Theoretical Mechanics And PracticalOrthodontics *SAM WEINSTEIN, D.D.S.,** andDONALD C. HAACK, M.S.,***Lincoln, NeOiaskaINTRODUCTIONContemporary education, receivingits nutrients from basic research, con-tinually refutes any policy of isolation-ism of the separate disciplines. Whilethe boundaries between the basicsciences, at least by definition, may besharp and definitive, any comprehen-sive research demands an interplay ofbodies of knowledge-a synthesis of dis-ciplines. The complexity of the prob-lems of the physical world, just asthose of the social, encourages abreakdown of isolationism. Particu-larly in the biological sciences is themultidisciplined approach becomingnecessarily apparent. The biochcinicalmarriage is a most solid and enduringone. The nuptial vows of biophysicsare more recent.As Rashcvsky suggests, "applicatioiiof mathematics to special biologicalproblems is not new, but a systematicmathematical biology is timely. It i3not now possible to `explain away'phenomena of life in terms of physics,but this approach may be dcvelopcdin the future. Since biological phcno-inena are closely related to physicalphenomena,-there is a desire to unifyall natural sciences."The attempt at explaining the ori-* Presented at the January, 1959 meeting ofthe Midwestern Component of the Edward H.Angle Society.** Associate Professor, Department of Ortho-dontics, University of Nebraska.*** Associate Professor of Engineering Me-chanics, Lecturer, Graduate Department ofOrthodontics, University of Nebraska.gin of life from non-living thiriqs ~ccnisnearer reality. Urey's classical work olthe production of amino acids by sui)-jecting certain simple gases to clectri-cal discharge suggests a rapport be-tween the viable and the nonviable-aunification of natural sciences.To those disciples of practicalityand office efficiency, it is acknowledg-ed that purely theoretical hypothesiz-ing may not have immediate practicalinterest of even urgent direct applica-tion to some experimental set-up, letalone positive correlation to this year'sincome. However, the history ofphysics reveals that pure theoreticaldevelopments led decades later to mostastonishing practical results. Today'seminently useful duality of the brni-son and cataclysm of atomic fission aresomc years removed from the theore-tical dreamings of Bohr and Einstein.Morc pragmatically, Gottlieb suggests:"The results of today's research is des-tined to be an integral part of thcpractitioner's work of tomorrow."In contemporary orthodontics, aunique situation attains in that thedentist must of necessity combine hisknowledge of the problems, sciences,and techniques of general dentistrywith sciences usually considered taii-gential to his field-such disciplinesas embryology, growth and develop-ment, anthropology, biochemistry, andparticularly the science of force action-mechanics.These additional disciplines are ~p-plicable to orthodontics, not in thesegregated sense, but as important in-177 178 WeinsteinJuly, 1959tegrated parts of the whole. It is prin-cipally with the science of mechanicsand the importance of its applicationto orthodontics that this paper is con-cerned.The physiological reactions whichpermit the movement of a tooththrough its bony environment cannotbe fully understood independent of aconcomitant understanding of the ac-tions of the initiating forces. Becauseof the classical work of Oppenheinl,Sandstedt, Moyers, Storey, etc., sonic:significant information is now avail-able concerning the biological changesoccurring during tooth movement.Though the mechanism of tooth move-ment is basically biological, it is ini-tiated by force action and, until suchtime as teeth can be moved by injec-tions or internal medication, the or-thodontist will be vitally conccrnedwith mechanics.Sicher, whose impact on the biology~f =r:h =n:ics has !xt.n significant.feels that in our contemporary at-tempts to surplant the early "mechan-istic" or gadget approach by a morescientific biological one, we have tend-ed to forget the pure physics.Furtherniorc, research into dic ti ucnaturc of the biological mcchanisnl oltooth movement is fruitless without aparallel understanding of the forcc ac-tion involved. Within the next decade,biophysical rcsearch in the field ot or-thodontics should answer a number ofimportant questions, soinc of M hichmight be:What is the quantitatiw relation-ship between rate of tooth inmement through its bony environ-ment and the reactivc pressiiieson the tooth root?What part is playcd by thc miis-culature and the geomctry of thesupporting bony structure in cs-tablishing positional stahilitv ofthe dentition?Can muscle tonus, i.e., thc forcewhich it exerts, he changed toaccommodate new positioiis ofstability of the teeth?What is the relationship of` prcs-sure and the immediate deforma-tion of the periodontal ligament?Can growth of bone tissue be re-tarded by mechanical means?THE IMPORTANCE