Minimizing biomechanical overload in implant prostheses: A computerized aid to design

Minimizing biomechanical overload computerized aid to design Brian

D.

Monteith,

in implant

prostheses:

A

MChDa

Medical University of Southern Africa, Faculty of Dentistry, Medunsa, South Africa Implant-supported prostheses must be able to withstand the load capabilities of individual patients to overload them. The gold alloy screw in the Branemark system is by intention the weakest component. Therefore, if cantilever lengths can be designed so that occlusal forces distributed to individual fixtures are limited to the gold screws’ ability to accept them, breakage-free performance may be assured. Models, such as that of Skalak, are capable of developing the required analytical processes to provide the information necessary to achieve this design. Unfortunately, the overt mathematical complexity of the Skalak model has militated against its routine use in the operatory. Its computational aspects are, however, eminently suited to computerization and indeed provide the basis for the computer program that is described in this article. This program is simple to apply clinically and, when used in conjunction with available load parameters of gold screw performance, can provide the clinician with a routine and scientific basis for rational implant prosthesis design. (J PROSTHET DENT 1993;69:495-502.)

I

n the decadesthat followed Brinemark’s introduction of the concept of osseointegration,numerous efforts have been applied to investigating the viability of the concept. Prominent amongthesewasthe project conducted by Zarb and his co-workers at the University of Toronto, the findings of which were reported in a seriesof three articles that discussedsurgicalresults,l prosthetic results,2and the problems and complications encountered.3 Zarb’s conclusionsendorsedthe longitudinal effectivenessof the Brinemark method. However, one noticeable feature among the problems and complications encountered during the Toronto study was the large number of gold screwsthat were reported to have fractured. Of 274 implants that were placed to support 49 prosthesesin 46 edentulous patients, 53 fractures of the gold alloy screws were noted. Similar observations emergedfrom a replication study conducted at the University of the Witwatersrand in which Shackleton et a1.4reached the conclusionthat “more than 50% of prosthetic problems are related to stress factors acting on the prostheses.”On the evidence, therefore, it is difficult to deny that screwfracture is indicative of an adverse load, whether due to (1) an impassive fit of the framework, (2) parafunctional contact movements, or (3) an unfavorable location of implant fixtures. Admittedly, the B&remark fixture assemblyhas been expressly designed

to fail sequentially,

from the top down,5

and consequentlyonewould expect the gold screwto be the first component to break. Becauseit is so readily accessiaProfessor and Chairman, Department of Prosthodontics. Copyright ‘: 1993 by The Editorial Council of THE JOURNAL PROSTHETIC oozz-3913/93/$1.00

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ble, this component is readily replaced. However, to have screwsfracturing asa normal event would not be conducive to sustained levels of patient confidence. Thus it would seemsensibleto find a way of individually custom-designing all implant prosthesesto maximize their ability to resist any tendency to overload them. THE PROBLEM Although proper attention to the management of biomechanicalloads and stresseson implant prosthesesis obviously vital to their success,reference to the relevant literature reveals that, compared with other aspects, this subject has attracted relatively scant attention from researchers.6As Zarb observed, “The quality of the science underscoring the clinical application of osseointegration appearsto virtually guaranteea complication-free surgical experience . . . Prosthodontic treatment, however, introducesa seriesof clinical stepsthat are largely empirical in nature . . . are borrowed or modified from the traditional clinical repertoire . . . and have not evolved as a result of careful scientific scrutiny.” Thus, the decision as to the length of cantilever is either (1) limited to a cautionary statement that it extend no more than 20 mm distal to the center of the distalmost mandibular fixtures7 or (2) made subject to a rule of thumb linking it to the anteroposterior dimension of the fixture grouping.5*8 The problem at issueis not a lack of a scientific basis, however. One needlook no further than the mathematical model that Skalakg describedin 1963,whereby the resultant of a vertical load P, applied to a curved beam, can be expressedin terms of the force which that load would induce at eachof the implant fixtures supporting that beam (Fig. 1). The underlying thesisof Skalak’s model is that an implant-supported prosthesis is akin to an engineering

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put. Expressed in these terms, the Skalak formula can be regarded simply as a directive to input various items of information into the right-hand side of an equation. These data are then processed through multiple mathematical manipulations, until the required output emerges on the left-hand side of the equation as the solution F1. The need for this process to be repeated as many times as there are fixtures in the design places it well beyond the capabilities of most hand-held calculators; however, this kind of iterative processing is particularly well suited to a programmed solution on a computer.

