ELECTRICAL PROPERTIES OF WET-COMPACT BONE

ELECTRICAL

PROPERTIES

OF

WET-COMPACT

BONE

G. N . R e d d y a n d S . S a h a D e p a r t m e n t of O r t h o p a e d i c Surgery Louisiana State University Medical Center S h r e v e p o r t , LA 71130

ABSRTACT T h e e l e c t r i c a l p r o p e r t i e s of f u l l y - w e t , b o v i n e - c o m p a c t b o n e a r e m e a s u r e d in t h r e e o r t h o g o n a l p l a n e s , u s i n g a d i f f e r e n t i a l technique. T h e m e a s u r e d f r e q u e n c y r a n g e is 1 k H z to 1 M H z . For a x i a l , r a d i a l , and c i r c u m f e r e n t i a l d i r e c t i o n s the s p e c i f i c r e s i s t a n c e s are 1 6 . 6 , 5 4 . 0 , and 3 5 . 8 k i l o o h m - c m ; t h e s p e c i f i c c a p a c i t a n c e s a r e 1 8 3 , 5 2 , and 7 3 p f - c m " ^ ; and the s p e c i f i c i m p e d a n c e s a r e 1 6 . 6 / - 1 .09 , 5 4 . 0 / - 1 .01 , and 3 5 . 8 / - 0 . 9 4 k i l o o h m - c m r e s p e c t i v e l y at 1 k H z . The m e a s u r e d electrical p r o p e r t i e s i n d i c a t e t h a t t h e w e t - c o m p a c t b o n e is a d i s p e r s i v e and a n i s o t r o p i c m a t e r i a l . T h e d i f f e r e n t i a l t e c h n i q u e u s e d in t h i s s t u d y p r o v i d e s an a c c u r a t e m e a n s to m e a s u r e t h e e l e c t r i c a l p r o p e r t i e s of b o n e . The r e s u l t s f u r t h e r i n d i c a t e that the m o i s t u r e c o n t e n t of b o n e d o m i n a t e s in d e t e r m i n i n g t h e e l e c t r i c a l p r o p e r t i e s of b o n e . INTRODUCTION S i n c e the f i n d i n g s that the d r y b o n e and dry c o l l a g e n are p i e z o e l e c t r i c ( F u k a d a and Y a s u d a , 1 9 5 7 , 1 9 6 4 ) , and w h e n the s u b s e q u e n t e x p e r i m e n t s s h o w e d t h a t w e t b o n e is a l s o p i e z o e l e c t r i c ( R e i n i s h and N o w i c k , 1 9 7 5 ) , s i n c e t h e n t h e e l e c t r i c a l e n h a n c e m e n t of o s t e o g e n e s i s h a s r e c e i v e d increasing attention. In t h e p a s t d e c a d e e x t e n s i v e r e s e a r c h h a s b e e n c o n d u c t e d for c l i n i c a l l y u t i l i z i n g this e f f e c t . Recently, electrical stimulation has found w i d e s p r e a d a c c e p t a n c e among o r t h o p a e d i c s u r g e o n s for t r e a t i n g n o n - u n i o n s and congenital p s e u d a r t h r o s e s ( B r i g h t o n and c o - w o r k e r s , 1 9 7 7 ; B a s s e t t , 1 9 8 1 ; M u l i e r and S p a a s , 1 9 8 0 ) . T h o u g h e l e c t r i c a l s t i m u l a t i o n is b e i n g u s e d s u c c e s s f u l l y in o r t h o p a e d i c c l i n i c s t o d a y , o u r u n d e r s t a n d i n g of the m e c h a n i s m of a c t i o n is s t i l l v e r y l i m i t e d . F u r t h e r w o r k is n e e d e d , t h e r e f o r e , to o p t i m i z e e l e c t r i c a l - s t i m u l a t i n g p a r a m e t e r s for m a x i m u m osteogenic effect. M a n y i n v e s t i g a t o r s r e c o g n i z e that c h a r a c t e r i z i n g the e l e c t r i c a l p r o p e r t i e s of b o n e is i m p o r t a n t f o r f u r t h e r progress

