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Biomechanical considerations in osseointegrated prostheses
Biomechanical osseointegrated Richard
Skalak,
Columbia
University,
considerations prostheses
Ph.D.* Bioengineering
Institute, New York, N.Y.
T
he successfulclinical results achieved with osseointegrated dental implants underscorethe fact that such implants easily withstand considerable masticatory loads.‘.’ In fact, one study showed that bite forces in patients with these implants were comparable to those in patients with natural dentitions.3 Extensive documentation of failure loadsin pullout and lateral loading of osseointegratedimplants is unavailable, and specific installations or design details are matters of clinical judgment determined largely by morphologic space limitations. Studies of the interface between titanium implants and bone show that a closecontact between a titanium implant develops during the healing period.4 This article attempts to analyze macroscopicstressdistribution and load transfer mechanismswhere closeapposition of bone to titanium implants is provided at the microscopic level. I will also attempt to provide some qualitative guidelinesregarding fixture placement and the mode of action that may be expected from the dental bridge (fixed partial denture)-osseointegrated fixture system. STRESS TRANSFER TO BONE
FROM IMPLANTS
A critical aspectaffecting the successor failure of an implant is the manner in which mechanicalstressesare transferred from the implant to bone. It is essentialthat neither implant nor bone be stressed beyond the long-term fatigue capacity. It is alsonecessaryto avoid any relative motion that can produce abrasion of the bone or progressive loosening of the implant. These requirements are met by osseointegratedimplants by virtue of the closeapposition of the bone to the implant at the angstrom level. Titanium is generally stronger and stiffer than bone. Presented A the Toronto Conference on Osseointegration Dentistry, ‘Toronto, Ont., Canada. *Prof’cssor, Department of Civil Engineering and hfrchanics.
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in Clinical Engineering
Young’s modulus of titanium is about 1.1 X 10” N/m* and it has a yield strength in tension of about 3 X lo* N/m’.’ Young’s modulus of cancellous bone at low stresslevels is of the order of 1OioN/m2 and has a tensile failure stressof about 5 x 10’ N/m2. Individual variations of bone properties are much larger than in different samplesof titanium becausethe latter are quite uniform. Cortical bone has a lower elastic modulus and strength than cancellous bone and is probably more variable. This means that at any interface betweenboneand titanium it may be expected that the bone or the bond of the bone to titanium will fail first rather than the titanium. Any failure of titanium is more likely to be at some overstressed section above the bone level rather than at the interface. An implant is osseointegratedwhen bone is allowed to heal around it in the absence of loading. The titanium implant and the bone may be regarded as having a perfect fit with no stressin either material prior to loading. The result is similar to the case in which a plastic or cementlike material is poured against a metallic surface, bonds to it, and hardens without any curing or shrinkage stresses.The close apposition of titanium and bone at the angstrom level meansthat under any subsequentloading, the interface movesas a unit without relative motion of the bone and titanium and with the possibility of transferring stress to all parts of the interface. In a screw that is tightened into bone immediately after the thread is tapped, the apposition is not uniform at the microscopiclevel. Only the loaded side of each thread on the screw will be in closecontact, and there will be stressesin the bone due to the screw tightening. A screw that is osseointegrated during an unloaded healing period will not have any such initial or internal stresses. An osseointegratedimplant in the form of a screw is able to transmit an axial tensile or compressiveload to the surrounding bone, primarily by compressionan the inclined faces of the screw. In this way it may be expected that the full shear strength
of the bone can be
843
SKALAK
HORIZONTAL TITANIUM
LOW/STRESS
THREADED
RO”!dDEO STRESS
TO REWCE CONCENTRATION
IMPLANT
TITANIUM
:
LOAD
B?NE
B,ONE
FRACTURE
SMOOTH TITAN!UM
PONE
IMPLANT
TITANIUM
CONNECTIVE TISSUE I
BONE
Fig. 2. Schematic plan of a fixed partial denture with horizontal load, P, in plane of prosthesis. Load P has eccentricity, e, with respect to center of 0, of six fixtures shown.
OSSEOINTEGRATED
NON-INTEGRATED
Fig. 1. Schematic sections of A, threaded implant showing detail of thread in close apposition to bone and, B, smooth implant indicating that a bond is required to prevent slip under shear. Microscopic schematicsectionsshowing, C, close ingrowth of bone (osseointegrated) and, D, implant with a layer of fibrous connective tissue between implant and bone (nonintegrated). (Modified from Albrektsson, T., Branemark, P-I., Hansson, H-A., Kasemo, B., Larsson, K., Lundstrom, I., Mcqueen, D., and Skalak, R.: The interface zone of inorganic implants in vivo: Titanium implants in bone. Ann Biomed Eng [In press.].)