OF THE CONCEPT OF EQUILIBRIUMThe principle of equilibrium isinanifcst in many branches of science,physical and biological. All bodies arein equilibrium with their surround-ings. Equilibrium controls the be-havior of the stars in the heaven andthe fish in the seas. The motion of theplanets of thc solar system and the nio-tion of the electrons of the atom aremanifestations of the same principle.The universality of the concept olcquilibrium is such that the fact rhatteeth are in equiiibrium with iiwbsurrounding environment cannot bcquestioned. The equilibrium withwhich orthodontics is primarily con-ccrned is the static equilibrium offorces. In order that the body, in thiscase a tooth, be in static cquilibrium,two conditions must be satisficd: 1.The vcctor sum of a11 forccs acting onthe tooth must equal zero, 2. the vectorsum of all moments of forccs acting onthc tooth relative to any point mustalso be zero. Forces which may act onthe tecth include those applied direct-ly by the surrounding musculature,forces due to natural functions, suchas mastication, forces due to pernicioushabits, forccs due to the prcsencc oforthodontic appliances, and thc i`etcc-five forces applied to the roots ol thcteeth by the surrounding bony struc-ture through the periodontal liga-ment.From the standpoint of the ortho-dontist, the idea of equilibrium of thc Vol. 29. No. 3MechanicsI79tooth can he further analyzed. In linewith the above hypothesis, it is ob-vious that the tooth must he in cquili-briurn at any particular instant. Now-ever, it may not be so self-evident thatthe teeth must also be in a mean stateof equilibrium extending over a con-siderable period of time. Over sucha period the effects of short term ran-dom forces can be expected to nullifyeach other so that the resultant toothmovement would be zero.Resultant forces of long durwionand repeated application cnter intothe mean equilibrium picture xiid un-der ordinary circumstances causemovement of the teeth. A rcisiiltantforce in this case may be describedas a sort of net force. For instance, apremolar subjected to a .1 07. forccexerted by the buccinator musculaturrand simultaneously subjected LO, say,a .3 oz. force exerted by thc tonguecould be said to be subjected to a .I!oz. force exerted by the tongue anddirected buccally. As long as the crow~iof a tooth is acted upon by a longterm resultant force, the mean equili-brium of thc tooth must be acconi-plished by the development of reac-tions exerted on the root through theperiodontal ligament. Such reactiveforces are the initiators of biologicalactions which culminate in toothmovement.It must be emphasized that dura-tion of application, as well as thevector properties of force, is importantin determination of the mean state ofequilibrium. It may be hypothesizedthat the product of force magnitudeand time controls the rate of toothmoveinen t.STABII-ITYAn additional area of theoreticalmechanics which is of great iniport-ance to the orthodontist is stability.The orthodontist is concerned withthe movement of teeth from positionsof malocclusion to positions of goodocclusion, but he should be concernedfurther with the stability of theteeth in their new positions. Puttingthe teeth into new positions of in-stantaneous static equilibrium is notenough. These positions must be onesof stable static equilibrium so that thcteeth will not tend to drift back totheir old positions of malocclusion orto new positions of malocclusion withthe passage of time.In general, a stable position is oneto which a body will return readilyand of its own accord if subjccted tominor displacement. That is, theminor displacement referred to willcause th.e body to be subjected toforces which will dictate a return to itsoriginal position. If, however, theminor displacement causes the body tobe subjected to forces tending to fur-ther increase the displacement, thebody is said to be in an unstable equil-ibrium position.Stability must camider the origin ofsome of the forces that act upon theteeth as previously mentioned, i.e.,those forces emanating from the mus-culature, natural functions, or perni-cious habits. These are the forceswhich must dictate whether or not atooth is in a stable position. It shouldbe noted that these forces do not ill-clude those exerted by the appliance,since consideration cif these applianccforces could bc justified only if thepatient were to wear some sort of re-tentive device indefinitely.Fischer points out, in connixtionwith hazards of treatment, that "thestability of the denture in malocclu-sion is thc result of the very sameforces that will be responsible for t.hefinal positioning of the teeth aftertreatment."Purely from the standpoint of niech-anics, stable positions of equilibriumarealways positions in which the ener- 180WeinsteinJuly, 1959gy stored in the system is a minimum.Since the laws ,of mechanics are appli-cable to the teeth individually and