Patent Abstract:
medical implants with non - equilibrium surface structures are disclosed . the surface treatment of the implants greatly enhances osseointegration , reduces time to recovery following implant surgery , reduces surgery - related infections , and improves outcomes . the implants , including dental implants and other implants for insertion into or attachment to bone , are applicable to treatment of a wide variety of medical conditions . the methods of altering the surface properties of medical implants include exposure of a crystalline surface material , such as metal or ceramic , to a short burst of high thermal energy or shock , resulting in the introduction of a non - equilibrium concentration of crystal lattice defects in a surface layer .

Detailed Description:
the critical phenomena occurring early in the osseointegration of a medical implant are heavily dependent on surface energy and adsorption of various chemical species to the surface of the implant that interfaces with bone . this invention provides novel methods to physically engineer and / or alter the surface energy , wettability , or adsorption characteristics of the implant material to enable better performance in terms of these physical phenomena and to ensure prompt and reliable osseointegration of the implant . one aspect of the invention is a method of treating a medical implant so as to promote protein adsorption and osseointegration . a medical implant is treated at an exposed surface of a crystalline surface material of the implant . treatment includes the application of a physical form of energy that is capable of causing structural defects and alterations in a surface layer of the crystalline surface material , and can also produce changes in the structure of the exposed surface itself . the changes in the surface layer and / or surface structure promote more rapid and more numerous adhesion of proteins and cells and accelerate the osseointegration process for implants that interface with bone . the medical implant can be any physical structure intended for surgical implantation into the body of a human or animal patient . especially preferred are medical implants that interface with bone when implanted in the patient , such as dental implants , joint replacements ( e . g ., hip , knee and other joint replacements inserted at one or more points into bone tissue ), prostheses inserted into bone , and various types of surgical hardware such as screws , rods , or plates ( e . g ., for facial or skull reconstruction ) that are designed for insertion into bone . the medical implant can be of homogeneous construction , i . e ., composed of one type of material , either pure or an alloy or composite , or of heterogeneous construction , i . e ., composed of different parts or sections having different types of materials . the medical implant and / or the crystalline surface material , can include or essentially consist of a metal or ceramic material , such as titanium , titanium oxide , alloys including titanium ; zirconium , zirconium oxide , alloys including zirconium ; aluminum , aluminum oxide , alloys containing aluminum ; cobalt - chromium alloys ; any of the 300 series stainless steels ; any of the 400 series stainless steels ; calcium phosphate , or hydroxyapatite ; or any combination thereof . the crystalline surface material can be a separate material that is bonded with a substructure or bulk material of the implant , or the crystalline surface material can be a surface region of a homogeneous or bulk material of the implant . the crystalline surface material contains a substantial fraction of a crystalline phase . preferably , the crystalline surface material is substantially entirely crystalline at least in a region at and near a surface of the implant to be treated to promote osseointegration . however , the crystalline surface material can contain an equilibrium concentration of crystal lattice defects prior to treatment according to the invention . after treatment according to a method of the invention , the crystalline surface material will contain at least a portion that has a non - equilibrium concentration of crystal lattice defects . crystal lattice defects for use in the invention include vacancies , dislocations , disinclinations , steps , and grain boundaries . vacancies are a preferred crystal lattice defect . the treatment according to the invention may be applied over the entire surface of the implant or only over one or more portions of the surface . preferably , the treatment is applied over the full extent of the implant surface that is intended to interface with bone . the treated surface includes or is entirely composed of the crystalline surface material as described above . treating the surface includes applying an energy source to the crystalline surface material so as to rapidly heat or shock the material . suitable energy sources that heat the material include pulsed or continuous ion beams , pulsed or continuous electron beams , pulsed or continuous lasers , and electric arcs . energy sources that induce a shock wave in the material include pulsed lasers , pulsed ion beams , and pulsed electron beams . shock energy sources can be differentiated from heat sources in that the creation of defects by shock is caused by homogeneous nucleation of the defects directly