developed(Fig. 1, A). In the caseof a smoothimplant, the interface bond itself must also be able to withstand the full shear stressdirectly without slip or rupture. The screw form doesnot require the bond to carry the full shear stress.It can develop a large load due to the closeapposition and predominantly compressivestresses at the interface of the screw threads. Surface roughnessand porosity of an osseointegrated implant can also have a beneficial interlocking effect similar to that of screw threads at a microscopic scale (Fig. 1, C’). Surface asperities can be assumedto be
844
small compared to the screw diameter, but large to molecular dimension so that close apposition of the bone and titanium surfaces can be achieved at the angstromlevel. Under theseco&tions the interlocking of the bone and titanium asperitiescan transmit shear stresses in a manner similar to that of the screwthread. A perfectly smooth surface will require the bond itself to carry the applied full shear stress(Fig. 1, B). The beneficial effects of surface roughness are obtained only if bone grows closelyinto the asperitiesof the implant surface. If a rough pin is placed in a freshly drilled hole, the surface roughnessmay touch the bone only at peaks and there may be stressconcentrations and abrasion under load. Similiarly, if a fibrous layer forms around an implant (Fig. 1, O), the surface roughness may lead to some relative motion and degradation of the bone. To achieve the beneficial effects of surface roughness,a true osseointegrationis necessarywith ingrowth of bone into the asperities of the implant. LOAD DISTRIBUTION SEVERAL SCREWS
TO
When a dental prosthesisor fixed partial denture is supported by several screws, the resulting combined structure forms a unit in which the distribution of any
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1983
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NUMBER
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RIOMECHANICAL
CONSIDERATIONS
IN OSSEOINTEGRATED
PROSTHESES
DISTRIBUTED VERTICAL
SUPPORT
Fl= P
LOAD
IP
&J’ A
1
2
CANTILEVER
3
F;W2P
lP
i-l
Fig. 3. Schematic sketch of a fixed partial denture with vertical load, P. Center of gravity of six fixtures shown is 0. Eccentricity of load is xpwith respect to y axis and yp with respect to x axis.
Fig. 4. Schematic load distribution with, A, distributed supports(fixtures) and small overhang and, B, closely spacedsupports (fixtures) with large overhang (cantilever).
applied load dependson the relative stiffnessesof the several membersinvolved, as well as the geometry of their arrangement. Such a structure is called statically indeterminate, indicating that the equations of statics alone are insufficient to determine the distribution of the acting loads. A complete analysis must take into account the deformations of the fixed partial denture and the jaw as curved, elastic beamsunder torsion and bending. In addition, the stiffnessof the screwsand of their connectionsto the bridge and jaw must be taken into account. In the absenceof such complete stress analyses,estimatesof load distribution may be madeby use of simplified models and/or simplified assumptions. Some commentsbasedon such approximations are therefore pertinent. Becausean osseointegratedfixture forms a closeand tight bond with the bone structure, it is to be expected that the responseto any loading is elastic, that is, that the deflection of a fixture is proportional to the load applied to it. On the other hand, when a stiff metallic fixed partial denture is used, it may be assumedto be relatively rigid compared to the screws,which have a smaller crosssection. The situation is similiar to that encounteredin the designof bolted joints5 In the dental
implant the mandible and the metallie fixed partial denture play the role of membersbeing bolted together by the implanted fixtures. On the assumptionthat the fixed partial denture is relatively stiff, the following formulas may be used to estimate the load on each screw. For a load P in the horizontal plane (in the plane of the bridge) as shown in Fig. 2, the horizontal load F, on the ith fixture is estimated by:
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P
PP
I?, = ,fip + = R,n, Z R: where E is the vector force on the ith fixture and P is the applied load, which acts in a direction indicated by the unit vector ~rp.As shown in Fig. 2, the radii Rj to each screw are measuresfrom the center of gravity of the screws, 0, which is chosen as the origin of the coordinates (x, y). The eccentricity of the load with respect to the origin is the distance e (Fig. 2). The summationin equation No. 1 is over the Rj for the total number of screws,N. The unit vector 5 is defined to be perpendicular to Ri for eachi. Equation NO. 1 holds for i=l, 2,... N. The first term represents an equal distribution of load P acting through the center of gravity 0. The secondterm in equation No. 1 repre-
845
SKALAK
TIGHT
CONNECTIONS 1P l-l u
/-n1 I
BRIDGE FIXTURE
l-l
BONE
l-l
Equation No. 1 and Fig. 2 apply to horizontal loads. The distribution of a vertical load P may be approximated by using similar assumptions and analysis (that is, it is again assumed that the deflections of the screws are linearly elastic and that the restoration is comparatively rigid). Referring to Fig. 3, the vertical load Fi on each screw is: Fi =; + P(Ax, + ByJ
@
I
0’ VIERENDIEHL
TRUSS
(2)
where N is the number of screws and (xi, yi) are the coordinates of the ith screw as shown in Fig. 3. The coefficients A and B in equation No. 2 depend on the location (xp, yJ of the load and are given by: A = (L,Y, - Lxx,)/(I:, where and
Fig. 5. A, Schematic sketch of a fixed partial denture tightly connected to supporting fixtures that are osseointegrated. B, Effective integral structure representing design shown in A is a Vierendiehl truss in which each joint is rigid and can carry bending moments. Two dotted-line sketches, C and D, show qualitative behavior and deflection of combined structure under vertical and horizontal loads.
sents the effect of the torsional moment about a vertical axis due to the eccentricity e of the load P. The end result of applying equation No. 1 to any particular prosthesis will generally be that the maximum load on any one screw will be less than the load P. The screw closest to the load (No. 1 in Fig. 2) will carry the largest load. A rough estimate for geometry similar to Fig. 2 will be F,, = 2P/N. When N = 6 as in Fig. 2, the maximum load per screw will then be of the order of P/3. The reduction of the load per screw by the combined action of several fixtures tied together by a stiff fixed partial denture will not be important if each screw can carry the maximum load P directly. In this case a light and flexible fixed partial denture would be sufficient. This may be the case in some lower jaw situations, but concerted action of several screws by use of a stiff fixed partial denture is probably essential in the upper jaw.
