PDF hosted at the Radboud Repository of the Radboud University
Nijmegen
The following full text is a publisher's version.
For additional information about this publication click this link.
http://hdl.handle.net/2066/23684
Please be advised that this information was generated on 2015-01-24 and may be subject to
change.
ARTICLES
Detection of dental
decay and its extent
using a.c. impedance
spectroscopy
C hiustoi’hku Long b ottom 1,
M arik-Charioti'i; D.N.J. Huysmans2, N igi-x B. Prrrs1,
Pkzkmysi.aw Los 3 and Pktku G. Biiuce:i
It
'Department of'Dental Health, University of Dundee Dental School,
Park Place, Dundee, DDl 4 HR, Scotland
riilKON: Insiliate /'or Dentai (Muletti Research, Deporti nenl of Cariolo$y
and Endodontolo^y, University of'Nijmv$en, Nijnu^en, The Nvtìierhmris
\School afCìiemistry, University of'St, Andrews, St. Andrews, Scollami
Correspontìence shouìd he addressed to C.L
Dental caries (decay), the most prevalent of diseases,
represents a health problem of immense proportions1, It
principally affects posterior (back) teeth on occlusal
(biting) and approxlmal (adjacent contacting) surfaces.
Caries starts as a subsurface demineralization of enamel,
may progress to the underlying dentine and, eventually, to
cavitation of the surface. Accurate diagnosis before
cavitation would permit targeted preventive treatment,
thereby significantly improving dental health and reducing
the need for expensive drilling and filling. Inaccessibility of
caries initiation sites and recent changes in lesion
morphology contribute to the relatively poor accuracy of
conventional diagnostic methods2. Among alternative
techniques, measurements of electrical resistance35 have
shown the most promise. Here we describe a new
experimental technique that demonstrates an outstanding
100% correlation between a.c, impedance measurements
of whole teeth and the actual extent of approximal caries in
vitro. Only relatively minor modifications should be
required to transfer the technique to in vivo applications.
Impedance spectroscopy, which involves the measurement of
current in response to the application of a sinusoidally varying
voltage over a wide frequency range'1,1', has been used to study
dental enamel”’*' and dentine1". The effects of a carious lesion on
the electrical properties of enamel and dentine in whole teeth
have not yet been studied systematically. The aims of this study
were ( 1 ) to characterize the complex impedance behavior of
whole extracted premolar teeth, measured at one or both of their
approximal surfaces; by a method which could in its essential
features be reproduced in a clinical situation, and (2 ) to identify
parameters of the complex impedance behavior of the teeth that
would be useful in distinguishing between degrees of carious in­
volvement. in order to establish a method of measurement that
could be reproduced in a clinical situation, it was necessary to
develop a contact electrode from a material that could be used in
a thickness of only a fraction of a millimeter, was flexible and
hydrophobic, and could be impregnated at specific sites with
electrically conducting material. Such a material was identified
and a device designed for in vivo use (Patent pending, University
of Dundee, 1995),
NATURE MUmCINK, VOLUMI- 2, NUMHKR 2, IT.URUAHY 19%
The sample of teeth that were studied consisted of 26 unre­
stored extracted premolar teeth, with varying degrees of carious
lesions in the approximal surfaces. The individual approximal
surfaces were assigned to one of three groups on the basis of their
direct visual appearance, sound (S) if no visible sign of caries was
apparent; white or brown spot lesion (indicative of demineraliza­
tion due to caries) with no detectable loss of surface enamel (L),
and cavita ted (C) if there was a carious lesion with an area where
there was obvious loss of surface enamel. For each group (S, L
and C) ten surfaces were measured. Subsequent to measurement,
the teeth were hemisectioned and serially sectioned to validate
the visual categorization of the teeth and to determine the true
extent of any caries in enamel or dentine.
The a.c. impedance measurements were carried out with the
teeth placed in a custom -built Perspex chamber. Details of the
chamber and the technique are given in the Methods section.
