H.S.

Yang, DDS, FhO

Assistant Professor of Prosthodontics
College of Dentistry
Chonnmn National University
A Two-Dimensional Stress Kwang-ju, Korea
Analysis Comparing Fixed
V.P. Thompson, DOS, PhD
Prosthodontic Approaches Professor, Director of Dental Materials
to the Tilted Molar Dental School
University of Maryland
Abutment Baltimore, Maryland

A two-dimensional finite element method was used to

analyze the changes in mechanical behavior of the
supporting structures when a fixed prosthesis replaced a
mandibular first molar. In the unrestored situation, as the
degree of bone résorption increased there was a
corresponding increase in stress in the periodontium. Tilting
of the molar abutment induced additional stress on the
mesial side of the root. The presence of a fixed prosthesis
markedly reduced the magnitude and distribution of stress
in the periodontium. The mechanical advantage obtained by
a fixed prosthesis was greater in the situation of a tilted
second molar with reduced bone support than with higher
bone levels. Int j Proslhodoni 1991,-4:416-424.

mandibular molar abutment that has tilted abutment selection. No clearly examined scientific
A mesially into the edentulous space is a com-
mon problem in fixed prosthodontics. Although
guidelines have been presented for the selection
of abutments with reduced alveolar bone leyel
the ideal abutment for a fixed prosthesis is an and/or severe inclination of one of the abutment
upright, sturdy tooth that is well supported by a teeth.
healtby periodontium, sucb a situation is rare, and The purpose of this study was to analyze the
tbe dentist must decide whether the extent of the stress levels in the supporting structures with
bone résorption and degree of abutment tilting is increasing bone loss and abutment tilting and to
acceptable for a fixed retainer. ascertain bow the addition of a fixed prosthesis
Some autbors' - claim that the tilted molar abut- modified these stresses and their distribution. A
ment for a fixed prosthesis will induce an unusual two-dimensional finite element method was used
strain in the periodontium and will eventually to determine the stresses in the prosthesis and sur-
destroy the supporting tissues. However, Hood et rounding structures as well as the displacement of
al' suggested that mesial tilting of less tban 30° the abutment teeth by forces of occlusion.
should not be a limiting factor for the molar abut-
ment, since the stresses induced in the periodon-
Materials and Methods
tium were markedly reduced following the
placement of a fixed partial denture. Many
Tbe finite element model was constructed of a
textbooks""-* propose that a crown/root ratio of
more than 1:1 should be avoided for abutments. mandibular posterior segment tbat included a
Another study' has sbown that teeth with consid- canine, premolars, (first molar missing), second
erably reduced bone support can be successfully molar, and supporting structures. A standard
used as abutments for fixed prostheses. There are intraoral radiograph was made of a periodontaiiy
some arguments"'^ regarding these theories on healthy mandibular premolar-molar area using the
paralleling technique. There was no bone résorp-
tion and no abutment tilting. The radiograph was
used to trace the outlines of each of the compo-
Reprint requests: Or Thompson, Department of General Den- nents and to construct the standard model {OH)
tistry. University of Maryland Dental School, 666 W Baltimore Three variations of the two-dimensional finite ele-
Street, Baltimore, Maryland 2120!. ment models were made: two with upright abut-