- Ix&) B = (1x,x, - I,,yJ/K - LJ,,) I,, = L: XT I,, = z VT I,, = 2 x,y,
(3) (4) (5)
(6)
The summationsindicated in equation Nos. 5 and 6 are taken over the N screws. The forces Fi given by equation No. 2 are vertical and the two terms in equation No. 2 add algebraically rather than vectorially asin equation No. 1. The ccordinates(xi, yi) of the ith screw are taken positive or negative according to the axes shown in Fig. 3. The origin 0 is the centroid of the screws.It follows that the fixtures near the load P will sustain larger forces Fi than on the oppo$ite side. The results of using equation No. 2 for geometry such as shown in Fig. 3 will show that the load per screw Fi will generally be lessthan the applied load P. A rough estimate for geometry similar to Fig. 3 is Fmax= 2P/N. Loads on a screw can be equal to or larger than the applied load P if the geometry is sufficiently altered, especially if cantilevers (unsupported overhangs) are incorporated into the design. In extreme casessuch as shown schematically in Fig. 4, the maximum load per screwmay reach 11%to 2 times the applied load P. This may be tolerable and safe if the capacity of a single screw is greater than the maximum applied load P. This often appears to be the case in the lower jaw. However, equation Nos. 1 and 2 indicate that where feasible, it is beneficial to spread out a given number of screws N as widely as convenient because this will generally reduce the maximum load per screw. Equation Nos. 1 and 2 deal with horizontal and vertical loadsseparately. The analysesare approximations that are valid for stiff fixed partial dentures that JUNE
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lie in a definite horizontal plane supported by vertical screws. A load force P in any direction can be resolved into horizontal and vertical components the effects of which may be computed separately by equation Nos. 1 and 2. The forces exerted on a particular screw may then be combined vectorially. In this way most general design and loading prosthesescan be conveniently computed.
SHOCK
RESISTANCE
CONNECTION OF FIXED PARTIAL DENTURES TO FIXTURES The firm connection of a fixed partial denture to osseointegratedfixtures results in a unified structure in which the fixed partial denture, the fixtures, and the bone act as a unit. P-.ich a design may reduce the maximum applied stressesat both the upper end of the fixture as well as the bone and can carry bending momentsas well as axial loadsand horizontal shearing forces. The unified structural behavior of osseointegrated fixtures tightly fastened to a fixed partial denture is schematically illustrated in Fig. 5, A. The entire structure acts like a Vierendiehl truss (Fig. 5, B), in which the membersare rigidly connectedat all joints so as to form a continuous structure with rectangular openings. Such a structure is unstable if the connections cannot carry bending moments.It would be stable only if the bottom joints (screwsto bone) were rigid and capable of carrying bending moments. However, the peak stresseswill generally be reduced if the upper joints (fixtures to fixed partial denture) are also rigid. It must be emphasizedthat any misalignment of the fixed partial denture to the osseointegratedfixtures will result in internal stressesin the fixed partial denture, the fixtures, and the bone. Such stresses cannot be detectedby visual inspection but may reduce failure loads substantially or even lead to failures without external loads. Rigid and accurate connections of fixed partial dentures to fixtures are therefore desirable. SHOCK RESISTANCE An osseointegratedimplant provides a direct and relatively rigid connection of the implant to the bone.’ This is an advantage becauseit provides a durable interface without any substantial change in form or duration. There is a mismatch of the mechanical properties and mechanical impedanceat the interface of titanium and bone that would be evident at ultrasonic frequencies. However, under a pulse of several milliseconds or more in duration, this mismatch will not have large effects. As a result, bone may be THE
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Fig. 6. A, Schematic sketch showing impact of a mass,M, at velocity z, onto a metallic fixed partial denture on fixtures that are osseointegrated with bone. System behaveslike a stiff spring with modulus, K, as shown. B, Same schemeas in A except that an acrylic resin sheath (for example, acrylic resin teeth) is placed over metallic fixed partial denture. Theoretical model includes a softer spring, K,, and dashpot, p, representing acrylic resin. C, Qualitative sketch of force versus time resulting from impact in casesA and B above. Impulse (area) for two casesis same,but peak force is much lessin B (curve h).