Designing

IF3 Fig. 1. Diagrammatic representation of Skalak’s modelg for determining distribution of a vertical load (P) to six implant fixtures (F) that support a fixed partial denture. Fixture coordinates and point of force application are expressed in terms of x and y axes that intersect at center of gravity of six fixtures (0). (Reproduced from Skalak R. J PROSTHETDENT 1983;49:843-8, with permission)

structure that assumes a rigid beam (the denture framework) secured by elastic bolts (the gold-alloy screws). This model has been subjected to theoretical analysis81 lo, l1 and has served as a baseline in finite element analysis,r2 where its suitability as a model for cases using B&remark implant fixtures has been confirmed. Consequently, it would appear to provide the opportunity of testing whether a cantilever for a given fixture arrangement would overtax the configuration. However, as shown in Fig. 2, the chief obstacle to the everyday use of the Skalak model in the operatory lies in its inherent complexity. Because of the suitability for computerization of Skalak’s computation, it seemed sensible to create a computer program that might provide the clinician with an uncomplicated, quick, yet effective way of bringing the scientific benefits of Skalak’s computation to bear on the design applications of everyday practice. This article will describe such a program, which can be used without the need for any mathematical knowledge or computational skills beyond those required to operate the most basic PC-based practice-management package.

THE

COMPUTER

PROGRAM

Computer applications generically involve only three basic functions: data input, data processing, and data out496

the computer

program

The source code for the computer program was developed by use of a hybrid application of two separate yet linkable programming languages: Turbo-Prolog and Turbo-C (Borland International, Inc., Scotts Valley, Calif.). The former is a versatile, fifth-generation computer language originally designed to address artificial intelligence applications, but with outstanding graphics abilities and a built-in recursion mechanism. The latter is a language renowned for its elegance of syntax and a “number-crunching” ability that is well-suited to the mathematical demands of the required computation. The reason for using the two languages was the need to use these inherent qualities. Thus, Turbo-Prolog’s attractive user interface and windows feature was ideal for the solicitation of input information. However, even though its built-in recursion mechanism is ideal for summing up data in performing functions A and B of the formula, it is inherently less capable than Turbo C of handling the algorithm that is needed to compute the center of gravity of the fixture grouping and to deal with the more mathematical aspects of the process. At various points in the processing, therefore, parameters are passed from Turbo-Prolog to Turbo-C, which mathematicaIly manipulates them and then passes the products back to Turbo-Prolog for final display of the output. Although these various functions were initially developed, tested, and de-bugged as individual modules, they were finally linked and compiled into a runtime version capable of being accommodated on a floppy disk and running directly under MS-DOS (Microsoft Corporation, Redmond, Wash.) on a personal computer.

Inputs

required

by the program

The Skalak equation requires four essential items of input information, (1) P-the force acting on the implant prosthesis; (2) N-the number of implant fixtures; (3) Xi and Yi-the coordinates of the various fixtures, relative to orthogonal axes that pass through the center of gravity of the fixture grouping; and (4) X, and and Y,--the coordinates of the point of force application relative to the same center of gravity axes. These items are elicited from the user in the order given here. However, the information necessary for two of the inputs-items 1 and 3-requires that certain preparatory procedures be completed before the program can be run.