169

170

BIOMEDICAL ENGINEERING II

of t h e c l i n i c a l u s e of e l e c t r i c a l s t i m u l a t i o n ( W a t s o n , 1 9 7 9 ; B e c k e r , 1 9 7 9 ; P l i s k i n and W i e n t r o u b , 1 9 7 9 ) . T h i s p r o g r e s s , it is e n v i s a g e d , c a n b e a c h i e v e d if t h e b a s i c u n d e r s t a n d i n g of t h e i n t e r a c t i o n s b e t w e e n e l e c t r i c a l s t i m u l a t i o n and t i s s u e are known. S i n c e t h e s e i n t e r a c t i o n s c a n be p r e d i c t e d if t h e e l e c t r i c a l p r o p e r t i e s of t h e m a t e r i a l s a r e k n o w n ( S t u c h y , 1 9 7 9 ; S c h o w n and F o s t e r , 1 9 8 0 ) . T h e p u r p o s e of t h i s s t u d y is to m e a s u r e t h e e l e c t r i c a l p r o p e r t i e s of b o n e ; n a m e l y , i t s s p e c i f i c i m p e d a n c e , p h a s e a n g l e , r e s i s t a n c e and c a p a c i t a n c e . It is p r o p o s e d to m e a s u r e t h e s e p r o p e r t i e s of b o n e o v e r a w i d e range of f r e q u e n c i e s to s t u d y i t s d i s p e r s i v e c h a r a c t e r i s t i c s ; a n d to a l s o e x a m i n e t h e m in t h r e e o r t h o g o n a l d i r e c t i o n s , to s t u d y i t s structural anisotropy. MATERIALS

AND

METHODS

In t h i s s t u d y t h e o v e r a l l i m p e d a n c e ( v o l u m e i m p e d a n c e ) of t h e b o n e s p e c i m e n is m e a s u r e d u s i n g a d i f f e r e n t i a l t e c h n i q u e (Reddy and S a h a , 1 9 8 2 ) . T h e p u r p o s e of u s i n g t h e d i f f e r e n t i a l method is to m i n i m i z e e r r o r s d u e to s t r a y c a p a c i t a n c e . In p r i n c i p l e , t o c a l c u l a t e b o n e i m p e d a n c e w i t h t h i s m e t h o d it is n e c e s s a r y to make two m e a s u r e m e n t s : o n e a r e f e r e n c e r e a d i n g (to p r e d e t e r m i n e the m e a s u r i n g s y s t e m ' s s t r a y c a p a c i t a n c e ) w i t h o u t a s a m p l e for m e a s u r i n g the s y s t e m ' s i m p e d a n c e ( Z ^ / )> ^ second reading w i t h a s a m p l e to m e a s u r e t h e c o m b i n e d e q u i v a l e n t impedance (Zgq/J^gq). T h e s a m p l e v o l u m e i m p e d a n c e ( Z g / e _ ) is t h e n g i v e n b y

F r o m the v o l u m e i m p e d a n c e ( Z g / e _ ) c a p a c i t a n c e ( C g ) c a n be c o m p u t e d / C o s θ , and

Rs

Cg

the v o l u m e r e s i s t a n c e ( R g ) as ( R e d d y and S a h a , 1 9 8 2 ) =

SinG

(2)

/ ω

For s p e c i m e n s w i t h a r e a ( A ) and l e n g t h ( L ) , the s p e c i f i c impedance (Zgp/6_gp), phase angle ( 6 g p ) , resistance ( R g p ) , c a p a c i t a n c e ( C g p ) are c o m p u t e d as Zsp| and in The and

θ gp eqn.

3,

=

Rsp

=

-tan-1

Rgp

=

/[(ωRspCsp)2

of

UV^,

, and

this

Cgp

and

(3)

(ωRspCgp),

(RgA)/L

further details Saha, 1982).

+

and

(4) =

technique

(CgL)/A, are

given

(5) elsewhere

(Reddy

RESULTS F i g u r e 1 s h o w s t h e s p e c i f i c I m p e d a n c e ( c o m p u t e d u s i n g e q n . 3 ) of b o v i n e - c o m p a c t b o n e in the a x i a l , r a d i a l , and circumferential d i r e c t i o n s as a f u n c t i o n of f r e q u e n c y . It c a n be s e e n t h a t t h e e f f e c t of c a p a c i t i v e r e a c t a n c e o n i m p e d a n c e is s i g n i f i c a n t only a f t e r 100 k H z . T h i s f l a t - i m p e d a n c e r e s p o n s e w i t h f r e q u e n c y is p a r t l y d u e to t h e d e c r e a s e of c a p a c i t a n c e w i t h frequency ( a p p r o x i m a t e l y 10 d B / d e c a d e ) ; a n d s e c o n d l y , d u e to i t s l o w c a p a c i t i v e (182 p f - c m " ^ , at 1 k H z , for axial specimens) component. T h e c o r r e s p o n d i n g p h a s e - a n g l e p l o t s a r e s h o w n in