Measurements of a.c. im pedance were carried out over a wide
range of frequencies, typically from 300 kHz to 1 Hz* Preliminary
experiments were carried out to establish reproducibility of the
technique. At least six measurements were carried out on each of
these teeth. Reproducibility was excellent, representing varia­
tions of less than a factor of two, which was minimal compared
with the variation of 100 in the resistances between the different
categories of tooth surfaces. The results of the measurements of a
representative tooth from each of the three categories St L and C
are presented in Fig, 1 .
The electrical response of any material can be represented by
an equivalent circuit. The equivalent circuit described in the
Methods section and derived for use in this experiment was fit­
ted to our data using a nonlinear least-squares procedure. In Pig.
1 the solid lines represent the best fit obtained, and the dots rep­
resent the data. The scale of the differences in the electrical
responses of the teeth in each of the three histological categories
is readily apparent.
The mean values (with standard deviations) for the total resis­
tances in Mfi (the sum of the two resistances in the equivalent
40
30-
20100
Z' /
MQ
Fig. 1 Examples of the complex plane plots of a representative
tooth from each of the three groups: S, shown in blue; L, shown in
black; and C, shown in red. The plot for the C group tooth Is en­
larged in the inset to facilitate visualization. The graphs plot the val­
ues for Z", the imaginary impedance, against Z', the real impedance,
at the various frequencies applied to each tooth.
2U5
»
Ci
%■
11 If, 11■
■
Ri|fj J
im-'
Wff
«.•■
■
..-l'' ■
m
«
ï
i.
#
tm..-
i
« M M W
W
W
» | W
« i*
&
#■
.# •
v
.
tfMi,
WÊSikü
:\(b
m
!
m
■
■
v
«y-
m
.
m
ai>i*
m
w
i."/■
/■
•■
& [ < &m
&
«
é
f i-
' $ m
r
J P
W -nm !
/ a} 4*/}»J i
i=
ïW/vY
iMi)
}{>
•
'■
’
A’
m
Vs-i.ï
àà*1*
■
•V/;
iîV 'V i/ i
I
y *
ÊÊ0$0M
®
ÉIllilÉlill
* l* lllip
miîi
i
Î m é ^ 0 M é 0 .
*
...............m
™
"
#
&
••
Ü
• *
V'fe ,vv^
ii'##
V ü ' m
■ ilp lliP p a
<
/.•
,0mÿWÊÊ
V.j' ^ •J;!.f
J V ^ V Y';
*', '
■'/<
■
■//A
!)':
m
m.
vî%;
iiilli
''y.i:!■
-1i'!
''W;
wm^tÈÊÈiÊiê
m
ff;M
w
iSÈÊËmÊÊË
>jV/? 'y '
Wsi
m $ m $ )
v n V
A
' . é
' é
■://'
¡•N - X i
'y à ï f r ''! -
ï ÿ
ÿ
m
*^ i:;;?•;Vi;-r;;:; »i-^J:>i / ':<»>.:]:
Sl®Sfc$&.....
i'//'!
:i i::i^:j!?
;i
#
W(.
■ ry - y /y
V x lv
m
iS ffP S S Î'ï'W ^ li^ i-'iS îîîfr’Æ ; ^
rlWéyHi:
Ji
ol
'..'.'.
:' . . . '• .: ..-■
------- !...'i:'.1 I\. ÿ l ■V.'.'.' ■.'.' .;'/ ^ :
'îi:ÿ?/
WtT,7\i<7i'ir»rny/i7/
M
■
V:.V.-
M
Éjg lla® ^
feilÉiilllllli
A
m
M
^
m
m
^
è
r
n
•vi'.'ik'':'
é
;-S<
■ « « illili^
piilliilÉii
M
&
M
,...<.,......... 1i?:W:.ü
^
'ii ‘\'y.y'yyJ.y,'y'/;’.'1j'.ft&içtiÆtv,<:l-.'->:.vi
tf> * i
i r< ir
m
m
I /: -! - ^ v i f v ^ i / ;
m
u
lî Ji
M
:v;•;•:
.v i i i i
W
.%
) iê ïW
>
M
4
'?/.■
à
m
g
m
r
n
ê
p
>y/;'<■:
ïy
i «■l
; ;; :
i
:■»;
. .