THE

of force. Designing prosthetic compothe capabilities of individual patients to overload them requires knowledge of the magnitude of the loading forces that such components will be required to bear. Assessing a patient’s occlusal force capability is of primary importance in this regard. Unfortunately, almost intractable problems surround its implementation, not only because of the enormous individual variability in occlusal force that is discernible in the literature,13 but also, as Carlsson and Haroldson’ have observed, that “. . . few measuring methods have been developed for routine clinical use.” These limitations have placed a decided limit on the use of Skalak’s model as a routine planning instrument. Researchers using t,he model have either expressed induced forces in terms of the magnification factor of the unit force applied,‘e or have worked with median values.15 Even if a simple and inexpensive device for measuring occlusai force becomes available, the problem would not be resolved. Preprosthetic force levels have been shown to increase 85 “( over the Z-month period following placement of osseointegrated prostheses.‘* Consequently, pretreatment evaluation of occlusal force in an edentulous patient would be patently insufficient to predict the eventual postintegration force capability that may develop. An indication of individual force determination may be provided by Wolff’s law, Ifi which states that, “Every change in the use or static relations of a bone leads not only to a change in its internal structure and architecture but also to a changein its external f’orm and function.” Variability in individual occlusal force can thus be quantified by examination of the muscular expression of occlusal function on associated bone morphology. Given that the chief muscular determinants of biting are the masseter and medial pterygoid muscles that enclose the angle of the jaw, it can be postulated that the bony morphology of the underiying gonial angle will provide a reliable expression of the inherent muscular biting power of any individual patient. Thus, the reaction of bone at the angle of the jaw will be in direct proportion to the tensile forces imparted by the masseter and medial pterygoid sling. A greater muscular force would result in greater buttressing and consequently a more acute angulation of the gonial angle, while the angulation in response to a lesser force would be more obtuse. A dual hypothesis” arising from this perception was that an increase in the contractile force of the muscles making up the masseter and medial pterygoid sIing wiII be accompanied by (1) an increase in the dimension of the interocclusal space and (2) a simult,aneous decrease in the angulation (or a sharpening) of the gonial angle. The first part of this hypothesis was tested on a sample of 130 dentate individuals, and a correlation between gonial angulation size and interocclusal space demonstrated a coefficient of correlation value of r = -0.7762.17 Regression analysis of the paired data provided a mathematical formula that permits cephalometric determination of interocclusal space in complete denture patients. This analysis has heen applied clinically for 10 years and found to he Determination

nents to withstand

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Fi = N’ + P(Axi + ByJ

Fig. 2. Computation required for calculating force magnitude generated at each implant fixture. Inputs required by computer program are: P, the force acting on prosthesis; IV, number of fixtures; Xi and Yi, coordinates of relevant fixture, relative to orthogonal axes through the center of gravity of fixture grouping; X, and Yp, coordinates of point of force application.

particularly successful in addressing

certain interocelusal space-related dysfunctional problems.‘s More recently, Nel et al.lg addressed the second part of the hypothesis and demonstrated a particularly strong correlation 0. = -0.91) between gonial angle values and occlusal force production in a dentate sample. With a coefficient of determination value of ? = 0.828 these data indicate that 82% of the variation in the one variable (occlusal force) can be attributed to its relationship with the other variable (gonial angle size) in each case. 2o This relationship has permitted a regression formula to be incorporated into the computer program that, given the input of a specific genial angle value, automatically calculates a “best” computed estimate of forcegenerating capability. Furthermore, in the light of the earlier observation that osseointegration will with time enhance an edentulous patient’s force generation to the equivalent of fully dentulous magnitudes,14 it seems appropriate to adopt a paradigm that is derived from fully dentulous data. The methodology of the act& cephalometric analysis involved has been described in detail elsewhere.r* Essentially, it involves identifying the cephalometric points of articulare and gnathion on a lateral cephaiogram and, from them, projecting tangential lines to the posterior and inferior aspects of the gonial angle (Fig. 3i. The angle they contain (measured in degrees) is the gonial angle value that is required to be input in the computer so as to predict the force capability of a particular subject. 497

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Fig. 3. Cephalometric gonial angle value gauged by measuring angle of intersection between tangential planes that pass through cephalometric reference points articulare and gnathion.

Determination and tranafer offixture location. To pickup the geometric positions of the implant fixtures from the working cast and register them on the computer, a transfer template is made. This template consists of a rectangular cut of acetate sheet that is laid over the working cast and the position of each fixture is carefully pricked into the upper acetate surface with a sharp instrument (Fig. 4). A rubber dam punch is then used to enlarge each penetration, which creates a series of circular holes in the acetate overlay that will have the same geometric pattern as that of the implant fixture grouping on the cast (Fig. 5). With the gonial angle determination and the template, the computer can now be programmed. Entering the gonial angle value for force computation andplanned number of fixtures. On start-up, the program displays an input window in which the user is prompted to enter the cephalometric gonial angle value as previously determined. On keying in the required information, the user is informed of the occlusal force value that would be typical for a specific angle, and is then prompted to key in the number of fixtures that are to be used. The user is now provided with a red screen on which a pair of eccentric yellow axes and a small white arrow are displayed (Fig. 6). The axes serve to assist the user in entering the various fixture positions. The arrow is the mouse