171

BIOMEDICAL ENGINEERING

Fig. 2. T y p i c a l v a l u e s of I m p e d a n c e s at 1 k H z a r e 1 6 . 6 , 5 4 . 0 , and 3 5 . 8 ; and the c o r r e s p o n d i n g p h a s e a n g l e s are - 1 . 0 9 , - 1 . 0 1 , and - 0 . 9 4 d e g r e e s r e s p e c t i v e l y . V a r i a t i o n of t h e s p e c i f i c resistance (Rgp) specific capacitance (Cgp) (computed 60

1 Axial Radial Circumferential

^

\

\ \

40

- ^^

105

10*

103

*\

106

Frequency (Hz)

Fig.

1

Specific function

i m p e d a n c e of w e t - c o m p a c t of f r e q u e n c y .

10*

bone

as

a

10* Frequency (Hz)

Fig.

2

Phase angle f u n c t i o n of

of t h e s p e c i f i c frequency.

impedance

as

a

u s i n g e q n . 5 ) a s a f u n c t i o n o f f r e q u e n c y a r e s h o w n in F i g s . 3 and 4 r e s p e c t i v e l y . T y p i c a l v a l u e s of t h e r e s i s t a n c e a n d c a p a c i t a n c e for the a b o v e d i r e c t i o n s at 1 kHz a r e : 1 6 . 6 , 5 4 . 0 , 3 5 . 8 k i l o o h m - c m ; and 1 8 3 , 5 2 , and 73 p f - c m ~ l respectively.

172

BIOMEDICAL ENGINEERING II CONCLUSIONS

AND

DISCUSSION

O u r r e s u l t s s h o w t h a t t h e e l e c t r i c a l p r o p e r t i e s of b o n e , n a m e l y , the s p e c i f i c r e s i s t a n c e , s p e c i f i c c a p a c i t a n c e , s p e c i f i c i m p e d a n c e are all f r e q u e n c y d e p e n d e n t . Our r e s u l t s a g r e e q u a n t i t a t i v e l y w i t h t h o s e by o t h e r s ( M a r i n o a n d c o - w o r k e r s , 1 9 6 7 ; R e i n i s h , 1 9 7 9 ) ; h o w e v e r , t h e a c t u a l v a l u e s and t h e r a t e of c h a n g e w i t h i n c r e a s e of f r e q u e n c y , as m e a s u r e d b y u s , a r e significantly different. T h i s is p r o b a b l y d u e to t h e f a c t t h a t our r e s u l t s are for f u l l y - w e t bone with very high conductivity, w h i l e t h e r e s u l t s of t h e o t h e r s a r e f o r p a r t i a l l y - w e t b o n e . Our

Radial Circumferential

103

105

10*

106

Frequency (Hz)

Fig.

3

S p e c i f i c r e s i s t a n c e ( R g p ) of t h e b o n e a s a f u n c t i o n of f r e q u e n c y .

103

10*

105

wet-compact

106

Frequency (Hz)

Fig.

4

S p e c i f i c c a p a c i t a n c e of t h e a f u n c t i o n of f r e q u e n c y .

wet-compact

bone

as

BIOMEDICAL ENGINEERING II

173

r e s u l t s a g r e e w i t h t h e v a l u e s of K o s t e r i c h ( 1 9 8 3 ) , w h o m e a s u r e d t h e d i e l e c t r i c p r o p e r t i e s of b o n e u n d e r near-normal physiological conditions. We found that the s p e c i f i c resistance i n t h e r a d i a l d i r e c t i o n to be a p p r o x i m a t e l y t h r e e t i m e s t h a t i n t h e c i r c u m f e r e n t i a l d i r e c t i o n a n d to be a p p r o x i m a t e l y t w o t i m e s h i g h e r t h a n t h a t in t h e a x i a l d i r e c t i o n ( F i g . 5 ) , d e m o n s t r a t i n g its a n i s o t r o p i c n a t u r e . T h i s is in c o n f o r m i t y w i t h t h e f i n d i n g s of C h a k k a l a k a l a n d c o - w o r k e r s ( 1 9 8 0 ) , a n d S a h a a n d co-workers ( 1982) . REFERENCES B a s s e t t , C . A . L . , S. N . M i t c h e l l a n d S . R . T r e a t m e n t of u n u n i t e d t i b i a l d i a p h y s e a l p u l s i n g e l e c t r o m a g n e t i c f i e l d s . J. B o n e 63A, 511-523.