'S !
W
iïk W
À
&
i #
P
m
y.
.,<.*■
W ; <.iîi
Ï Â i :;i;;
i ■',';'.;''-:'.'î .
WÊ M Ü fÊr M ;Ê
Ë
Ê
H
llllw lillB iliW
m
kl’',i/.o.l XU\
$ :■ Î Ï K
i i i V
. :
s:
, <<.■■i.... ./,x' | ’, ;; i: : : s-'fi<',■<■';!<,'•:<y
-■<iv,--1;
<••. •/"--(.
i v -■
v ; f!.;^>;.'>. r
y,',;■
v
/ : : . :yy..-■fÿ/:Jif'£
%
;
m
s i
mmmmK
m^m k
i m m ï
> '•! 2
»
M
%
v .r >
m
* * y .
j h
H
J,V..<'NW
ƒ,J,—î'ii- '..i 6/!,' x*'.ll<0 i iI•>• i'***^
MiàMmÊsêÊÈËmm§mmm
W :0
ry-'.ï':
^myMxS
)/k^^0^$0é0M
ü iî.\
î î 'i i ^ ^ 'ÿ
V<;V # ;4
.-,: •W 0 / $ i
:(i
^ !- ‘rJ
■
■
■
■
/! W
O /J'
l l l l
% y j i ::('- m *
v?;K! ■X<-\-'ï>XÇ< <
■¡J:'ï 0 $
x c
r n
W
'■
vi\
'& ■
< '/ f f i
M
S i
:•■>. i
$ f c : / s h 'i ù \
w ;\
ï£iï?si'4V JRi'^M</J>/^yS.'-\^.
-.1
y'.\
',:■
'.■
:
.-V
'.'^^■.■\,Jyli\y'.iyt//r:>¿¿y.i
X '/ i "
îi ;
!
'0ÈM
i^0^yW
è^M
^pi'A
W 0^^Ê^^ÊiÉ!âi
m
• v .v 4
^
:î\I
■ rZ
C^?i/.VA'- ' ^V. WrJU>r^-jV/ii i i:!^
Æ
W0M0 &ÊWÊM^MMWÿMi
WSI. $é§0MMÈÊMfÊSâêM^ÊÉm
': > .! i : ' ! -
p
■
:&
.ÿ &
(tÔ
"
■y i v .
m
, '> ■
.
.
W ÊIÊÊÈ ê
?
4
s/yy-f!
'«KM/.-.ïte érM & U tâfr'M 'r'- - - '.................
...
■>.!,
•/< f<.
■kl;>
■y;-/'
•l /•
>>■/'*
y >f<
&
(/Vti* A(y>-'
W «:
» fc » e ^
# ^
^
^
# * ç. fe
#
^
^
fr.
fr.
^
#
w * ft-. * ^
^ y «i,
» #
a-
^
^ ^ * * * * * «■ « ^ «■ * «• *• * «
^
^
^ ^ ^ ® K ^ * * * * w * * "''
.* « «.
6
» « « -« -« «
«: *; «; « ♦- * « *
<1
«V ç, 0b «i
# - 4« «•
fc :* « •- *- #•
* if «i
* # « »
W
* H <- îî * * #
«r f. *
^
•W'
•S'%
.SJz
$
-V¿
=*£.
*í
"7**iÁ
.F l
&■
»v.' cîI â .
M -%
't4:
^
^S¡£- -''
V>V -5
>ÿ"
.
•^áScsiíÉ."
,<r-
' JVy.'-.'.'-V.'
•Sí’-f
M iW
M m
'.í'.
Vv^áxXÍ.
:*■
•vS
■
:,!.v
1 ^ :
.w l
#■
TV—
rS:>ïT
i^ V
■J--?
ÄX^T^:'
%■-%
»•9ÄV-
-5v
-ÍÍTTv\.
^ w
:;l v ^ '
#»***
¿S¿" ■'"¿.
c -
^r‘ ■
>.-;
)^'. -«sVC-Ä ;#
.--y;-
à
v.-:.
