micromotion of dental implants has been defined as minimal displacement of an implant body relative to the surrounding tissue which can not be recognized with the naked eye   ( figure 1 ) . various authors have shown that excessive micromotion may interfere with the process of osseointegration of dental implants [ 2 , 3 ] . although exact data are missing , it has been postulated that micromotion between implant and bone must not surpass a threshold value of 150 micrometer ( m ) for successful implant healing [ 46 ] . in traditional loading protocols , where implants are allowed to heal undisturbed for periods of several months , the issue of implant micromotion is of limited importance . with the advent of modern treatment concepts including early and immediate loading of dental implants [ 7 , 8 ] , with implants being restored early in the healing phase , the issue of implant micromotion has gained significant importance [ 4 , 5 ] . numerous reports trying to relate clinical parameters to the phenomenon of implant micromotion can be found in the dental literature [ 811 ] . the nonuniform nomenclature , the varying experimental settings , and the partially contradicting results presented on the one hand indicate the complexity of the topic but on the other hand emphasize the need for clarifying basic engineering principles . from a biomechanical perspective , successful osseointegration of dental implants depends on the way mechanical stresses and strains are transferred to the surrounding bone and tissues . the multiple factors hereby affecting stress and strain transfer include the type of loading that occurs , the type of implant - bone interface being present , the length and diameter of the implant , implant geometry and its surface texture , and the quality and quantity of the surrounding bone [ 1319 ] . only by understanding the most critical of these variables , strategies for optimizing implant stabilization can be developed . for determining how implant mobility , often referred to as micromotion , relative motion , micromovement , and so forth , or implant loading affects bone response , a closer look at implant deformation , bone deformation , and stress or strain at the implant - bone interface is required . in this context , it was the purpose of this paper to mechanically describe the phenomenon of micromotion occurring between implant and alveolar bone using simple spring models , continuum mechanics models , and 3d - finite - element models simulating varying contact types between implant and bone [ 2123 ] . three basic scenarios reflecting different anchoring situations of dental implants were considered . in scenario 1 , the implant rests on an apically located fixed surface but neither has contact to cortical bone nor to trabecular bone at the vertical walls of the implant ( figure 2 ) . in this situation , maximum implant deformation under vertical loading occurs in the coronal part and diminishes gradually towards the apex . as a result , micromotion between the implant and the vertical walls of the socket also decreases towards the apical part of the implant . axial deformation of the implant as a consequence of vertical loading can be calculated according to 
 ( 1)u = fea / l = fc 
 with f standing for the vertical force applied , e being the young 's modulus of the implant , a being the cross section of the implant , l being the length of the implant , and c being the stiffness of the implant . maximum micromotion uc  at the cortical area can then be calculated according to 
 ( 2)uc=ulh 
 with h reflecting the height of cortical and trabecular bone around the implant . for scenario 2 , the fixed apical rest of the implant was altered by adding a layer of elastic trabecular bone apically to the implant . here , an axial force acting on the implant predominantly causes compression of the elastic material the implant is resting on . due to the drastically smaller elastic modulus of trabecular bone as compared to titanium , the deformation of the implant can be neglected and the relative movement between implant and bone is independent from the region of the implant considered ( figure 3 ) . in this situation , implant displacement may be calculated according to 
 ( 3)u = fesa / h[1+lhese]=fcs[1+ ] , 
 where es is the young 's modulus of the trabecular bone and h the height of the bone underneath the implant . taking into account that the young 's modulus of the implant is much greater than the young 's modulus of the trabecular bone ( e  es )  it is accepted   1  and furthermore the approximation for the micromotion 
 ( 4)uc=ufcs. consequently , micromotion at the cortical area of the implant and the relative micromotion between implant and bone are identical , both being related to the stiffness cs- of the trabecular bone underneath the implant . further approximating the clinical situation of an osseointegrated implant , in scenario 3 the implant is elastically supported by surrounding cortical and trabecular bone . due to the fixed contact between implant and bone , micromotion at this interface neglecting the deformation of the implant ( e  es ) the implant displacement may be calculated according to 