overstressedor fractured if impact loads are applied to the fixture or to a tightly connected fixed partial denture. Large impact loadscan be generatedduring chewing if a hard object is suddenly and inadvertently encountered. The situation is shown in Fig. 6, A and B, as a mass(M) with a velocity (v) impacting onto a bridge supported by an integrated implant. The impulse (the integral of force over time) required to bring massM to rest is constant, that is, it can be accomplishedby a large force acting over a short time or a small force acting over a longer time. 847
SKALAK
In the case of an unprotected metallic fixed partial denture, the entire construction acts like a stiff unit, and it will therefore produce large forces with little deflection over a short time (Fig. 6, A). The time history of the force generated is shown schematically as curve a in Fig. 6, C. It is a short pulse with a high peak force. It is this peak stress that is likely to produce fracture. In Fig. 6, B, the sketch is shown of an implant with a fixed partial denture covered in turn by acrylic resin or other plastic sheath that is molded in the form of teeth. Such plastics have a lower modulus of elasticity and provide some internal damping. Such a sheath is represented in Fig. 6, B, by a spring parallel to a dashpot or viscous element.6 This unit, usually called a Kelvin body, is mechanically in series with the springs representing the implant and the bone below it. The spring constant K, of the acrylic resin is assumed to be smaller (more compliant) than that of the metallic implant or bone. Under these conditions the same impact of mass M will result in a force-time history as illustrated by curve b in Fig. 6, C. The duration is longer and the peak force is correspondingly less. This is the shock-absorbing action. It is interesting to observe that from a mechanical standpoint, the shock-absorbing action would be the same if the soft layer were between the metal implant and the bone. In the natural tooth the periodontum, which forms a shock-absorbing layer, is in this position between the tooth and the jaw bone. As far as shock resistance goes, it could as well be located on the tooth surface; but then it would also have to play the role of the enamel as a wearing and cutting surface and would have to be replaced as it wore down. Acrylic resin can be replaced if it is subject to excessive wear, but the reported clinical experience ’ shows that this is not necessary for several years, at least in most instances. It is, therefore, practical to use acrylic resin teeth on a metallic fixed partial denture to achieve appropriate shock-absorbing action.
SUMMARY
AND
REFERENCES 1.
2.
CONCLUSIONS
On the basis of the previous discussions, several conclusions may be drawn. 1. The close apposition of bone to the titanium implant is the essential feature that allows a transmission of stress from the implant to the bone without any appreciable relative motion or abrasion. The absence of any intermediate fibrotic layer allows stress to be transmitted without any progressive change in the bond or contact between the bone and implant.
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2. The use of a threaded screw provides a form of interlocking with the bone on a macroscopic scale that allows full development of the strength of the bone in shear or compression. A smooth, cylindrical implant may require an adhesive bond for satisfactory performance, but a screw shape is able to work as long as the apposition of bone and implant is close, whether or not a true adhesive bond is developed. 3. The distribution of a vertical or lateral load applied to a fixed partial denture depends on the number, arrangement, and stiffness of abutment fixtures used, as well as the form and stiffness of the fixed prosthesis itself. In general a stiff fixed partial denture will distribute loads to several fixtures more effectively. A flexible prosthesis may be adequate if the strength developed by each fixture is able to carry the full load that is applied. Cantilevered ends of a fixed partial denture increases the loading on the first screw nearest the cantilevered end. Moderate overhangs may be tolerated if the fixtures are sufficiently strong. 4. A tight connection of the fixed partial denture to fixtures provides a combined structure that can act in concert with the bone to provide a greater strength than that of the fixture or the jaw bone alone. 5. The osseointegrated implant provides a direct contact with bone and therefore will transmit any stress waves or shocks applied to the fixtures. For this reason it is advisable to use a shock-absorbing material such as acrylic resin in the form of acrylic resin artificial teeth in the fixed partial denture. This arrangement allows for the development of a stiff and strong substructure with adequate shock protection on its outer surface.
3.
4.
5. 6.
Branemark, P-I., Hansson, B. O., Adell, R., Breine, U., Lindstrom, J., Hallen, O., and Ohman, A.: Osseointegrated Implants in the Treatment of the Edentulous Jaw. Stockholm, 1977, Almquist and Wiksell. Adell, R., Lekholm, U., Rockier, B., and Branemark, P-I.: A 15-year study of osseointegrated implants in the treatment of the edentulous jaw. Int J Oral Surg 6:387, 1981. Haroldson, T., and Carlsson, G. E.: Bite force and oral function in patients with osseointegrated oral implants. Stand J Dent Res 85:200, 1977. Albrektsson, T., Branemark, P-I., Hansson, H-A., Kasemo, B., Larsson, K., Lundstrom, I., Mcqueen, D., and Skalak, R.: The interface zone of inorganic implants in vivo: Titanium implants in bone. Ann Biomed Eng (In press.) McGuire, W.: Steel Structures. Englewood Cliffs, N.J., 1968, Prentice-Hall, Inc. Flugge, W.: Viscoelasticity. Waltham, Mass., 1967, Blaisdell Publishing Co.
JUNE
1983
VOLUME
49
NUMBER
6
Skalak,
Columbia
University,
considerations prostheses
Ph.D.* Bioengineering
Institute, New York, N.Y.
