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0099-2399/85/1105-0203/ 02.00/0
JOURNAL OF ENDODONTICS
Copyright 9 1985 by The American Association of Endodontists
Printed in U ,S,A.
VOL. 11, NO. 5, MAY 1985
Th e Ba lanced Force Co nce pt for Inst rum entation o f
Curved Cana ls
E l Con cepto de Fue rza Ba lancead a para la
Instrumentacion de Conductos Curvos
J a m e s B . R o a n e , B S , D D S , M S , C l y d e L . S a b a l a , B S , D D S , a n d M a n v i l le G . D u n c a n s o n , J r . , D D S , P hD
C a n a l c u r v a t u r e h a s a lw a y s i n t ro d u c e d c o m p l e x i ty
i n to c a n a l p r ep a r a t io n . T h e b a l a n c e d f o r c e c o n -
c e p t , d e v e l o p e d b y t ri al a n d e r r o r e x p e r i m e n t a t io n
o v e r t h e p a s t 1 2 y r, i s p r o p o s e d a s a m e a n s o f
o v e r c o m i n g t h e c u r v a t u r e i n f lu e n c e . I ts c o n c e p t s
u s e f o r c e m a g n i t u d e s i n o r d e r t o c r e a t e c o n t ro l o v e r
u n d e s i r a b l e c u t t i n g a s s o c i a t e d w i t h c a n a l c u r v a t u r e .
R o t a t io n i s p r o m o t e d a s t h e m e a n s f o r m a i n t a i n in g
m a g n i t u d e a s a c o n t ro l a n d c o u n t e r c l o c k w i s e d i r e c -
t i o n o f r o t a t i o n p r o v i d e s f i n i t e o p e r a t o r c o n t r o l . D i a -
g r a m m a t i c e v a lu a t io n s , m a t h e m a t i c a l c a l c u la t io n s ,
b e n d i n g m o m e n t s , t e s t c a n a ls , s e c t i o n e d t e e th , a n d
c l in i c a l r a d i o g r a p h s a r e p r e s e n t e d t o d o c u m e n t
e a c h s t e p o f t h e c o n c e p t . T h e c o n c e p t c o m e s t o
f r u it io n w i t h t h e i n t r o d u c t i o n o f a n e w K - t y p e f il e
d e s i g n .
L a c u r v a t u r a d e l c o n d u c t o s i e m p r e r e p r e s e n t b u n a
c o m p l e j id a d e n l a p r e p a r a c i o n d e l m i s m o . E l c o n -
c e p t o d e f u e r z a b a l a n c e a d a d e s a r r o l la d o a t r a v e s
d e e x p e r i m e n t a c i b n p o t e n s a y o y e r r o r d u r a n t e l o s
u l ti m o s 1 2 a ~ o s , s e p r o p o n e c o m o u n m e d i o d e
s u p e r a r l a i n f lu e n c i a d e l a c u r v a t u r a . S u s c o n c e p t o s
u s a n m a g n i t u d e s d e f u e r z a a f in d e I o g r a r el co n t r o l
d e l c o r te i n d e s e a b l e a s o c i a d o c o n l a c u r v a t u r a d e l
c o n d u c t o . S e p r o m u e v e l a ro t ac ib n c o m o m e d i o d e
m a n t e n e r l a m a g n i t u d c o m o c o n t r o l , y la d ir e c c io n
d e r o t a c i 6 n e n s e n t i d o c o n t r a r i o a la s a g u j a s d e l
r e lo j p e r m i t e u n d e f i n i d o c o n t r o l a l o p e r a d o r . S e
p r e s e n t a n e v a l u a c i o n e s d i a g r a m & t i c a s , c a l c u l o s
m a t e m a t i c o s , m o m e n t o s d e t o r s i6 n , p r u e b a s d e
c o n d u c t o s , d i e n t e s s e c c i o n a d o s y r a d io g r a f i a s c l i n -
i c a s p a r a d o c u m e n t a r c a d a p a s o d e l c o n c e p t o , q u e
s e v e c o m p l e t a d o c o n l a i n t r o d u c c i 6 n d e u n n u e v o
d i s e ~ o d e l i m a s ti p o K .
R oo t c u r v a t u r e i s a fr eque n t oc c u r r enc e i n t he hum a n
den t i t i on and w hen a c u r v a t u r e i s p r es en t , endodon t i c
2 3
p r epa r a t i on o f t he as s oc i a t ed pu l p c ana l s y s t em be -
com es d if fi cu l t. In fac t , curva ture in t rod uce s such com -
p l ex i t y t ha t t o t a l i n s t r um en t i ng c onc ep t s hav e been
dev e l oped t o dea l w i t h t he c u r v ed c ana l ( 1 - 5 ) . Ev en
w i t h t hes e , i t i s c om m on p l ac e f o r a c ana l l o c a t ed w i t h in
a c u r v ed r oo t t o be en l a r ged t o a s m a l le r fi na l d i am e t e r
than i t wou ld be i f i t were loca ted w i th in a s t ra igh t roo t .
Jus t i f i ca t ion fo r such a l te ra t ion i s s imp ly the fac t tha t a
c u r v a t u r e i n t r oduc es f ac t o r s i n t o p r epa r a t i on w h i c h , i f
no t c on t r o l l ed du r i ng en l a r gem en t , w i l l c aus e t r ans po r -
t a t ion , l edge f o r m a t i on , an d ev en pe r f o r a ti on ( 1 - 4 , 6 ,
7 ) . The m o r e s e v e r e t he c u r v a t u r e o f t he r oo t , the m o r e
one t ends t o r educ e t he i n t ended p r epa r a t i on d i am e t e r
i n an e f f o r t t o p r ev en t i rr ev e r s ib l e dam age o f t he c ana l
w a l l. R ed uc i ng t he p r epa r a t i on s i z e unde r s uc h c i r c um -
s t anc es appea r s t o be l og i c a l f o r t w o r eas ons : ( a )
s m a l l e r d i am e t e r p r epa r a t i on m eans l es s c u t t i ng o f t he
cana l wa l l s and consequent l y a lesser l i ke l ihood fo r
ex p r es s i on o f undes i r ab l e c u t t ing e f f ec t s and ( b ) s m a l l
d iameter f i l es a re more f l ex ib le and there fo re less l i ke ly
t o c aus e t r ans po r t a t i on du r i ng en l a r gem en t .
The c u r v a t u r e p r ob l em ap pea r s t o be s o l v ed by s m a l l
p r epa r a t i on d i am e t e r s un t i l one ex am i nes w ha t t ha t
so lu t ion sacr i f i ces in cana l debr idement and re l i ab i l i t y
o f t he f ina l s ea l . Sm a l l e r p r epa r a t i on d i am e t e r s r educ e
t he am oun t o f m ec han i c a l and c hem i c a l c l eans i ng o f
t he c ana l s pac e . Se v e r a l s t ud i es appe a r t o i nd ic a t e l es s
c om p l e t e r em ov a l o f deb r i s w h en s m a l l non f la r ed p r ep -
a r a t i ons a r e us ed ( 8 - 10 ) w h i l e o t he r s r e l a t e t o t he
f lush ing e f fec t o f i r r i gan ts and ind ica te tha t i r r i gan ts a re
no t e f f ec t i v e i n w as h i ng deb r i s f r om a s m a l l d i am e t e r
cana l (11-13) . F ina l l y , A l l i son e t a l . (14) ind ica te tha t
p r epa r a t i on s i z e / des i gn has an i n fl uenc e up on t he f ina l
s ea l. They f ound t ha t t he bes t s ea l w a s ac h i ev ed w hen
a s t e p b a c k p r e p a r a t io n w a s u s e d .