 ( 5)u = fcs1(1+(cs / cs)+(cc / cs ) ) . under the circumstances of scenario 3 , no relative micromotion between implant and bone exists . the displacement of the implant equals the micromotion depending on the stiffness of both cortical and trabecular bone surrounding the implant . further approximating clinical reality , continuum mechanics models were considered revealing implant displacement due to elastic deformation of bone when no contact between implant and bone was modelled in a plane strain fe - model ( figure 5 ) . this model correlates with scenario 2 described above ( figure 3 ) . simulating contact between implant and bone , bone is also elastically deformed in the cervical portion of the implant when an axial load is exerted ; however , no relative micromotion between implant and bone occurs at the interface ( figure 6 ) , and the implant displacement ( micromotion ) is related to the elastic properties of the cortical and trabecular bone . for a more realistic representation of clinical conditions , three - dimensional fe models   of dental implants with and without threads were generated ( figure 7(a ) ) which were subsequently embedded in a bony socket consisting of cortical and trabecular bone and an intermediate layer surrounding the implant ( figure 7(b ) ) . the geometry of the models was generated with a cad program ( solidworks 2011 , solidworks deutschland gmbh , haar , germany ) and imported in a fe program ( ansys workbench 12 , ansys inc . , canonsburg , pa , usa ) . combining both components , three - dimensional fe models ( figure 7(c ) ) were obtained for evaluating micromotion between implant and bone when an axial vertical force of 200  n was exerted which reflects an average biting force [ 24 , 25 ] . different stages of osseointegration were simulated by altering the elastic modulus of the intermediate bone layer [ 2123 ] . the contact type between implant and bone could be modified as friction free , only transferring compressive forces and allowing for sliding and gap formation , to friction ( friction coefficient 0.3 ) and force fit , respectively . in general , isotropic linear model parameters were applied , defining the contact type between the different layers of bone as  bond .  out of the large number of possible solutions for solving contact problems , the augmented lagrange method was chosen as accompanying optimization method . this method was applied for defining all contacts not allowing contacting components to penetrate each other . based on the results of previous investigations [ 22 , 23 ] indicating that the size of the models was sufficient for evaluating micromotion , model dimensions were reduced to a minimum and the borders of the models were fixed . depending on model type , 160000 hexaeder elements and 600000 to 650000 nodes were used to set up the models using the elastic modules given in table 1 . based on the fact that the elastic values and the strength limits of biologic materials in vivo  such as the bone - implant interface  are highly complex , only two states of osseointegration were considered ( starting point and end point of osseointegration ) . these different states were modelled by different elastic values in the areas ( 1 ) and ( 2 ) in figure 7(b ) . results of all simulations were recorded as von mises equivalent stress in addition to contour plots of global displacement .   for calculating relative displacement between implant and bone ( relative micromotion ) , a total of six corresponding nodes at the implant bone interface were established as reference marks . as the displacement of a specific reference mark on the implant represents both displacement of bone and implant , the displacement of the corresponding reference mark on the bone ( figure 8) was subtracted . simulating 200  n axial force acting on an osseointegrated cylindrical implant with no friction between implant and bone caused a symmetric loading situation of the bone surrounding the implant with maximum loading and maximum displacement occurring at the apical part of the implant ( figures 9(a ) and 10(a ) ) . adding threads to the implant led to a decrease both in loading and displacement occurring at the apical part of the implant . simultaneously , greater distribution of loading and displacement was observed at the vertical walls of the implants ( figures 9(b ) and 10(b ) ) . introducing friction between implant and bone ( figures 9(c ) and 10(c ) ) further decreased global displacement and resulted in a more homogeneous distribution of loads as compared to the force fit situation ( figures 9(d ) and 10(d ) ) , where load transfer predominantly occurred in the cervical area of the implant , where cortical bone was modelled . for freshly inserted implants with a soft intermediate layer of bone modelled around the implants , the introduction of a friction coefficient led to a considerable reduction in micromotion between implant and bone as well as to reduced displacement of all reference marks on the implant . overall , comparable values for micromotion were recorded at all corresponding reference marks ( figure 11 ) . simulating an osseointegrated implant in general reduced all displacement values by about 50% compared to the situation of a freshly inserted implant . again the introduction of a friction coefficient led to a considerable reduction in micromotion between implant and bone as well as to reduced displacement of all reference marks on the implant . in contrast to a freshly inserted implant , the distribution of micromotion depended on the location of the reference mark . whereas in the cervical aspect some minor micromotion in the range of 0.75  m could be found , at the most apical reference almost no relative displacement between implant and bone occurred ( figure 12 ) . within the limitations of this investigation , the effect of friction phenomena and implant design ( cylindrical versus threaded ) on stress distribution and implant displacement could be demonstrated . both the introduction of friction between implant and bone as well as the addition of threads to a cylindrically shaped implant resulted in the reduction of implant displacement under an axial load of 200  n. simultaneously , a more homogeneously distributed loading situation at the implant bone interface could be observed . changing the contact type between implant and bone to force fit resulted in load transfer predominantly occurring in the cervical part of the implant surrounded by stiffer cortical bone . this is in strict contrast to a situation with no friction modelled resulting in maximum loading of bone surrounding the periapical region of the implant . from a clinical perspective , these findings indicate that screw - shaped implants are advantageous while bone quality probably plays the most important role in achieving sufficient primary implant stability for immediate loading . based on a comparison of freshly inserted and osseointegrated implants it could be shown that the healing status affects the occurrence of micromotion phenomena along the implant bone interface . for a soft implant bone interface , reflecting early stages of osseointegration , micromotion remained on a constant level regardless of the location considered . simulating mature bone reflecting an osseointegrated implant , the introduction of a friction coefficient between implant and bone dramatically changed the distribution of micromotion along the implant bone interface . in addition to generally reduced levels of micromotion as compared to a freshly inserted implant , a decrease in micromotion was noted . it may be seen as a limitation of this study that only one specific value for axial loading of the implants was chosen . based on studies by brunski and coworkers , axial components of biting forces can range from 100 to 2400  n , while the exact values depend on factors such as location in the mouth and nature of food . for patients having implant - supported dentures , axial closure forces ranging from 45 to 255 furthermore , besides the pure mechanical aspects addressed in this paper , also biologic factors play an important role in the process of osseointegration of dental implants . following implant placement , the healing period starts with the adherence of serum proteins , followed by the attachment and proliferation of mesenchymal cells . bone remodeling occurs as an adaptation to the implants environment . with these processes occurring simultaneously to mechanical loading in an immediate loading situation , the interaction of both mechanical and biologic factors seems to be critical to the integration of the implant . given the nonuniform distribution of micromotion between implant and bone , it appears questionable whether currently available methods for experimentally determining this phenomenon provide meaningful data . the only valid approach for evaluating micromotion phenomena at the implant - bone interface appears to be finite element analysis . however , care has to be taken to set proper materials and interface characteristics as these parameters may greatly influence the outcome .
micromotion of dental implants may interfere with the process of osseointegration . using three different types of virtual biomechanical models , varying contact types between implant and bone 
 were simulated , and implant deformation , bone deformation , and stress at the implant - bone interface were recorded under an axial load of 200  n , which reflects a common biting force . without friction between implant and bone , a symmetric loading situation of the bone with maximum loading and displacement at the apex of the implant 
 was recorded . 
 the addition of threads led to a decrease in loading and displacement at the apical part , but loading and displacement were also observed at the vertical walls of the implants . introducing friction between implant and bone decreased global displacement . in a force 
 fit situation , load transfer predominantly occurred in the cervical area of the implant . for freshly inserted implants , 
 micromotion was constant along the vertical walls of the implant , whereas , for osseointegrated implants , the distribution of micromotion depended on the location . in the cervical aspect some minor micromotion in the range of 0.75  m could be found , while at the most apical part almost no relative displacement between implant and bone occurred .