The Imeinationsi journal of Proiihodontics 416 Volurre 4, Number S, 1991

 Yang/Thompson Fi«ed Prosthodontic Approaches lo the Tiited Molar Ahulment

Table 1 Symbols for Finite Element Designs a gold crown on the tilted second molar (OTL) to
Symboi Design restore the normal otclusal plane was analyzed.
The designs and their symbols are given in Table
OH No restoration, tiigh bone level (C/R ratio 1:1.5) 1.
OL No restoration, iow bone level (C/R ratio 1:0.6)
OTL In all models, the lower border of the mandible
Goid crown on second moiar, tilting ot second
moiar, low bone ievel was considered fixed and the mesial border was
3H Tiiree-unit restoration, higii bone ievei supported, allowing movement in the mesiodistal
3L Three-unit restoration, low bone ievei direction. A 1-kg unit ocdusai force with a 15°
3TL Tinree-unit restoration, tilting of second moiar, low
bone ievei mesial vector was applied on all of the fossae, mar-
4H Four-unit restoration, high bone ievel ginal ridges, and cusps of the occlusal surface of
4L Four-unit restoration, low bone ievei each looth (f^ig 1). When a prosthesis was present,
4TL Four-unit restoration, tiiting of second molar, low loading of its fossae and cusp tips was added to
bone levei
the total loading of the structures (compare Figs 15
and 16). Mechanical properties of the materials
were taken from the previous literature (Fig 2 and
Table 2 Mechanical Properties ol Materials Table 2). The amount of tooth mobility reported
in the model after finite element analysis calcula-
Young's modulus Poisson's tion was compared to the actual amount of mobil-
Materials (kg/cm^l ratio
ity observed in the mouth.'" The elastic modulus
Enamel" 8.26 X 10' 0.33 for the periodontal ligament (PDL) was selected
Dentin^' 2.14 X 10' 0.31 from several available to give model results that
PDL" 7.03 X 10' 0.45
Compact bone" 1.45 X 10'
best correlated with this literature value. The elastic
0.30
Canceilous bone" 2.15 X 10^ 0.30 constant and Poisson's ratio of the materials"'^
Casting gold'= 8.46 X 10' 0.40 (Table 2) as well as the data concerning coordinates
and geometry of each node and element were
recorded in a personal computer. The basic finite
element model (Fig 1) was composed of 413 ele-
ments and a crown/root ratio for each tooth of ments and 476 nodes, which varied with bone
either 1:1.5 or 1:0.6, and the other wilh upright level and restoration. The linear plane stress analy-
premolars but with 35° of mesial tilt of the second sis program of Supersap version 9.01/387E (Algor
molar and all teeth with a crown/root ratio of 1:0.6, Inc, Pittsburgh, Pa) was used to solve the two-
Each of these three models was considered and dimensional static stress analysis problems. The
analyzed with the following variations; (1) no res- calculated numeric data were transformed into
toration, (2) a Ihree-Ltnit fixed prosthesis, and 0) a color graphics to better visualize mechanical phe-
four-unit fixed prosthesis. Additionally, a model of

Fig 1 Two-dimensional finite element model at high bone Fig 2 Coior code tor the materials present canceilous bone
ievel. Arrows indicate appiied ioad. Nodes marked with a tri- (green), compact bone (red), periodontai ligament ¡yeiiow),
angle are fixed in X and Y direction. Nodes with circles are dentin (blue), gold aiioy (pink), and enamei ¡brown).
tixed in Y direction.

•4, Number 5, t99I 417 Tiie internstiona al of Prosthodontii

 Fixed Prosthodontic Approaches to the Tilted Molar Abutmerii Yang/Thompsi

Fig 3 (Leit) Shear stress

magnitude and associated
color lor Figs 4 through 12.
(Units are kg/cm=.)

Fig 4 ¡Rigfit) Stress distri-

Dution witti no restoration and
ideal bone hsigtit (OH).
Stresses are widely distrib-
uted in ttie conical bone.

Fig 5 Stress distribution with no restoration anO iow bone Fig G Stress distnbution with iow done level, a goid crown,
level (QL). Stress concentration is observed in the periodon- and tiiting ot second molar (OTL). Additional high stress is
tium around the root apex. generated in the periodontium on the mesial side of ttie sec-
ond molar.

nomena in the models. The maximum compressive seiected for presentation, as it weii represented the
stress, maximum tensile stress, and maximum shear other stress patterns. Oniy piots of maximum shear
stress in each element of the models v^-ere calcu- stress are presented in this paper ¡Figs 3 through
lated and plotted. 12),
To verify convergence of the finite element In the supporting structures, relativeiy high
model, the number of eiements was increased in stresses were found in the corticai bone. As the
the basic model (OH) and in the four-unit fixed height of aiveolar bone around the freestanding
prosthesis modei with low bone level (4L1, The teeth was reduced, the iocaiized stress in the per-
number of eiements was increased in the basic iodontium increased (Figs 4 and 5), There were
modei (OL) to 3,042 (3,282 nodes) and to 3,078 some differences in the iocation and distribution
eiemenls ¡3,322 nodes) in the four-unit fixed pros- of the iocaiized stress concentration between the
thesis modei ¡4L). The calculated results were upright and tiited abutments. The freestanding,
aimost identical to those shown beiow, indicating mesiaiiy tilted molar abutment induced additionai
convergence for this modei. stress on the mesial side of its root and in the asso-
ciated periodontium (Fig 6).
Results Ail of the fixed partiai dentures modified and
reduced the stress in the periodontium, but high
The stress distribution patterns for each type of stress concentrations were observed within the
stress were simiiar. Maximum shear stress was metal structure, particulariy in the connector areas