T
he successfulclinical results achieved with osseointegrated dental implants underscorethe fact that such implants easily withstand considerable masticatory loads.‘.’ In fact, one study showed that bite forces in patients with these implants were comparable to those in patients with natural dentitions.3 Extensive documentation of failure loadsin pullout and lateral loading of osseointegratedimplants is unavailable, and specific installations or design details are matters of clinical judgment determined largely by morphologic space limitations. Studies of the interface between titanium implants and bone show that a closecontact between a titanium implant develops during the healing period.4 This article attempts to analyze macroscopicstressdistribution and load transfer mechanismswhere closeapposition of bone to titanium implants is provided at the microscopic level. I will also attempt to provide some qualitative guidelinesregarding fixture placement and the mode of action that may be expected from the dental bridge (fixed partial denture)-osseointegrated fixture system. STRESS TRANSFER TO BONE
FROM IMPLANTS
A critical aspectaffecting the successor failure of an implant is the manner in which mechanicalstressesare transferred from the implant to bone. It is essentialthat neither implant nor bone be stressed beyond the long-term fatigue capacity. It is alsonecessaryto avoid any relative motion that can produce abrasion of the bone or progressive loosening of the implant. These requirements are met by osseointegratedimplants by virtue of the closeapposition of the bone to the implant at the angstrom level. Titanium is generally stronger and stiffer than bone. Presented A the Toronto Conference on Osseointegration Dentistry, ‘Toronto, Ont., Canada. *Prof’cssor, Department of Civil Engineering and hfrchanics.
THE
JOURNAL
in
OF PROSTHETIC
DENTISTRY
in Clinical Engineering
Young’s modulus of titanium is about 1.1 X 10” N/m* and it has a yield strength in tension of about 3 X lo* N/m’.’ Young’s modulus of cancellous bone at low stresslevels is of the order of 1OioN/m2 and has a tensile failure stressof about 5 x 10’ N/m2. Individual variations of bone properties are much larger than in different samplesof titanium becausethe latter are quite uniform. Cortical bone has a lower elastic modulus and strength than cancellous bone and is probably more variable. This means that at any interface betweenboneand titanium it may be expected that the bone or the bond of the bone to titanium will fail first rather than the titanium. Any failure of titanium is more likely to be at some overstressed section above the bone level rather than at the interface. An implant is osseointegratedwhen bone is allowed to heal around it in the absence of loading. The titanium implant and the bone may be regarded as having a perfect fit with no stressin either material prior to loading. The result is similar to the case in which a plastic or cementlike material is poured against a metallic surface, bonds to it, and hardens without any curing or shrinkage stresses.The close apposition of titanium and bone at the angstrom level meansthat under any subsequentloading, the interface movesas a unit without relative motion of the bone and titanium and with the possibility of transferring stress to all parts of the interface. In a screw that is tightened into bone immediately after the thread is tapped, the apposition is not uniform at the microscopiclevel. Only the loaded side of each thread on the screw will be in closecontact, and there will be stressesin the bone due to the screw tightening. A screw that is osseointegrated during an unloaded healing period will not have any such initial or internal stresses. An osseointegratedimplant in the form of a screw is able to transmit an axial tensile or compressiveload to the surrounding bone, primarily by compressionan the inclined faces of the screw. In this way it may be expected that the full shear strength
of the bone can be
843
SKALAK
HORIZONTAL TITANIUM
LOW/STRESS
THREADED
RO”!dDEO STRESS
TO REWCE CONCENTRATION
IMPLANT
TITANIUM
:
LOAD
B?NE
B,ONE
FRACTURE
SMOOTH TITAN!UM
PONE
IMPLANT
TITANIUM
CONNECTIVE TISSUE I
BONE
Fig. 2. Schematic plan of a fixed partial denture with horizontal load, P, in plane of prosthesis. Load P has eccentricity, e, with respect to center of 0, of six fixtures shown.
OSSEOINTEGRATED
NON-INTEGRATED
Fig. 1. Schematic sections of A, threaded implant showing detail of thread in close apposition to bone and, B, smooth implant indicating that a bond is required to prevent slip under shear. Microscopic schematicsectionsshowing, C, close ingrowth of bone (osseointegrated) and, D, implant with a layer of fibrous connective tissue between implant and bone (nonintegrated). (Modified from Albrektsson, T., Branemark, P-I., Hansson, H-A., Kasemo, B., Larsson, K., Lundstrom, I., Mcqueen, D., and Skalak, R.: The interface zone of inorganic implants in vivo: Titanium implants in bone. Ann Biomed Eng [In press.].)
