stress / strain redistributions occurring within mandibular bone as a result of prosthodontic treatments are highly complex and an understanding of the biomechanical factors ( strains ) initiating bone remodelling due to prosthodontic procedures has not been conclusive so far .
for this reason an in - depth understanding of the biological activity in the supporting abutments and bone structures is required as a means for possible improving the outcomes of such restorations .
therefore a detailed biomechanical model becomes essential , especially in typical clinical cases , in order to develop a computational biomechanical simulation capable of identifying the quantitative mechanical response to fixed prosthodontic treatment .  
fixed partial dentures are commonly used as a conservative prosthodontic treatment option in restorative dentistry with proven clinical reliability [ 2 , 3 ] and have played an integral role in the rehabilitation of oral function for years .
however , the rigid construction of fpd systems changes the local biomechanical status , whereby bone may model and remodel to accommodate a new loading environment .
thus a critical factor that determines the long - term success of fpds is how occlusal forces are transferred to the surrounding root abutments , periodontal ligament ( pdl ) , and bone .
bone remodelling is dependent on the maximum load experienced throughout its load history ; however , remodelling is also characterised by the number of daily cycles that are consistent with mastication [ 5 , 6 ] . in typical three - unit fixed partial dentures ,
the tooth root abutment - bone interface must be able to tolerate changes in occlusal force behaviour without instigating adverse bone tissue responses . in this sense , understanding the effect of biomechanics on biological response is a key step to optimal design of an fpd .
in general , the three main biomechanical issues related to an fpd are (  1 ) mechanical loading , (  2 ) transmission of the load to the interfacial tissues , and (  3 ) biological reactions of surrounding tissues to the transmitted load .  
frost 's mechanostat theory is one of such which defines a threshold minimum effective strain ( mes ) as a mechanical stimulus to trigger bone remodelling .
an mes remodelling threshold has been suggested in the range of 0.00080.002 unit bone surface strain , below which it is suggestive of bone resorption and above which it is indicative of bone apposition .  
clinically , an fpd can be established immediately upon tooth extraction or more often upon extraction socket healing .
resorption is an inevitable consequence of extraction of a natural tooth due to local bone disuse .
although the resorption may not be eliminated completely , its severity can be reduced by ensuring that the prosthesis transmits mechanical loads to the underlying bone structure properly [ 13 , 14 ] .  
previous investigations [ 15 , 16 ] conducted on fixed prosthodontics have mainly focused on technical complications and stress peaks within the prosthetic devices . while in other clinical scenarios ,
tooth - implant systems incorporating an fpd has been evaluated [ 1719 ] for assessing bone - implant osseointegration . despite their relevance , limited studies have been reported on the biomechanical responses of mandibular bone as a consequence of fixed prosthodontics .
indeed , the complexity of biological reactions surrounding an fpd have made it very difficult to draw general conclusions about the prognosis of restorative treatments with fpds in general dental practice .  
this paper aims to establish the stress / strain patterns in mandibular bone to identify the initial status of remodelling stimulus , thereby correlating the finite element ( fe ) results with clinical observation . in order to achieve a precise quantitative analysis of the initial mechanical responses to loading on an fpd ,
a biomechanical model is essential as the detailed anatomical configuration of dental structures could largely affect their behaviours [ 21 , 22 ] .
for this reason , computerized - tomograph- ( ct- ) based 3d finite element analysis ( fea ) techniques will be employed in this study to understand the biomechanics in the pdl - bone interface contiguous to abutments of an fpd .
it is expected that an increased knowledge in this region can help establish a quantitative relationship associated with biological reactions such as bone remodelling .
this study primarily focuses upon mandibular bone predictive or modelled strain responses as a direct result of mastication .
three - dimensional computational models of a section of the mandible with teeth were established in this study , representing the right mandibular premolar , first and second molars , and their supporting dental apparatus with / without a three - unit fixed partial denture .
the finite element models employed in this study were constructed primarily using computerized tomography ( ct ) images , digital edge detection technique , and computer aided design ( cad ) methods [ 2325 ] .   in the present paper ,
models a and b are of prefixed prosthodontics initially upon first molar extraction and following a healing period of 12-months without fpd construction , respectively .
models c and d are presented following the three - unit fpd established upon initial tooth extraction and after a 12 month healing period . the extracted tooth model ( models a and c ) simulated the removal of the first right molar and the wounded bone structure , immediately after extraction .