through the application of a high applied stress ( i . e ., a shock wave ). this is a physically different mechanism from thermally generated crystalline defects , which follow the arrhenius rate equation for thermally activated phenomena . shock waves produce mechanically induced defects without appreciable heating . the shock produces a pressure pulse which directly increases the internal energy of the solid through a material constant known as the grueneisen constant . this rise in internal energy over very short time periods allows the spontaneous nucleation and formation of lattice defects . furthermore , shock deformation produces a very dense dislocation tangle network in its wake — an additional source of crystal defects in the shocked region that resists annealing during subsequent heat treatment and is far in excess of the defect density possible using conventional means of surface deformation such as rolling , burnishing , or media blasting ( leslie 1973 ). the energy input to the crystalline surface material is generally of high intensity and brief duration . for example , an ion beam or electron beam source is preferably operated in the range of 100 kv ( kilovolts ) to 10 mv ( megavolts ) for the beam voltage , 1 a ( amp ) to 1000 a for the beam current , and is applied to the crystalline surface material for a duration of about 10 nanoseconds to about 100 microseconds . a pulsed laser pulsed can have a pulse width from about 10 picoseconds to about 1 millisecond , a pulse energy from about 1 picojoule per pulse to about one joule per pulse , wavelength from about 375 nm to about 1550 nm , and a pulse repetition rate from a single pulse to about 1 million pulses per second . multiple pulses can be delivered either as one continuous train of pulses , or as plural packets separated by a rest interval . in order to produce a shock wave by pulsed laser , the pulses must be spaced such that there is sufficient time for the material to cool between pulses , or to avoid excessive heating so that the pulsed mechanism of generating defects using shock waves does not default to the thermal method of generating defects using rapid heating and quenching . this time delay may be estimated from the characteristic heat conduction time , which is given by : where x is a characteristic length in cm and α is the thermal diffusivity of the material in units of cm 2 / s . for example , for titanium , the thermal diffusivity is 0 . 042 cm 2 / s . the characteristic length depends on both the surface area irradiated by the beam as well as the average depth of the zone directly affected by the heat source in question . therefore , the cube root of this affected volume may be taken as a representative characteristic length . for example , using a pulsed ion or electron beam with an energy of 500 kev , the spot size may be as large as 5 mm , but the depth directly affected by the laser will be very shallow and will be on the order of 1 to 5 micrometers or less ( dave , 1995 ). therefore the characteristic volume for this case is the area of the spot times the depth , or 1 × 10 − 4 cm 3 . taking the cube root , we get 0 . 05 cm as a characteristic length . therefore using equation 1 we calculate that to avoid excessive heating , it would be preferable to space pulses such that the pulse interval is no shorter than 0 . 015 seconds , which corresponds to a maximum pulse frequency of 67 hz . if the heat sink conditions are not ideal and heat extraction from the implant is poor , it is preferable to pick a much lower pulse rate than the highest allowable to ensure proper removal of heat in between pulses and to make sure the process operates in a purely mechanical as opposed to thermal regime for defect generation . treatment with a high energy beam or laser is preferably carried out in an environment that is essentially oxygen free , such as in a vacuum or in the presence of an inert gas ( e . g ., nitrogen , argon , or another inert or noble gas , or a mixture of such gases ). the presence of oxygen during the treatment would produce undesirable chemical reactions , such as the formation of oxides , which could alter the implant material or its crystalline structure . the surface layer to be treated , or formed during treatment , is a thin layer located at an exposed surface of the implant . the surface layer can have a thickness from about 10 nanometers to about 25 microns , or is less than about 10 microns . a surface layer thickness of about 10 microns is preferred . a surface layer that is too thin will not provide a significant effect on protein adsorption or osseointegration , whereas a surface layer that is too thick can alter the physical properties of the implant , or could promote delamination from the bulk material of the implant . in one embodiment of a method of treating a medical implant , the implant is first treated with an energy source as described above so as to heat the crystalline surface material and form a surface layer that includes crystal lattice defects . the surface layer material can include an equilibrium concentration of crystal lattice defects prior to heating , where the equilibrium concentration is established by the process of fabricating the implant ( e . g ., by an ordinary metal annealing process ). however , during the heating step , a higher , non - equilibrium