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cursor and can be moved about the screen in a way that corresponds to movement of the mouse on the user’s desktop. Entering the fixture locations. As prompted on the screen, the fixture positions are entered into the program in reverse order, starting at the intersect and working from the left of the screen to the right. The acetate template is taped to the screen with masking tape so that one terminal punch-hole is centered on the intersect and the opposite terminal punch-hole is placed on the yellow transverse axis line toward the right of the screen (Fig. 7). Fixture locations are then entered by successively clicking the mouse on each hole position in turn, pressing the spacebar after each entry to register that position. Registration is confirmed by the appearance of a small yellow circle at each location, joined to the previous entry by a fine white line. The latter is coincidental with the algorithm the program uses to compute the center of gravity of the fixture arrangement and provides visual evidence that the Turbo-C module that effects this function is operating correctly. With all of the fixture positions entered, the yellow orientation lines disappear, and are replaced by blue axes (Fig. 8) with their intersect the center of gravity of the fixture arrangement. As required by the Skalak formula, the x and y coordinates of each fixture location need to be recalculated in terms of these axes; however, this task is performed both automatically and invisibly by the program. Entering the force location. The user is now prompted to indicate the desired cantilever termination point, which represents a “worst case” loading location. As before, this location is recorded by positioning the cursor arrow at the desired spot and clicking the left button of the mouse. A small white bar appears on the screen to mark the spot, while further down on the screen, the coordinates of the point relative to the blue axes are displayed (Fig. 8). These coordinates are expressed in centimeters, and the scaling factor built into the program ensures that a centimeter measured on the screen corresponds to a standard centimeter. Therefore, once a decision has been reached as to optimum cantilever dimension, direct measurements can be taken from the screen and transferred to the working cast with dividers. output With all of the required input successfully entered, the user can activate the processing and output functions of the program by pressing the spacebar. At once, a list of fixtures in numerical order is scrolled down the screen-each accompanied by its associated force allocation, expressed in newtons (Fig. 8). Because one desires to optimize the cantilever dimension, the program provides the opportunity to sample various alternate cantilever lengths. As long as the user enters

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Fig. 4. Geometric arrangement of fixture assembly is taken from cast by pricking position of each fixture into acetate template with a sharp instrument. Fig. 5. Fixture assembly transfer template trimmed and ready for application to computer screen. Location holes in template are enlarged by use of rubber-dam punch. Fig. 6. Computer screen in readiness for input of fixture assembly pattern. White arrow is the mouse cursor. Fig. 7. Transfer template taped to screen with distal-most location holes oriented on yellow axes. Final registration (fixture 1) is about to be entered. White line connecting previously registered positions is generated by algorithm responsible for computing center of gravity and provides visual evidence that it is functioning properly. < y > in response to the prompt, “Would you like to recalculate using alternate cantilever parameters ?,” the program will provide the opportunity to enter multiple choices. With each new choice, the forces that pertain to that particular cantilever termination point will be listed, until a force profile emerges that will assure a design that will preclude the danger of implant overload. APPLICATION The purpose of eliciting load distribution values as described in the previous section is to minimize the possibility of biomechanical overload in implant prostheses by designing them to withstand overload. The gold alloy screw in the B&remark system is the weakest component; con-

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sequently, cantilever lengths should be designed so that occlusal forces distributed to individual fixtures do not result in gold-screw fracture. Because tensile forces usually cause gold-screw failure, the physical behavior of a screw under t,ension should be reviewed. The immediate response to tensile force application is screw elongation (Fig. 9). As is typical of most metals, this elongation is initially elastic, linearly proportional to the amount of tensile load applied. On removal of the load, the screw will return to its original length. With increasing magnitudes of force, however, a point will be reached beyond which the elongation of the screw will no longer be linearly proportional to the increase in load. This point is the elastic limit or yield st,rength of the screw, be-