bone morphology upon extraction results in the localised extraction sockets which vary between 2.0 and 4.5  mm   with a width decrease up to approximately 50% as well as an unchanged the mesial / distal attachment .
the healed tooth model ( models b and d ) incorporates the first right molar bone socket area of extraction after a 12-month healing period .
the fresh bone socket is healed with a pocket depth of 1.1  mm , width of 7.6  mm , and mesial / distal attachment levels of 0.3  mm .
this study will compare the mechanical strains within mandibular bone between the extracted and healed scenarios with prefixed prosthodontics and fpd situations .  
models a , b , c , and d ( figure 1 ) were the basis for the comparative fe analyses that were conducted in abaqus 6.6.1 ( abaqus , inc , providence , ri ) .
the models consisted of a 10-node quadratic tetrahedral solid mesh . to establish these four models ,
relevant convergence tests were performed to determine the best balanced accuracy and efficiency of numerical simulation , as in , which led to a global element edge length of 1  mm to ensure the sophistication of the models and an optimal computational cost . finally , models a , b , c , and d consisted of 124  196 ( dof : 897  516 ) , 115  675 ( dof : 836  202 ) , 124  520 ( dof : 900  975 ) and 116  781 ( dof : 847  851 ) quadratic elements , respectively .  
the models were subjected to occlusal forces which functionally varied for each tooth and the fpd .
loads of 50  n , 100  n , and 150  n were applied to the second premolar , first molar , and second molar , respectively ( figure 1 ) .
vaillancourt   suggested that an adequate functional loading of 50  n is sufficient for a premolar .
schwarz   stated that the molar region can endure mastication forces of up to 3 times greater than the force experienced in the canine region .
thus , mastication forces in this study are classified within an upper range of normal bitting forces [ 30 , 31 ] .
three - dimensional surface - to - surface contact with solid foods was modelled with a friction coefficient of 0.2 , as defined in abaqus ( figure 1 ) .  
all the materials were presumed linear , elastic , homogeneous , and isotropic for the analyses as widely adopted in existing literature [ 33 , 34 ] ( table 1 ) .
the periodontal ligament ( pdl ) stress - strain experienced in this paper is well fitted to the linear elastic range for the strains of higher than 5% but less than 20% .
although pdl is viscoelastic in nature , the isotropic elastic properties were assigned as the load response lies within the linear elastic range .
bone in this study is also modelled isotropically like previous studies [ 26 , 36 ] .
isotropic models of the mandible were able to distinguish meaningful strain differences when replicating functional loading , which have been widely accepted by clinicians when evaluating patients .  
the fe analyses of models a , b , c , and d primarily focused upon the stresses and strains within the alveolar and cortical bony tissues .
the biomechanical differences due to mastication in the pre - fpd and fpd cases are evident within the contiguous bone .
numerical values for strains in the extracted and healed cases were taken from distal , mesial , lingual , and buccal sites .
comparisons between the models were made through the von mises stresses , principal stresses , and equivalent strains .
firstly , von mises stresses were evaluated to provide distortion energies as an indicator to overall tissue deformation .
then , the first and third principal stresses were characterised to highlight tension and compression behaviours in these specific sites , where the nature of these stresses may affect bone remodelling .
finally , the equivalent strains were acquired to enable a measure of quantifying instigators into bone remodelling .
equivalent strain represents an aggregate elastic distortion within the bony tissues , which can be calculated from components of principal strains ( e 1 , e 2 , e 3 ) as follows : 
 ( 1)e=(12[(e1e2)2+(e2e3)2+(e3e1)2])1/2 . 
  according to frost 's remodelling theory ,
the equivalent strain is considered one of the most appropriate indicators of effectively predicting bone remodelling .
the finite element analyses indicated that the elevated von mises stresses occurred in the cortical ridges of functionally loaded teeth , suggesting high distortion energy distributions there .
the maximum von mises stresses are located around the second molar roots at the lingual site in model a and the distal region in models b , c , and d. their corresponding values are 37.5  mpa , 36.2  mpa , 27.3  mpa , and 23.3  mpa , respectively .  
the maximum first principal stresses in mandibular bone of models a and b ( without fpd ) were situated at the cortical ridge about the mesial aspect of the second molar , which were 10.2  mpa and 11.5  mpa , respectively .