lournai of Frost hod ont ii 418 • 4, Number 5, 1991

 Vang/Thompson ed Prosthodontic Approaches to the Tilted Molar Abutment

Fig 7 Stress distribution with high bone level and a three- Fig S Strass distribution with low bone level and three-unit
unit restoration (3H¡. Stress is relieved in the periodontium prosthesis (3L). The fixed restoration markedly reduced the
but stress concentration is seen in the connectors ot the fixed stress in the periodontium.
prosthesis.

Fig 9 Stress distribution with low bone level, tilted second Fig 10 Stress distribution with ideal bone height and tour-
molar, and three-unit fixed restoration (3TL). The fixed res- unit tixed prosthesis (4H]. Splinfing increases the stress in
toration not only reduces the stress level but also modifies the gold restoration but decreases the stress in the sup-
the pattern of stress distribution. No stress concentration is porting structures.
found in fhe periodontium around the tilted molar.

Fig 11 Stress distribution with low bone level anä four-unit Fig 12 Stress distribution with low bone level, filted molar,
prosthesis (4L), Stress level in the periodontium is reduced and four-unit fixed restoration (dTL). The fixed prosthesis
in both premolars by using a second abutment. tavors the tilted abutment with reduced bone support. No
stress concentration occurs in the periodohtium around the
abutments. (Compare to Fig 6.)

Volume 4, Numbers, 1991 419 The IntErnationa

 Fixed Piost h odontic Approaches lo Ihe Tilletl Molar Abutm Yang/Thompson

Table 3 Maximum Stresses in the Material ot Each Design

Compressive 129 225 225 147 177 195 113 112 126
Bone Tensile 82 157 197 94 152 160 63 79 81
Shear 64 112 113 73 89 97 56 56 63
Compressive 9 32 35 10 17 21 8 13 17
PDL Tensile 4 15 17 3 12 12 2 7 7
Stiear 5 16 17 5 9 11 5 8 10
Compressive 62 116 135 134 165 168 124 152 149
Tootti Tensile 45 80 13B 55 68 74 55 72 78
Stiear 33 58 79 67 83 84 62 76 75
Compressive 108 136 156 148 148 167 169
Gold Tensile 71 146 166 128 152 173 129
Shear 89 81 93 104 87 100 114

(Figs 7 through 12). To compare the magnitude of (Figs 13 through 16). The displacements were all
stress in each model, the peak stress for each mate- magnified by a factor of 10 for ease of visualization.
rial in each model was tabulated (Table 3). The The greatest mobility of the second molar abut-
maximum compressive stresses for the freestand- ment was observed with tilting and no fixed partial
ing teeth in the normal (OH) and reduced bone denture (Fig 14). A marked reduction in mobility
models (OL) were 129 and 225 kg/cm^ in the bone was observed in this abutment after placement of
and 9 and 32 kg/cm- in the PDL, respectively. In a fixed partial denture (Fig 16). The mesial and
the restored situation, the maximum compressive apical displacements in micrometers at the tnesial
stresses for the four-unit fixed partial denture with cusp tip of the second molar and the cusp tip of
reduced bone level (4L and 4TL) were 112 and 126 the second premolar when subjected to the stan-
kg/cm^ in the bone and 13 and 17 kg/cm^ in the dard loading conditions are listed in Table 4.
PDL, respectively. The maximum compressive The displacements of the freestanding molar
stresses of the three-unit and four-unit fixed partial abutment with normal bone level, low bone level,
dentures in the high bone level group (3H and 4H) and tilted molar abutment (OFi, ÛL, and OTL] were
were 136 and 148 kg/cm- in the bone and 10 and 87, 225, and 408 jim in the mesial direction and
8 kg/cm^ in the PDL, respectively. 64, 155, and 365 iim in the apical direction, respec-
To compare the mobility of an abutment tooth tively. The mesial displacement of the molar abut-
from model to model, the deflections were traced ment after placement of a three-unit fixed partial