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Fig. 8. Blue axes intersect at calculated center of gravity. Cantilever termination point has been marked on the screen (small white bar) and its coordinates displayed relative to blue axis lines. Outputs, an expression of forces in newtons that would be generated at each successive implant position, are instantaneously computed and listed in order on screen. Option to recalculate with alternate cantilever parameters is provided in program. Fig. 9. Gold screw elongation in response to tensile load is of elastic nature and increases in direct proportion to any increase in load (green urea). Beyond yield strength of the screw, further loading elicits an increasingly plastic elongation of screw (red area) until fracture occurs at point of ultimate tensile strength. Fig. 10. Hazard bandsdepict gold screwresponseto both the magnitude and frequency of load application. Fig. 11. Analytic exercise showsforce values that could account for fracture of all five gold alloy screws.3

yond which full dimensionalrecovery is no longer possible. Thus, any further load application will lead to increasing permanent deformation, until a load correspondingto the ultimate tensile strength of the metal is reached, at which fracture of the screw will occur. It is evident that elastic elongation of the gold screw would permit the joint between the gold cylinder and the abutment cylinder in the Branemark systemto open, with a possibledeleterious shift in the leveragesapplied to the implant. To ensurethat this shift doesnot occur, it is important that eachgold screwbe tightened, or preloaded to a value of 10 Ncm.21Preloading of the gold screw ensures that the gold cylinder fits securelyagainstthe abutment. As 500

a result of this preloading, additional external force application may not result in screw tension, but instead may cause a decreasein the compressiveforce acting on the screwjoint.21 Preloading enablesthe system to withstand loads of up to 250 N before the preload is overridden and opening of the joint occurs.Indeed, asreported by Ranger% et aLzl repeatedvertical loading of 200N, which is well below the opening point of the screw joint, resulted in “ . . . neither screwbreakagenor loosening,evenat l,OOO,OOO cycles.” Recent observationslink load to frequency of application (Fig. 10). Point A, for example, marks the ultimate tensile strength of the gold screw, where at a singleload applica-

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tion of 600 N5’ ?l, a2a fracture of the screw will occur. Point B marks the yield strength of the gold screw, which coincides with a tensile load of 400 N.21, 22 In theory, then, the gold screw, within its elastic range, should be capable of withstanding sustained cyclic loads of 1400 N without fracturing.

Interpreting

the force

values

To arrive at a clinically applicable interpretation of the force values that the program produces, the force spectrum depicted in Fig. 10 has been split into three color-coded hazard bands. The green band, predictably, represents a zone of safety. It accommodates loads of up to 250 N, which as long as proper attention is paid to details such as closeness of framework fit,23 are unlikely to lead to gold-screw failure no matter what the frequency of application might be. The amber-colored hazard band covers the region between 250 N and 300 N and can be construed as a zone of caution. It is at tensile loads within this range that the preload in the screw joint is likely to be overriden.21 Although the gold screw at these magnitudes of force is still operating well within its elastic range, the opening up of the joint consequent to the loss of the preload, and the accompanying introduction of alien leverage patterns is likely to have unexpected repercussions. It is noted that Patterson and Johns,15 although using the Skalak model in conjunction with a totally different analysis technique, arrived at an essentially identical conclusion regarding the vulnerability of the gold screw to cyclic loads in this region. Patterson and Johns’” used a Haigh diagram to demonstrate that the midline fixture of a five-implant configuration, when subjected to a tensile force of 273.13 N, will fall just outside of a “safe envelope” contained beneath the Cook-SnowLanger line of their diagram. In terms of Fig. 10, such a force would fall midway within the amber hazard band, which emphasizes the importance of adequately maintained levels of preloading. The red band covers the range from 300 N upward to the ultimate tensile strength, at which a single load of 600 N will cause the gold screw to break. This zone indicates maximum hazard and should be avoided. As indicated by the connecting line between points A and B, forces in descending magnitude from the 600 N singularity point of ultimate tensile strength will be tolerated over a broadening frequency band. However, any dimensionalaccommodation by the gold screw at these levels will be nonelastic and must inevitably lead to fatigue fracture. In the hypothetical caseused to illustrate the computer application, the assumptionswere that an individual with a gonial angle of 111 degreeswould typically have an occlusalforce of 125N. With a force of this magnitude applied to the extremity of a cantilever, at a point 2.49cm distal to the transverse axis of a five-unit fixture arrangement, the induced-force outputs (Fig. 8) reveal that, of the five fixture responseslisted, only one would give sufficient