it is noted that the freshly extracted case has a slightly lower tensile stress peak than the healed case .
the maximum first principal stresses in models c and d ( with fpd ) were located about the distal region of the second molar and were 25.1  mpa and 21.9  mpa , respectively , in which the fpd in the healed case presents a 15% lower tensile stress peak .
it is noted that all these first principal stress peaks are positive , indicating a tension in the surrounding areas .  
the maximum third principal stresses in the mandibular bone were situated in the lingual region of the cortical ridge in models a , b , c , and d , where the peak values were 58.1  mpa , 57.7  mpa , 16.9  mpa , and 15.5  mpa , respectively .
it is noted that all these third principal stress peaks are consistently negative , indicating a compressive nature at these sites .
a comparison of the first and third principal stress peaks about the first molar are summarised in table 2 .  
as shown in figure 2 , the peak equivalent strains on the ridged regions of the cortical bone were located in the lingual area in models a and b ( without fpd ) , showing 0.00132 and 0.00131 , respectively . in models c and d ( with fpd ) , the maximum equivalent strains were situated around the root apex of the second premolar , yielding 0.00785 and 0.00667 , respectively . the minimum equivalent strains models a , b , c , and d are 9.46  10 , 1.334  10 , 9.48  10 , and 2.267  10. it is noted that the equivalent strain in the ridged regions of the cortical bone is of primary interest in determining initiation of bone remodelling .
the corresponding average values for the equivalent strain in the mesial sides around the first molar region in models a , b , c , and d were 0.0002 , 0.0006 , 0.0005 , and 0.0012 , respectively , while they were 0.0006 , 0.0008 , 0.0013 , and 0.002 on the distal sides , respectively .  
tooth extraction significantly altered the equivalent strain concentrations around the first molar ( figure 3 ) .
the average lingual strains in models a , b , c , and d were 0.0002 , 0.0005 , 0.0002 , and 0.0004 , while the average buccal strains were 0.0001 , 0.0002 , 0.0002 , and 0.001 , respectively .
in order to gain understanding of the consequences of fpd treatment , it is essential to establish a sound knowledge of the physiological characteristics of all the supporting tissues within such an oral environment .
a fundamental design criterion for an fpd is to institute compatibility with its surrounding living tissues .
the vitality of bone about an fpd is of primary importance as the condition of bone can in turn affect the stability of the fpd considerably . from the clinician 's point of view , it is imperative that the selected abutment teeth for the fpd are supported by adequately healthy alveolar bone [ 41 , 42 ] .
however , it has remained unclear how the alteration of local oral condition induced by extraction of natural tooth and construction of fpd could affect the alveolar bone .
therefore there is a need to quantify the mechanical responses of alveolar bone due to construction of fpd . in this
study the stress and strain distributions were examined in the pre - fpd and post - fpd cases within the mandible .  
tooth extraction leads to immediate changes in local bone morphology and loadings , which consequently alter the biomechanical responses in the surrounding bone bed .
frost 's mechanostat theory suggests that the minimum effective strain ( mes ) in the range of 0.00080.002 enables the dynamics of bone turnover to reach equilibrium . in this study ,
the equivalent strains in the different scenarios yielded the strains within , above , and below frost 's bone adaptive mes remodelling range .
the fe analyses showed that the equivalent strains in the cortical ridge of the first molar in the mesial , distal , and buccal regions in model d ( healed with fpd ) were within the equilibrium range ( figures 4 and 5 ) . this is a realistic indication that an fpd treatment could better maintain an appropriate bone remodelling equilibrium , thereby preserving a healthy status of bone .  
it is also seen that models c and d incorporating the fpd undergo overall higher equivalent strain than models a and b ( figure 2 ) .
the higher magnitude of equivalent strains is evident and logical as the two abutment teeth are supporting a mastication load suitable for three native teeth .
thus the strains within the abutments will be significantly greater than its prebridgework counterparts as the loading condition has substantially increased . from figure 2 ,
the cortical strains in the freshly extracted tooth models a and c are observed to be much lower than their native counterparts   due to removal of part of mastication load , suggesting that resorption may occur around the cortical ridge .
the resorption is an expected outcome as upon extraction a reduction in ridge height subsequently follows .  
figure 5 also displays a considerable increase in strains around the apical third tooth root and root apex of the extracted tooth in models a and c. this higher strain concentration suggests that it would be a site of bone apposition .
this is a probable scenario as clinically upon extraction the process of bone healing involves the formation of bone within the extraction socket .
it can also be noted that with the presence of bridgework , the strains within the mandibular bone are noticeably higher due to restoration of normal masticatory function ( figure 2 ) .  