concentration of crystal lattice defects is produced in the surface layer . following the heating step , the surface layer is thermally quenched so as to preserve a non - equilibrium concentration of crystal lattice defects in the surface layer . the heating step is accomplished using one or more of the energy sources described above . the quenching step is necessary in order to prevent the material from re - establishing equilibrium and thus to preserve the non - equilibrium concentration of defects . thus , thermal quenching must be more rapid than the approach to equilibrium . the speed of thermal quenching can be calculated as described below . in many cases , sufficiently rapid thermal quenching can be accomplished by rapidly removing or turning off the energy source and allowing the thermal energy within the surface layer to dissipate within the attached bulk material by conduction . equilibrium and non - equilibrium concentrations of such defects can be calculated based on the material and conditions used , as described below . these concentrations also can be directly measured by visualization of the crystalline structure of the treated or untreated surface layer , or a portion thereof , using transmission electron microscopy . for example , a thin section of the surface layer can be cut out using an ion beam , and the section can be placed into a transmission electron microscope , with which the individual atoms and their arrangement can be seen . using the electron microscope , defects in the lattice structure can be counted in a known volume of the material to give the defect concentration . in another embodiment of treating a medical implant , shock deformation of a crystalline surface material is performed . the shock deformation creates a shock wave in the crystalline surface material , resulting in the mechanically - induced formation of a non - equilibrium concentration of crystal lattice defects in a surface layer of the material . the foregoing methods of treating a medical implant may induce surface structural alterations in addition to producing a non - equilibrium concentration of crystal lattice defects . typically , the surface structural modifications result in the smoothing of the surface , with the elimination of all or nearly all surface features ( i . e ., structures protruding above the surface plane ) and surface voids ( i . e ., structures dipping below the surface plane ) having an average or root mean square size ( i . e ., diameter ) of about 10 microns or less , or in some embodiments 5 microns or less . surface features or voids larger than about 5 or 10 microns in size remain generally unaffected , and are available as a residual surface roughness that can be useful in promoting osseointegration . however , removal of small surface features and voids can improve the performance of the implant by removing points where contamination with inorganic or organic matter ( including microbes ) can accumulate . the smoothing of a medical implant surface on a fine length scale ( i . e ., removal of surface features of less than 5 or 10 microns in size ) is thought to contribute significantly to reducing inflammation following implantation surgery . such small surface features are potential sites for trapping both organic and inorganic contamination . their removal thus reduces the extent of the immune response required to eliminate these contaminants . the treated implant therefore presents a cleaner or more readily cleanable surface . the surface structure of a medical implant can be determined using scanning electron microscopy ( sem ) or atomic force microscopy . comparison of the surface structure using these methods before and after the treatment process can be used to determine the effects of the treatment on surface structure . a characteristic of the methods of treating a medical implant according to the invention is that they result in the formation and preservation of a non - equilibrium concentration of crystal lattice defects in a surface layer . in some embodiments of these methods , the surface layer formed by the treatment is disposed at the surface of the implant , and resides above and optionally in direct contact with a bulk material layer that does not have a non - equilibrium concentration of crystal lattice defects , but instead has an equilibrium concentration of crystal lattice defects , or is essentially devoid of crystal lattice defects . the present invention also contemplates medical implants made by any of the foregoing methods of treating the surface of the implant . medical implants according to the present invention have several advantageous properties . they possess a surface layer which contains a non - equilibrium concentration of crystal lattice defects . those defects , which are present at a higher concentration than found in conventional implants , promote more rapid and more extensive protein binding to the implant , which in turn leads to cell attachment and eventually to the firm attachment of bone tissue to the implant ( osseointegration ) as well as adhesion to neighboring tissues such as skin , cartilage , connective tissue , and other tissues . the surfaces of conventional implants contain only an equilibrium concentration of crystal lattice defects , because they are made by processes that allow the concentration