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causefor alarm. With a computed load responseof -278 N, fixture 3 would fall within the amber zone, which would be an indication to incorporate a shorter cantilever into the final design.Applying the 20 mm cantilever limitation rule in this particular casewould safely place all force values within the bounds of acceptability. However, this finding should not be construed as an intimation of its universal applicability. Fig. 11 illustrates the importance of considering the geometric configuration of the fixture arrangement before applying the 20 mm rule. For this analysis (Fig. II), a tracing has been used of a casein which all five gold screwsfractured.” Although the cantilever length wasin strict accordancewith the rule, an arbitrary force application of 100N would have resulted in three of the fixtures experiencing tensile loads in the red hazard zone of Fig. 10. For fixture 4, the load would have been in excessof the gold screw’sultimate tensile strength of 600 N. Applying the computer program’s facility to sampleshorter cantilever lengths, the clinician can quickly determine a cantilever dimension that will be below the threshold of excessivelevels of force dispersal.To assistin this process,and to alert the user to the possibility of untoward levels of force generation, a watchdog facility has been incorporated in the program. This watchdog checks each force prediction as it is being calculated. If a tensile force prediction between the magnitudesof 250and 300 N (the amber zone) is detected, an immediate warning is flashed to the screen: Force on this fixture is likel~v to override 10 Ncm preload. . _. Similarly, tensile force generation in excessof 300 N (the red zone), will result in the warning: THIS FIXTURE IS IN DANCER OF COMPONENT FAILURE!

FUTURE

DIRECTIONS

There is a needto review and refine the precision of this program’s predictive abilities as an ongoingpriority. This review requiresconstant measurementof the veracity of its output against available research data, giving critical attention to both the quality of its input and the appropriatenessof its processes.

Quality force

of input:

The question

of occlusal

The useof gonialanglesizeasa predictor of occlusalforce will always be open to question, becauseit will always remain only an approximation. However, the useof a median value is also an approximation. Patterson and John@ madeuseof a medianvalue of 143N in applying the Skalak model to predict component fatigue in Branemark implants. They admitted that valuesfour times aswell ashalf as much as this figure can be found in the literature. The advantage of the gonial angle predictor is that it allowsone to addressboth extremes, together with the entire spectrum of possibilities in between. The implications of this opportunity are clear: future studies will require that the correlation between occlusalforce and gonla1angle size be 501

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extended to involve a far greater sample size, thereby enhancing both the precision and the practical relevance of the statistic. In addition, clinical studies are underway to test the reliability of this method as a predictor of biomechanical overload in both retrospective and prospective clinical cases.

Appropriateness of the Skalak

of processes: Suitability model as a predictor

Recent research studieslo* l1 have cast some doubt on the validity of Skalak’s root assumption of infinite rigidity of bridge and jawbone. Investigating the Skalak principle, Mendelson and Brunskill constructed an experimental model that consisted of rigid steel plates joined by from four to six semicircularly arranged load-sensing bolts. When external loads were applied to the top plate, axial load dissemination to the various “implant” bolts agreed with mathematical predictions by use of Skalak’s formula. However, when the solid square upper plate was substituted with a more denture-like U-shaped plate, it was found that the Skalak predictions tended to underestimate loading on the implants closest to the point of external force application and overestimate loads on those further away. These observations were confirmed in a separate experiment that featured fixtures screwed into a rigid aluminum block and supporting a silver palladium metal framework of the Branemark type. The results of both experiments led Brunski’O to suspect the influence of bridge flexibility. By using models developed at the University of Sheffield that incorporate the elastic rigidity of the prosthesis (EI), he was able to make predictions that were closer to the experimental values obtained than those calculated according to Skalak.lO Subsequently, Elias and Brunski12 confirmed these observations by using 3-D finite element analysis. However, suspecting that the bone/implant interface would confer an in vivo stiffness far less than the rigid lower element in the experimental models would allow, these workers modified their hardware so as to give expression to stiffness values as reported for Branemark implants in bone (1 to 10 N/PM). The significant effect of this modification was that it brought the predictions obtained from the finite element analysis back into line with those of the Skalak model. Which of the experimental assumptions reviewed will ultimately provide the truest mirror of clinical reality will eventually emerge as the result of adequate in vivo experiment. At present, according to Patterson and Johns,15 “ . . . more sophisticated models do not appear to have been developed, [while] . . . data from clinical experiment are also not available”; consequently, data obtainable by applying Skalak’s method “. . . are probably the best available.” In the meanwhile, and in the light of this affirmation, there seems to be little reason to doubt the usefulness of the Skalak model as the basis for prosthesis design.

