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1264

JACC Vol . 27, No. 5

Apr i l 1996:1264-9

I n V i t r o F l o w E x p e r i m e n t s f o r D e t e r m i n a t i o n o f O p t i m a l G e o m e t r y o f

To ta l a v o pulm o na ry o nn ec t io n fo r Surg ica l Re pa ir o f h i ldren

W i t h F u n c t i o n a l S i n g l e V e n t r i c l e

S H I V A S H A R M A , M D , F A C C , S E A N G O U D Y , B S ,* P E T E R W A L K E R , P H D ,*

S A M I R P A N C H A L , M S , * A N N E N S L E Y , B S ,* K I R K K A N T E R , M D , t V I N C E N T T A M , M D , ~

D E R E K F Y F E , M D , P H D , A J I T Y O G A N A T H A N , P H D *

Atlanta, Georgia

Objectives.

This s tudy sou ght to eva luate the e f fec t o f o ff se tt ing

c a v o p u l m o n a r y c o n n e c t i o n s a t v a r y i n g p u l m o n a r y f l o w r a t i o s t o

d e t e r m i n e t h e o p t i m a l g e o m e t r y o f t h e c o n n e c t io n .

Background.

P r e v i o u s i n v e s t ig a t o r s h a v e d e m o n s t r a t e d e n e r g y

c o n s e r v a t i o n w i t h i n t h e s t r e a m l i n e d c o n t o u r s o f t h e t o t a l c a v o -

p u l m o n a r y c o n n e c t io n c o m p a r e d w i t h t h a t o f t h e a t r i o p u l m o n a r y

c o n n e c t i o n . H o w e v er t h e i r s u r g i c a l d e s i g n o f c o n n e c ti n g t h e t w o

c a v a e d i r e c t l y o p p o s i t e e a c h o t h e r m a y r e s u l t i n h i g h e n e r g y

l o s s e s . O t h e r s h a v e i n t r o d u c e d a u n i d i r e c t i o n a l c o n n e c t i o n w i t h

s o m e a d v a n t a g e s b u t w i t h c o n c e r n s a b o u t t h e f o r m a t i o n o f

a r t e r i o v e n o u s m a l f o r m a t i o n i n t h e l u n g e x c l u d e d f r o m h e p a t i c

v e n o u s r e tu r n . T h u s a n o p t i m a l s u rg i ca l d e s i g n h a s n o t b e e n

d e t e r m i n e d .

M ethods.

I n t h e p r e s e n t m o d e l s t h e c a va l c o n n e c t i o n s w e r e

of fse t through a range o f 0 .0 to 2 .0 d iameters by 0 .5 super ior cava

d i a m e t e r i n c r e m e n t s . F l o w r a t i o s w e r e f i x e d f o r s u p e r i o r a n d

in fer ior cavae and var ied for right and le f t pu lmo nary ar teries as

70:30 60:40 50:50 40:60 and 30:70 to s t imu la te vary ing lung

r e s i s ta n c e . P r e s s u r e m e a s u r e m e n t s a n d f l o w v i s u a l i z a t io n w e r e

don e a t s teady f lows o f 2 4 and 6 l i ters /ra in to s imula te res t and

exercise.

Results.

O u r d a t a s h o w t h a t t h e e n e r g y l o s s e s a t t h e 0 . 0 -

d i a m e t e r o f f se t w e r e d o u b l e t h e l o s s e s o f t h e 1 . 0 a n d 1 .5 d i a m e t e r s

w h i c h h a d m i n i m a l e n e r g y l o s s e s . T h i s r e s u l t w a s a t tr i bu t ab l e t o

c h a o t i c p a t t e r n s s e e n o n f l o w v i s u a l i z a t i o n i n t h e 0 . 0 - d i a m e t e r

of fse t . Energy sav ings were more ev ident a t the 50 :50 r ight / le f t

p u l m o n a r y a r t e ry r a ti o . E n e r g y l o s s e s i n c r e a s e d w i t h i n c r e a s e d

total f low rates.

Conclusions.

The resu l t s s trong ly sugges t the incorporat ion o f

cava l o ff se ts in fu ture to ta l cavopulm onary connect ion s .

