resistance R
)he resistance decreases rapidly as a
increases
R ; ?PI ; 8 l B AaG)he units of R are Pa #!3s
narrowin* of an artery leads to a lar*e
increase in the resistance to 'lood flow&'ecause of aGter#.
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9olu#e %low Rates
,ffect of restrictions and 'loc4a*es2
$Series& whole flow is reducedstopped
$Parallel& flow partially reduced& increased in
other parts of the networ4
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)ransport Syste#
closed dou'le!pu#p syste#2
Syste#ic
irculation
Kun*
irculation
Keft side of heart
Ri*ht side of heart
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)ransport Syste#
Structure of the Heart
/nferior "ena ca"a
=fro# lower 'ody>
Superior "ena ca"a
=fro# upper 'ody>
orta
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)ransport Syste#
5ranchin* of 'lood "essels
$teries 'ranch into arterioles& "eins into
"enulesrteries
rterioles
apillaries
9enules
9eins
Heart
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)ransport Syste#
apillaries
$%ine "essels penetratin*
tissues$Main route for *asnutrient
e
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)ransport Syste#
5lood is in capillary 'ed for a few seconds
* of #uscle has a "olu#e of a'out
0F##3=density of #uscle E*#c#3or
000 *#3>& hence there are a'out
L04# of capillaries with a surface area of
E@ #@assu#in* a typical capillary is@0m in dia#eter.
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Pressures
Kar*e pressure "ariations throu*hout the
syste# =note 4Pa ; 7.3N ## H*>
$7 4Pa =@N ##H*> after left "entricle
$@ 4Pa =N ## H*> after syste#ic syste#
$3.G 4Pa =@N ##H*> after ri*ht "entricle
5lood pressure #onitor on ar# #easures@0 ##H* systole and 80 ##H* diastole for a
healthy youn* person
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Pressure
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Pressure
,ffect of *ra"ity on pressure
$Density of 'lood E .0G
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Pressure
onse:uences
$9aricose "eins
+or#ally =e.*.& durin* wal4in*> #uscle action helpsreturn "enous 'lood fro# the le*s
(ne!way "al"es in le* "eins to pre"ent 'ac4ward
flow
Defecti"e "al"es #eans poolin* of 'lood in le*"eins
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Pressure
cceleration
$onsider upward acceleration& a! au*#ents *ra"ity
$effecti"e *ra"ity ; aO&$Pressure difference ; =aO&>h
Pressure at head reduced.
,.*.& a; 3*
Pheart!head; .0G
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Rate of 'lood flow
5lood lea"es heart at E 30 c#s
/n capillaries& flow slows to E ##s
$Surprisin* ! continuity should i#ply hi*her
flow
$Recall indi"idual capillaries only E@0# in
dia#eter& 'ut "ery #any hence total crosssection e:ui"alent to a tu'e 30 c# in dia#eter
usin* esti#ate of @@N < 0Fcapillaries in 'ody
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,ffect of onstrictions
5ernoulli effect
$+arrowin* of tu'e *i"es increased "elocity& 'ut
reduced pressure
/ncreasin* "elocity at o'struction leads to a
transition fro# la#inar to tur'ulent flow
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,ffect of onstrictions
)ransition fro# la#inar to tur'ulent flow
characterised 'y"eynold's ()m*er, +
%low
rate
Pressure
Ka#ina
r
)ur'ulen
t
Qc
$ritical "elocityc Qc
$c;+"
$%or #any fluids&+E000
$e.*& in the aorta
="-c#>& cE 0.G#s
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,ffect of onstrictions
pparent that one can *et a rapid increase
in flow as a function of pressure in the
la#inar re*ion& 'ut relati"ely slow intur'ulent re*ion
$Durin* e
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%urther Readin*
ll inPhysics of the Body, Cameron,
Skofronick and Grant, Ch. 8,
Measure#ent of 'lood pressure
$Section 8.G
Physics of heart disease
$Section 8.0