T h e g o a l s o f a n e n d o d o n t i c t r e a tm e n t a r e to r e m o v e
t he c ana l s s o f t t i s s ue c on t en t s as c om p l e t e l y as pos -
s ib le , e l im ina te as comp le te ly as phys ica l l y poss ib le any
m i c r ob i a l e l em en t s , and c r ea t e a s i t ua t i on w i t h i n t he
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2 0 4 R o a n e e t a l
c a n a l t h a t c a n p r e v e n t m i c r o b e s o r t o x i c s u b s t a n c e s
f r o m p a s s i n g t h r o u g h t h e c a n a l s y s t e m t o t h e a p i c a l
s u p p o r t i v e s t ru c t u r e s . T o r o u t in e l y a n d d e p e n d a b l y a c -
c o m p l i s h t h e s e g o a l s e a c h t i m e a c a n a l i s p r e p a r e d , i t
s e e m s r e a s o n a b le to d e m a n d t h e s a m e c o m p l e t e n e s s
o f p r e p a r a t i o n f o r e a c h c a n a l r e g a r d l e s s o f w h e t h e r i t
i s s tr a i g h t o r c u r v e d . Va r i a t io n s i n th e s i z e o f p r e p a r a -
t i o n s s h o u l d o c c u r i n r e s p o n s e t o r o o t o r c a n a l s i z e
r a t h e r t h a n t h e d e g r e e o f r o o t c u r v a t u r e . I f s u c h w e r e
p o s s i b l e , s p e c i f i c a l l y d e f i n e d s t a n d a r d i z e d c a n a l p r e p -
a r a t i o n s b a s e d o n i n t r a c a n a l m o r p h o l o g i c a l n e e d s a n d
n o t r o o t c u r v a t u r e c o u l d b e u s e d . T h i s i s n o t p r e s e n t l y
t h e c a s e a n d t o b e c o m e c a p a b l e o f s u c h p r e p a r a t i o n
w i l l r e q u i r e a d v a n c e m e n t i n t h e e x i s t i n g p r e p a r a t i o n
t e c h n o l o g y . O u r g o a l o f p r e p a r a t i o n b a s e d u p o n r o o t
s i ze ra ther than curva ture was in i t i a l l y env is ioned by
R o a n e i n 1 9 7 0 a n d , a s a r e s u l t o f 1 2 y r o f tr ia l a n d e r r o r
e x p e r i m e n t a t i o n , a p r e p a r a t i o n t e c h n i q u e h a s b e e n d e -
v e l o p e d w h i c h a p p e a r s t o a c c o m p l i s h t h e s p e c i f i e d
g o a l s . T h i s a r t i c l e i s a n a t t e m p t t o d e s c r i b e t h a t t e c h -
n i q u e t e r m e d t h e b a l an c e d f o r c e c o n c e p t , t o s u p p o r t
i t s va l id i t y , and to make i t s concepts ava i lab le so tha t
o t h e r s m a y a l s o e x a m i n e a n d t e s t i ts v a li dit y.
R T I O N L E
T h e b a l a n c e d f o r c e c o n c e p t w a s d e r i v e d f r o m t h e
p h y s i c a l l a w w h i c h s t a t e s : f o r e v e r y a c t i o n t h e r e i s a n
e q u a l a n d o p p o s i t e r e a c t i o n . T o d e v e l o p t h e c o n c e p t ,
t h i s l a w w a s u s e d t o i d e n t i f y a n d d e f i n e a c t i o n s a n d
r e a c t i o n s t h a t o c c u r d u r i n g c a n a l p r e p a r a t i o n i n o r d e r
t o s t u d y t h e m a n d a t t e m p t t o d e f i n e a s e q u e n c e o f
e v e n t s a n d m o t i o n s t h a t c o u l d b e u s e d t o c o n t r o l
e n d o d o n t i c i n s t r u m e n t s d u r i n g p r e p a r a t i o n . Su c c e s s f u l
m o t i o n s w e r e r e t a i n e d a n d a p r e p a r a t i o n m e t h o d d e -
f i n e d w h i c h d i r e c t e d h i g h m a g n i t u d e f o r c e s a g a i n s t
s m a l l m a g n i t u d e f o r c e s t o d e v e l o p a b a l a n c e o f a c t i o n
t o r e a c t i o n , m a k i n g i t p o s s i b l e t o i g n o r e c u r v a t u r e d u r -
ing cana l p repara t ion .
T o u n d e r s t a n d t h e b a l a n c e d f o r c e c o n c e p t i t i s n e c -
e s s a r y t o s t u d y t h e d e s i g n o f p r e p a r a t i o n i n s t r u m e n t s ,
d e v e l o p a t h o r o u g h k n o w l e d g e o f t h e i r c h a r a c t e r i s t i c s ,
a n d l e a r n t o r e c o g n i z e t h e i r c o m p l e t e c a p a b i l i t i e s a s
w e l l a s t h e i r s p e c i f i c b e h a v i o r d u r i n g m o v e m e n t . W i t h
t h i s a c c o m p l i s h e d t h a t k n o w l e d g e m a y b e u s e d t o
s e l e c t a n i n s t r u m e n t w h i c h p r o v i d e s e n o u g h v a r i a t i o n
i n c a p a b i l i t i e s t o a l l o w t h e u s e r a m e a n s o f i n s t r u m e n t
c o n t r o l w h e n c a n a l c u r v a t u r e i s e n c o u n t e r e d .
C l i n i c a l u s a g e a n d s u b s e q u e n t p h y s i c a l a n a l y s i s i n -
d i c a t e t h a t i t i s b e s t t o s e l e c t a t ri a n g u l a r c r o s s - s e c t i o n
K - t y p e f i l e . T h i s t y p e o f p r e p a r a t i o n i n s t r u m e n t o f f e r s
s e v e r a l a d v a n t a g e s o v e r o t h e r c r o s s - s e c t i o n a l d e s i g n s
a n d i n s t r u m e n t t y p e s , w h e n a b a l a n c e o f f o r c e s i s b e in g
s o u g h t . M o s t i m p o r t a n tl y , t h e K - t y p e d e s i g n p r o v id e s
c u t t i n g e d g e s w i t h i d e n t i c a l r a k e a n d c l e a r a n c e a n g l e s
( 1 5 ) r e g ~ d l e s s o f t h e d i r e c ti o n o f m o v e m e n t . S i n c e
t h e s e a n g l e s r e m a i n u n c h a n g e d b y d i r e c t i o n o f a p -
J ou r na l o f
E n d o d o n t i c s
p r o a c h w i t h t h e c u t t i n g s u r f a c e , t h e K - t y p e i n s t r u m e n t
m a y b e u s e d a s a b i d i r e c t i o n a l c u t t i n g t o o l w i t h o u t a
loss o f e f f i c iency (16) (F ig . 1 ) . B id i rec t iona l cu t t i ng
m e a n s t h a t t h e o p e r a t o r h a s t w o m o r e c u t t i n g d i r e c -
t io n s a v a ila b le w i t h a K - t y p e i n s t r u m e n t t h a n w o u l d b e
a v a i l a b l e i f a H e d s t r o m - t y p e i n s t r u m e n t w e r e u s e d .
Se c o n d , w h e n a t r ia n g u l a r c o n f i g u r a t i o n i s s e l e c t e d t h e
c r o s s - s e c t i o n a l m a s s o f e a c h f i l e i s r e d u c e d , t h e f l u t e
d e p t h i s i n c r e a s e d , a n d t h e m a g n i t u d e o f t h e b e n d i n g
m o m e n t o r r e s t o r i n g f o rc e , a s i t w i ll b e r e f e r re d t o
here , i s decreased.