•ií-'
: T v. *
■ V '
Ä
.
asaafirè
fc o -
£•
.o,
*?■ '¿.•/'•.''•<■■''■'■
-S&Jï
V
£
ÿtoutff
•f*S :¿
•.
*$*
*Á >
5^5
** i
S = ¿-
>'•
":
3-i
*3*. ^ 5
v:- -í;.-t<-
$-
„ Ä ■
v tsrte ^ S :
•^s.-.-.. i'.
'• ^ T '
" "
M .
sa^.
;V.
y
'/,'•'. . ^A~
--g<
c>^èV'
:S # '
*'•
::-r:
V
¿¿“3$
*■
;■
/■
;'
^néhtfig-
v<'
31»
Æ
■
’£■
1
jg
.<*'■
aj.
*."T.*'■
-*
Í&&C-
fi •■^¿ÍC
■z
:-v
«.
.¡S^SSta' -Vi;
■ I«'
'*&£■
âè-.:
VéÇb.o
•¿S;-f
.Ä * .
V--:',.
«
:=^>9^
tiSBS?
•5t
• '% #
'‘SStïÆ'
>'
.r
. ^ t;
% ;
v i-
W
Vs> S í
■&**&
■4.
'k.
1^1. ■5^'
«?»:
'^5C' ..
sp- •7P-
fs. 1
-
'■
:■Ci-•.fc.
:^ * ^ '
,^ •st^.
.'
'^ Ä -
>j.
_---.' ---
dRWiC'
J .
■.. .
.Ä iS U
'■ S^:
.VP'
%■
■si'.
^.:Ï*=S$.
*•.
■üfeuCjig'
f
fl V
11»-ir.
^ Ä :
jW v w
'■-'" ■'¿'
jjnigyrw ^
%:'
...
».
^5?'
SS’
-
l á :
#"
1:
ir^ewa^--
■£=“ £
5?y»S**f
Ì
'.w #
f% _ ß '
m
-
,^-
‘^ 0
*•
•*.
^
'Ü3..J!A(Ç-:
>jv
iW ^ntlí
^ ,- ' T'
■'i-'
ïo .
*
»•spsw^.
?T
-íBr-'
Ä
*
.y*-
~v;-.çt ’ v¡-
^>
^:,^ '
IVrfr
f-tì
ffln-r; l-fe
•«r
••«fe..
••:«• ä :
.Jr.
A.
^Vigccá*^- '
«fr.
^y*=*£-
:>-v
S?5'
.:C Tro
'¥•• ' -# :
■».
.•-.•OCjJÍ?::^:v
.X‘--v- iÿ¿r-;
»•
•V -
:% S -
.ts6B«et:
f
V' •>i.■&-••*
-7::
•£-
}g% :.ik
.
•r'
-■¿r
«rtiaräfii.
S'
/ri',-
íí=>-,vír-
Â.¿i-.X Ï :
,-^vSs^te:
.•I»-
^ r ' *i.)■./
‘',s'
A;>‘ ■
:^ ..
••¿¡i'
&/&£■
,?/•• rv:
% *#
•■Séí^wltf;:
•■'y:-»w.
■
v.^‘f.v. •/,••
.^- r^-.
=€:
'ï>
1 -.
7i’:
- ^é-
•y-
::vÿoj rt>-.
, ^ # ;:
.'S.
•■isatoyÇ;
S&T..
% % Í-
C^Vm.
«S i.,
"i# ï ^ '
• .V .
Í?•’^ s 5>.
p
:Í8--
-'v;
r-*--•iïir.v
.».
'is w |.í*Í;^v.
»V.'.vV
>**• -Ji..
::i-V |»S
r-
4Äs'. ...
•ft-
,a s p í '
.'.Tv
Vf—
■ % #'
dît-..
•^îl:
:■».
:X¿
”^'.. ../j.
'•'S**,.
/5t.
4rr-25=îÇ:
■Æ
•**i.
•SP;
.re.
^P = ^:
■i3r
•%SS
c # #
"% ß
pjport'é
Ä : .%
•i7^iiewäv>.