J

Am CoU Car dio l 1996;27:1264-9

Th e h i s to ry o f su rg i ca l m a n a g e m e n t o f p a t ie n t s w i th a fu n c -

t iona l s ing le ventr ic le has bee n ch arac te r ized by modifica tions,

m a n y o f w h ic h w e r e d o n e t o r e d u c e c o m p l ic a t io n s a n d i m p r o v e

th e fu n c t io n a l o u t c o m e o f c h i l d re n (1 -3 ) . O n e o f t h e m a jo r

m o d i f i c a t i o n s fo l l o w e d th e p io n e e r in g w o rk o f d e Le v a l e t a l .

(4) , who demonst ra ted tha t pu lsa t i le va lve less cavi t ies l ike the

r ig h t a t r i u m a n d v e n o u s c o n n e c t io n s a t sh a rp a n g l e s c o n t r i b -

u t e d t o e n e rg y l osses . Co n c o m i t a n t ly t h e y d e v e lo p e d th e t o t a l

c a v o p u lm o n a ry c o n n e c t io n w i th a n a s to m o s i s o f t h e i n fe r io r

a n d su p e r io r c a v a d i r e c t l y o p p o s i t e e a c h o th e r o n t h e r i g h t

p u lm o n a ry a r t e ry ( i . e . , w i th z e ro o f f se t o f c a v a e f ro m e a c h

o th e r ) . A su b se q u e n t s t u d y (5 ) c o m p a r in g t h e t r a d i t i o n a l

Fo n ta n a t r i o p u lm o n a ry c o n n e c t io n w i th t h e t o t a l c a v o p u lm o -

n a ry c o n n e c t io n d e m o n s t r a t e d l o w e r sy s t em ic v e n o u s p re s -

From the Chi ldren 's Hear t Cente r , Emory Univer s i ty School of Medic ine ;

*Cardiovascula r F lu id Mechanics Labora tory, Geo rgia Ins t itute of Technology,

School of Chemica l Engineer ing; and tEgles ton Chi ldren 's Hospi ta l a t Emory

University, Atlanta, Georgia. Sean Goudy was supported by a National Science

Founda t ion Fe l lowship, Washington, D.C.

Manuscr ipt r ece ived Jun e 22, 1995; revised manuscr ipt r ece ived N ovember

10, 1995, accepted No vem ber 22, 1995.

Address for cor respondence : Dr . Shiva Sharma, The Chi ldren 's Hear t

Cente r , 204 0 Ridgewood Dr ive NE, At lanta , Georgia 30322.

su re s a n d a l o w e r i n c id e n c e o f a t r i a l a r rh y th m ia i n t h e l a t t e r

g ro u p o f p a t i e n t s. Th e t o t a l c a v o p u lm o n a ry c o n n e c t io n c o n -

c e p t w a s e x t e n d e d fu r th e r b y La k s e t a l. (6 ) b y d e v e lo p m e n t o f

th e u n id i r e c t i o n a l c a v o p u lm o n a ry c o n n e c t io n i n w h ic h t h e

su p e r io r v e n a c a v a a n d i n fe r io r v e n a c a v a w e re c o n n e c t e d

exc lusive ly to the le f t and r igh t pu lmonary a r te r ies , respec-

t ive ly , wi th c rea t ion of a fenest ra t ion in the infe r ior channe l .

Th e t h e o re t i c a d v a n ta g e s o f th i s m o d i f i c a t i o n w e re t h a t i t

p ro v id e d e v e n l o w e r i n fe r io r v e n a c a v a l p re ssu re s a n d o b l ig a -

to ry su p e r io r v e n a c a va l f lo w to t h e l e f t l u ng . I t a l so m a tc h e d

the re la t ive ly h igher in fe r ior vena cava l f low to the la rger

volume of the r igh t lung .

D e s p i t e t h e s e i m p r o v e m e n t s , c o n c e r n s r e m a i n a b o u t b o t h

these designs. In th e ze ro-offse t design , d iss ipat ive energ y

losses a re be l ieved to b e h igh a t th e s i te of co l li s ion of the cava l

f lo w s . In t h e u n id i r e c ti o n a l c o n n e c t io n , h e p a t i c v e n o u s b lo o d i s

comple te ly exc luded f rom the le f t lung by design . Sr ivastava e t

a l. (7) r e p o r t e d t h e d e v e lo p m e n t o f p u lm o n a ry a r t e r i o v e n o u s

m a l fo rm a t io n i n t h e l u n g se q u e s t e re d f ro m h e p a t i c v e n o u s

b lo o d in t h e i r p a t i e n t s w i th c a v o p u lm o n a ry c o n n e c t io n s , u n -

d e r sc o r in g t h e n e e d fo r h e p a t i c v e n o u s p e r fu s io n t o b o th l u n g s .