A t r i a n g u l a r f i l e h a s a c r o s s - s e c t i o n a l a r e a o r m a s s
t h a t i s 3 7 . 5 % l e s s th a n t h a t o f a s q u a r e f il e o f t h e s a m e
standard ized s i ze . Th is po in t i s ver i f i ed by ca lcu la t ing
t h e a re a o f tw o # 4 0 file s , a s s u m i n g o n e t o b e m a n u -
f a c t u r e d w i t h a t r i a n g u l a r a n d t h e o t h e r w i t h a s q u a r e
c r o s s - s e c t i o n . T h e a r e a o f a t r i a n g u l a r c r o s s - s e c t i o n f il e
i s d e t e r m i n e d u s i n g t h e e q u a t i o n s b - - 3 R / 1 7 3 2 a n d
A = b / 4 x 1 . 7 3 2 . I n t h e s e e q u a t i o n s b r e p r e s e n t s t h e
length o f one s ide o f an equ i la te ra l t r i ang le , R the
c i rcumrad ius o r one-ha l f o f the cu t t i ng d iameter , i . e . 1 /2
o f 0 . 4 0 m m , a n d A t h e a r e a o f t h e t ri a n g le . Su b s t i tu t e
t h e k n o w n v a l u e s a n d f i n d b = 3 ( 0 . 2 ) / 1 . 7 3 2 - - 0 . 3 4 6
m m . W i t h t h e v a l u e t h u s o b t a i n e d f o r b , t h e s e c o n d
e q u a t i o n m a y b e s o l v e d f o r t h e c r o s s - s e c t i o n a r e a : A =
0 . 3 4 6 / 4 x 1 . 7 3 2 = 0 . 0 4 9 9 m m 2 . F o r a s q u a r e f ile , t h e
FiG 1. W is a l ine draw n tange nt to the c i rcumference of cut c at a
po in t o f contac t w i th one cut t ing e dge o f a t r i angu lar shaped K - type
instrument. W is us ed to descr ibe the c learanc e angles U and V into
the f l u te space assoc ia ted w i th that cu t t i ng edge. T hey are equa l and
are 60 de gree s by def ini tion. P is a tangen t l ine dra wn in a s imilar
fashion to intersect one edg e of a square K- type instrument. I t is
used to def ine the c l earance ang les Q and R whi ch are equa l and 45
degre es by definit ion. The s ides of the squa re and tr iangle are let tered
a and b, respectively , and the area s are sh ded for co mpa r ison. I t i s
easy to recognize that the square has a cross-sect ional area which
is much larger than tha t of the t riangle, i .e. 37.5 greater . The rake
angle for both the t r i ang le and squa re may be measured as the ang le
betw een the radial line d and the l ines b an d a, respect ively . B oth
shapes produce neg at i ve rake ang les ; how ever , the t r iang le en joys a
15-degree more favo rable angle. Nei ther the rake n or the c learance
angle is al tered for ei ther by the di rect ion of m ovem ent.
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Vol. 11 N o. 5 Ma y 1985
e q u a t i o n s a = d/1 414 and A - - a 2 a r e r equ i r ed . I n t hes e
a r ep r es e n t s t he l eng th o f one s i de o f t he s qua r e , d t he
c u t t i ng d i am e t e r o f t he fil e o r 0 . 40 r am , and A t he a r ea
o f t he s qua r e . Subs t i t u t e t he k now n v a l ues and f i nd : a
= 0 . 4 / 1 . 41 4 = 0 . 282 m m . By us i ng t ha t f o r a , t he a r ea
equa t i on i s s o l v ed t hus l y : A = ( 0 . 282 )2 - - 0 . 07 95 m m 2 .
R es u l t s o f the p r ec ed i ng c a l c u l a t i ons r ounded t o t w o
s i gn i f i c an t num be r s i nd i c a t e t ha t w hen t he c u t t i ng r a -
d ius i s 0 .4 mm ( i .e . a 4 0 f il e ), a t r i ang le has a c ross -
s ec t i ona l a r ea o f 0 . 05 m m 2 w h i l e a s q ua r e h as an a r ea
o f 0 . 08 m m 2 . W i t h t he r ec ogn i t i on t ha t c u r v a t u r e c o u l d
b e c o n s i d e r e d a s a c o n s t a n t a c t i n g u p o n b o t h s h a p e s
and t ha t t he am oun t o f m e t a l , i . e . t he c r os s - s ec t i ona l
a r e a , va r ie s b e t w e e n t h e t w o s h a p e s , t h e n o n e s h a p e
m a y b e c o m p a r e d w i t h t h e o t h e r u s i n g a p e r c e n t a g e
r a t i o bas ed upon t he i r c r os s - s ec t i ona l a r eas . By us i ng
t h i s m e t hod , i t bec om es appa r en t t ha t a t r i angu l a r f i l e
h a s o n l y 6 2 . 5 % a s m u c h c r o s s - s e c t i o n a l a r e a a s a
s qua r e f i l e o f equa l c u t t i ng r ad i us and i f geom e t r y had
no a f f ec t upon bend i ng , t he t r i angu l a r f i l e w ou l d be
ex pec t ed t o dev e l op on l y 62 . 5% as l a r ge a r es i s t i ng
l oad ( r es to r i ng f o r c e ) aga i ns t t he c ana l w a l l a s a s qua r e
f i l e as s um i ng bo t h w e r e p l ac ed t h r ough t he s am e c u r -
va ture . C l in i ca l ly spe ak ing , a t r i angu la r f il e i s p red ic ted
to be m ore f lex ib le and to ap p ly a li gh te r res to r ing fo rc e
aga i ns t t he w a l l o f a c u r v ed c ana l du r i ng p r epa r a t i on .
Th i s m eans , t ha t t he t r i angu l a r g r ound i ns t r um en t w i l l
be l es s l ik e ly t o t r ans p o r t a c ana l w a l l du r i ng p r epa r a -
t ion . I ts K - t y pe b i d ir ec t iona l de s i gn a l l ow s t he o pe r a t o r
t o s e l ec t any o f f ou r po t en t i a l c u t t i ng app r oac hes , i . e .
i n s e r ti on , w i thd r aw a l , c l oc k w i s e , o r c oun t e r c l oc k w i s e
r o t a t ion . F i gu r e 1 p r ov i des a g r aph i c c om pa r i s on be -
t w een t he t r i angu l a r and s qua r e , i . e . c u t t i ng edge c on -
f igura t ion , rake , and c learance ang les .
By r ec ogn i z i ng t ha t geom e t r y has an i n f l uenc e upon
s t ruc tu ra l p roper t ies o f mater ia l s , i t i s des i rab le to es -
t ab l i s h a r e l a t i ons h i p be t w een t he r es t o r i ng f o r c e and
t he c r os s - s ec t i ona l geom e t r y r a t he r t han on l y t he a r ea
as j us t p r ev i ous ly c o ns i de r ed . To do t h i s it m us t be
r ec ogn i z ed t ha t t he r es t o r i ng f o r c e m ay be m eas u r ed
t h r ough i ts oppos i ng f o r ce , t he angu l a r de f l ec ti on be nd -
i ng m om en t . Va l ues hav e been ex pe r i m en t a l l y de t e r -
I m i n e d fo r b e n d i n g m o m e n t s b e t w e e n v a r io u s g e o m e t r ic
s hap es and w e r e r ec en t l y r epo r t ed by K r upp e t a l. (17 ).
I n t he i r s t udy , t he am oun t o f f o r c e r equ i r ed t o p r oduc e
a 60 - deg r ee angu l a r de f l ec t i on o f a t r i angu l a r s i z e 30
U n i t ek f i l e w as one - t h i r d l e s s t han t ha t r equ i r ed t o
p r oduc e an equa l de f l ec ti on o f a s q ua r e s i z e 25 U n i t ek
f i l e . The i r g r aphs i nd i c a t ed t ha t a bend i ng m om er ) t
s l i gh t l y g r ea t e r t han 40 g - c m de f l ec t ed t he s i z e 30
t r i angu l a r f i l e 60 deg r ees w h i l e a bend i ng m om en t
s l i gh t l y g r ea t e r t han 60 g - c m w as r equ i r ed t o de f l ec t
t he s i z e 25 s qua r e f i l e equa l l y . A dec r eas e i n t he
r es t o r i ng f o r c e r epo r t ed as bend i ng m om en t oc c u r r ed
in sp i te o f a g rea ter cu t t i ng rad ius , i .e . la rger ins t rum ent
s ize o f the t r i angu la r f i l e . The square f i l e i n th i s case
Balanced Force Concept 205
has 83% as l a r ge a c r os s - s ec t i ona l a r ea as t ha t o f t he
c om pa r ab l e t r i angu l a r f i l e y e t i t gene r a t es abou t one
and one-ha l f t imes as la rge o f a res to r ing fo rce , i .e .
b e n d i n g m o m e n t o f 6 0 v e r s u s 4 0 g - c m . B y r e c o g n i zi n g
t ha t t he r es t o r i ng f o r c e i s a s t a t ic a l ly ap p l ied l oad w h i c h
ho l ds t he f il e s c u t t ing s u r f ac es a ga i ns t t he c u r v a t u r e i n
a s ing le d i rec t ion and tha t i t i s the load wh ich i s re -
s pons i b l e f o r a s t r a i gh t en i ng o f t he c u r v e du r i ng
p r epa r a t i on , one c an p r ed i c t t ha t a s qua r e f i l e i s m o r e
l i ke ly to uncont ro l l ab ly s t ra igh ten the cana l , to cu t ex -
cess ive ly a t i t s t i p , and there fo re i s more l i ke ly to ledge
a p r epa r a t ion . The d i f fe r enc e in r es t o r i ng f o r c e m agn i -
t ude c oup l ed w i t h ou r un r epo r t ed c l i n i c a l and ex pe r i -
m en t a l obs e r v a t i ons l ead us t o c onc l ude t ha t a s qua r e
s h a p e s h o u l d b e a v o i d e d w h e n e v e r p o s s i b l e , b u t e s -
pec ia ll y w hen us i ng l a r ge i ns t r um en t s i z es .