of such defects to reach equilibrium . the equilibrium concentration of defects in near surface layers of conventional implants promotes protein adhesion , cell adhesion , osseointegration , and tissue adhesion to a lesser degree than the implants of the present invention . another aspect of the invention is a method of treating a medical condition . the method includes implanting into a human or animal patient , such as by surgery , a medical implant that has been treated by any of the methods of the invention . the method can include further steps , such as testing for or monitoring the progress of osseointegration or the presence of infection after the implant surgery . the medical condition can be any condition requiring the use of a medical implant in a patient , such as an implant that interfaces with bone . thus , the medical condition can be the insertion of a dental implant into a jaw bone , the replacement of a joint such as a hip joint , or the repair of a bone fracture . the methods described herein encompass a wide range of length scales and physical phenomena ranging from the sub - angstrom level to the millimeter scale . examples include : the fundamental physics of metals ( angstroms ); surface thermodynamic and quantum - mechanical properties ( angstroms and below ); molecular processes at bone contact surfaces ( angstroms to nanometers ); protein adsorption to bone contact surfaces ( nanometers ); cellular attachment to protein scaffolds ( micrometers ); and bone growth , mineralization , and eventual attainment of full biomechanical stability of the implant ( micrometers to millimeters ). the bulk energy and the surface energy of a crystalline surface material can be altered by the presence of crystalline defects . one such defect is called a vacancy . crystalline vacancies are the absence of an atom on a lattice . this is shown in fig1 in the case of a two dimensional lattice as an example . the crystal lattice 1 is a regular array of atoms with a specified symmetry . vacancies can either occur at the surface 2 or in the interior 3 of the crystal . location 4 in fig1 represents an interstitial atom , or an atom that has been displaced from the lattice and now occupies a site between other atoms , or an interstitial site . when a vacancy forms , the atom that used to occupy the vacancy site either becomes an interstitial atom or jumps to another vacancy site . this combination of a vacancy and an interstitial is known as a frenkel pair ( kittel 2005 ). vacancies have a specific energy of formation . at a given temperature , there is an equilibrium concentration of vacancies as specified by conditions of thermodynamic equilibrium . this concentration is given by ( haasen 1986 ): where c v is the equilibrium concentration of vacancies at absolute temperature t , e vf is the free energy of formation of a vacancy , s vf is the entropy of formation of the vacancy , and k is the boltzmann constant . when a metal surface is suddenly subjected to a large temperature pulse over a very short period of time , the equilibrium vacancy concentration would rise quickly according to equation 1 . this rapid heating will create frenkel pairs . in order to determine how fast these frenkel pairs can form on rapid heating of a crystal , it is first necessary to estimate the time needed to get to equilibrium . the first assumption for an equilibrium time might be made based on the phonon spectrum of the crystal . the phonon spectrum , or the total assembly of quantized states of vibration of a crystal , approaches equilibrium on the order of 10 − 11 sec ( seitz and koehler 1956 ). point defects however take longer to form since there has to be a vibration fluctuation of sufficient strength to knock the atom out of its lattice position . an equation describing the rate of frenkel pair generation is given by ( koehler and lund 1965 ): where c pair is the concentration of frenkel pairs , w is a characteristic atomic vibration frequency which is typically taken to be 10 13 ( kittel 2005 ), e pair is the energy of pair formation , t is the absolute temperature , and k is the boltzmann constant . for titanium , the energy of formation of a vacancy in equation 1 is 1 . 2 electron volts or ev ( novikov et al 1980 ), but the energy of formation of a frenkel pair in equation 2 is higher , between 3 and 5 ev ( he and sinnott 2005 ). assuming that the temperature to which the metal surface is raised is 1273 k ( 1000 c ), then according to equation 2 the rate of generation of frenkel pairs is approximately 79 . 6 per second . the equilibrium concentration of frenkel pairs is given by ( koehler and lund 1965 ): substituting in the values shown above , the equilibrium concentration is approximately 1 × 10 − 6 or 1 ppm . therefore , dividing this number by the frenkel pair generation rate , the equilibrium time is estimated to be 1 . 