Fu r th e rm o re , t h e u n id i r e c ti o n a l d e s ig n d o e s n o t a l l o w fo r

v a r i a t i o n s i n p u lm o n a ry r e s i s t a n c e t o a d ju s t p u lm o n a ry b lo o d

©1996 by the Am er ican Col lege of Cardiology 0735-1097/96/ 15.00

Published by Elsevier Science Inc. SSD I 0735-1097(95)00598-6

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J A C C V o l. 2 7, N o . 5 S H A R M A E T A L . 265

A p r il 1 9 9 6 :1 2 64 -9 E X P E R I M E N T S F O R F O N T A N O P E R A T I O N O P T I M I Z A T I O N

1 3 . 5 m m

- ml.-Im -

v c

mm TI RP ~ ~ LP mrn

~ I V C

1 3 . 5 m m

Figure 1. Schematicof 1.0-diameter offset model showing dimensions

used. IVC = inferior vena cava; LPA = left pulmo nary artery; RPA =

right pulmon ary artery; SVC = superior ven a cava.

f low between the two lungs. T here fore , whi le a l lowing for

ci rculatory mixing of sys temic venou s re turn, w e s tudied the

effects of varying caval offsets at various right and left pulmo-

nary ar tery f low rat ios (varying pulmonary res is tance) to

de te rmine the op t ima l combina t ion for min imiz ing ene rgy

losses.

e t h o d s

Dete rmin at ion of glass m odel s izes. To obtain real is t ic

s izes of the inferior and su perior vena cavae and r igh t and lef t

pu lmon ary a r t er i e s, an 8-yea r o ld boy wi th a Fontan ope ra t ion

underwent magne t i c re sonance imaging MRI)with a Philips

Medical Sys tems ACS 1.5-tes la scanner. The magnet ic reso-

nance images were then t ra nsferre d to an ISG al legro graphics

works ta t ion for image s egmenta t ion and th ree -d imens iona l

recons t ruc tion . F rom the com pute r recons t ruc t ion , t he s izes o f

in fe r io r and supe r ior vena cavae and r igh t and l e f t pu lmon ary

arter ies were measured.

Exper imen ta l sys tem and condi t ions . F igure 1 represen t s

the configurat ion and dimensions of the 19-ram (1.0-diameter

offset ) mo del th at was ma de of cus tom -crafted Pyrex glass. A11

in le t and ou t l e t duc ts had an inne r d i amete r o f 13 .5 mm and

were -15 cm long. Five models were cons tructed with offsets

of 0.0 mm (0.0-diameter offset ) , 8 mm (0.5-diameter offset ) ,

19 mm (1.0-diameter offset ), 25 m m (1.5-diameter offset ) and

30 m m (2.0-diameter offset ) . f f s e t was defined as the horizo n-

ta l dis tance between the caval midpoints (Fig. 1) . A 2-ram

diame te r ho le was dr il l ed in to each in l e t and ou t l e t condu i t t o

measure the di fferent ia l s ta t ic pressure decrease within the

mode l s . The ho les were used to inse r t f l a t - t i pped me ta l

ca the te rs tha t were connec ted to a p res sure t ransduce r . The

flow rat ios for the superior and inferior cavae were f ixed a t

40:60, respectively, which was used to reflect the higher

superior vena caval f low seen in infants and young chi ldren

(8,9) . The f low rat ios to the r ight and lef t pulmonary ar ter ies

we re var ied as follows: 30:70 , 40:60, 50:50, 60:40 and 70:30.

Pressure measurements were carr ied out a t 2, 4, and 6 l i ters /

min. An aqueo us solut ion of glycerin wi th a me an (+_SD)

kinematic viscosity of 3.5 _+ 0.1 centistokes was used to

repr odu ce the kinem at ic viscosi ty of bloo d. T he viscosi ty was

measured a t a l l s tages of data col lect ion to ensure that i t

r ema ined cons tan t.

By maintaining a cons tant head different ia l between the

supply and dump tanks , s teady f low was produced. We used

three ro t am ete rs to measure the f low: one m easured the to t a l

f low; anothe r mea sured in ferior caval f low; the las t meas ured

the h ighe r f low of e i the r the r igh t o r l e f t pu lmonary a r t ery . A

mul t ip le - range DP 15TL Va l idyne pres sure t ransduce r w i th a

no . 24 d iaphragm was used to m easure the pres sure dec rease

across each mod el , using the inferior vena caval inle t as the

re fe rence po in t fo r each measurem ent . We co l l ec ted da ta for

10 s and averag ed these data to ge t a s ingle mean value for the

s ta t ic pressure decrease .

Flow visualization. To visualize flow through the glass

mod els , neutra l ly buo yant spherical 100-p,m Am berl i te part i -

c les wer e adde d to th e water/glycerin solut ion and i l lum inated

with whi te l ight . The experimental f low condi t ions were the

same as those desc r ibed for p res sure measurement s . The

mot ion of the pa r t i c l e s a s they t rave led th rough the mode l s was

recorded wi th a v ideo camera . F low pa th l ines were ob ta ined

by black-and-white pho tograp hy of the mod els using a 35-mm

cam era with 400-ASA speed f i lm with a shu t ter speed o f 1/15

and 1/30 s .

Data analys is . Afte r col lect ing s ta t ic pressure (Pi,s) a t each

of the condui t measurem ent por t s and the a s soc ia t ed vo lumet -

r ic flow (Qi) , the d ata we re analyzed to calculate the veloci ty

(u) through each of the condui ts and the power losses associ-

a t ed w i th each to t a l cavopulmonary connec t ion conf igura t ion .

Using the veloci ty data and de ns i ty data (p) , the dyna mic

pres sure (Pi,ke) was ca lculate d as follows:

P i , k e =

1/2pu2.

Next , us ing the Bernoui l l i equat ion, both the ra te of kinet ic

energy losses (Eke,loss) and the ra te of p otent ia l energy losses

(Es,loss) w ere calculated:

Es,lo~.,= (Qiv~ P¢c~+Q~c Psvc.s)-(Q,v. P~pa,s+Qlm Plp~.s),

E k e ,, o s s = ( Q i v c . P i v c , k e + Q s v c . P s v c , k e ) - ( Q r p a . P r p a , k e + Q l p a . P t p a , k e ) .

Final ly, summing the separate contr ibut ions of the power

losses (rate of en ergy losses), th e tot al po we r losses (EtotaUoss)

were calculated as fol lows:

Eto ta l , los s = Eke , los s + Es , loss .

A fte r calculating the to tal pow er losses for all cases studied, we

ident i f ied the na dir of the po wer losses a t 2 l i ters /min and used

that q uant i ty as the refere nce value. Th e refere nce value (Xref)

was then u sed to calculate the re la t ive percen t change of a l l the

cases studied:

Change = ( X i - X r e f ) / X r e f X 1 0 0 ° ~ .

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1 2 6 6 SHA RM A T AL. JACC Vol. 27, No. 5

EXPERIMENTS FOR FONTAN OPERATIONOPTIMIZATION April 1996:1264-9

o

o~

( 3 .

2 . 5

2

1.5

1

0 . 5

0

-0 . 5

--.~ 0.0 Diam eter Of fset KE) I

X 0.0 Diame ter Of fset PE)

.0 D iame ter Of fset PE)

1.0 D iame ter Of fset KE)

I ~ 0 .0 D iame ter Of fset Tota l)

[ • 1.0 Diam eter Offset Total )

, , ; , I , , i i I i i , , [ , , , ¢ I , , , , I , , , , I

7 0 / 3 0 6 0 / 4 0 5 0 / 5 0 4 0 / 6 0 3 0 / 7 0

Flow Split RPNLPA)

Figure

2. Graph of poten tial (PE) and kine tic (KE) energy osses for

the 0.0- and 1.0-diameteroffsetat total flow ate o f 2 liters/min. Other

abbreviations as in Figu re 1.

R e s u l t s

Flow energet ics Com parison o f potent ial an d k inetic energy

changes .