Ä ..
'-'S
•Ä .
ÇîSssîfes^.
>3r.
^■w-.V.'
■
■
• .'•:
ïSb-
%ss*&--
■^^.■iS?.
s-
î
.■•SS«T?5>;
¿&'■
J’■
.■
:'■
■.--;v
iS-
■
X-,
. *V
AÎ?:^=Ç'-
R.
-,'l..
4
- V.* .
VK-p ù iÜ :
":;Í '
:k .V |.
-2
Ä lt
,.¿&s;:í-.-.
M í
=33.
*,•• i¿>•:^ ' -
Ä - s-
^4#
îç.
w%-.'§
tfí.
?•
%
«ik,,
iÜ5:-
.c o c jì:-
-*•
¿S5
T*^rMfg
$
/iv^eöR jÄ
k
'W
■n *
fW ¥i|.
^ '.i___V
W
f
-tqÿteuoft'!ÿ
■
nX
,Ä .
'•;i ^
¿
:^ r
»-s« « #■■•?■
'^ :«y.é-
■ ?wwS'
J0
*Vs *# Í.
lí6r<
ä#üÄss*ft-
,:^ r :^.
*^V
.r _ ’
.■yciiapg.
■.V
•% ;
•Ä-:
s if :
^ '• 4 #
?r-
-■XCTiLVi-i!^
i®?
••'¿V
UI
.^ I^ ^ 1
...
^.V jïï-
*i—
TÍ¡*W $'
i:--.
•.ÄK.
/_
$*§■
.^ - -7:-.
•^ 7 ,
•>'.' ■'V.,
;/y
4<^ ft
■< * v ■
*•
^¿ái;
•áf-
#%:
¿ sísi,.
-Sîs5«ç«h^ ’
''
’
1
#•*ic* » •
.sja^j'.i'.üí-
?t o -
ñ
t i
|a?rU^
^
rí«5:
“ w «è:
â |
î# #
^■aSûî«5''
:&■
$ **§ :
'^üi^
í-
^ J '%
^\*
31S=j4?
,t^Ç ;i-
.Ä : -V
Â' ' a;■
;V
;
,
.^v
..■
.»■
^
r?:ÆôSî#
qDUMlb;
--Çvimy
ásei^:
'V
V s^ •c^-
^ s ;
ifB T n if-
—r\^,V
?•..
..v .
^ iâ ? :
a'.
sa#-
■-
■$-S*»lf5Í
’W S ***■
'fe * * ;
■
?jTO>!f
3?'
.?•
*
i;.VJ .Jr
^S6M6âfiÇ;
JfST
4&
'
.is.'.'.s%
%fcST :k''
•ÍK:
Ar'
'^ ? r -
.:-?^:vÿ:.
.
æ;-
■■f Ï'
*ÏS
• # ^ :-‘î ; ' •••;
&
Ä
■>.
#■
SW
s£. .S
!»
-ai-
1
¿í8 **.
■S'
O S*.
ÍRWSfc
■f
1.'
jg rt.
£*&*»*£
' ’*¡ú¿f
«•SS*8J5^
***#■
■WW'
:«st:
■
í^
V -4 Í
i. .r.;.
'v ^ g ..
■>?W'
Sák.
.(•'•
%■:
N*V
*%■
.. ^ •
&***■
'$ $ 0 % :
.SBsçÇJSÂ-.'
..ijii ;i-ril 1.1,V;
:>>
:■>:
¿fe4
.p lf&nJX Î
■#':
''*&}&■
«-•jípsssÍ
í?f
—-1».'.' ■' *-1•' ■
IS ®
:^;"'
^eüS^;'
■
\
;X \ .
/.«M.ff->ivS '
Iß
•Ü¿É
*
”
- - *.
< p*& .
^■.s1
.*•-TÓOg^
5r-'.,...^
,ÿ > ~
v/ - ...* * y
'':^ 0 :
LN.-.Í-. S'.-
....vx
S%
vcS^èà?'
;i:;v{-v.'v:-:-
;i á í :
Ä-.V.V.. ...