The nex t s t ep i n unde r s t and i ng how t o m a i n t a i n
p r epa r a t i on s i z e p as t a c u r v e i s l ea r n ing t o i den t if y t he
d i r ec t i on and l oc a t i on f o r ex p r es s i on o f t he r es t o r i ng
f o r c e w h i c h i s gene r a t ed b y e l as ti c d i s to r t i on w i t h i n an
i ns t r um en t w h en i t i s pas s ed t h r ough a c ana l c u r v a t u r e .
I den t i f i c a t i on a l l ow s r ec ogn i t i on o f w he r e t he l oads
c onc e n t r a t e and p r ov i des i n f o r m a t i on us e f u l in l ea rn i ng
how t o p r ev en t e f f ec t i v e ex p r es s i on o f t hos e l oads i n
undes i r eab l e a r eas . I t i s i m po r t an t t o l ea r n t o c on t r o l
t hes e f o r c es in o r de r t o p r ev en t t hem f r om bec om i ng a
m a j o r i n f l uenc e du r i ng c ana l en l a r gem en t as t he i r
e x p r e s s io n c a n p r o d u c e d i s a s t ro u s r e s u lt s . T o a c c o m -
p li sh c on t r o l i t is nec es s a r y to c o m p a r e t he m ag n i t ude
o f l oads , app l y t he r u l e t ha t f o r ev e r y ac t i on t he r e i s an
equa l and op pos i t e r eac t i on , and f i na ll y i den t if y m o t i ons
w h i c h w i l l d i r ec t t he f o r c es app l i ed by t he ope r a t o r i n
s u c h a m a n n e r t h a t t h e y w i ll m a s k t h o s e g e n e r a t e d b y
c u r v a t u r e . W hen s uc h a ba l anc e i s es t ab l i s hed , t he
cana l may be en la rged th rough i t s o r ig ina l ax is , a t l eas t
in the ap ica l th i rd o f the cana l . In the process t ranspor -
ta t ion i s e l im ina ted o r a t l eas t d i sp laced coronaUy whe re
i t i s l e s s l i k e l y t o hav e s e r i ous c ons equenc es . The
des i r ed ba l anc e o f f o r c es c an be gene r a t ed s i m p l y by
r o t a t ing t he i ns t r um e n t s t o p r od uc e c ana l en l a r gem en t .
Th i s i s t r ue s i nc e r o t a t i on d i r ec t s den t i na l ha r dnes s
aga i ns t t he r es t o r i ng f o r c e o f t he c u r v ed i ns t r um en t
a n d s i m u l ta n e o u s l y u s e s t h a t h a r d n e s s t o c r e a t e t h e
c u t t ing l oads . R o t a t i on p r ev en t s ex p r es s i on o f t he c u r -
v a t u r e - gene r a t ed r es t o r i ng f o r c e v ia m a gn i t ude , a t l eas t
fo r a l im i ted range o f f i l e s i zes . F igure 2 i l l us t ra tes the
ba l anc e o f fo r c es gene r a t ed by r o t a t ion . T he r e la t iv e
m agn i tudes o f t he f o r c e gene r a t ed f r om den t i na l r es i s t-
anc e and t he r es t o r i ng f o r c e gene r a t ed i n t he i ns t r u -
m en t by a c u r v a t u r e a r e no t de fi ned ; how ev e r , pe r f o r m -
anc e t es t s dem ons t r a t e t he v a l i d i t y o f t he as s um p t i on
t ha t t he r es t o r i ng f o r c e i s o f l e s s m agn i t ude t han t he
forces c rea ted f rom dent ina l res is tance (F igs . 3 and 4) .
The m agn i t ude o f den t i na l r es i s t anc e i s a f unc t i on o f
den t i na l ha r dnes s and gene r a t es a f o r c e du r i ng p r epa -
ra t ion wh ich remains re la t i ve ly cons tan t fo r each cana l .
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2 0 6 R o a n e e t a l
FIG 2. T he e n l o s i n g i r l e representsdentinas i t contacts he cutt ing
edges of a f i le. R represents he internal force appl ied by den tinal
hardnessas i t is vectored oward the center of the instrument.S is a
restoring orce appl ied against he curva ture by the f i le attempting o
return to i ts original straight condi t ion. S remains stationary as the
instrument s rotated whi le R rotates wi th the blades. As long as R
remains greater than S, the instrumentwil l not tran spo rt the cana l;
however, should he f i le be pul ledout rather han rotated his formula
fai ls and S appl ies the primary cutting load . Transportation wi l l
frequently occur under such condi t ions.
T h e m a g n i t u d e o f t h e r e s t o r i n g f o r c e d e v e l o p e d
w i t h i n a f i le i s a fu n c t i o n o f t h e f i l e s m a s s , g e o m e t r y ,
a n d c o m p o s i t i o n a s w e l l a s t h e r a d i u s a n d a r c o f t h e
i n s t r u m e n t a t i o n c u r v e . I t s e x p r e s s i o n i s in v e r s e l y r e -
l a t e d t o t h e d i s t a n c e f r o m t h e c u r v e t o t h e i n s t r u m e n t
t ip . C o n s e q u e n t l y , t h e r e s t o r i n g f o r c e i s a v a r i a b le f o r c e
a n d i t w i l l in c r e a s e : ( a ) i f t h e m e t a l m a s s i n c r e a s e s ,
e i t h e r a s a r e s u l t o f s h a p e o r i n s t r u m e n t d i a m e t e r ; ( b )
i f t h e r a d i u s o f t h e c a n a l c u r v a t u r e i s d e c r e a s e d ; ( c ) i f
t h e a r c o f t h e c a n a l c u r v a t u r e i s in c r e a s e d ; o r ( d ) if t h e
d i s t a n c e f r o m t h e c u r v e t o t h e f il e t i p is d e c r e a s e d . B y
u s i n g t h e s e r e l a t io n s h i p s , o n e c a n i d e n t if y s p e c i f ic c a n a l
a l t e r a t io n s t h a t m u s t b e a c h i e v e d i n o r d e r t o a c c o m p l i s h
l a r g e p r e p a r a t i o n s i z e s a r o u n d c u r v a t u r e s w i t h o u t u n -
d e s i r e a b l e r e s u l t s , i . e . t r a n s p o r t a t i o n , l e d g e s , a n d p e r -
f o r a t i o n s . I n i ti a ll y , t h e r a d i u s o f t h e c u r v e s h o u l d b e
i n c r e a s e d b y c r e a t i n g a c a n a l a c c e s s ( 1 , 4 , 5 ) , i . e .
o p e n i n g t h e c o r o n a l e n d a n d s t r a ig h t e n i n g t h e c u r v a t u r e
( F i g . 5 ) . T h i s e f f e c t i v e l y i n c r e a s e s t h e r a d i u s a n d d e -
c r e a s e s t h e a r c o f t h e c a n a l c u r v a t u r e b y a l l o w i n g t h e
i n s t r u m e n t a s t r a i g h t e r p a t h t o t h e a p e x . T h e r e s u l t i n g
s t r a i g h t e r i n s t r u m e n t g e n e r a t e s a l e s s e r r e s t o r in g f o r c e
a l o n g i t s c u t t i n g e d g e s a n d t i p . T h e l i g h t e r l o a d s p r o -
d u c e l e s s d e n t in r e m o v a l a n d t h e c a n a l is e n la r g e d
u s i n g c u t t i n g p r e s s u r e s e q u a l t o t h a t o f s m a l l e r . in s t r u -
m e n t s . A s a c o n s e q u e n c e , l a r g e r d i a m e t e r i n s t r u m e n t s
m a y b e u s e d b e f o r e t r a n s p o r t a t i o n , l e d g i n g , o r p e r f o -
r a t i o n a r e l i k e l y . T o a v o i d a p i c a l e x p r e s s i o n , p r i m a r i l y
l e d g in g , t h e d i s t a n c e f ro m . t h e c u r v e t o t h e i n s t r u m e n t
t ip m a y b e i n c r e a s e d b y e x t e n d i n g t h e f il e t i p b e y o n d
t h e a p e x b e f o r e i n t r o d u c i n g t h e n e x t l a rg e r i n s t r u m e n t .