Figure 2 shows representative curves of changes in

the kinetic, po tentia l and tota l energy for the 0.0- and 1.0-

diameter offset models at 2 liters/min. The net rate of kinetic

energy changed only with flow ratio, which affected flow

velocity and reached maximal losses at 50:50 right/left pulmo-

nary ar tery f low ratio. In con trast , the po tentia l energy losses of

each of the models var ied w ith offset, f low ratio and f low rate .

Com parison of kinetic and poten tia l energy changes, d epicted

in Figure 2, revealed that the p otentia l energy changes were

more than tenfold greater than the kinetic energy changes

calculated.

C om par i son o f t o t a l pow er l os se s w i t h changes i n o f f se t f l ow

rat io and total f low.

Tota l power losses a re summar ized in

Figure 3, which gives a composite of the tota l power losses

versus offset and f low ratio a t 6 l i ters/min. Figure 3 shows

tha t a s the of f se t was inc reased f rom 0 .0 to 0 .5 supe r ior vena

Figure

3. Surfaceplot o f po wer losses versus offsetand flowsplit at 6

liters/rain. Abbreviations as in Figu re 1.

E

30.0

20.0

10.

0

s v c

ffset

i t ( R P A )

caval diameters, the power losses decreased signif icantly.

Wh en the of f se t was inc reased fur the r f rom 0 .5 to 1 .0

super ior vena cava l d iamete r s , the re was an addi t iona l

dec rease in the pow er losses bu t le ss marked than the in i t ia l

dec rease . Therea f te r , fur the r inc reases in of f set r e su l ted in

no sign if icant change in powe r losses, and the losses for 1.0-,

1.5- and 2.0-diameter offsets did not appear to be signif i-

can t ly d i ffe ren t f rom o ne anothe r .

The power losses var ied with varying pulm onary f low ratios

(Fig. 3 and 4). The power losses were least at the 50:50 flow

split, mo dera te at th e 40:60 and 60:40 flow splits and highes t at

the 30:70 r ight/ left pulmonary ar tery f low spli t and the la t ter

chang e was more obvious at th e 0.5-diameter offset.

Figure 4 demonstra tes that the power losses were greatly

magnif ied a t increased tota l f low rates. There w as a 2,000

increase in power loss in the 1.5-diameter offset from the

lowest flow of 2 liters/min to the h ighest at 6 liters/rain, and for

the zero offset there was 4,200 increase fo r a similar increase

in total flow.

F low visua l iza t ion . F igure 5 demonst ra te s the e f fec t o f

offset a t a co nstan t f low spli t for the 60:40 r ight/ lef t pulmo -

nary ar tery case . The ze ro-d iam eter offset case (Fig. 5, top)

dem onst ra te s tha t the re la tive ly pa ra l le l pa th l ines of flow in

the two cavae turned in to a d isorganized pa t te rn of pa th

lines a t the si te of coll ision of f low. The 0.5-diameter offset

case (Fig. 5, middle) demonstra tes a vigorous vortex a t the

of f se t s i te of the cavae . The vor tex appea rs to cushion the

caval flows so that there is a ben d in sup erior vena caval f low

toward the le f t pu lmonary a r te ry and a s l igh t bend in

infe r ior vena cava l flow toward the r igh t pu lm onary a r te ry .

The h ighe r of f se ts a lso dem onst ra ted a vor tex , bu t i t was le ss

we l l de f ined and le ss v igorous than the 0 .5-d iamete r of f se t

(1.0-diameter offset [Fig. 5, bottom]) . Other than the differ-

ence in the vor tex , the f low pa th l ines f rom the 0 .5- to

2 .0-d iamete r of f se ts appea red s imi la r . Downst ream pa th-

l ines in bo th pu lmon ary a r te r ie s ha d he l ica l secondary flow

patterns for all offsets.