' !^ ó < ^ ::^ ;
Æ-
% :% ÿ
■3»*^
•"••■ >i:-
.sr--^s^;i
7C».
';:
Â'' 'Í-:-.
s#
..
••p S i^ p x -
a
rW
■
-1\ ^ t
V.Sg!=*r-,
c':.
- -.y:;.
' ::^ s p '
.Wf
.«fe..
fS a s #
*
%#
'^SàVP
.Ä ,
'■
’-
S*s*¿
•:K-: -<:.
•:s:
w tß ■&’■
■
. ' V-,
•TV * —
A
¿r
'NÇ'■
-.vi.'
"W
"V.
j£.'-
.*
$&#§■
*V
. '.X 1 ' *
f
&
-T^yjj¿f£
•Ä i
.'Í.V
«sj(SNÇ^'
■^S
^v;
-.■^■
:- -\ _'.
S-' ■':&
• : ^ Ä .
•%:
'jfeSsftfc'.
^ísat^'
•r^jfeay-
^•''-Tíf-
. 1 1 1 U-
SVA^¿.
i
¿S
1
f
.iim iÇ.
S*
î>.
Ä .
W l'
.uk . .1rV
■PiSefi.
W ":
£.
I
AS&' 'i
Tjjiiüîy^'
X*
.■
>.
*»r
/■•{ÎTJr
*fcv,
■>/
V.
V- ^ ¿ :
*r~
V-
ít^ s
•ÿ jS S ^ .
ífefr,
li
:4 •ií..¿;'
s■
Ä?
,?■• -i
fî* :4
.^»R. :.v
^É È #'
£**$
 w ÿ'
&
'ìL
ü1*
?.•
s:
,'i ; ;§ :
:-.:Sv
Ä--
:^ : -¿530=
f'i^ ;I--
MJ.-neiÍC.
&
Æ
'?:■
5,
SV¡'.
< í« ^ %
••ís*'
:i§-
\y
■
■
■
’
y'
. . # %
.r^ ^ X
■V'
g s« ^’
'N-''. _s.
Æ',-
•Sv
;g-:»Vri'
••*;v • •í*'¿:'v
 :â
.*->.- •*.*.*..VV
.-'TJÿ••As.
ajÿiitigo.;'
sp.
$■
tN
•. j í ^ | .
" . Ä ' ä .
:fÄ '
.W.-
.Äi2,
/.V
JT
■ ^=^'
'••
íf
.'■'v'.
iSfaiaijí/
•X—
T^îWîSÇ1
.??•
•'^j
•:^:-
Äv
f e á
:í^ :
.«Stíáfe
•Í h # "
*0.
?s\
' • % ^ '
••‘
fe:
iri
>»•
-3?r.
•»:••
ViVb. -Bbss
'35!=»^'.
-ÎSs^^^Ç
«c
%
Ä:
■■0: Ê
x'(.
’
.v*,
-:-z.
* . ' ''
% '%
• $ :
:,vf;
•s§-
3|t %
i -
W
' S
'
.-I#
;
•NÏ.
: á : :"
1«
iife
n
•íí:
•-;-
: £
/-■
.•-X
w
#'•
•i;-i;-.
si':
'X .fc1-1.
*
'■
ìk?•>
sÿ
.V«.
i¿:
.s'
•-&V
^ • ' 'iii
■
• X.
W
✓5'.
IVI
.V * .
Í?.
•-•e- -
5 ;:
S';-
.*•
V í.
-ä
>-
.ne,.
■V ■
>:
•Xf!
V .
" ^
.•>;
/V
■
..V
.H&Q-
¿V
•S;-
N> 1
¿
y
■
■
ag-.
■•V.
Ä:
Í-. •.?.••
'•>' ■
^
•S':
x*^
I :
:•>>-V .
S:- •**:
&■
&-
•V:
:¿
-V
Æ
,óv
L
'ra.
,'*ryiW W ;
•;«^-
.■ájis's
-Si-
'vVM
N^:';
'¿¿asá
.
•^sjaíáíR'
s-.