45 × 10 − 8 seconds , or on the order of tens of nanoseconds . at lower temperatures , this equilibrium time will be longer . for example , at 700 c or 973k , this equilibrium time is on the order of 1 microsecond . at the melting point of titanium , the equilibrium time is much shorter , and is approximately 1 × 10 − 10 sec , or a tenth of a nanosecond . therefore it is seen that the time required to reach an equilibrium concentration of vacancies varies from a tenth of a nanosecond at the melting point to close to a microsecond at one half the melting point . after a supersaturation of vacancies is created , the vacancies tend to anneal out to try to reduce the free energy of the system . alternatively they tend to form lower energy cluster configurations . therefore , the faster the quench rate , the more likely the supersaturated vacancy concentration is to be preserved . kauffman and smith ( 1965 ) have studied this effect and found that a quenching temperature or cooling rate of 10 4 degrees k per second or higher would be expected to avoid excessive vacancy annealing and to maintain the highly non - equilibrium microstructure produced in the method of the present invention . surface defects such as steps , vacancies , dislocations , disinclinations , and grain boundaries are known to play an important role in controlling the mechanical and chemical properties of surfaces . with regards to adsorption , modification of the electronic density and the electronic potential around defects leads to different adsorption behavior as compared to the rest of the surface ( persson 1992 ). the adsorption of atoms and molecules to defect sites can be understood qualitatively by considering that adsorbed atoms help to “ complete ” the missing electron density at the defect sites . this can be done either through an electrostatic interaction , such as physical adsorption through weak van der waals forces , or chemisorption through the formation of covalent bonds between adsorbed atoms and a metal ( or metal oxide ) surface ( feibelman et al 1996 ). some previous work ( vakarin 2003 ) has found a correlation between the number density of free defects and the adsorbate cluster size . such a specific size effect modifies the thermodynamic and kinetic properties ; for example , the adsorbate surface diffusion coefficient is proportional to the density of free defects . the preferential binding of adsorbate atoms to defect sites is schematically illustrated in fig2 . in the first view , the surface of the metal is schematically portrayed as a lattice consisting of sites with no defects 5 and defect sites 6 . adsorbed molecules 7 first attach to the defect sites . as more molecules adsorb to the surface , the adsorbed layer grows out in islands 8 from the initial nucleation sites and begins to fill up the surface . eventually the entire metal surface is covered with adsorbed molecules 9 . protein adsorption is dominated by considerations of surface energy , intermolecular forces , ionic , and electrostatic interactions , in addition to considerations of hydrophobictiy or hydrophillicity . proteins are biological heteropolymers that are composed of amino acid units . certain amino acids have a side chain that may be charged based on the details of the solution chemistry ( e . g ., ph , ionic strength ) and environment it is in . it is through these charged amino acid side chains that proteins are able to adsorb to multiple sites on a metal surface ( dee 2002 ). as shown schematically in fig3 , protein adsorption is dependent on both the properties of the molecule 10 as well as of the surface 11 . see dee ( 2002 ). with respect to protein adsorption on medical implant surfaces , the effect of surface roughness is well - documented and leads to approximately a 30 %- 50 % increase in the adsorption kinetics ( rechendorff 2006 ). the interaction of a protein molecule with a surface is dominated by the amino acid interactions . a larger protein 12 has more links with the surface made by the amino acids 13 as compared to smaller proteins 14 and 15 . this is schematically shown in fig4 . it is expected that the increased surface energy will provide more energetically favorable sites or activated sites for amino acids to attach to , again speeding up the kinetics of protein adsorption . alternatively , in proteins that are folded but have less stability of the folded state , the increase in the number of surface active sites may in fact encourage folded proteins to unfold and become adsorbed to the surface through additional amino acid chain interactions . see dee ( 2002 ). wound healing around a dental implant is characterized by three distinct phases : initial formation of blood clot occurs through a biochemical activation , followed by cellular activation , which in turn is followed by a cellular response ( stanford and schneider 2004 ). the various events occurring at the implant interface include the following ( see also anil et al 2011 and ramazanoglu et al 2011 ): 1 ) dental implant surfaces come into contact with various blood components during surgery . 2 ) the blood wets the dental implant much as any viscous fluid will wet a metal surface . 3 ) various proteins get adsorbed onto the metal surface . 4 ) the most important of these proteins is human plasma fibrinogen ( hpf ), which partakes in blood coagulation , facilitates adhesion and aggregation of platelets ( silvennoinen et al , 2011 ). 5 ) fibrinogen is converted to fibrin . 6 ) complement and kinin systems get activated . 7 ) migration of bone cells will occur through the fibrin of a clot . 8 ) since fibrin is adherent to the metal surface , migration of osteogenic cell populations towards the metal surface will occur . 9 ) migration of these cells will however cause retraction of the fibrin scaffold . 