Fig 13 Deflection ot the dental structures with ioading and Fig 14 Defiecticn with reduced bone level and upright molar
normai bone level. Green lines indicate the outline before abutment. (Magnitude ot displacement X 10.]
loading. White iines show ttie contour after ioading. (Magni-
tude of displacement x 10.¡

The Inl e ma liona I journal oí Prosthodontii 420 Volume 4. Numbers, 1991

 Vang/Thompson Fixed Prosthodontic Approaches to the Tilted Molar Abulment

Table 4 Displacement of Mesial Cusp Tip in Each is possible with otber stress analysis methods. The
Design (^m)
finite element method has long been used in tbe
Second rnolar Second premolar field of biomechanics, and its validity in designing
Design Mesial
and analyzing prostheses has been established in
Apical Mesiai Apical
dentistry."
OH 87 64 77 30 The stresses that occur in the periodontium are
OL 255 155 283 54
OTL 408 365 280
an important factor in regulating the remodeling
53
3H 36 33 36 48 process ofthe alveolar bone. It is a well-accepted
3L 55 43 55 72 theory that excessive compressive stress reduces
3TL 75 55 78 89
4H
the blood supply in the periodontal membrane,
28 30 28 36
4L 42 37 41 50
leading to bone résorption, while tensile stress
4TL 52 40 53 57 leads to bone deposition."' Although they were
well distributed, bigh stresses in the cortical bone
surrounding the abutment teeth were found in the
model. The highest stresses for upright teeth
denture with normal bone height, reduced bone occurred in the periodontium around the root
height, and tilted molar abutment {3H, 3L, and 3TL1 apex, not at the crestal bone. Tbe tilted molar
were 36, 55, and 75 (im, while with multiple ante- induced an additional stress concentration in the
rior abutments (4H, 4L, and 4TL) the displacements periodontium around the alveolar crest on the
mesial side of the mesial root. As the height of the
were reduced to 28, 42, and 52 um, respectively
alveolar bone decreased around the abutment
(Table 4).
without a fixed prosthesis, there was a correspond-
Tbe modifying effects of the fixed prosthesis,
ing increase in the magnitude of all stresses. The
abutment tilting, and bone résorption on the stress
major differences between the tilted and upright
distributions and mobility of the supporting struc- abutment at the same bone height were the loca-
tures can be evaluated by comparing these results. tion and the distribution pattern of tbe stress con-
centration (Figs 4 through li. Table 3).
Discussion
The maximum compressive stresses for the four-
The finite element method of stress analysis is a unit prosthesis in the low bone level group (4L and
mathematical engineering method of approxima- 4TL] were 112 and 126 kg/cm^ in the bone and
tion that divides a structure into a finite number of 13 and 17 kg/cm^ in the PDL, respectively. These
elements whose mechanical behavior is specified values were similar to those calculated for the high
by a finite number of parameters. If input data and bone level model without a fixed prosthesis. When
assumptions in making a finite element model are comparing the stresses between the unrestored
appropriate, the output will be more accurate than group and the four-unit fixed restoration, the mag-

Fig 15 Deflection with reduced bone ievei and lilting oí the Fig 16 Deflection after tfie placement ot a fixed prosthesis
moiar. The greatest mobility cf the second molar is seen. on tiited abutment with reduced bone support. A marked
(Magnitude of dispiacement X 10.) reduction in the abutment mobility is seen compared to Fig
15. (Magnitude ot dispiacement X 10.)