J o u r n a l o f E n d o d o n t i c s
O v e r e x t e n s i o n i s g e n e r a l l y c o n s i d e r e d t o b e u n d e s i r a -
b l e a n d t h e c o n s e q u e n c e s o f l e v e r a g e a r e b e s t m a n -
a g e d b y m o d i f ic a t i o n o f t h e i n s t r u m e n t t i p in o r d e r t o
g a i n b a l a n c e t h r o u g h t h e r e m o v a l o f th e t e r m i n a l c u t t i n g
p o i n t s .
M o d i f i c a t io n o f t h e i n s t r u m e n t s t i p i s a r e c e n t i n n o -
v a t io n a n d h a s p r o d u c e d p e r h a p s t h e m o s t d r a m a t i c
c h a n g e i n i n s t r u m e n t r e s p o n s e w i t h i n t h e c o n c e p t s o f
b a l a n c e d f o r c e s . I t e n t a i l s r e m o v a l o f t h e c u t t i n g s u r -
f a c e s t h a t p r i m a r i l y e x p r e s s t h e s t a t i c r e s t o r i n g f o r c e
a n d t h e r e f o r e t h e s u r f a c e s t h a t a r e p r i m a r i l y re s p o n s i b l e
f o r c a n a l t r a n s p o r t a t i o n . P r o p e r r e m o v a l o f t h e s e c u t -
t i n g p o i n t s p r o v i d e s b e t t e r i n s t r u m e n t c o n t r o l t h a n a n y
p r e v i o u s l y r e c o g n i z e d m e t h o d , i n c l u d i n g c a n a l a c c e s s
p r e p a r a t i o n ( F i g . 5 ) . T h e m o d i f i e d i n s t r u m e n t i s n o t
p r e s e n t l y a v a i la b l e o n a c o m m e r c i a l s c a le . A p h o t o -
g r a p h o f t h e m o d i f i c a t i o n i s p r e s e n t e d i n F i g . 6 a l o n g
s i d e t h a t o f a n o r m a l t i p t o e m p h a s i z e t h e t e r m i n a l
p o i n t s . T h e s e p o i n t s c u t i n r e s p o n s e t o a r e s t o r i n g
f o r c e p r o d u c e d w h e n t h e c u r v a t u r e d e f l e c t s t h e f i l e
FIG 3. Th is electron micrograph of a prepared canal n a mandibular
incisor reveals ingual movem ent of the preparation. The access n
this ooth appliedpressure o the f i le shaft which should havecaused
movem ent facial ly. The obse rvationof a tape red preparation o th e
l ingual supports the balance of force magn i tude concept. M issing
dentin o the l ingualunbalanceddentinal esistance o that side and
al lowed the f i le to be pus hed away from the F wal l m asking enti rely
th e expressionof any restoring o rce along he F wa l l.
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Vol. 11 No. 5 May 1985 Balanced Force Concept 207
FiG 4. P resented are four cases that were prepared us ing the ba lanced force concept . The m in imum ap i ca l p repara t i on d iameter was 0 .45 m m.
The secon d m olar in A w as com ple ted us ing s tandard fi les and t i p overex tens ion whereas the o ther th ree cases were com ple ted us ing m odi f ied
instruments.
6 4 TE $
L I D D EN
2 h N h L
4 CCE $ $
FtG 5. Th i s graph i c representa t ion A and ac tua l molar cana l access B i ll us t ra te how an a ccess preparat i on a l te rs the curvature s e f fec t upon
enlarging instruments. B an d C are the areas of dent in rem oval which a re responsible for ang ular change. The cha nge in instrum ent entry angle
before and a f ter canal access is i l lus trated as the angle a and repres ents a reduct ion in the arc of the canal s curvature. Spac e created by the
access a l l ows the canal curvature to be expresse d in the i ns t rument as though the rad ius o f the curve had been i nc reased. The curve becom es
more genera l i zed and d i s t r i bu tes throughout th e cana l l ength , thereby de c reas ing the curvature- re l a ted orces and the i r express ion.
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2 0 8 R o a n e e t a l
J o u r n a l o f E n d o d o n t i c s
i s ev ident t ha t use o f t he ba lanced fo rce concepts ,
especial ly with mod if ied instruments, ena bles one to
prepare a curved acry l ic cana l much la rger than c lass i-
ca l t echn iques , w i tho ut p roduc ing ap ica l t ranspo r ta t ion .
Fi le t ip modif icat ion and u se of the balanced force
F IG 6 . P r e s e n t e d a r e t w o t r ia n g u l a r K - t y p e f il e s . File A h a s a s t a n d a r d
t i p w i t h d is t i n c t p o i n t s c r e a t e d w h e n i t s c u t ti n g e d g e s a r e t e r m i n a t e d
w i t h a s t a n d a r d i z e d t i p .
File B
i s a p r o t o t y p e m o d i f ie d i n s t r u m e n t w i t h
a p a r a b o l i c ti p . T h i s c o n f i g u r a t i o n e l i m i n a t e s t h e t e r m i n a l p o i n t s a n d
p r o d u c e s s u p p o r t i n g t r ia n g u l a r p la n e s w h i c h d i s t r i b u t e lo a d s t o k e e p
t h e m b e l o w c u t t in g m a g n i t u d e . P e n e t r a t i n g c a p a c i t y i s m a i n t a i n e d a s
t h e f l u te d e p t h s a r e u n c h a n g e d a n d t h e t h r e e o r i g in a l c u t ti n g e d g e s
a r e r e p la c e d b y s i x n e w e d g e s .
f rom i t s pass ive o r zero fo rce s t ra igh t l ine pos i tion (F ig .
7) . The res tor ing fo rce when present is t ransmi t ted to
the f i le t ip through i ts metal shaf t which acts as a lever
arm.
A l te r ing the ins t rument t ip removes i t s capab i l i t y t o
respond to e las tic d is to r t ion in a concent ra ted area and
t he r eby m anda t es t he ex p r es s ion o f t hos e f o rc es ov e r
the length o f each cu t t ing edge ra ther than a t t he f i le
t ip. Th us, with the terminal poin ts removed, internal
d is to r t ions es tab l ished by the cana l curva ture gene ra te
a res tor ing fo rce wh ich is p ropo r t ioned over the cu t t ing
edges and .d ispersed enough to a l low the re la t ive ly
la rger ma gn i tude o f dent ina l hardne ss to de ny not icab le
express ion . Conse quent ly , t he f i le s s t ra igh t p ro fi le be-
comes unapparent in the comple ted prepara t ion . I n t ro -
duc t ion of t ip modif ication int rodu ces an abi li ty .to en-
la rge a curved can a l even a long i t s ins ide w a l l com-
p le te ly to the apex . Th is ab i li ty does not app ear to ex is t
w i th in the methods tes ted to da te us ing s tandard
ground K- type inst ruments. (Fig. 8) . I f the resul ts seen
in F ig . 8 are comp ared w i th tho se o f Weine e t a l . (2 ), i t
s, , A
I
Z
F IG 7 . T h is h y p o t h e t i c a l c a n a l c u r v a t u r e i s s e p a r a t e d i n t o i t s c o m p o -
n e n t p a r t s .
Point A
i s t h e a x i s o f t h e cu rve , r i s t h e ra d i u s , a n d a
d e f i n e s i t s a rc . W h e n a t h e o re t i ca l f i le i s p a ss e d a ro u n d t h i s cu rve , i t
d e v e l o p s i n t e r na l f o r c e s a s a r e s u l t o f m o l e c u l a r c o m p r e s s i o n a n d
e x p a n s i o n w i t h in i t s m a s s . T h o s e f o r c e s , i . e . r e s t o r in g f o r c e s , a r e
s u b s e q u e n tl y e x p r e s s e d a t t h e f il e ti p o v e r t h e / e v e r
FT
C h a n g i n g
t h e c u r v e b y a l t e ri n g it s a r c o r r a d i u s c a n a l t e r th e m a g n i t u d e o f t h e
r e s t o r i n g f o r c e , w h i l e c h a n g i n g t h e l e v e r le n g t h b y m o v i n g
t ip T
a w a y
f r o m t h e c u r v e h e l p s t o r e d u c e e x p r e s s i o n b y d e c r e a s i n g t h e l e v e r a g e
a d v a n t a g e f o r t h e r e s t o r i n g fo r c e . C a n a l a c c e s s m a y b e u s e d t o
c h a n g e t h e c u r v a t u r e w h i l e fi le o v e r e x t e n s i o n c a n b e u s e d t o i n c r e a s e
t h e l e ve r a rm . F i l e t i p m o d i f i ca t i o n d o e s n o t a f f e c t t h e l e ve r ; i t s i m p l y
p r e v e n t s e x p r e s s i o n o f t h e g e n e r a t e d f o r c e s . F Z i n d i c a t e s t h e f i le ' s
o r i g i n a l s t ra i g h t co n d i t i o n a n d d e t e rm i n e s t h e ze ro f o rc e l in e , i .e . n o
re s t o r i n g f o rce .
F IG 8 . P r e s e n t e d a r e t w o a c r y l ic c a n a l m o d e l s w h i c h h a v e b e e n
e n l a r g e d f r o m a n o r i g i n a l d i a m e t e r o f s i z e 2 0 t h r o u g h a f i le s i z e 5 5
u s i n g t h e b a l a n c e d f o r c e c o n c e p t . Sample A w a s p r e p a r e d w i t h
s t a n d a r d i n s t r u m e n t s u s i n g 0 . 5 - m m s t e p b a c k s e v e r y o t h e r f i l e s i z e .
I t w a s t h e b e s t o f a s e r i e s a n d s h o w s s l i g h t o u t w a r d t r a n s p o r t a t i o n
a p i ca l l y . Sample B w a s p r e p a r e d u s i n g m o d i f i e d f i le s a n d n o s t e p b a c k .
I t is t y p i c a l o f t h e s e r i e s a s n o a p i c a l t r a n s p o r t a t i o n w a s s e e n i n t h e
e n t i r e g r o u p . E n l a r g e m e n t a p p e a r s t o h a v e b e e n a c c o m p l i s h e d a lo n g
b o t h i t s i n n e r a n d o u t e r w a l l t o t h e f o r a m e n .
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Vol . 11 No. 5 May 1985
c onc ep t c an enab l e one t o eas i l y en l a r ge a c ana l f r om
a s i z e 20 t o a s i z e 55 f i l e w i t hou t r ec ogn i z ab l e t r ans -
po r t a t i on i n t he p r es enc e o f r a t he r s i gn i f i c an t c ana l
c u r v a t u r e .
T E C H N IQ U E C O N S I D E R T I O N S
To u t i l i z e t he ba l anc ed f o r c e c onc ep t s , i n s t r um en t a -
t i on s hou l d be r e f i ned i n t o p l ac em en t , c u t t i ng , and
remova l o f each f i l e us ing on ly ro ta ry mot ions . P lace-
m en t i s ac c om p l i s hed us i ng c l oc k w i s e r o t a t i on ( 18 ) and
l igh t, i nw a r d p r es s u r e . C u t t i ng i s ac c om p l i s hed us i ng
c oun t e r c l oc k w i s e r o t a t i on ( 19 ) and i nw a r d p r es s u r e
ad ju s ted to ma tch the f i le s s t re ngth , i .e . very l i gh t fo r
s m a ll i n s t r um en t s and heav y f o r v e r y l a r ge ins t r um en t s .
C l ean i ng o r deb r i s r em ov a l i s ac c om p l i s hed us i ng one
t o t w o n o n c u t t i n g n o p r e s s u r e o r s l i g h t o u t w a r d p u l l
c l oc k w i s e r o t a t i ons . C l ean i ng i s no r m a l l y c om p l e t ed
on l y a f t e r t he des i r ed l eng t h has been r eac hed and
m a i n t a i ned w i t h c oun t e r c l oc k w i s e r o t a t i on . Ax i a l r ec i p -
r oc a t i on o r f il ing m o t i on i s us ed on l y t o p r oduc e c ana l
t r ans po r t a t i on , t o f la r e t he c o r ona l a r ea , and du r ing t he
in it ia l ope n ing o f ca lc i fi ed cana ls . Such m ot ion vo ids the
ba l anc ed f o r c e f o r m u l a t i on a nd i t s us e s hou l d be l im i t ed
t o ex t r em e l y s m a l l d i am e t e r i n s t r um en t s o r t o t ha t
po r t i on o f t he c ana l w h i c h i s c o r ona l t o t he c u r v a t u r e ,
ex c ep t w he r e t r ans po r t a t i on w i l l s e r v e t o r em ov e a
p r eex i s t i ng l edge o r s hel f. W h en unm od i f i ed i ns t r u -
m e n t s a r e u s e d , th e w o r k i n g d e p t h s h o u l d b e s h o r t e n e d
by 0 . 25 m m w i t h eac h c hange t o t he nex t l a r ge r s i z e
i ns t r um en t i n o r de r t o p r ev en t ac c um u l a t i on o f t i p c u t s
a t a s ing le po in t . I f accumula ted , t i p cu ts w i l l c rea te a
m ec han i c a l l edge . The s t epbac k p r ec au t i on i s no t nec -
es s a r y w hen t he t i p s a r e m od i fi ed a nd f il ing ac t i on m ay
be us ed m o r e f r ee l y w i t hou t d r as t i c l o s s o f c on t r o l.
T h e r e a s o n f o r c l o c k w i s e p l a c e m e n t a n d c o u n t e r -
c l oc k w i s e c u t t i ng m ay no t be appa r en t a t f i r s t . To
unde r s t and t ha t c onc ep t , one has t o aga i n ana l y z e f i l e
des i gn and pos t u l a t e t he r eac t i ons p r oduc ed by v a r i a -
t i ons o f mot ion or d i rec t ion . The cu t t i ng edges inc l ine
dow n a K - t y pe f i l e s ha f t a t app r ox i m a t e l y 45 deg r ees
f rom the ver t i ca l ax is (F ig . 6 ) . By s tandard ized spec i f i -
c a t i on , t he c i r c um r ad i us i nc r eas es f r om t he t i p t ow a r d
t he hand l e and t he f l u t es s p ir a l c l oc k w i s e . The r es u l t is
s i m p l y t ha t a l oad de li v e red by c l oc k w i s e r o t a t ion pu l ls
a w a y f r o m t h e o p e r a t o r a n d m o v e s t h e i n s tr u m e n t
ap i c a l l y , w h i l e a l oad de l i v e r ed by c oun t e r c l oc k w i s e
r o t a t ion pu s he s t ow a r d t he ope r a t o r and m ov es t he fi le
ou t o f t he c ana l (F ig . 9 ) . As a c ons equ enc e o f t h is , t he
ope r a t o r m ay s ens e t he t o t a l o f a l l f o r c es du r i ng c oun -
t e r c l oc k w i s e r o t a t i on , t o r que p l us ou t w a r d m ov em en t ,
w h i l e he o r s he s ens es on l y t he t o r que po r t i on o f a
c l oc k w i s e r o t a t i on . The unno t ed i nw a r d m ov em en t i n
t ha t c as e p l ac es t he i ns t r um en t f u r t he r i n t o t he c ana l
and ex c es s i v e l y em beds i t s c u t t i ng edges i n t o den t i n .