developed(Fig. 1, A). In the caseof a smoothimplant, the interface bond itself must also be able to withstand the full shear stressdirectly without slip or rupture. The screw form doesnot require the bond to carry the full shear stress.It can develop a large load due to the closeapposition and predominantly compressivestresses at the interface of the screw threads. Surface roughnessand porosity of an osseointegrated implant can also have a beneficial interlocking effect similar to that of screw threads at a microscopic scale (Fig. 1, C’). Surface asperities can be assumedto be
844
small compared to the screw diameter, but large to molecular dimension so that close apposition of the bone and titanium surfaces can be achieved at the angstromlevel. Under theseco&tions the interlocking of the bone and titanium asperitiescan transmit shear stresses in a manner similar to that of the screwthread. A perfectly smooth surface will require the bond itself to carry the applied full shear stress(Fig. 1, B). The beneficial effects of surface roughness are obtained only if bone grows closelyinto the asperitiesof the implant surface. If a rough pin is placed in a freshly drilled hole, the surface roughnessmay touch the bone only at peaks and there may be stressconcentrations and abrasion under load. Similiarly, if a fibrous layer forms around an implant (Fig. 1, O), the surface roughness may lead to some relative motion and degradation of the bone. To achieve the beneficial effects of surface roughness,a true osseointegrationis necessarywith ingrowth of bone into the asperities of the implant. LOAD DISTRIBUTION SEVERAL SCREWS
TO
When a dental prosthesisor fixed partial denture is supported by several screws, the resulting combined structure forms a unit in which the distribution of any
JUNE
1983
VOLUME
49
NUMBER
6
RIOMECHANICAL
CONSIDERATIONS
IN OSSEOINTEGRATED
PROSTHESES
DISTRIBUTED VERTICAL
SUPPORT
Fl= P
LOAD
IP
&J’ A
1
2
CANTILEVER
3
F;W2P
lP
i-l
Fig. 3. Schematic sketch of a fixed partial denture with vertical load, P. Center of gravity of six fixtures shown is 0. Eccentricity of load is xpwith respect to y axis and yp with respect to x axis.
Fig. 4. Schematic load distribution with, A, distributed supports(fixtures) and small overhang and, B, closely spacedsupports (fixtures) with large overhang (cantilever).
applied load dependson the relative stiffnessesof the several membersinvolved, as well as the geometry of their arrangement. Such a structure is called statically indeterminate, indicating that the equations of statics alone are insufficient to determine the distribution of the acting loads. A complete analysis must take into account the deformations of the fixed partial denture and the jaw as curved, elastic beamsunder torsion and bending. In addition, the stiffnessof the screwsand of their connectionsto the bridge and jaw must be taken into account. In the absenceof such complete stress analyses,estimatesof load distribution may be madeby use of simplified models and/or simplified assumptions. Some commentsbasedon such approximations are therefore pertinent. Becausean osseointegratedfixture forms a closeand tight bond with the bone structure, it is to be expected that the responseto any loading is elastic, that is, that the deflection of a fixture is proportional to the load applied to it. On the other hand, when a stiff metallic fixed partial denture is used, it may be assumedto be relatively rigid compared to the screws,which have a smaller crosssection. The situation is similiar to that encounteredin the designof bolted joints5 In the dental
implant the mandible and the metallie fixed partial denture play the role of membersbeing bolted together by the implanted fixtures. On the assumptionthat the fixed partial denture is relatively stiff, the following formulas may be used to estimate the load on each screw. For a load P in the horizontal plane (in the plane of the bridge) as shown in Fig. 2, the horizontal load F, on the ith fixture is estimated by:
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JOURNAL
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DENTISTRY
P
PP
I?, = ,fip + = R,n, Z R: where E is the vector force on the ith fixture and P is the applied load, which acts in a direction indicated by the unit vector ~rp.As shown in Fig. 2, the radii Rj to each screw are measuresfrom the center of gravity of the screws, 0, which is chosen as the origin of the coordinates (x, y). The eccentricity of the load with respect to the origin is the distance e (Fig. 2). The summationin equation No. 1 is over the Rj for the total number of screws,N. The unit vector 5 is defined to be perpendicular to Ri for eachi. Equation NO. 1 holds for i=l, 2,... N. The first term represents an equal distribution of load P acting through the center of gravity 0. The secondterm in equation No. 1 repre-
845
SKALAK
TIGHT
CONNECTIONS 1P l-l u
/-n1 I
BRIDGE FIXTURE
l-l
BONE
l-l
Equation No. 1 and Fig. 2 apply to horizontal loads. The distribution of a vertical load P may be approximated by using similar assumptions and analysis (that is, it is again assumed that the deflections of the screws are linearly elastic and that the restoration is comparatively rigid). Referring to Fig. 3, the vertical load Fi on each screw is: Fi =; + P(Ax, + ByJ
@
I
0’ VIERENDIEHL
TRUSS
(2)
where N is the number of screws and (xi, yi) are the coordinates of the ith screw as shown in Fig. 3. The coefficients A and B in equation No. 2 depend on the location (xp, yJ of the load and are given by: A = (L,Y, - Lxx,)/(I:, where and
Fig. 5. A, Schematic sketch of a fixed partial denture tightly connected to supporting fixtures that are osseointegrated. B, Effective integral structure representing design shown in A is a Vierendiehl truss in which each joint is rigid and can carry bending moments. Two dotted-line sketches, C and D, show qualitative behavior and deflection of combined structure under vertical and horizontal loads.
sents the effect of the torsional moment about a vertical axis due to the eccentricity e of the load P. The end result of applying equation No. 1 to any particular prosthesis will generally be that the maximum load on any one screw will be less than the load P. The screw closest to the load (No. 1 in Fig. 2) will carry the largest load. A rough estimate for geometry similar to Fig. 2 will be F,, = 2P/N. When N = 6 as in Fig. 2, the maximum load per screw will then be of the order of P/3. The reduction of the load per screw by the combined action of several fixtures tied together by a stiff fixed partial denture will not be important if each screw can carry the maximum load P directly. In this case a light and flexible fixed partial denture would be sufficient. This may be the case in some lower jaw situations, but concerted action of several screws by use of a stiff fixed partial denture is probably essential in the upper jaw.