•4, Number 5, i99I 421 ' Tiie international Journal ot Prosthodondcî

 Fixed Proslhodoniic Approaches to rhe Tilted Molar Abuln Vang/Ttiompsoii

nitude of compressive stress in the periodontium to its abutment (3,3%), fracture of the fixed res-
was reduced approximately 50% by the placement toration (2,1%), or fracture of abutment teetn
of a prosthesis in the low bone level model (4L (2.4%). ,
and 4TL), while a 10% reduction was seen in the Based on this stress analysis, the possible prob-
bigb bone level mode! (4H) (Figs 10 through 12, lems associated with a fixed restoration using the
Table 3). A fixed prosthesis not only reduced the tilted molar abutment witb reduced bone support
stress level but also more uniformly distributed would be (1 ) breakage of the prosthesis at the con-
stresses in the periodontium. This result comple- nector area and (2) failure of cementing media at
ments other stress analysis research on fixed the second molar as a consequence of the high
prostheses.'^''' These results also support the clin- stress concentrations in those regions. Deteriora-
ical report of Nyman and Ericsson,^ who ques- tion of the periodontium as a result of increased
tioned the validity of "Ante's law,"'"
occlusal loading seems unlikely.
Note that when a prosthesis was present, a major Stress distribution patterns were similar in the
portion of the masticatory forces applied were dis- three-unit and four-unit fixed restorations. When
tributed within the metal structures. the first premolar was included as a second abut-
Relatively high principal stress ranging from 128 ment, lower stress was observed in each tootb and
to 173 kg/cm- was seen in the region of the con- periodontium around tbe premolars than before
nectors (Figs 7 through 12). When a fixed pros- splinting (Figs 7 through 12]. Splinting of the pre-
thesis was present, the 1-kg load was applied lo
molars increased the peak stress level in the inter-
all cusps, fossae, and marginal ridges of the pros-
nal structure of the fixed prosthesis but decreased
thesis (note the vectors in Fig 16]. This increased
the stresses in the abutment teeth, PDL, and sup-
the total force borne by the abutments, yet defor-
porting bone (Table 3).
mation in the prosthesis absorbed and distributed
the forces and reduced the overall stress level The mesial and apical displacement of the teeth
within the periodontal structures in comparison to increased with increasing bone résorption and
the unrestored situation. abutment tilting, and it decreased after placement
of a fixed prosthesis (Fig 13 through 16]. The four-
When a tilted abutment was present, stress con- unit prosthesis exhibited slightly less displacement
centration occurred within the gold alloy at the than the three-unit prosthesis (Table 4). At the
occlusal half of the mesial surface of the molar same bone level but witbout a fixed restoration,
abutment and tbe connector area between the the tilted molar exhibited greater mobility than the
pontic and tbe second premolar (Figs 9 and 12],
upright molar. This implies that the PDL supports
No stress concentration was observed in the per-
the load more efficiently when the force is applied
iodontium including the region of the alveolar
along the long axis of the root. The tilted second
bone crest. This suggests that a molar abutment
molar without a prosthesis exhibited the greatest
with 35° of mesial tilting may not be detrimental
to the periodontium, as the magnitude of stresses mobility when occlusal force was applied. This ver-
in the periodontium was reduced by approximately tical displacement of the tilted second molar sup-
50% after placement of a fixed prosthesis. Addi- porting the three-unit prosthesis was less than that
tionally, no stress concentration was observed on calculated in the presence of a normal bone level
the lateral side of the root. Although high stress without a restoration.
concentrations were found at the connector areas,
a fixed prosthesis markedly reduced the stress level Limitations of the Study
in the supporting periodontal structures in all sit-
uations. The mechanical advantage (reduction of To construct a finite element model, it is usually
peak stress level in the periodontium and reduction necessary to simplify the system by making several
of tooth mobility) afforded by a fixed prosthesis assumptions. The assumption required for analysis
was greatest for tbe tilted molar with a reduced of stress distribution by using a two-dimensional
bone level as compared to a normal bone level. finite element metbod was that the stresses in a
buccolingual direction were negligible and stress
Nyman and Ericsson's long-term study' of fixed components in any direction were independent of
partial denture abutments witb reduced bone sup- tbe buccoiingual dimension. In this regard, the
port indicated tbat none of the patients exhibited above analysis is a first approximation and the
recurrent periodontal breakdown or occlusal over- result should be interpreted as qualitative. In addi-
loading. Only 8% of the 332 restorations had failed tion, although biological materials such as dentin
by the 5- to 8-year recall. All of recorded failures PDL, and bone are anisotropic and inhomoge-
were from either loss of retention of the retainer neous, and usually exhibit nonlinear stress-strain

The International tournai of Prosihodontii 422 : A, Numbers, 1991

 Yang/Thompson ed Prosthodontic Approaches to the Tilted Molar Abutment

relationships, the materiais invoived were ideaiized 2. The freestanding tiited molar Induced addi-
as homogeneous, isotropic, and iineariy eiastic. tionai stress on the mesiai side of the roots
The laci< of good characterization data on biolog- and in the locai periodontium.
ical materiais iimits the accuracy of these resuits. 3. A fixed restoration reduced and modified the
Particuiarly, the physicai properties for the PDL stresses in the periodontium by distributing
avaiiabie in the iiterature exhibit a large variation. the major portion of occiusai force within the
The PDL has viscoeiastic properties and tooth metai structure.
mobiiity varies considerably with the individuai. 4. The greatest improvement in stress reduction
The mechanical behavior of PDL changes noniin- and distribution in the periodontium and a
eariy depending on the magnitude and duration of concomitant mari<ed reduction of tooth
the ioad appiied. Aiso, the PDL has different prop- mobiiity were achieved by the fixed prosthesis
erties in compression than in tension, and these on the tilted moiar abutment with reduced
are not weii described in the avaiiabie literature. bone support.
As was recently noted, progress in finite eiement 5. Muitipie abutments more uniformiy distrib-
analysis wiii be limited untii better defined physical uted the stresses than the singie abutment and
properties for enamel, dentin, the PDL, and can- reduced the amount of cusp dispiacement.
cellous and cortical bone'^ are available. We are
not in a position to verify the model developed
other than to note clinical data supporting these References
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Aithough these two-dimensionai models of den- patient be rehabilitated biologicaliy and mechanically by
means of crowns and fixed bridges? ; Ont Dent Assoc
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significant ciinicai impiications. The better distri- (iCE. / Prosthet Denf 196a;l9:483-488.
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1975:34:415-421.
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tissues to support fixed bridge work. / Ciin Periodontoi
a fixed prosthesis can be a successfui restoration 19e2;9:409-4l4.
with a tilted moiar abutment tooth having severeiy 8- Penny RE, Kraal IH: Crown-to-root ratio: Its significance
reduced bone support. It must be assumed that in in restorative dentistry. / Prostfiet Dent 1979:42:34-38.
such a situation the periodontium is healthy, iong- 9. Rosenstiel SF, Land MF, Fujimoto |- Contemporary Fixed
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42-49.
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Conclusions of three- and four-unit bridges. / Oral Refiabii
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4, Number 5, 1991 423 The Internaironai jOLrral of ProsthodoniK

 Fised ProsthodorilLc Apptoaches lo the Tilled Molar Abutment Yarg/Tliompson

16. Reitan K: Clinical and histological observations on tooth 9. Tesk |A, Anusavice K): Summary conference on design of
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Literature Abstract-

The Effect of Some Chlorhexidine-Containing

Mouthrinses on Salivary Bacterial Counts
This study evaluated the effect of four chlorhexidine mouthwash formulations on salivary bacterial
counts after a single rinse. Ten healthy young adult volunteers rinsed with the 0.2%, 0.12%, and two
0.1% formulations (all except for one ot the two 0.1% formulations commercially available) according
to manufacturers' instructions. The 0 2%, 0.12%, and commercially unavailable 0,1% tormulations
produced similar large and prolonged reductions in salivary bacterial counts during a 7-hour period.
The commercially avállatele 0.1% formulation produced minimal effects on salivary bacterial counts not
much different than the saline rinse control. The results were consistent with comparative plaque
inhibitory studies of the formulations and suggest that the described method is a quick and simple
way of screening products for antimicrobial and antiplaque potential.
Addy M, Jenkins S, Newsambe R. J Ciin PsnoúonroM 991:18(2)90-93. References: 19. Reprints: Martin Addy,
Department of Periodontology. Dental School. University df Wales College of Medicine, Cardiff CF4 4XY, United
Kingdom.-Slepiien A. Wagner. UP Abstract/Book Review Editor

Journal of Prosthodontu 424 •4, Number 5, 1991