T h e d e s c r i b e d m o v e m e n t s a r e a c o n s e q u e n c e o f v e c -
t o r ed f o r c es c r ea t ed w hen t he app l i ed t o r que i n t e r ac t s
p o w /
a l a n c e d F o r c e C o n c e p t
209
MOVEMENT
FIG 9. This i l lustration indicates the reactions which occur along the
blade inc l ines of a K - type f i le dur ing c lockwise and cou nterc loc kwise
rotat ion. Dent in s tr ikes the inc line opp osi te the rotat ing force deb r is
is ref lected to the de nt in s ide whi le a por t ion of the torqu e is vectore d
causing the i ns t rument to move i n to the cana l when the torque i s
c l ockwise and out o f the cana l when the torque i s counterc l ockwise.
Inward movement is labeled power and is used to place the instru-
me nt into canals . Outw ard m ovem ent is labeled control . I t is used to
i nc remental ly d i sengage the cut t ing ed ges and may be opposed by
the ope rato r pushing inw ardly to pro duce a f ini te c ontrol over the
cutting force.
wi th the c ana l wa l l a long the b lade inc lines. The resu l t -
an t fo r c es m ov e t he i ns t rum en t i n to t he c ana l w hen t he
t o r que i s app l i ed c l oc k w i s e and as t he i ns t r um en t
m ov es i nw a r d l y i t s s t anda r d i z ed t ape r f o r c es t he c u t -
t ing b l ades de epe r i n t o t he c ana l w a l l s . In o t he r w o r ds ,
a t a g iven po in t w i th in a cana l , the cu t t i ng rad ius
i nc r eas es as t he f i l e m ov es i nw a r d l y . C onv e r s e l y t ha t
r ad i us dec r eas es as t he f i l e m ov es ou t w a r d l y . I nw a r d
m ov em en t i s a r es u l t o f c l oc k w i s e i ns t r um en t r o t a t i on
w h i l e ou t w a r d m ov em en t i s a r es u l t o f c oun t e r c l oc k -
w i s e i ns t r um en t r o t a t i on ( F ig . 9 ). H enc e , no t on l y does
t he ope r a t o r s ens e t he f u l l l oad w h i l e r o t a t i ng t he
i ns t r um en t c oun t e r c l oc k w i s e bu t a l oad o f den t i n t oo
g r ea t t o s hea r w i ll c aus e t he f il e t o m ov e ou t w a r d l y and
t ha t m ov em en t w i l l s i m u l t aneous l y dec r eas e t he dep t h
o f c u t t i ng edge pene t r a t i on i n t o t he den t i n . The de -
c r eas e i n pene t r a t i on dep t h c on t i nues un t i l t he ope r a -
t o r s app l ied i nw a r d p r es s u r e e x c eed s t he s hea r
s t r eng t h o f t he t o t a l engaged den t i n and a c u t r es u l t s .
Th is re la t ionsh ip f i n i te l y ad jus ts app l ied fo rce aga ins t
8/20/2019 3.- Fuerzas Balanceadas_2
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2 1 R o a n e e t a l
t h e e n g a g e d d e n t i n a n d g i v e s t h e o p e r a t o r c o m p l e t e
c o n t r o l o v e r e a c h c u t t i n g a c t i o n . W i t h t h e u s e o f t h i s
s y s t e m , t h e o p e r a t o r m a y r e c o g n i z e t h e a c c o m p l i s h -
m e n t o f a c u t w h e n a s l i g h t p o p i s f e l t . C o n t i n u i n g
c o u n t e r c l o c k w i s e r o ta t io n p a s t 1 2 0 d e g r e e s , o n c e d e n -
t a l c u t t in g i s r e c o g n i z e d , e n l a r g e s t h e c a n a l t o t h e f i le s
c u t t i n g d i a m e t e r a s e a c h b l a d e w i l l h a v e r e a c h e d t h e
b e g i n n i n g p o s i t i o n o f a n o t h e r b y t h a t p o i n t . F u r t h e r
c o u n t e r c l o c k w i s e r o t a t io n h e l p s t o e n s u r e f ul l d i a m e t e r
e n l a r g e m e n t a n d r e m o v a l o f d e n t i n w h i c h m a y h a v e
c o m p r e s s e d a w a y f r o m t h e f i r s t b l a d e p a s s . U p o n
c o m p l e t i n g e a c h c u t , t h e f i l e i s a g a i n p o s i t i o n e d f o r
c u t t in g b y u s i n g a c l o c k w i s e p l a c e m e n t s t r o k e o f o n e -
h a l f o r l e s s r e v o l u ti o n . E a c h p l a c e m e n t i s fo l l o w e d b y a
c o u n t e r c l o c k w i s e c u t t i n g r o t a t i o n . T h i s s e q u e n c e i s
r e p e a t e d u n t i l t h e w o r k i n g d e p t h h a s b e e n a c h i e v e d
a n d t h e c a n a l i s f u l l y e n l a r g e d b y c o u n t e r c l o c k w i s e
r o t a t io n . W h e n e n l a r g e m e n t h a s b e e n a c c o m p l i s h e d , a
f i n a l c l o c k w i s e c l e a n i n g r o t a t i o n i s u s e d t o l o a d c a n a l
d e b r i s i n t o t h e f l u t e s a n d t o e l e v a t e t h a t d e b r i s a w a y
f r o m t h e a p i c a l f o r a m e n . C l e a n i n g h e l p s t o p r e v e n t
d e b r i s a c c u m u l a t i o n w i t h i n t h e c a n a l w h e r e d e b r i s w i l l
a c t t o u p s e t t h e b a l a n c e o f f o r c e s a n d a l s o h e l p s
p r e v e n t e x c e s s i v e l o s s o f d e b r i s i n t o t h e a p i c a l t i s s u e s .
C l o c k w i s e l o a d i n g o f d e b r i s i s a n o n e n l a r g i n g m o t i o n
in tended on ly to fac i l i t a te remova l .
D I S U S S I O N
U t i li z a ti o n o f t h e c o n c e p t o f b a l a n c e d f o r c e s e n a b l e s
o n e t o p r o d u c e e n l a r g e m e n t o f c a n a l s p a s t s e v e r e
c u r v a t u r e s w i t h o u t c o m p r o m i s e o f e n l a r g e m e n t c o n -
c e p t s o r p r e p a r a t i o n d i a m e t e r s . Ex a m p l e s o f c l i n i c a l
c a s e s c o m p l e te d u s in g t h e m e t h o d o l o g y d e s c r i b e d a r e
p r e s e n t e d i n F ig . 4 . W i t h o u t m o d i f ie d t i p s it is n e c e s s a r y
t o e x t e n d t h e i n s t r u m e n t s l i g h t l y b e y o n d t h e a p e x i n
o r d e r to p r e v e n t t r a n s p o r t e d w a l l s a n d l e d g e fo r m a t i o n .
W h e n o v e r e x t e n s i o n i s u s e d , t h e t i p m u s t b e r e t r a c t e d
t o l ie w i t h i n t h e c a n a l s p a c e a t l e a s t o n e o r t w o i n s t r u -
m e n t s i z e s b e f o r e c o m p l e t i n g t h e d e s i r e d p r e p a r a t i o n
d i a m e t e r i n o r d e r t o e n s u r e e s t a b l i s h m e n t o f a c o n s t r i c -
t i o n o r l e d g e . I n t h o s e c a s e s , t h e l e d g e c r e a t e d b y t h e
l a s t o n e o r t w o i n s t r u m e n t s b e c o m e s t h e a p i c a l s t o p
a n d s e r v e s t o p r e v e n t o v e r e x t e n s i o n o f g u t t a - p e r c h a
d u r i n g t h e f il lin g p r o c e d u r e . F i g u r e 4 A p r e s e n t s a c a s e
c o m p l e t e d i n t h i s f a s h i o n . T h i s p r o c e s s i s n e i t h e r c o m -
p le te ly accu ra te nor c li n ica ll y des i rab le and it ma y be
e l i m i n a t e d i n t h e f u t u r e t h r o u g h t h e u s e o f t h e m o d i f i e d
ins t rum en ts . E x tens ive c l in i ca l t r i a l s o f the mod i f ied f i l es
h a v e d e m o n s t r a t e d t h i s c o n c l u s i o n t o b e t ru e . Se v e r a l
c a s e s a r e p r e s e n t e d i n F ig . 4 ( B t o D ) w h i c h r e v e a l th e
cl in ical value of f i le t ip modi f icat ion.