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REFERENCES 1. Zarb GA, Schmitt A. The longitudinal clinical effectiveness of osseointegrated implants: the Toronto study. Part I. Surgical results. J PROSTHET DENT 1990;63:451-7. 2. Zarb GA, Schmitt A. The longitudinal clinical effectiveness of osseointegrated implants: the Toronto study. Part II. The prosthetic results. J P~o~~~~~D~~~1990;64:53-61. 3. Zarb GA, Schmitt A. The longitudinal clinical effectiveness of osseointegrated implants: the Toronto study. Part III. Problems and complications enc0untered.J PROSTHETDENT 1990;64:185-94. 4. Shackleton JL, Carr L, Slabbert JCG, Lownie JF. Prosthodontic complications and problems of fixture-supported prostheses [Abstract]. J Dent Res 1992;71:1113. 5. Rangert B, Jemt T, J&n&s L. Forces and moments on Branemark implants. Int J Oral Maxillofac Implants 1989;4:241-7. 6. Davis DM, Zarb GA, Chao Y-L. Studies on frameworks for osseointegrated nrostheses: Part 1. The effect of varying the number of supporting abutments. Int J Oral Maxillofac Imp&s 1988;3:197-201. implant system. Clinical and lab7. Beumer J, Lewis SG. The Branemark oratory procedures. St Louis: Ishiyaku EuroAmerica, 1991:73. and occlusal rehabilita8. Hobo S, Ichida E, Garcia LT. Osseointegration tion. Tokyo: Quintessence Publishing 199Oz278. 9. Skalak R. Biomechanical considerations in osseointegrated prostheses. J PROSTHETDENT~~S~;~%~~~-~. 10. Brunski JB. Forces on dental implants and interfacial stress transfer. In: Laney WR, Tolman DE, eds. Tissue integration in oral, orthopedic and maxillofacial reconstruction. Chicago: Quintessence Publishing, 1992:108-24. 11. Mendelson M, Brunski JB. Force distribution among dental implants: measurements from laboratory models [Abstract]. J Dent Res 1991; 70:460. 12. Elias J, Brunski JB. 3-D Finite element analysis of axial loads on dental implants [Abstract]. J Dent Res 1991;70:460. 13. Brunski JB. Biomechanics of oral implants: future research directions. J Dent Educ 1988;52:775-87. 14. Carlsson GE, Haraldson T. Functional response. In: Branemark P-I, Zarb GA, Albrektsson T, eds. Tissue-integrated prostheses. Chicago: Quintessence Publishing, 1985:155-63. 15. Patterson EA, Johns RB. Theoretical analysis of the fatigue life of fixture screws in osseointegrated dental implants. Int J Oral Maxillofac Implants 1992;1:26-33. 16. Wolff J. In: Blakiston’s New Gould Medical Dictionary, 1st ed. Philadelphia: Blakiston Company, 1949. 17. Potgieter PJ, Monteith BD, Kemp PL. The determination of free-way space in edentulous patients-a cephalometric approach. J Oral Rehabil 1983;10:283-93. 18. Monteith BD. The role of the free-way space in the generation of muscle pain among denture-wearers. J Oral Rehabil 1984;11:483-98. 19. Nel MS, Potgieter PJ, Benninghof W, van der Merwe S. Bite force: the morphologic relation. J Dent Assoc South Afr (in press). statistics, 4th ed. London: Prentice20. Freund JE. Modern elementary Hall International, 1974. 21. Rangert B, Gunne J, Sullivan DY. Mechanical aspects of a Branemark implant connected to a natural tooth: an in vitro study. Int J Oral Maxillofac Implants 1991;6:177-86. 22. Jemt T, Carlsson L, Boss A, JBrnBus L. In viva load measurements on osseointegrated implants supporting fixed or removable prostheses: a comparative pilot study. Int J Oral Maxillofac Implants 1991;6:413-7. in 391 consecutively inserted fixed 23. Jemt T. Failures and complications prostheses supported by Briinemark implants in edentulous jaws: a study of treatment from the time of prosthesis placement to the first annual checkup. Int J Oral Maxillofac Implants 1991;6:270-6. Reprint requests to: DR. BRIAN D. MONTEITH, DEPARTMENTOFPROSTHOWNTICS, P.O.MEDUNSAO~O~ SOUTH AFRICA

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