figure 4 
				 relates the equivalent strains to the mes remodelling range suggested by frost , where significant difference can be observed between the counterparts with or without the fpd construction .
model a suggests that resorption may occur in the mesial / distal / lingual / buccal areas of the cortical ridge , but apposition in root apex and about the root surface within the apical third .
model b indicates that resorption may appear in the mesial / lingual / buccal regions , making the buccal - lingual ridge thinner and lower .
model c ( fpd ) implies resorption in the mesial / lingual / buccal sites and remodelling equilibrium around distal region .
model d appears to perform best in terms of the effective strain level and shows possible occurrence of resorption on the lingual side only .  
since pdls are of special importance to bone remodelling , figures 6 and 7 provide the equivalent strain values observed within the pdls of the premolar and molar in all the models .
it is seen that the regions of bone resorption and apposition can correlate to those strains developed in the pdl .
nevertheless , the equivalent strains within the pdl are higher than those observed within the mandibular bone due to its much lower young 's modulus .   to better observe the strain distribution in pdl , figure 8 plots the equivalent strains in the different regions versus the distance from the root apex .
it is shown that in all dentitions , the highest equivalent strains are at the root apex .
in addition , the equivalent strains in the prebridgework models are considerably lower than those in the fpd - models .
this is a realistic outcome as the two abutments are supporting a masticatory load of three dentitions after the fpd treatments .
quantifying the response within the pdl can provide the indicators as to whether the appropriate mechanical signals are indicative to bone remodelling .  
furthermore , the anticipation of bone resorption in the extracted models a and c can be seen as a step in the healing process of extraction as alveolar bone atrophy posttooth extraction is a well - known phenomenon [ 44 , 45 ] . from figure 3 , it is noted that the fpd treatment results in the fresh extraction site experiencing a considerably higher equivalent strain , thereby somewhat better preserving the ridge height and reducing bone loss .
as summarized in table 3 , considerable better apposition volumes ( in percentage ) can be anticipated in the bridgework models c and d. much greater bone volumes , 45.93% and 40.57% , respectively , in the freshly - extracted fpd and healed fpd models , reach the equilibrium of bone turn - over , compared with much higher resorption volumes of 86.20% and 86.97% in the corresponding non - fpd models .
this clearly indicates the primary importance of timely fpd treatment , not only for restoring the normal masticatory function but also for maintaining bone quantity and quality .  
the present study defines the initial biomechanical responses and possible adaptive changes within surrounding bone with or without construction of fpd .
it is revealed that the application of an fpd leads to a noticeable alteration in normal stress / strain patterns undergone within the alveolar bone . as a consequence ,
this paper suggested that the response of the bone - fpd interface ( pdl and adjoining bone ) to functional load is crucial to the long - term success of the prosthetic treatment .
this initial status of biomechanics can be associated with specific biological cellular reactions as a consequence of biomechanical stimuli .
the results provide supportive evidence that an fpd treatment in a healed extraction site would help maintain a proper equilibrium of bone turnover .
enumerating the adaptive ability of bone to multiple respective loading situations attained by using remodelling processes and bone remodelling algorithms will be our future work .
 an understanding of functional responses in oral bone is a crucial component of dental biomechanics . 
 the purpose of this study was to investigate the potential biological remodelling response during mastication on the mandibular pre- and post - insertion of a fixed partial denture ( fpd ) . 
 a series of three - dimensional ( 3d ) finite element analysis ( fea ) models were presented pre- and postextraction to determine the biomechanical responses to masticatory loading in the anterior mandible . 
 equivalent strains were analysed at lingual / buccal and mesial / distal areas of the premolar to molar region and quantified to anticipate bone remodelling response . 
 mandibular bone incorporating an fpd experienced substantially greater stress / strain magnitudes than that prior to placement of fixed prosthodontics , which is suggestive of engagements of bone remodelling . 
 the results suggest similar outcomes to those reported clinically . developing a simulation reflecting the outcomes of restorative treatment can provide meaningful insight into restorative treatment planning , clinical outcomes , and fixed prosthodontics designs . 
1. Introduction
2. Material and Methods
3. Results
4. Discussion