O N L U S I O N S
T h e b a l a n c e d f o r c e c o n c e p t o f i n s t r u m e n t a t i o n i s
s i m p l y a n e x p a n s i o n o f t h e c o n c e p t o f r e a m i n g c a n a l s .
I t d i f fe r~ p r imar i ly i n tha t the cu t t i ng mo t ion i s i n ten t ion-
J o u r n a l o f E n d o d o n t i c s
a l l y c o u n t e r c l o c k w i s e a n d m a y b e a c c o m p l i s h e d a t a n y
l ev e l w i t h o u t b l o c k a g e , e s p e c i a l l y w h e n m o d i f ie d i n s t ru -
m e n t s a re u s e d . I n s t r u m e n t p l a c e m e n t is a c c o m p l i s h e d
b y c l o c k w i s e r o t a t i o n a n d i s c a p a b l e o f p r o d u c i n g s i g -
n i fi c a n t lo a d s o n a n i n s t r u m e n t t i p w i t h o u t r e q u i ri n g t h e
a p p l i c a t i o n o f i n w a r d p r e s s u r e b y t h e o p e r a t o r . T h i s
f a c t e n a b l e s s m a l l i n s t ru m e n t s , i .e . 8 a n d 1 0 , t o b e
c r u s h e d p a s t c a l c i f i c a t i o n s a n d a l l o w s o n e t o o p e n
ca lc i f i ed cana ls rap id ly . In add i t i on , th i s approach to
c a l c i f i e d c a n a l s a p p e a r s t o r e d u c e t h e i n c i d e n c e o f
s e c o n d a r y b l o c k a g e f r o m l o o s e n e d p a r t i c l e s .
T h e b a l a n c e d f o r c e c o n c e p t i s s i m i l a r t o r e a m i n g i n
t h e fa c t t h a t c l o c k w i s e r o t a t i o n o f e a c h i n s t r u m e n t m u s t
b e l i m i t e d t o n o m o r e t h a n 1 8 0 d e g r e e s i n o r d e r t o
prevent over inser t ion o f the ap ica l por t ion o f the ins t ru -
m e n t i n t o d e n t i n . Su c h o v e r i n s e r t i o n c a u s e s t h e t i p t o
c e a s e t u r n in g a n d a l l o w s t h e r o t a t i n g f o r c e t o u n w i n d
t h e f ile c o r o n a l t o t h a t p o i n t a n d i n c r e a s e s t h e l ik e l ih o o d
o f i n s t r u m e n t s e p a r a t i o n ( 2 0 ) . Ea c h p l a c e m e n t l o a d i s
f o l lo w e d b y a c u t t i n g m o t io n , c o u n t e r c l o c k w i s e r o t a t io n
o f 1 2 0 d e g r e e s o r g r e a t e r . T h i s a c t i o n c o m p l e t e l y e n -
la rges the cana l to the f i l e d iameter , f rees the ins t ru -
m e n t , a n d p r e p a r e s i t f o r p l a c e m e n t t o a d e e p e r d e p t h
w h e n th e n e x t c l o c k w i s e r o t a t io n i s s u p p l i e d . C l o c k w i s e
p l a c e m e n t a n d c o u n t e r c l o c k w i s e c u t t i n g r o t a t i o n s a r e
r e p e a t e d u n t i l t h e d e s i r e d d e p t h o r w o r k i n g l e n g t h i s
r e a c h e d . O n o c c a s i o n t h e f il e b e c o m e s f ill ed w i t h d e b r i s
a n d w i l l h e s i t a t e t o a c c e p t t h e n e x t p l a c e m e n t m o t i o n .
W h e n t h a t o c c u r s , t h e f i l e m u s t b e r e m o v e d , c l e a n e d ,
a n d t h e n r e i n s e r t e d b e f o r e i n s t r u m e n t a t i o n m a y p r o -
gress . Upon re inser t ion , p repara t ion i s con t inued un t i l
t h e d e s i r e d w o r k i n g d e p t h i s o b t a i n e d a n d t h e c a n a l
d i a m e t e r h a s b e e n e n l a r g e d b y c o u n t e r c l o c k w i s e r o t a -
t io n o f a t l e a s t 1 2 0 d e g r e e s . A g r e a t e r a n g l e o f r o t a t io n
i s d e s i r e d , i. e. o n e o r t w o r e v o l u ti o n s , b u t c a n n o t b e
safe ly accom pl i shed in a l l cana ls . Th is i s espe c ia l l y t rue
w h e n a n e x t r e m e l y s h a r p c u r v a t u r e e x i s t s a s s u c h a
curva ture can eas i l y cause fa t igue fa i l u re and resu l t i n
i n s t r u m e n t s e p a r a t i o n . C a n a l s w h i c h a r e e v e n l y c u r v e d
throughout the i r l eng th p roduce l i t t l e l i ke l i hood o f f rac -
t u r e w h i l e t h o s e e x h i b i t i n g s h a r p c u r v a t u r e c o n c e n -
t r a t e d i n a s m a l l s e g m e n t o f t h e r o o t r e q u i r e c a r e f u l
r o t a t i o n w i t h m i n i m u m o r l i m i t e d c l o c k w i s e J c o u n t e r -
c l o c k w i s e m o v e m e n t , i . e. 1 2 0 d e g r e e s e i t h e r d i re c t io n .
En l a r g e m e n t i s n o t i c e a b l y s l o w e r i n s u c h s i t u a t i o n s .
Sh a r p c u r v a t u r e s l o c a t e d p r im a r i ly i n t h e a p i c a l o n e -
t h i r d o f a c a n a l p r e s e n t t h e g r e a t e s t d i f f i c u l t y a s t h e y
d o n o t a l l o w m u c h a l t e r a t i o n o f t h e c u r v a t u r e a n g l e o r
r a d i u s v ia c a n a l a c c e s s a n d t h e i r i n f lu e n c e i s e x p r e s s e d
t h r o u g h a v e r y s h o r t le v e r a rm .
T o s u p p o r t t h e b a l an c e d f o r c e c o n c e p t a n d e s t a b li s h
i ts s a f e t y , w e h a v e a c c u m u l a t e d d a t a r e la t iv e t o i n s tr u -
me nt fa il u re dur in g c l in i ca l u se (20) . In tha t s tud y ins t ru -
m e n t d a m a g e w a s r e l a t e d t o t h e d i r e c t i o n o f r o t a t i o n
w h i c h p r o d u c e d t h e o b s e r v e d f a u l t s o r f a i l u r e i n o r d e r
t o d e t e r m i n e t h e r i s k o f i n s t r u m e n t s e p a r a t i o n a n d i t s
r e l a t i o n s h i p t o t h e d i r e c t i o n o f r o t a t i o n . T h e d a t a o b -
8/20/2019 3.- Fuerzas Balanceadas_2
9/9
Vol. 11 N o. 5 May 1985
t a i n e d h e l p s t o e x p l a i n o u r a p p a r e n t d i s r e g a r d f o r r e -
p o r t e d c o u n t e r c l o c k w i s e i n s tr u m e n t w e a k n e s s 2 1 , 2 2 ) .
T h e f in d in g s o f p r ep ar a t io n s p r o d u ced in p las t i c can a l
b l o c k s u s i n g t h e b a l a n c e d f o r c e c o n c e p t w i l l b e p r e -
sen t ed in a su b seq u en t a r t i c l e .
D r . R o a n e s a s s o c i a t e p r o f e s s o r a n d c h a ir m a n , D e p a r t m e n t o f E n d o d o n t i c s ,
U n i v e r s i ty o f O k l a h o m a C o l l e g e o f D e n t i s t r y , O k l a h o m a C i ty , O K . D r . S a b a l a i s
a s s o c i a t e p r o f e s s o r , D e p a r t m e n t o f E n d o d o n t ic s 0 U n i ve r s it y o f O k l a h o m a C o l -
l e g e o f D e n t i s t r y . D r. D u n c a n s o n i s a s s o c i a t e p r o f e s s o r a n d c h a i r m a n , D e p a r t -
m e n t o f D e n t a l M a t e r i a l s , U n i v e r s i t y o f O k l a h o m a H e a l t h S c i e n c e s C e n t e r ,
O k l a h o m a C it y , O K .
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