Gaston (1981). fractures with and J o i n t S u r g . ,

B e c k e r , R . O ( 1 9 7 9 ) . T h e s i g n i f i c a n c e of e l e c t r i c a l l y stimulated o s t e o g e n e s i s : More questions than a n s w e r s . Clin. Ortho., 141, 266-274. B r i g h t o n , C . T . , Z . B . F r i e d e n b e r g , Ε . I . M i t c h e l l , a n d R. E . B o o t h , ( 1 9 7 7 ) . T r e a t m e n t of n o n - u n i o n w i t h constant-direct current. Clin. Orthop., 124, 106-123. C h a k k a l a k a l , D . , M . W . J o h n s o n , R. A . H a r p e r a n d J. L . K a t z ( 1 9 8 0 ) . D i e l e c t r i c p r o p e r t i e s of f l u i d s a t u r a t e d b o n e . I E E E Trans. Bio-Med. Eng., 27, 95-100. F u k a d a , E . , a n d I. b o n e . J. P h y s .

Y a s u d a ( 1 9 5 7 ) . On the p i e z o e l e c t r i c Soc. Japan, 12, 1158-1162.

F u k a d a , E . , and I . Y a s u d a ( 1 9 6 4 ) . P i e z o e l e c t r i c c o l l a g e n . J. A p p l . P h y s . , 3 , 1 1 7 - 1 2 1 .

effect

effects

in

K o s t e r i c h , J. D . , K. R . F o s t e r a n d S. R. P o l l a c k (1983). D i e l e c t r i c p e r m i t t i v i t y and e l e c t r i c a l c o n d u c t i v i t y of s a t u r a t e d b o n e . I E E E T r a n s . B i o m e d . E n g , 30( 2) , 8 1 - 8 6 . M a r i n o , A . Α . , R. determination 367-378.

0. of

of

fluid

B e c k e r and C. H. B a c h m a n ( 1 9 6 7 ) . Dielectric b o u n d w a t e r of b o n e . P h y s . M e d . B i o l . , 12 ,

M u l i e r , J. C , a n d F. S p a a s ( 1 9 8 0 ) . O u t - p a t i e n t t r e a t m e n t of s u r g i c a l l y r e s i s t a n t n o n - u n i o n s by i n d u c e d pulsing current — clinical r e s u l t s . A r c h . Orthop. T r a u m a t . surg . 9 7 , 293-297. P l i s k i n , J . S . , and S . W i e n t r o u b ( 1 9 7 9 ) . T h e e l e c t r i c a l s t i m u l a t i o n of b o n e h e a l i n g : s o m e p o l i c y i s s u e s . P r o c . I E E E , 67 , 1 3 5 2 - 1 3 5 3 . R e d d y G. N . a n d S . S a h a ( 1 9 8 2 ) . A d i f f e r e n t i a l m e t h o d m e a s u r i n g e l e c t r i c a l c h a r a c t e r i s t i c s of b o n e . J. B i o e l e c t r i c i t y . 1(2) , 173-194 . R e i n i s h , G. B . , and A . p r o p e r t i e s of b o n e

S. as

Nowick ( 1 9 7 5 ) . a f u n c t i o n s of

for

Piezoelectric moisture content.

174

BIOMEDICAL ENGINEERING II N a t u r e , 253 , 6 2 6 - 6 2 7 .

R e i n i s h , G. B . and A . S. N o w l c k ( 1 9 7 6 ) . E f f e c t of m o i s t u r e t h e e l e c t r i c a l p r o p e r t i e s of b o n e . J. E l e c t r o c h e m . S o c , 123, 1451-1455.

on

S a h a , S . , Μ · V . K a m a t h a n d J. A . A l b r i g h t ( 1 9 8 1 ) · E l e c t r i c a l i m p e d a n c e c h a r a c t e r i s t i c s of c o m p a c t b o n e . T r a n s . 1st A n n . B R A G S M e e t . , 25^. S c h w a n , Η . P . , a n d K . R. F o s t e r ( 1 9 8 0 ) . RF f i e l d interaction with biological systems: electrical properties a n d b i o p h y s i c a l m e c h a n i s m s . P r o c . I E E E . , 68 , 1 0 4 - 1 13 . S t u c h l y , M . A . ( 1 9 7 9 ) . I n t e r a c t i o n of r a d i o f r e q u e n c y a n d microwave radiation with living systems. Radiat. Environ. B i o p h y s . , 16 , 1 - 1 4 . W a t s o n , J. ( 1 9 7 9 ) . T h e e l e c t r i c a l s t i m u l a t i o n healing, Proc. IEEE, 67, 1339-1352

of

bone