10 ) therefore the ability of the fibrin scaffold to strongly adhere to the metal surface during the phase of wound contraction is critical to determining whether or not the migrating cells will reach the implant surface . 11 ) platelets are activated as a result of interactions of platelets with the implant surface . 12 ) thrombus formation and blood clotting results . 13 ) platelets are the source for growth and differentiation factors which act as signaling molecules for recruitment and differentiation of undifferentiated mesechymal stem cells at the implant surface . 14 ) other proteins which could promote cell adhesion and osseointegration include fibronectin and vitronectin . this list is not intended to provide a complete picture of all of the possible processes involved during the osseointegration process . the time dependence of these various physical , chemical and biological processes for a dental implant is shown in anil et al 2011 . despite the considerable complexity of this physical - chemical - biological sequence of events , the essential steps within the first six days after implantation are wetting of the metal surface by blood and plasma components and the concomitant adsorption of proteins to the metal surface . both of these phenomena are heavily influenced by surface energy and surface science considerations . in view of this osseointegration process , three objectives of the present invention are : 1 ) to improve wetting and wettability of the surface through alteration of the surface energy by introduction of a non - equilibrium concentration of crystal lattice defects ; 2 ) to improve adsorption of proteins through creation of a non - equilibrium surface concentration of defects which serve as preferred adsorption sites ; and 3 ) to smooth the surface at dimensions less than several microns so as to seal up sites which could trap organic and inorganic contaminants . the first mechanism by which the non - equilibrium defect concentration in the near - surface layer on the metal medical implant can be created is through rapid thermal surface treatment . fig5 shows the sequence of a heat source 16 interacting with the surface of the metal medical implant 17 . a region of heated material 18 is created in the zone directly affected by the heat source . the heat source can be one of the following : an ion beam , operating in pulsed or continuous mode ; an electron beam , operating in pulsed or continuous mode ; a laser , opeating in pulsed or continuous mode ; or an electric arc , operating with straight or reverse polarity . the timeframe for the heat source to interact with the crystalline surface material must be fast . the on - heating equilibrium time for the vacancy concentration to reach the value for the elevated temperature is given by considering equations 2 and 3 and can vary in general from as small as 10 nanoseconds at temperatures approaching the melting points of most common engineering metals , ceramics , and alloys to as large as 100 microseconds at temperatures at one half to one third of the melting point for most commonly used engineering metals , ceramics , and alloys . therefore , the preferred characteristics of the heat source would be an interaction time of about 10 nanoseconds to about 100 microseconds . a short pulse is required to limit the depth of material that is heated or melted , so that the heat accumulated in the surface layer can be quickly dissipated . in continuous sources , this relevant time is the beam interaction time , i . e ., the beam radius divided by the beam velocity . the time of pulsed heating or the interaction time with the beam must be small so as to limit the total volume of near - surface material that is heated and therefore to allow a quick quench . for this reason , isothermal heating of the entire implant followed by quench will not work , because the stored thermal energy in the bulk material of the implant below the surface layer becomes too large to allow a rapid cooling rate . therefore , the goal is to minimize the stored thermal energy in the near - surface layer . for continuous heat sources such as continuous electron beams , ion beams , lasers , or electric arcs , the situation is illustrated in fig6 . it is assumed that the continuous heat source 19 moves across the surface of the metal medical implant 20 and creates a transient region which is heated 21 . the moving heat source has diameter 22 and travel speed 23 such that the velocity 23 will be fast enough to keep the interaction time small and the stored thermal energy in the near - surface region small as well . the interaction time is governed by the desired cooling rate , which must be about 10 4 degrees k per second or greater . therefore the relationship between travel velocity , beam diameter , cooling rate , and maximum temperature achieved may be estimated as follows . first , it is possible to approximate the cooling rate by relating it to the travel speed using a convective derivative : where v is the travel speed in the direction x , t is time , and t is temperature . it is possible to approximate the thermal gradient by considering the mathematical solution to the steady state thermal field produced by a travelling point heat source on a semi - infinite plane , which is given by rosenthal ( 1946 ): where t is the temperature at location r from the center of the heat source , r is the distance which in this case will be set to the radius of the heat source ( i . e ., d / 2 ), k is the thermal conductivity of the material , q is the power level of the heat source , v is the travel speed of the heat source , t is the time , and x is the distance along the axis the heat source is moving . differentiating with respect to x and we get the thermal gradient as : so then , combining equations 8 and 4 and taking the absolute value to get the magnitude , we get the relationship for the critical travel speed as a function of the desired cooling rate , the power of the heat source , and the diameter of the heat source : the desired cooling rate will be between 10 4 and 10 6 degrees kelvin per second . the required travel speed can then be set based on equation 9 for any given material or heat source type . now we make one more substitution , which relates to the peak temperature that is to be achieved at the interface . using equation 5 and evaluating the rise in temperature at x = d / 2 , y = 0 , z = 0 , we get : as an example , we can calculate the travel speed required to obtain a non - equilibrium concentration of vacancies using an electron beam to perform the rapid surface heat treatment . the following parameters would be used in the calculation : the desired cooling rate is 10 5 degrees c ./ second ; the diameter of the beam is 0 . 15 cm ; and the temperature increase is 1200 degrees c . then , the desired travel speed will be 8 . 3 cm / s . to get to a cooling rate of 10 6 deg . c ./ sec , a travel speed of 83 cm / s would be needed . therefore , according to equation 11 it is possible to determine the required travel speed for any given beam power , temperature rise , beam diameter , and material type so that a non - equilibrium concentration of vacancies will be trapped in the near - surface layer of the metal . this actually applies for any metal in this approximate relationship since in equation 11 the “ k ” cancel out top and bottom . the “ k ” is implicit in the δt because the rise in temperature is related to the thermal properties of the material . as a specific example of how the present invention can produce the desired non - equilibrium structures on the surface of any metal implant , consider the following example in which a commercially available titanium dental implant made out of commercially pure titanium grade 4 was provided by basic dental implant inc . and was first subjected to media blast and acid etching in order to create a surface that is standard for current implants widely in use . the initial surface of the implant is shown in fig7 and is shown after both the media blast and acid etch have taken place . the implant was then exposed to a pulsed ion beam with the following range of parameters : beam waveform ( time ) 150 ns square pulse beam waveform ( spatial ) gaussian beam pulsewidth 150 ns peak current 20 ka peak voltage 350 kv average energy fluence at target in j / cm 2 4 j / cm 2 implants made according to example 1 were placed in human patients . small batches of 6 implants were placed into 4 to 6 patients ( some patients received more than 1 implant ). the patients were recalled at 2 weeks and at four weeks following the surgery . typical results were as follows . after 4 weeks , the bone did not show wound bone remodeling at all , and the implant ( in all cases tested ) showed nearly 100 % osseointegration , which was demonstrated by the lack of a decrease in radio opacity at the implant surface during the healing period . there was also no invagination of any type at the crest of bone as typically seen in conventional titanium implants . the average osseointegration time was 30 days for one set of 6 patients , and there were greatly diminished clinical indications of pain and inflammation as observed by the implant medical care providers and as directly communicated by study subjects . when the surfaces of the implants placed in this study were examined under very high magnification ( see fig9 ), they were observed to be very smooth on a length scale of less than 10 micrometers , but had appreciable surface roughness retained from media blasting on length scales of 50 - 100 micrometers . adell , r . et al . a 15 - year study of osseointegrated implants in the treatment of the endentulous jaw . int . j . of oral surg ., 10 , pp . 387 - 416 . anil , s ., et al . ( 2011 ). dental implant surface enhancement and osseointegration , implant dentistry — a rapidly evolving practice , ilser turkyilmaz ( ed . ), isbn : 978 - 953 - 307 - 658 - 4 , intech , available from : www . intechopen . com / articles / show / title / dental - implant - surface - enhancement - and - osseointegration ballo , a . m ., et al . ( 2011 ). dental implant surfaces — physicochemical properties , biological performance , and trends , implant dentistry — a rapidly evolving practice , ilser turkyilmaz ( ed . ), isbn : 978 - 953 - 307 - 658 - 4 , intech , available from : www . intechopen . com / articles / show / title / dental - implant - surfaces - physicochemical - properties - biological - performance - and - trends branemark p i et al ( 2010 ). bone response to laser - induced micro - and nano - sized titanium surface features . submitted to nanomedicine . 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