Figure 6 demonstra tes the effects of f low spli ts a t a

cons tan t 1 .5-d iamete r of fse t. The 70:30 r igh t / le f t pu lmonary

a r te ry case (Fig. 6 , top) dem onst ra te s tha t the pa ra l le l pa th

l ines of f low in the supe r ior vena cava co l l ide wi th the

condui t wa l l and sp l i t toward the le f t and r igh t pu lmonary

a r te rie s , and the pa th l ines of the infe r ior vena cava appea r

to be d i rec ted toward the r igh t pu lmo nary a r tery . The 30:70

case (F ig . 6 , middle ) demonst ra te s tha t the infe r ior vena

cava l f low sp l i t s toward le f t and r igh t pu lmonary a r te r ie s ,

whereas the supe r ior vena cava l f low appea rs to b end toward

the lef t pulm on ary ar tery only. In the 50:50 flow split (Fig. 6,

bo t tom) , the supe r ior vena cava l pa th l ines appea r to bend

toward the le f t pu lmona ry a r tery , and th e infe r ior vena cava l

pa th l ines co l lide wi th the c ondui t wa l l and sp li t, w i th the

la rge r component go ing toward the r igh t pu lmonary a r te ry

a n d t h e sma l l e r c o mp o n e n t t o w a r d t h e l e f t p u lmo n a r y

a r te ry . The f low pa th l ines for the 40:60 r igh t / le f t pu lmon ary

artery f low spli t were similar to thos e for t he 50:50 f low split .

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J A C C V o l . 2 7 N o . 5 S H A R M A E T A L . 267

A p r il 1 9 9 6 :1 2 6 4 -9 E X P E R I M E N T S F O R F O N T A N O P E R A T I O N O P T I M I Z A T I O N

_=

E

o

@

Z

o

a r

3

_=

2 0 0

1 0 0

7 0 8 0 5 0 4 0 3 0

o f T o t a l

Flow to FIPA

0 o o l z

=

Z~~0 4 ]

3 0 0 0

t

2

,=

f_,

1 0 0 0

7JO 6 5 0 4 0 3 0

o f T o t a l F l o w t o R P

Figu re 4. Percent difference in energy loss at 2 top) and 6 liters/min

bottom) relative to the nadir at 2 liters/min. Circles = 0.0-diameter

offset; s o l id t r ian g les = 0.5-diameter offset; solid squares = 1.0-

diameter o ffset;op e n t r ian g les = ] .5-diameter offset; o p e n s q u a r e s =

2.0-diameter offset.

i s c u s s i o n

W h e n t h e i m p o r t a n c e o f c o n s e r v i n g e n e r g y i n a s i n g l e -

v e n t r i c le s u p p o r t e d c i r c u l at i o n w a s r e a l i ze d , r e c e n t m o d i f i c a -

Figure 5. Still photographs o f representative m odels at 60:40 r ight/lef t

pulm onary ar tery ratio for 0.0- top) , 0.5- middle) and 1.0-diameter

offset bottom).

t i o n s o f t h e F o n t a n o p e r a t i o n f o c u s e d o n s t r e a m l i n i n g f l o w

t h r o u g h t h e c o n n e c t i o n s . I n v i t r o e x p e r i m e n t a l w o r k b y d e

Le v a l e t a l. 4 ) h a s c o n t r ib u te d s ig n i f i c a n t ly to th e d e v i s in g o f

t h e s e m o d i f i ca t i o n s . O u r p r e v i o u s in v i t r o w o r k 1 0 ) p o i n t e d

o u t t h e a r e a s o f e n e r g y lo s s i n a t r i o p u l m o n a r y c o n n e c t i o n s . I n

t h e p r e s e n t r e p o r t w e d e s c r i b e o u r e x p e r i m e n t a l w o r k i n

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1 2 6 8 S H A R M A E T A L . J A C C V o l . 2 7 N o . 5

E X P E R I M E N T S F O R F O N T A N O P E R A T I O N O P T I M I Z A T I O N A p r il 1 9 9 6: 1 26 4 -9

Figure 6. Still photographs of representative right/left pulmon ary

artery flow sp lits at fixed 1.5-diameter offset: 70:30 flow split (top),

30:70 flow split (m iddle) and 50:50 flow split (bottom).

determining the optimal geometry of tota l cavopulmonary

connection that would keep en ergy losses to a m inimum. The

study utilized patient-de rived sizes of glass mo dels an d realistic

f low rates found in children. T he quanti ta t ive portion of ou r

wo rk was sup ported by extensive flow visualization studies.

Relat ion between f low energetics and f low vi sual izat ion

E f f e c t o f o f f s e t

The present s tudy demonst ra ted tha t the

introduction of caval offsets significantly reduced energy con-

sumption within the connections. At the 0.0-diameter offset,

f low visualization demonstra ted that the high energy losses

meas ured were du e to intensely disorganized f low patterns and

secon dary flows. A t th e 0.5-diameter offset, energy losses were

-4 0 lower tha n tha t at the 0.0-diameter offset at 6 liters/min.

This finding is confirmed by the flow visualization, which

revealed that the vortex at the site of the anastomosis at the

0.5-diameter offset effectively cushio ned th e collision o f the

converging caval flows and redu ced th eir interacti on and, thus,

power losses (Fig. 5, top and middle) . Further , a t the 1.0- and

1.5-diameter offset, the energ y losses were -5 0 lower tha n

that at the 0.0-offset at 6 liters/min (Fig. 3). We believe that

significantly lower ene rgy losses were m easu red in the 1.0- and

1.5-diameter offsets because o f furthe r reduc tion in caval flow

interaction. This interaction was stronger for th e 0.5-diameter

case a nd m anifested as a mo re vigorous centra l vortex than the

vortices a t the high er offsets. Fo r this reason, th e 0.5-diameter

offset was n ot as efficient in minimizing energy losses as the 1.0-

or 1.5-diameter offsets.

E f f e c t o f f l o w s p l i t

In addit ion to determining the effect of

offset on p ow er losses, the presen t stud y evalu ated the effect of

variable pulm ona ry flow ratio a nd its effects on pow er losses.

Our results show that the power losses associated with the

respective offsets were lowest when the pulmonary resistance

was equ ally distr ibuted ( i .e ., 50 :50 pulmonary f low ratio, as

explained in the Appendix). In addition, our results show that

at a pulm ona ry resistance equivalent to a 60 :40 and 40:60

right/ left pulmo nary ar tery f low ratio, power losses were com-

parably low for a given model and tota l f low rate a nd were a lso

nearly symmetric (Fig. 4). These experimental results are

consistent with theory (see Appendix).

Surgical applications.

O f f s e t

Although preliminary, our

study has potential surgical applications. The study separated

the caval offsets with th e least energ y losses (1 .0 and 1.5

diame ter) f rom those with re la tively low (0.5 and 2.0 diam eter)

and high losses (0.0 diam eter). These results imply that futu re

surgical designs should definitely have an offset and that the

1.0- or 1.5-diameter offset wou ld be m ore desirable. H owever,

our surgeons (V.T., K.K.) believe that anatomic space con-

straints in som e situations m ay allow a maximal offset of only

0.5 mm in diameter. Our results show that in these situations,

energ y losses would be also lower tha n a t the 0.0-offset case.

P u l m o n a r y f l o w r a t i o

The optimal offsets were found to

main ta in low losses through a rang e o f pulmo nary f low ratios,

with the n adir a t the 50:50 f low ratio. The impo rtance of this

f inding l ies in the fact that m any postoperative patients with a

tota l cavopulmonary connection develop a te lectasis , dia-

phragm paralysis or pleural effusions, which can lead to an

alteration in pulmonary resistance. Because of the bidirec-

t ional option of f low in our proposed design, pulmonary

redistribution can occur without significant energy losses.

T o t a l f lo w

The present experiments w ere don e a t varying

tota l f low rates to simulate the rest and activity cardiac o utpu t

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JACC Vol. 27, No. 5 SHARM A ET AL. 1269

April 1996:1264-9 EXPERIM ENTS FOR FONTA N OPERAT ION OPTIMIZATIO N

seen in children. Although the differences between the best

and w orst cases for en ergy loss were significant, they were still

relatively sm all at low flow rates of 2 liters/rain. W hen the flow

rate w as increased to 6 liters/rain, these differences increased

20-fold, underscoring the need for offset.

Mixing The experimental models, by vir tue of not being

unidirectional, enab led m ixing of caval flows. In the 30:70,

40:60 and 50:50 f ight/ lef t pulmonary ar tery f low splits , there

was clear visualization of inferior caval flow toward both the

r ight and lef t pulmonary ar ter ies. In the other models, the

central vortex app eared to facilitate mixing. The im portan ce of

mixing l ies in the provision o f hepatic venous blood to both

lungs. It was convincingly dem on strate d by Srivastava et al. 7)

that exclusion of hepatic venous blood from a lung can result

in the deve lopment of pu lmon ary a rte r iovenous ma lformat ion

in that lung. The factors in hepatic venous blood th at prevent

this complication have not been isola ted and therefore cann ot

be quantified. Nevertheless, future surgical designs should

allow at least some mixing to occur, and our experiments

suggest that this mixing can occur at most flow splits and

offsets.

Conclusions. Th e presen t study investigated the effect of

caval offset and varying pulmo nary vascular resistance and

cardiac output on the energy losses associa ted with the tota l

cavopulmo nary connection. These effects were then re la ted to

flow visualization. Fr om these investigations o ur results indi-

cate that an offset should be incorporated into future tota l

cavopulmonary c onn ection designs, and th e ideal offset shou ld

be 1.0 to 1.5 mm in diameter . These offsets consume the least

amount: of en ergy whe n vascular resistance is equally distrib-

uted between both lungs. Furthermore, increases in cardiac

outp ut are associated with increased energy consum ption. Our

future work will investigate the effect of both curvature and

pulsatility on the energy losses associated with the total

cavopulm onary connection.

We acknowledge he secretarial help of Ellen Troutman and Leigh Swisher, The

Children's Heart Center, Atlanta, Georgia.

ppendix

Theoret ical A nalys is

I t can be shown by the Po iseu i l le and Bernou i l l i equa t ions tha t ou r

exper imen ta l re su l t s a re cons is ten t wi th p rev ious ly accep ted theor ies .

The Po iseu i l le equa t ion re la tes the change in s ta t ic p ressu re to the

vo lumetr ic f low ra te :

Q =/3 • APs,

where ]3 = pd4/(128t, AL); APs = change in s ta t ic p ressu re ; d =

d iamete r ; /z = v iscos i ty ; and AL = change in leng th ' , Q = vo lumetr ic

flow rate'. .

F igure 2 o f ou r resu l t s shows the change in k ine t ic and po ten t ia l

energy losses ve rsus f low ra t io fo r severa l rep resen ta t ive cu rves .

M o r e o v e r , F i g u r e 2 s h o w s t h a t t h e m a g n i t u d e o f t h e k i n e t i c p o w e r

l o s s e s a r e m u c h s m a l l e r t h a n t h e m a g n i t u d e o f t h e p o t e n t i a l p o w e r

losses . The k ine t ic and po ten t ia l power losses a re the change in the

dynamic and s ta t ic p ressu res , re spec t ive ly , mul t ip l ied by the vo lum etr ic

f low ra te :

P s , l o s s =

Q x A P s ,

P k e , l o s s =

Q

× A P k e

I f we assum e tha t the dy namic p ressu re i s much sm al le r than th e s ta t ic

p ressu re te rms , we can make the assumpt ion tha t the change in to ta l

p ressu re i s approx imate ly equa l to the change in s ta t ic p ressu re .

AP = APk~ + AP ~,

A P t o t a I -~

AP~.

Fur the rmo re , i f the change in s ta t ic p ressu re i s approx imate ly equa l to

the to ta l p ressu re , we can subs t i tu te the s ta t ic p ressu re in to the

Bernou i l l i equa t ion fo r the change in to ta l p ressu re :

AE = Q

X A P t o t a l ,

AE ~ Q x AP~,

whe re E = to ta l power . F ina l ly , i f we so lve the Po iseu i l le equa t ion fo r

the change in s ta t ic p ressu re and subs t i tu te the resu l tan t equa t ion in to

the Bernou i l l i equa t ion fo r the change in s ta t ic p ressu re , the resu l tan t

equa t ion revea ls tha t the change in power losses a re p ropor t iona l to

t h e s q u a r e o f t h e v o l u m e t r i c f l ow r a t e :

aPs = (l/H) • Q, aXE

~ Q 2 / ~ .

In our sys tem we se t the inpu t energy by se t t ing the inpu t f low ra te fo r

a g iven to ta l f low ( i. e. , the super io r and in fe r io r vena cava l f low ra tes

a re se t a t 40 and 60 o f the to ta l f low, respec t ive ly ) . F ina l ly , u s ing

the p rev ious t runca ted equa t ion , when the energy losses assoc ia ted

wi th eac h o f the respec t ive o f fse ts a re ca lcu la ted , the 50 :50 f low ra t io

consumes le ss energy regard less o f the o f f se t o f the mode ls .

e f e r e n c e s

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