- Ix&) B = (1x,x, - I,,yJ/K - LJ,,) I,, = L: XT I,, = z VT I,, = 2 x,y,
(3) (4) (5)
(6)
The summationsindicated in equation Nos. 5 and 6 are taken over the N screws. The forces Fi given by equation No. 2 are vertical and the two terms in equation No. 2 add algebraically rather than vectorially asin equation No. 1. The ccordinates(xi, yi) of the ith screw are taken positive or negative according to the axes shown in Fig. 3. The origin 0 is the centroid of the screws.It follows that the fixtures near the load P will sustain larger forces Fi than on the oppo$ite side. The results of using equation No. 2 for geometry such as shown in Fig. 3 will show that the load per screw Fi will generally be lessthan the applied load P. A rough estimate for geometry similar to Fig. 3 is Fmax= 2P/N. Loads on a screw can be equal to or larger than the applied load P if the geometry is sufficiently altered, especially if cantilevers (unsupported overhangs) are incorporated into the design. In extreme casessuch as shown schematically in Fig. 4, the maximum load per screwmay reach 11%to 2 times the applied load P. This may be tolerable and safe if the capacity of a single screw is greater than the maximum applied load P. This often appears to be the case in the lower jaw. However, equation Nos. 1 and 2 indicate that where feasible, it is beneficial to spread out a given number of screws N as widely as convenient because this will generally reduce the maximum load per screw. Equation Nos. 1 and 2 deal with horizontal and vertical loadsseparately. The analysesare approximations that are valid for stiff fixed partial dentures that JUNE
1983
VOLUME
49
NUMBER
6
BIOME,CHANICAL
CONSIDERATIONS
IN OSSEOINTEGRATED
PROSTHESES
lie in a definite horizontal plane supported by vertical screws. A load force P in any direction can be resolved into horizontal and vertical components the effects of which may be computed separately by equation Nos. 1 and 2. The forces exerted on a particular screw may then be combined vectorially. In this way most general design and loading prosthesescan be conveniently computed.
SHOCK
RESISTANCE
CONNECTION OF FIXED PARTIAL DENTURES TO FIXTURES The firm connection of a fixed partial denture to osseointegratedfixtures results in a unified structure in which the fixed partial denture, the fixtures, and the bone act as a unit. P-.ich a design may reduce the maximum applied stressesat both the upper end of the fixture as well as the bone and can carry bending momentsas well as axial loadsand horizontal shearing forces. The unified structural behavior of osseointegrated fixtures tightly fastened to a fixed partial denture is schematically illustrated in Fig. 5, A. The entire structure acts like a Vierendiehl truss (Fig. 5, B), in which the membersare rigidly connectedat all joints so as to form a continuous structure with rectangular openings. Such a structure is unstable if the connections cannot carry bending moments.It would be stable only if the bottom joints (screwsto bone) were rigid and capable of carrying bending moments. However, the peak stresseswill generally be reduced if the upper joints (fixtures to fixed partial denture) are also rigid. It must be emphasizedthat any misalignment of the fixed partial denture to the osseointegratedfixtures will result in internal stressesin the fixed partial denture, the fixtures, and the bone. Such stresses cannot be detectedby visual inspection but may reduce failure loads substantially or even lead to failures without external loads. Rigid and accurate connections of fixed partial dentures to fixtures are therefore desirable. SHOCK RESISTANCE An osseointegratedimplant provides a direct and relatively rigid connection of the implant to the bone.’ This is an advantage becauseit provides a durable interface without any substantial change in form or duration. There is a mismatch of the mechanical properties and mechanical impedanceat the interface of titanium and bone that would be evident at ultrasonic frequencies. However, under a pulse of several milliseconds or more in duration, this mismatch will not have large effects. As a result, bone may be THE
JOURNAL
OF PROSTHETIC
DENTISTRY
Fig. 6. A, Schematic sketch showing impact of a mass,M, at velocity z, onto a metallic fixed partial denture on fixtures that are osseointegrated with bone. System behaveslike a stiff spring with modulus, K, as shown. B, Same schemeas in A except that an acrylic resin sheath (for example, acrylic resin teeth) is placed over metallic fixed partial denture. Theoretical model includes a softer spring, K,, and dashpot, p, representing acrylic resin. C, Qualitative sketch of force versus time resulting from impact in casesA and B above. Impulse (area) for two casesis same,but peak force is much lessin B (curve h).
overstressedor fractured if impact loads are applied to the fixture or to a tightly connected fixed partial denture. Large impact loadscan be generatedduring chewing if a hard object is suddenly and inadvertently encountered. The situation is shown in Fig. 6, A and B, as a mass(M) with a velocity (v) impacting onto a bridge supported by an integrated implant. The impulse (the integral of force over time) required to bring massM to rest is constant, that is, it can be accomplishedby a large force acting over a short time or a small force acting over a longer time. 847
SKALAK
In the case of an unprotected metallic fixed partial denture, the entire construction acts like a stiff unit, and it will therefore produce large forces with little deflection over a short time (Fig. 6, A). The time history of the force generated is shown schematically as curve a in Fig. 6, C. It is a short pulse with a high peak force. It is this peak stress that is likely to produce fracture. In Fig. 6, B, the sketch is shown of an implant with a fixed partial denture covered in turn by acrylic resin or other plastic sheath that is molded in the form of teeth. Such plastics have a lower modulus of elasticity and provide some internal damping. Such a sheath is represented in Fig. 6, B, by a spring parallel to a dashpot or viscous element.6 This unit, usually called a Kelvin body, is mechanically in series with the springs representing the implant and the bone below it. The spring constant K, of the acrylic resin is assumed to be smaller (more compliant) than that of the metallic implant or bone. Under these conditions the same impact of mass M will result in a force-time history as illustrated by curve b in Fig. 6, C. The duration is longer and the peak force is correspondingly less. This is the shock-absorbing action. It is interesting to observe that from a mechanical standpoint, the shock-absorbing action would be the same if the soft layer were between the metal implant and the bone. In the natural tooth the periodontum, which forms a shock-absorbing layer, is in this position between the tooth and the jaw bone. As far as shock resistance goes, it could as well be located on the tooth surface; but then it would also have to play the role of the enamel as a wearing and cutting surface and would have to be replaced as it wore down. Acrylic resin can be replaced if it is subject to excessive wear, but the reported clinical experience ’ shows that this is not necessary for several years, at least in most instances. It is, therefore, practical to use acrylic resin teeth on a metallic fixed partial denture to achieve appropriate shock-absorbing action.
SUMMARY
AND
REFERENCES 1.
2.
CONCLUSIONS
On the basis of the previous discussions, several conclusions may be drawn. 1. The close apposition of bone to the titanium implant is the essential feature that allows a transmission of stress from the implant to the bone without any appreciable relative motion or abrasion. The absence of any intermediate fibrotic layer allows stress to be transmitted without any progressive change in the bond or contact between the bone and implant.
848
2. The use of a threaded screw provides a form of interlocking with the bone on a macroscopic scale that allows full development of the strength of the bone in shear or compression. A smooth, cylindrical implant may require an adhesive bond for satisfactory performance, but a screw shape is able to work as long as the apposition of bone and implant is close, whether or not a true adhesive bond is developed. 3. The distribution of a vertical or lateral load applied to a fixed partial denture depends on the number, arrangement, and stiffness of abutment fixtures used, as well as the form and stiffness of the fixed prosthesis itself. In general a stiff fixed partial denture will distribute loads to several fixtures more effectively. A flexible prosthesis may be adequate if the strength developed by each fixture is able to carry the full load that is applied. Cantilevered ends of a fixed partial denture increases the loading on the first screw nearest the cantilevered end. Moderate overhangs may be tolerated if the fixtures are sufficiently strong. 4. A tight connection of the fixed partial denture to fixtures provides a combined structure that can act in concert with the bone to provide a greater strength than that of the fixture or the jaw bone alone. 5. The osseointegrated implant provides a direct contact with bone and therefore will transmit any stress waves or shocks applied to the fixtures. For this reason it is advisable to use a shock-absorbing material such as acrylic resin in the form of acrylic resin artificial teeth in the fixed partial denture. This arrangement allows for the development of a stiff and strong substructure with adequate shock protection on its outer surface.
3.
4.
5. 6.
Branemark, P-I., Hansson, B. O., Adell, R., Breine, U., Lindstrom, J., Hallen, O., and Ohman, A.: Osseointegrated Implants in the Treatment of the Edentulous Jaw. Stockholm, 1977, Almquist and Wiksell. Adell, R., Lekholm, U., Rockier, B., and Branemark, P-I.: A 15-year study of osseointegrated implants in the treatment of the edentulous jaw. Int J Oral Surg 6:387, 1981. Haroldson, T., and Carlsson, G. E.: Bite force and oral function in patients with osseointegrated oral implants. Stand J Dent Res 85:200, 1977. Albrektsson, T., Branemark, P-I., Hansson, H-A., Kasemo, B., Larsson, K., Lundstrom, I., Mcqueen, D., and Skalak, R.: The interface zone of inorganic implants in vivo: Titanium implants in bone. Ann Biomed Eng (In press.) McGuire, W.: Steel Structures. Englewood Cliffs, N.J., 1968, Prentice-Hall, Inc. Flugge, W.: Viscoelasticity. Waltham, Mass., 1967, Blaisdell Publishing Co.
JUNE
1983
VOLUME
49
NUMBER
6