tothe dentition as a whole, it must beconcluded that stable positions of thedentition and its elements are posi-tions in which the energy stored inthe system is minimal. Here the sys-tem in which energy is stored must beconsidered to be the teeth, the perti-nent bone structure, and particularly,the surrounding musculature. In someinstances there may be but one stablelocation for a tooth or segmcnt of thedentition, but in many circumstancesthere may be multiple positions inwhich stability will be achieved. Anexample of such multiple positions ofstability would be molar crossbite.The maloccluded position is stable,since there is no tendency for thetooth to move from this position or tocorrect itself. This malocclusion repre-sents one of several energy minima.When this crossbite is cui-Iecied oribdontically, a new position oE Ininimiimenergy is achieved and tlie result isalso stable.Relapse of the treated dentition in-dicates that the teeth were left in un-stable positions at the conclusion oftreatment. Stability of the dentitionneed not imply that the teeth are sta-tionary, since growth may present achanging set of conditions to which theteeth become adapted by appropriatemovements. It can, however, be cate-gorically stated that every relapse isthe end result of instability. MECHANICS OF MATERIALSAnother subdivision of mechanicswith important ramifications in ortho-dontics is that of the mechanics of ma-terials. Where mechanics as a whole isconcerned with the forces of motions,mechanics of materials, in partic:ular,is concerned with stresses, mains, anddeformations. Since orthodontic forcesare exerted through the medium of- . -.fabricated appliances, it is necessarilyapparent that a knowledge of themechanical properties of the materialsinvolved is most essential. Each appli-ance as constructed by the orthodon-tist has certain essential mechmicalcharacteristics, such as strength, stilf-ness, and resilience (energy storagecapacity). These properties of the ap-pliance are dependent upon thc in-trinsic properties of the material,strength, stiffness, hardness, and re-silience, as well as the extrinsic prop-erties characteristic of the appliancedesign, such as shape and size. Im-portant quantitative characteristics ofthe appliance are dictated by the lawsof mechanics of materials, and are ofdirect concern in that they control themagnitude of the forces exerted bythe appliance, the deformation of theappliance, and the rate at which forcewill be dissipated. Since these proper-ties govern the basic mechanics of theance for a thorough undersranding ofthis essential tool.---1:,--- .LA.. -,..,, -c *.trn .e* ;,,7,,nvt.appi1aiic.c uicy alc VI ULLL ~~tSUMMARY1. Scientific orthodontics requires amultidisciplined approach. No singlebranch of basic science can be suffi-cient support for its complete under.standing.2. Of particular importance to or-thodontics is the science of theoreticalmechanics- the science of force action.Unfortunately, most graduate studentsin orthodontics are not sufficientlyprepared in this area by their under-graduate or professional training.3. The importance of ;in under-standing of force action should be self-evident in view of the fact that forcemust be relied upon to initiate biolo-gical reaction in the iriovement ofteeth.4. The concept of equilibrium isessential to an understanding of theforces acting upon individual teeth Vol. 29. No. 3 Mechanics181or upon segments of the dentition.Such forces must include not dvthose acting upon the crowns bur alsothe reactions upon the roots.5. Since one of the criteria of suc-cessful treatment is the absence of re-lapse, stability is of primarv tonc-ernin orthodontic therapy. Theoreticalmechanics is the key to understandingand recognizing the characteristic\ 01stable and unstable conditions.6. The application of orthodonticforces through fabricated appliancesmakes essential an understanding ofthe mechanical properties of the ina-terials of which these appliance., aremade. Mechanics of material., is thediscipline embodying such know-ledge.309 Andrew HallREFERENCESRashevsky, N. : Mathematical Biophysics,Univ. Chicago press, Chicago 1938.Wald, George: "The Origin of Life",Physics and Chemistry of Life-flcientificAmericam, Simon and Schuster, New York,1965.Gottlieb, Bernard. : ` ` Histological Consider-ations of The Supporting Tissues of theTeeth", J.A.D.A. 30: 1859-1883, 1913.Oppenheim, Albin : ` ` A Possibjlity ForPhysiologic Orthodontic Movement ", A.J.O. and 0.8. 30: 277-327, 345-368, June1944.Standstedt, C. : " Einige Beitrage ZurTheorie Der Zahuregolierung ' I, NordiskTandlafiaretidscrift, 1904-1905.Moyers, Robert E.: "Peridontal Membranein Orthodontics", J.A.D.A. 40: 22-27 Jm-uary 1956.Storey, Elsdon : ` ` Bone Changes AssociatedWith Tooth Movement, A RadiographicStudy", Australian J. of Dentistry 67 :57, April 1953.Fischer, Bercu: Orthodontics, W. B. Saup-ders, Phil., 1952.