%íl
%
':-:> ;^;-
'S'V:
•TV
'.C;
;v..
m
■i":'-
■-_-t
’
.*<;•
,.M
'
f ü. V
g - .vrr
Ä
•r,v>
. « . ' 4
•ví. í;
1
¡.0;
'■
Í|:
i
->i
#■
■S'-.
Cf.
ÍÍH
v£*H.
'Vs
>jS"'
•-Í:
:^::
:ss
Ä'
<Z".
^sS üt.
•^ ae« 1-'
'•'^v
%
% *#
•?
■
'*W
Mm
•Sí.
:É '
•ft-
.v;-
S iç,
¿5:
i
t-
Ir>.-';
1=*ÖW6*=»
%
f
3 8 ^ ’*^í
■
'■^V
" I:
■
,gp-.4gfe.
i
W
■
y.-'
7 -«
§
!*V'
£
I»'
1
■?r
f.-
I
i
vi-
•>y
s*'
;n-v.
v
^;
s*:'*
« s * ;
§
■* ' ^
%
■mm:
VÇ.
;:S:
m
ÍV:*
•1?/
.•¥>.
%
' ICÍSS*
, %
Üil
■ %>5
■
f
“'-/.i1.■
>-.;;■
.
¿V
•SSSSwÄ.
*•
■
.r^,/ — .
■ W œ *?»
' % * # '
-äJ
Ä'.
■
■i-
ir..
:í n -
f# ïê .
f-'^:-
i-,-.;
V-¿
# j # á wsg;-'
^&=£é¡É '
ÿ W W ! S:
■á:
Æ'
JS.
Vv:
.\'.v
;S;
•.i;'
^:.>íi¿i4^;.
ÉS:
<îï,
■
,<?S~ v ¿
-£:%:••'
?¡-v
j Ä
•■Ä-.
Ä : : '^áí'
I
&
Sí'
¿
jèS
É
*
«
:£\
•.'■
%
•.•"'s.
'^• . -s>
I
vV
■^*.\
•'«.
■
r_x\
:í^'
:?l•'■
—
.
y~\
Æ
?
&
£ s .
-'s
'ÖX
'■
i'':::•
>V:
f:
!•:
•-C1
•'S'
• <Z'
.sV-
y.'
■
:S::
s i'
:'rí:
•j S -
•;■_lujSS:'
v w
•y.
-s.
v»
*-"s
•••*■
Ts
s
•^:.
's£
•*/•
i
■ifc.
X?.:
l-V'
.!.S
$ %
•y~
s•rr*:
\'J"
sm f'
*.v*
r:.
'^i.x
i r ^ ' X,
■bs:'" ' v-?55
-V1**.
. Â % s .
A-*.
ví.
■
.“.■
■
:^ -
•■*5'
•!\vi
Ä;v-:'
;>■.'
5 ¿vir^ ■
••V/,, ••
■raft:
■'Mï-
I
■
¥í,c^
•Ä --
s>:
:.v::.'
,4
S Ä
V'/
%
#Äi.
I
.;-*,•
:A'
:>X-r
7'fi.
•:/•.*
i-
'.\!y>-
......
•'Æ?.
' '-VC'
' ■■■
■
■■
O;■
.
.
-X''X:.
:v.*.
Æ-iy
■V\'
.X*.
->T?CVA
XV .*
■
-X-:
.•^i-
|r
3':
. JiXs.
*-V.
•
7;C:
.•V.
xS^-
M
•i
“'
\Nt*
:jv.'
^
;-
:& i. '% :
•cs¿- ' ' ' ;"?rro
••X-.
,xV
55Vï;:
-ÿ'-
Ä
.•5&V
j*sü. -iv-
7S.V:
:>:■
m
'■¿h,
&r-y
$
9ii
,-c
•-V
Vf
■&
- l ó '.
;.V,
IÄ -
■>v'
•F ä E -^ '
v;-;:.'.:-ÿ
•
x'A
-f-
I
Í ^ É sfe.
% w er
VTrr?=
< v .'
.»S
;Á>
e r i: