Prostorove pomeï ry v distaâ lnõâm uâ seku dolnõâho oblouku Space in the distal region oflower arch

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Prostorove pomeÏry v distaÂlnõÂm uÂseku dolnõÂho oblouku

Space in the distal region oflower arch

* MUDr. Bc. ZdeneÏk Haken, * MUDr. Hana TycovaÂ, ** Mgr. KaterÏina LangovaÂ

* Ortodonticke oddeÏlenõÂ, Stomatologicka klinika1.LFUK aVFN v Praze

* Department of Orthodontics, Clinic of Dental Medicine, 1st Medical Faculty of Charles University in Prague ** Katedra leÂka rÏske biofyziky, LF UP Olomouc

** Department of Medical Biophysics, Medical Fakulty, Palacky University in Olomouc Souhrn

Je pojednaÂn vyÂvoj prostoru v lateraÂlnõÂm uÂseku dolnõÂho oblouku. Byla provedena analyÂza prostoru distaÂlneÏ od prvnõÂho staÂleÂho molaÂru. Byl sledovaÂn lineaÂrnõ parametr Ar-Pg, uÂhly ANB a Goniovy uÂhel. Do souboru byli zarÏazeni jedinci, u kteryÂch byly k dispozici dva kefalometricke snõÂmky, zhotovene v obdobõ prÏed a po pubertaÂlnõÂm ruÊstoveÂm spurtu.

CõÂlem praÂce bylo vyhodnotit velikost zmeÏny meÏrÏenyÂch lineaÂrnõÂch a uÂhlovyÂch parametruÊ po probeÏhleÂm puber-taÂlnõÂm ruÊstoveÂm spurtu a zjistit, zda existuje zaÂvislost mezi meÏrÏenyÂmi parametry na dolnõÂ cÏelisti a prostorem di-staÂlneÏ od prvnõÂho staÂleÂho molaÂru.

Po probeÏhleÂm ruÊstoveÂm spurtu bylo zjisÏteÏno statisticky vyÂznamne zmensÏenõ GonioveÂho uÂhlu a uÂhlu ANB. Byla prokaÂzaÂna korelace mezi velikostõ zmeÏny Ar-Pg a prostorem distaÂlneÏ od prvnõÂho dolnõÂho molaÂru. Korelace mezi velikostõ zmeÏny GonioveÂho uÂhlu, uÂhlu ANB a prostorem distaÂlneÏ od prvnõÂho dolnõÂho molaÂru nebyla prokaÂzaÂna (Ortodoncie 2010, 19, cÏ. 3, s. 27-34).

Abstract

The space development laterally in the lower arch was discussed. The space analysis was performed in the region distally from the first permanent molar. The linear parameter Ar-Pg, angles ANB and Gonion were registe-red. The sample included patients with two cephalograms - one taken prior and the other after the growth spurt. The aim of our work was to assess the change of linear and angular parameters after the growth spurt, and try to find out the relation between the measured parameters in the mandible and the space distally from the first per-manent molar.

After the finished growth spurt we indicated statistically significant decrease of the Gonion and ANB angles. The correlation between the change Ar-Pg, and the space distally from the first lower molar was proved. The re-lation between the change of Gonion, ANB angles and the space distally from the first lower molar was not found (Ortodoncie 2010, 19, cÏ. 3, s. 27-34).

KlõÂcÏova slova:distaÂlnõ steÏsnaÂnõÂ, prostorova analyÂza, erupce druheÂho molaÂru. Key-words:distal crowding, space analysis, second molar eruption

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Introduction

The evaluation of space condition in permanent dentition the segmental analysis on models is used. In mixed dentition the Moyers analysis is necessary. Using these methods we can judge the space suffi-ciency after eruption of lateral teeth. However, this is only the space in front of the first permanent molar.

Sometimes the space behind the first permanent mo-lar is paid less attention. In permanent dentition, we often take it into the consideration only if we have to solve some unfavourable situation. During the second phase of change of dentition as well as in the early sta-ges of second permanent molar eruption the space beyond the first permanent molar does not have the final size. Moreover, in the space is often found not only the second molar but also the third molar germ.

The impacted teeth are most often the lower third molars. On the other hand, the impaction of second permanent molar is rather rare. Prece [1] gives preva-lence of 0.06%. The space for the second molar in den-tition is determined also from the evolutionary view-point. The impaction of second molar may occur so-metimes under the known circumstances; however, sometimes we cannot determine the cause.

This study aims to make the space analysis of the lower dental arch, distally off the first permanent molar. The analysis was performed before and after the growth spurt. We monitored the linear parameter Ar-Pg and ANB and Go angles. We also measured the space located distally off the lower first molar (Dist). The aim of the study was to evaluate the changes in li-near and angular parameters after the finished growth spurt, and to find the correlation between the parame-ters given above and the space located distally off the first permanent molar (Dist).

Material and method

Only the patients with a lateral cephalometric pictu-res before the growth spurt (upper limit stated as CVMSII stage inclusive), and after the growth spurt (lo-wer limit set at CVMS IV, inclusive). To determine the stage of skeletal development, we used a modified evaluation of cervical vertebrae according to Baccetti [2, 3]. The age range was 7-18 years. The mean age of patients before the growth spurt was 9.9 years, and after the growth spurt 14.7 years.

At the beginning 134 patients were chosen; later the patients who underwent extractions were left out, as well as X-rays of an insufficient quality.

The sample consisted of 80 patients treated with fi-xed appliances at the Department of Orthodontics, 1st Medical Faculty Charles University in Prague. There were 22 males and 58 females in the sample.

UÂvod

Pro posouzenõ prostorovyÂch pomeÏruÊ ve staÂleÂm chrupu pouzÏõÂvaÂme metody segmentaÂlnõ analyÂzy saÂd-rovyÂch modeluÊ. Ve smõÂsÏeneÂm chrupu maÂme k dispozici Moyersovu analyÂzu. TõÂmto postupem muÊzÏeme s urcÏi-tou pravdeÏpodobnostõ posoudit dostatecÏnost pro-storu, ktery maÂme k dispozici pro prorÏezaÂnõ postran-nõÂho uÂseku chrupu. Jedna se vsÏak pouze o prostor vy-mezeny prÏed prvnõÂm staÂlyÂm molaÂrem.

Prostor distaÂlneÏ od prvnõÂho staÂleÂho molaÂru neÏkdy unika pozornosti. Ve staÂleÂm chrupu si jej cÏasto vsÏõÂ-maÂme a zÏ s potrÏebou rÏesÏit neprÏõÂznivou situaci. Ve druhe etapeÏ vyÂmeÏny chrupu, ani v pocÏaÂtecÏnõÂch staÂdiõÂch erupce druheÂho staÂleÂho molaÂru, nema prostor za prvnõÂm staÂlyÂm molaÂrem definitivnõ velikost. NavõÂc v tomto prostoru se veÏtsÏinou nachaÂzõ vedle druheÂho molaÂru i zaÂrodek trÏetõÂho molaÂru.

K retenci dochaÂzõÂnejcÏasteÏji u trÏetõÂch dolnõÂch molaÂruÊ. K retenci druheÂho staÂleÂho molaÂru dochaÂzõ naopak zrÏõÂdka, Prece [1] uvaÂdõ prevalenci 0,06 %. Druhy molaÂr ma i z hlediskaevoluce svuÊj prostor v chrupu vymezen. K retenci druheÂho molaÂru muÊzÏe dochaÂzet zaokolnostõÂ, jejichzÏ podstata je znaÂmaÂ, jindy vsÏak pravou podstatu tohoto neprÏõÂzniveÂho jevu spõÂsÏe odhadujeme.

CõÂlem teÂto praÂce je proveÂst prostorovou analyÂzu v zubnõÂm oblouku dolnõ cÏelisti, distaÂlneÏ od prvnõÂho staÂ-leÂho molaÂru. Pro analyÂzu bylavybra naobdobõ prÏed apo pubertaÂlnõÂm ruÊstoveÂm spurtu. Byl sledovaÂn lineaÂrnõ znak Ar-Pg a uÂhly ANB aGo uÂhel. MeÏrÏen byl i prostor di-staÂlneÏ od prvnõÂho dolnõÂho molaÂru, oznacÏeny jako Dist. UÂkolem praÂce je vyhodnotit velikost zmeÏny meÏrÏenyÂch li-neaÂrnõÂch auÂhlovyÂch parametruÊ po probeÏhleÂm pubertaÂl-nõÂm ruÊstoveÂm spurtu. DalsÏõÂm cõÂlem je stanovenõÂkorelace mezi zmõÂneÏnyÂmi parametry a prostorem distaÂlneÏ od prvnõÂho staÂleÂho molaÂru, znakem Dist.

MateriaÂl a metodika

Do souboru byli zarÏazeni pouze pacienti, u kteryÂch byl zhotoven profilovy rentgenovy snõÂmek v obdobõ prÏed spurtem (shoraohranicÏeno stadiem CVMS II, vcÏetneÏ) av obdobõ po ruÊstoveÂm spurtu ( zdolaohrani-cÏeno stadiem CVMS IV, vcÏetneÏ). Pro urcÏenõ stadia vy-zraÂvaÂnõ skeletu bylapouzÏitamodifikovana metoda hodnocenõ krcÏnõÂch obratluÊ podle Baccettiho [2, 3]. VeÏ-kove rozmezõ ve sledovaneÂm souboru bylo 7-18 let PruÊmeÏrny veÏk pacientuÊ v obdobõ prÏed ruÊstovyÂm spur-tem byl 9,9 roku apo spurtu 14,7 roku.

ZaÂkladnõÂ vyÂbeÏr cÏõÂtal 134 pacientuÊ, kterÏõÂ splnÏovali podmõÂnku dvou daÂlkovyÂch rentgenuÊ zhotovenyÂch ve zmõÂneÏnyÂch ruÊstovyÂch faÂzõÂch.

Z tohoto zaÂkladnõÂho vyÂbeÏru byli vyrÏazeni pacienti, u kteryÂch bylauskutecÏneÏnaextrakcÏnõ leÂcÏba . Da le byly vyrÏazeny rentgenove snõÂmky, u kteryÂch nebylo mozÏno

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Before the measurement all cephalograms were di-gitalized. We used scanner Epson Perfection V700 Photo, resolution 6400 x 9600 dpi. For the monitor out-put the maximum resolution of 100 dpi was selected. The analysis was performed on the graphic screen EIZO 22º, model S2242W, high-definition resolution 1920 x 1200 dpi.

The digitalized pictures were processed with PCdentÒsoftware, Dialog MIS, and with Excel of MS

Office 2007. Before the analysis, each X-ray was cali-brated with reference distance and scale.

Ricketts growth analysis of the mandible served as the basic model for the method used in our study [4]. Constructed and anatomical cephalometric points [4, 5, 6] were used as reference points in the cephalome-tric analysis.

Gonion angle and the angle ANB were used from angular measurements. Linear distance Ar-Pg showed the length of the mandible.

Following are the points and lines which are not used so frequently:

SPo (suprapogonion) - the point on the anterior sur-face of symphysis. Ricketts located the point in the area where convexity of mental protuberance transfers into concavity, i.e. between the points B and Po. The most accurate results are obtained by the use of cra-nial edge of cortical crest, ventrally surrounding symp-hysis.

Xi (point Xi) - the constructed point on the mandible ramus, found between (or on some of) the contours of the mandible channel (for the construction of the modi-fied point Xi - Fig. 1).

M (point M) - the constructed point at the crossing of perpendicular lines V-ref. and H-ref. (Xi-SPO) at the place of the most distal surface of the crown of the lo-wer first molar (Fig. 1).

Modified construction of Xi point:

The modification of the Ricketts method is based on the choice of adifferent reference line. Ricketts employed Frankfurt horizontal. However, this was not acceptable for our work due to insufficient repro-ducibility. Therefore, we used S-N line in our work as this line may be determined with sufficient accuracy.

The construction of Xi point involved several steps. First we plotted atangent to the most inferior point of mandibular notch that goes parallel with S-N line. Then we drew a straight line parallel with S-N line, so that it became the tangent to the lower border of the mandi-ble at the place where convexity of the mandimandi-ble angle transforms into concavity of the lower border of the mandible. Finally, we plotted tangents to the anterior and posterior concavity of the mandible ramus per-pendicular to S-N line.

z duÊvodu nõÂzke technicke kvality spolehliveÏ odecÏõÂst meÏrÏene znaky.

Soubor byl sestaven z 80 jedincuÊ leÂcÏenyÂch fixnõÂm aparaÂtem naortodontickeÂm oddeÏlenõ 1. LFUK aVFN v Praze. Ve sledovaneÂm souboru bylo 22 muzÏuÊ a58 zÏen. PrÏed vlastnõÂm meÏrÏenõÂm byla provedena digitalizace vsÏech kefalometrickyÂch snõÂmkuÊ. PouzÏit byl skener Epson Perfection V700 Photo s optickyÂm rozlisÏenõÂm 6400 x 9600 dpi. Pro vyÂstup namonitor bylo zvoleno maximaÂlnõ rozlisÏenõ 100 dpi. AnalyÂzabylaprova deÏna nagrafickeÂm monitoru EIZO 22º model S2242W s vy-sokyÂm rozlisÏenõÂm 1920x1200 boduÊ.

Takto digitalizovane snõÂmky byly zpracovaÂny po-mocõÂprogramu PCdentÒ, spolecÏnosti Dialog MIS a

po-mocõ Excelu sady MS Office 2007. KazÏdy rentgenovy snõÂmek byl prÏed analyÂzou kalibrovaÂn pomocõ refe-rencÏnõ vzdaÂlenosti ameÏrÏõÂtka.

ZaÂkladem pro odvozenõ metodiky teÂto praÂce se stala Rickettsova ruÊstova analyÂzadolnõ cÏelisti [4]. Jako referencÏnõ body byly prÏi analyÂze rentgenovyÂch snõÂmkuÊ vyuzÏity beÏzÏneÏ pouzÏõÂvane konstruovane aantomicke kefalometricke body [4, 5, 6].

Z uÂhlovyÂch rozmeÏruÊ byl meÏrÏen Goniovy uÂhel auÂhel ANB. DeÂlku dolnõ cÏelisti prÏedstavoval rozmeÏr Ar-Pg.

Z boduÊ aliniõÂ, ktere nejsou beÏzÏnou soucÏaÂstõ nejcÏa -steÏji pouzÏõÂvanyÂch analyÂz vyjõÂmaÂme zejmeÂna :

SPo (suprapogonion) - bod nachaÂzejõÂcõ se naante-riornõÂm povrchu symfyÂzy, Ricketts jej umõÂstil do oblasti kde konvexitakosteÏneÂho bradoveÂho vyÂbeÏzÏku prÏechaÂzõ v konkavitu, mezi body B a Po. Prakticky se ukaÂzalo, zÏe pro jeho nejprÏesneÏjsÏõ stanovenõ je vyÂhodne pouzÏõÂt kra-niaÂlnõ okraj hrÏebene kompakty, ktera ventraÂlneÏ ohrani-cÏuje symfyÂzu.

Xi (bod Xi) - konstruovany bod naveÏtvi dolnõ cÏelisti, nachaÂzejõÂcõÂse mezi nebo naneÏktere z kontur mandibulaÂrnõÂho kanaÂlu (konstrukce modifikovaneÂho bodu Xi -Obr. 1)

M (bod M) - konstruovany bod vznikajõÂcõ proteÏtõÂm kolmyÂch liniõ V-ref. aH-ref. (Xi-SPO) v mõÂsteÏ nejdistaÂl-neÏjsÏõÂho okraje korunky dolnõÂho prvnõÂho molaÂru (Obr. 1)

Popis modifikovane konstrukce bodu Xi:

Modifikace puÊvodnõ Rickettsovy metodiky spocÏõÂva ve volbeÏ odlisÏne referencÏnõ linie. Ricketts pouzÏil Frank-furtskou horizontaÂlu, cozÏ z duÊvodu nedostatecÏne re-produkovatelnosti nebylo pro nasÏe uÂcÏely akceptova-telneÂ. V teÂto praÂci bylapouzÏitalinie S-N, kterou lze urcÏit s dostatecÏnou prÏesnostõÂ.

VlastnõÂkonstrukce bodu Xi probõÂhala v neÏkolikakro-cõÂch. Nejprve sestrojenõ tecÏny k nejinferiorneÏjsÏõÂmu bodu incisura mandibulae, ktera je soucÏasneÏ paralelnõ s liniõ S-N. DaÂle sestrojenõ prÏõÂmky paralelnõ s liniõ S-N tak, aby tvorÏilatecÏnu k dolnõÂmu okraji hrany mandibuly v mõÂsteÏ, kde konvexitauÂhlu mandibuly prÏechaÂzõ v

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kon-The intersection of diagonals of the rectangle thus construed is Xi point. It is always between the contours of mandible channel or in some of them, in the middle of the mandible ramus.

Ricketts method [4] became also the basis for the construction of reference lines.

Constructed lines

H-ref. (horizontal reference line, Xi-SPo) - horizontal reference line used in our work, and constructed as the connecting line of the points Xi and SPo. The line repre-sents the axis of the mandible body.

V-ref. (vertical reference line) - constructed as the perpendicular to Xi-SPo line at the point M (Fig. 1).

The method should be designed and modified so that it represents as best as possible the space in the alveo-lar process, i.e. the space where the second and third permanent molar germs erupt. Therefore, the point M was constructed, as it relates to the axis of the mandible body, and the space changes of the point best corre-spond to the actual space changes in the developing dental arch. The changes are then expressed as the change of distance between Xi and M points (i.e. Dist.). All parameters were measured in two profile cepha-lometric pictures included into the analysis according to the given criteria. The first picture was taken prior to the growth spurt (the parameter measured was mar-ked as 1), and the second one after the finished growth spurt (the parameter measured was marked as 2).

Statistical data were processed with the help of SPSE software, version 16.

All parameters, with the exception of Ar-Pg2 and ANB1, showed normal distribution. The data with ab-normal distribution were also processed in pairs (Ar-Pg1 and Ar-Pg2, ANB1 and ANB2). Therefore, we used parameter tests (Student's pair t-tests). However, the results were verified and proved with non-parametric methods (Wilcoxon tests).

Using correlation analysis, we tried to find the rela-tionship between individual parameters observed (change in Go angle, change of Ar-Pg, and change in ANB) and the change of the distance Dist. The correla-tion analysis was performed as the calculacorrela-tion of Pearson's correlation coefficients. The correlation was considered as significant on the level of p<0.01. By repeated measurements of selected parameters in 44 patients, we stated the mean error of measure-ment of angular parameters 0.28°, and of linear para-meters 0.28 mm.

Results

Growth spurt led to the mean reduction of Go angle by ±1.74° (± 3.74°), ANB angle by ±1.44° (± 1.53°) (Table 1).

kavitu dolnõ hrany mandibuly. Sestrojenõ tecÏen k prÏednõ a zadnõ konkaviteÏ ramene mandibuly tak, aby byly kolme k linii S-N.

PruÊsecÏõÂk uÂhloprÏõÂcÏek takto zkonstruovaneÂho obdeÂl-nõÂku je bodem Xi. NachaÂzõ se vzÏdy mezi konturami mandibulaÂrnõÂho kanaÂlu nebo naneÏktere z nich, v po-myslneÂm strÏedu ramene mandibuly.

Zaza klad konstrukce referencÏnõÂch liniõ bylatakteÂzÏ vzata puÊvodnõ RickettsovapraÂce [4].

Konstruovane linie

H-ref. (horizontaÂlnõ referencÏnõ linie, Xi-SPo) -hori-zontaÂlnõ referencÏnõ linie zvolena pro tuto praÂci, kon-struovana jako spojnice boduÊ Xi aSpo. Ve sve pod-stateÏ tato linie vyjadrÏuje osu teÏladolnõ cÏelisti.

V-ref. (vertikaÂlnõ referencÏnõ linie) - konstruovana jako kolmice nalinii Xi-SPo v bodeÏ M (Obr. 1).

Pro zvolenou metodiku je duÊlezÏiteÂ, zÏe bylanavrzÏena aupravenatak, aby co nejleÂpe postihlaprostor alveolu dolnõ cÏelisti, tj. prostor ve ktereÂm se prorÏezaÂvajõ zaÂrodky druhyÂch atrÏetõÂch staÂlyÂch molaÂruÊ. Proto byl konstruovaÂn bod M, ktery dle nasÏeho naÂzoru, je v nejteÏsneÏjsÏõ souvi-slosti s osou teÏladolnõ cÏelisti ajeho prostorove zmeÏny tak nejleÂpe odpovõÂdajõ skutecÏnyÂm prostorovyÂm zmeÏ-naÂm ve vyvõÂjejõÂcõÂm se zubnõÂm oblouku. Tyto zmeÏny jsou pak vyjaÂdrÏeny zmeÏnou vzdaÂlenosti boduÊ Xi aM abyly v teÂto praÂci ozna cÏeny jako znak Dist.

MeÏrÏenõÂ vsÏech znakuÊ bylo provaÂdeÏno nadvou profi-lovyÂch rentgenogramech, zarÏazenyÂch dle selekcÏnõÂch kriteriõÂ teÂto praÂce. PrvnõÂ byl zhotoven prÏed ruÊstovyÂm

Obr. 1:Konstrukce modifikovaneÂho bodu Xi areferencÏnõÂch liniõÂ Fig. 1:Construction of the modified Xi point and reference lines

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The mean change of Ar-Pg was +9.98 mm (±3.84 mm) (Table 2).

Student's pair t-tests proved that after the finished growth spurt the values of angles Go (p = 0.0001) and ANB (p <0.0001) showed statistically significant decrease, while the parameters Dist. and Ar-Pg (p <0.0001 in both) showed statistically significant in-crease.

Verification of the results for parameters Ar-Pg and ANB with Wilcoxon serial tests proved the conclu-sions.

The correlation analysis was performed as the cal-culation of Pearson's correlation coefficients. It was proved that between the values change Dist, and change Ar-Pg exists statistically significant medium size positive correlation (Table 4). The situation is illu-strated with a dot chart (Fig. 2) with a regressive straight line illustrating the tendency of the relations-hip. There was found no statistically significant corre-lation between the other parameters and the change in Dist.

Discussion

Growth represents an important factor influencing the final sagittal position of jaws. Of course, the growth of jaws affects dental relationship of the upper and lo-wer dental arches. Increasing jaws bases should be accompanied with sufficient increase of space for in-clusion of all teeth. Whenever we evaluate dental disc-repancy and plan the resulting intercuspation we should take into account the dynamics of the jaws de-velopment.

pubertaÂlnõÂm spurtem (oznacÏenõ meÏrÏeneÂho znaku 1) adruhy po ruÊstoveÂm pubertaÂlnõÂm spurtu (oznacÏenõÂmeÏ-rÏeneÂho znaku 2).

ZpracovaÂnõÂ statistickyÂch dat bylo provedeno po-mocõÂ programu SPSE verze 16.

VsÏechny znaky, kromeÏ Ar-Pg2 a ANB1, vykazovaly normaÂlnõ rozlozÏenõÂ. Vzhledem k tomu, zÏe i data, ktera nemeÏlanormaÂlnõ rozlozÏenõÂ, bylazpracovaÂvaÂna paÂroveÏ (Ar-Pg1 aAr-Pg2; ANB1 aANB2) byly ke zpracova nõ pouzÏity parametricke testy (Studentovy paÂrove t-tes-ty). VyÂsledky byly vsÏak oveÏrÏeny apotvrzeny pomocõ neparametrickyÂch metod (Wilcoxonovy testy).

DaÂle bylapomocõÂ metod korelacÏnõÂ analyÂzy hledaÂna zaÂvislost mezi jednotlivyÂmi sledovanyÂmi znaky (zmeÏna Go, zmeÏnaAr-Pg azmeÏnaANB) azmeÏnou Dist. Kore-lacÏnõÂ analyÂzabylaprovedenavyÂpocÏtem PearsonovyÂch korelacÏnõÂch koeficientuÊ. Korelace byla povazÏovaÂna za signifikantnõÂ na uÂrovni p<0,01.

OpakovaÂnõÂm meÏrÏenõ vybranyÂch znakuÊ u 44 jedincuÊ bylastanovenapruÊmeÏrna chybameÏrÏenõ pro uÂhlove znaky 0,28°apro lineaÂrnõ znaky 0,28 mm.

VyÂsledky

RuÊstovyÂm spurtem dosÏlo k pruÊmeÏrneÂmu zmensÏenõÂ hodnoty Go uÂhlu o ±1,74°(±3,74°), daÂle v tomto ob-dobõÂ dosÏlo k pruÊmeÏrneÂmu zmensÏenõÂ hodnoty uÂhlu ANB o ±1,44°(±1,53°) (Tab. 1).

PruÊmeÏrna zmeÏnaAr-Pg dosaÂhlahodnoty + 9,98 mm (±3,84mm) (tab. 2).

StudentovyÂmi paÂrovyÂmi t-testy bylo prokaÂzaÂno, zÏe po probeÏhleÂm ruÊstoveÂm spurtu dosÏlo k statisticky vyÂ-znamneÂmu snõÂzÏenõÂ hodnot uÂhluÊ Go (p = 0,0001) aANB (p<0,0001) ake statisticky vyÂznamneÂmu

zvyÂ-Tabulka 1:UÂhlove rozmeÏry Table 1:Angle measurements

Tabulka 2:LineaÂrnõÂ parametry Table 2:Linear parameters

N - pocÏet, number, Min. -minimaÂlnõ hodnota, minimum value, Max. - maximaÂlnõ hodnota, maximum value, Mean - pruÊmeÏr, SD - smeÏrodatna odchylka, standard deviation

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The space before the lower first permanent molar was evaluated by Moyers [5] and others [6, 7, 8, 9, 10]. The space behind the lower first permanent molar was dealt with - in relation to the inclusion of third mo-lars - by Richardson [12, 13], Bishara [14], Zachrisson [15], Sable [16], Ledyard, Kaplan and a number of other authors.

The development of the space for the inclusion of teeth in the mandible during the growth spurt was the goal of our study, i.e. it dealt with the period when the space for the inclusion of second and third perma-nent molars is created. The sample of our patients was selected according the skeletal growth stage. The sample consisted of 72% girls, and 28% boys. This difference in number is due to the difference in skeletal maturation related to sex. The eruption of second mo-lars and finished treatment very often did not coincide with CVMS IV stage in boys. The growth spurt in boys was not finished very often with erupted second mo-lars, and therefore, these patients could not be inclu-ded in the sample.

sÏenõÂ hodnot parametruÊ Dist aAr-Pg (p<0,0001 v obou prÏõÂpadech).

Validizace vyÂsledkuÊ pro parametry Ar-Pg a ANB Wil-coxonovyÂmi porÏadovyÂmi testy tyto zaÂveÏry potvrdila.

KorelacÏnõ analyÂzabylaprovedenavyÂpocÏtem Pearso-novyÂch korelacÏnõÂch koeficientuÊ. Bylo prokaÂzaÂno, zÏe mezi velicÏinami zmeÏnaDist azmeÏnaAr-Pg je statisticky vyÂznamna strÏedneÏ silna pozitivnõ zaÂvislost (viz. Tabulka 4). Situace je znaÂzorneÏnabodovyÂm grafem (Obr. 2) s pro-lozÏenou regresnõ prÏõÂmkou naznacÏujõÂcõ trend tohoto vztahu. Mezi ostatnõÂmi znaky a znakem zmeÏnaDist sta-tisticky vyÂznamna korelace nalezena nebyla.

Diskuse

Pro konecÏne sagitaÂlnõ postavenõ cÏelistõ ma velky vyÂ-znam ruÊst. RuÊst cÏelistõ se bude samozrÏejmeÏ promõÂtat i do dentaÂlnõÂho vztahu hornõÂho a dolnõÂho zubnõÂho ob-louku. Se zveÏtsÏovaÂnõÂm baÂzõ cÏelistõ ocÏekaÂvaÂme dosta-tecÏny prÏõÂruÊstek prostoru pro zarÏazenõ vsÏech zubuÊ. PrÏi hodnocenõÂdentaÂlnõÂdiskrepance i prÏi plaÂnovanõÂvyÂsledne artikulace je nutne s dynamikou vyÂvoje cÏelistõ pocÏõÂta t.

Tabulka 3:ZmeÏny ajejich signifikace Table 3:Changes and significance

sx- strÏednõÂ chybapruÊmeÏru, standard error of the mean, t - StudentuÊv t-test, Student t-test

Tabulka 4.KorelacÏnõÂ koeficienty mezi zmeÏnami sledovanyÂch znakuÊ azmeÏnou Dist. Table 4.Correlation coefficients between changes of parameters ane the change in Dist.

** Korelace je signifikantnõÂ na hladineÏ vyÂznamnosti 0.01, correlatiom is sigmificant on the level 0.01

Obr. 2:Korelace mezi zmeÏnou Ar-Pg azmeÏnou rozmeÏru Dist. Fig. 2:Correlation between the change in Ar-Pg and the change of Dist.

Ve smõÂsÏeneÂm chrupu se hodnocenõÂm prostoru prÏed prvnõÂm staÂlyÂm dolnõÂm molaÂrem zabyÂval Moyers [5] aneÏkterÏõÂ dalsÏõÂ autorÏi [6,7,8,9,10]. Prostor zadolnõÂm prvnõÂm staÂlyÂm molaÂrem zkoumali, zejmeÂnaz hlediska zarÏazenõÂ trÏetõÂch molaÂruÊ, Richardson [12, 13], Bishara [14], Zachrisson[15], Sable [16], Ledyard, Kaplan amnozõÂ dalsÏõÂ.

Tato praÂce bylazameÏrÏenanavyÂvoj prostoru pro za-rÏazenõ zubuÊ v dolnõ cÏelisti v pruÊbeÏhu pubertaÂlnõÂho ruÊ-stoveÂho spurtu, tj. naobdobõÂ, kdy se mimo jine utvaÂrÏõ prostor pro zarÏazenõ druhyÂch atrÏetõÂch staÂlyÂch molaÂruÊ. JednõÂm z hlavnõÂch kriteriõ vyÂbeÏru do souboru bylo ruÊ-stove staÂdium skeletu. KonecÏny analyzovany soubor tvorÏilo 72 % dõÂvek a28 % chlapcuÊ. Tento nepomeÏr je vyjaÂdrÏenõÂm odlisÏnosti ve vyzraÂvaÂnõ skeletu v zaÂvislosti

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The mild anteriorotation, which is the most frequent growth type, ¹closesª the Go angle and reduces the ANB angle.

Most authors of cephalometric analyses use their own interval and mean value of Gonion angle: Hasund 123°(±7.2), Jarabak 130°(±7), Williams 126°(±6).

The mean value of Gonion angle obtained through our measurements is similar to that given by Hasund (Table 1). Before the growth spurt: 123° ± 6.0; after the finished growth spurt: 121° ± 6.5. The Go angle usually decreases in population during the growth spurt. This fact brings about also changes in the posi-tion of the mandible. The point B rotates in anterior di-rection, and ANB angle value changes, too. In her work, Richter [17] measured Gonion angle in the con-trol (untreated) group, and reported the mean reduc-tion by 1.89°in the period between the age of 11 and 15. The decrease is probably due to the change in the mandible position caused by its rotation, and due to the different rate in the growth of the maxilla and the mandible. This, of course, affects dental occlusion. The interval and mean value of ANB angle is not so different in individual analyses: Hasund 2.3°(±1.8), Ja-rabak 2°(±3), Williams 3°(±1.3). The mean value of ANB angle obtained through measurements within this work (Table 1) is similar to that given by Hasund. Before the growth spurt: 3.5° ±2.7; after the finished growth spurt: 2.1° ±2.4.

Dibbets [18] measured gains in the length of the mandible Ar-Pg distance. The method proved to have the best reproducibility.

From Ricketts work [5] we derived the measurement of Xi-M, i.e. Dist. (the space distally off the first lower molar). The mean change of Dist (Xi-M) was +7.75 (±2.90) mm. Forsberg [19] gives the mean size of the lower permanent second molar in males 11.00 mm (±0.50), in females 10.20 mm (±0.49). Thus we can as-sume that a major part of the space for the eruption of these teeth has its origin in the resorption of the ante-rior border of ramus mandibulae. The space allowing inclusion of the lower second molar, which is created during the growth spurt, is proportional to the size of this tooth. The use of mechanics using the space to solve crowding may result in the easier impaction of second molars; and most probably, third molars re-main impacted.

Conclusion

In 80 patients in the growth spurt period 160 lateral cephalograms were analyzed.

After the finished growth spurt statistically signifi-cant reduction of Gonion angle and angle ANB was proved.

napohlavõÂ. ProrÏezaÂnõ druhyÂch molaÂruÊ adokoncÏenõ leÂcÏby se u chlapcuÊ cÏasto neshodovalo s prÏõÂtomnostõ staÂdiaCVMS IV. RuÊstovy spurt u chlapcuÊ s prorÏeza-nyÂmi druhyÂmi molaÂry nebyl tedy veÏtsÏinou dokoncÏen atito jedinci museli byÂt vyrÏazeni ze souboru.

PrÏi mõÂrne anteriorotaci, cozÏ je nejcÏasteÏjsÏõ ruÊstovy typ, dochaÂzõ k ¹zavõÂraÂnõª Go uÂhlu azaÂrovenÏ k zmensÏo-vaÂnõ uÂhlu ANB.

VeÏtsÏinaautoruÊ kefalometrickyÂch analyÂz pouzÏõÂva vlastnõ interval a pruÊmeÏr hodnot GonioveÂho uÂhlu: Ha-sund 123°(±7,2), Jarabak 130°(±7), Williams 126°(± 6). StrÏednõ hodnotaGonioveÂho uÂhlu vyplyÂvajõÂcõ z meÏrÏenõ v teÂto praÂci (Tabulka 1) se nejvõÂce blõÂzÏõ HasundoveÏ ana-lyÂze. PrÏed spurtem, pruÊmeÏr 122,95° ± 6,0. Po spurtu, pruÊmeÏr 121,21° ±6,5. V pruÊbeÏhu ruÊstoveÂho spurtu se u veÏtsÏiny populace hodnota Go uÂhlu zmensÏuje. Tato skutecÏnost s sebou nese i zmeÏnu polohy dolnõ cÏelisti. Bod B rotuje smeÏrem vprÏed, meÏnõ se velikost uÂhlu ANB. Richterova [17] ve sve praÂci nameÏrÏilananeleÂcÏene kontrolnõ skupineÏ, v obdobõ mezi 11. a15. rokem, pokles GonioveÂho uÂhlu pruÊmeÏrneÏ o 1,89°. Toto zmensÏenõ lze prÏicÏõÂst zmeÏneÏ polohy dolnõ cÏelisti zpuÊsobene jejõ rotacõ aodlisÏneÂmu tempu v ruÊstu maxily a mandibuly. Z toho plynoucõ vliv nadentaÂlnõ okluzi je zrÏejmyÂ.

Interval a pruÊmeÏr hodnot uÂhlu ANB v jednotlivyÂch analyÂzaÂch se nelisÏõÂ tolik, jako je tomu u GonioveÂho uÂhlu. Hasund 2,3° (±1,8), Jarabak 2° (± 3), Williams 3°(±1,3). StrÏednõÂ hodnotauÂhlu ANB vyplyÂvajõÂcõÂ z meÏ-rÏenõÂ v teÂto praÂci (Tabulka cÏ. 1) se opeÏt nejvõÂce blõÂzÏõÂ Ha-sundoveÏ analyÂze. PrÏed spurtem, pruÊmeÏr 3,5° ±2,7. Po spurtu, pruÊmeÏr 2,1° ±2,4.

Dibbets [18] pouzÏil pro meÏrÏenõÂ prÏõÂruÊstkuÊ v deÂlce dol-nõÂ cÏelisti vzdaÂlenost Ar-Pg. Tato metodika se ukaÂzala jako nejleÂpe reprodukovatelnaÂ.

Z Rickettsovy praÂce [5] bylo odvozeno meÏrÏenõ vzdaÂ-lenosti Xi-M oznacÏene jako znak Dist (prostor distaÂlneÏ zaprvnõÂm dolnõÂm molaÂrem). PruÊmeÏrna zmeÏnaDist (Xi-M) byla+7,75 (±2,90 mm). Forsberg [19] uvaÂdõ pruÊmeÏr-nou velikost druheÂho staÂleÂho dolnõÂho molaÂru u muzÏuÊ 11,00 mm (±0,50 mm) a10,20 mm (±0,49 mm) u zÏen. Z toho lze usuzovat, zÏe znacÏna cÏaÂst prostoru pro prorÏe-zaÂnõ teÏchto zubuÊ vznika resorpcõ prÏednõÂho okraje ra-mus mandibulae. Prostor pro zarÏazenõ druheÂho dol-nõÂho molaÂru, ktery se dotvaÂrÏõ v pruÊbeÏhu ruÊstoveÂho spurtu, je svou velikostõÂteÏsneÏ proporcionaÂlnõÂk velikosti tohoto zubu. PouzÏijeli v ortodonticke leÂcÏbeÏ me-chaniku, ktera tento prostor vyÂznamneÏ vyuzÏõÂva pro rÏe-sÏenõ steÏsnaÂnõÂ, lze se domnõÂvat zÏe snaÂze muÊzÏe dojõÂt k re-tenci druhyÂch molaÂruÊ, trÏetõ molaÂry s nejveÏtsÏõ pravdeÏpo-dobnostõ zuÊstanou retinovaÂny.

ZaÂveÏr

Bylo analyzovaÂno 160 bocÏnõÂch kefalogramuÊ u 80 je-dincuÊ v pruÊbeÏhu ruÊstoveÂho spurtu. Po probeÏhleÂm

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ruÊ-The medium positive relationship was proved bet-ween the amount of change in space distally off the lo-wer first permanent molar and the change in Ar-Pg di-stance.

No statistically significant relationship was proved between the change of space distally off the lower first permanent molar and Gonion or ANB angles.

The authors have no comercial, proprietary, or finan-cial interests in the products or companies described in this article.

stoveÂm spurtu bylo prokaÂzaÂno statisticky vyÂznamne zmensÏenõ GonioveÂho uÂhlu aANB.

Bylaproka zaÂnastrÏedneÏ silna pozitivnõ zaÂvislost mezi velikostõ zmeÏny prostoru distaÂlneÏ zaprvnõÂm staÂ-lyÂm dolnõÂm molaÂrem azmeÏnou vzdaÂlenosti Ar-Pg.

NebylaprokaÂzaÂnastatisticky vyÂznamna zaÂvislost ve-likosti zmeÏny prostoru distaÂlneÏ zaprvnõÂm staÂlyÂm dolnõÂm molaÂrem ani na zmeÏneÏ Go uÂhlu ani na zmeÏneÏ uÂhlu ANB.

AutorÏi nemajõ komercÏnõÂ, vlastnicke nebo financÏnõ zaÂ-jmy na produktech nebo spolecÏnostech popsanyÂch v tomto cÏlaÂnku.

Literatura/References

1. Prece, J. W.: The incidence of unerupted permanent teeth and related clinical cases. Oral. Surg. 1985, 59, cÏ. 8, s. 420-425.

2. Franchi, L.; Baccetti, T.; McNamara, J.A.: Mandibular growth as related to cervical vertebral maturation and body height. Amer. J. Orthodont. dentofacial Orthop. 2000, 8, cÏ. 3, s. 335-340.

3. Baccetti, T.; Franchi, L.; McNamara, J.A.: An improved version of the cervical vertebral maturation (CVM) me-thod for the assessment of mandibular growth. Angle Orthodont. 2002, 72, cÏ. 4, s. 316-323.

4. Ricketts, R. M.: Cephalometric analysis and synthesis. Angle Orthodont. 1961, 31, cÏ. 3, s. 141-156.

5. Ricketts, R. M.: A principle of arcial growth of the mandi-ble. Angle Orthodont. 1972, 42, cÏ. 4, s. 368-385. 6. Moyers, R. E.: Handbook of orthodontics. 4th ed.,

Chi-cago: Year Book, 1988.

7. Hasund, A.; Segner, D.: Individualizovana kefalometrie. 1. vyd., Praha: HansaDont, 1994.

8. Williams, S.: KoncepcÏna ortodoncia, II. Rast a ortopeÂdia. Bratislava: Ing. Juraj HalabrõÂn, 2005.

9. Proffit, W. R.; Fields, H. W.: Contemporary orthodontics. 4th ed., St. Louis: Mosby, 2007.

10. Bishara, S. E; Staley, R. N.: Mixed-dentition mandibular arch length analysis: a step-by-step approach using the revised Hixon-Oldfather prediction method. Amer. J. Orthodont. 1984, 86, s. 130-135.

11. Tanaka, M.; Johnston L.E. The prediction of the size of unerupted canine and premolars in a conteporary ortho-dontic population. J. Amer. dent. Assoc. 1974, 88, s. 798-801.

12. Richardson, M. E.: The early developmental position of the lower third molar relative to certain jaw dimension. Angle Orthodont. 1970, 40, cÏ. 3, s. 226-230.

13. Richardson, M. E.: The effect of mandibular first premo-lar extraction on third mopremo-lar space. Angle Orthodont. 1989, 59, cÏ. 4, s. 291-294.

14. Bishara, S. E.: Third molars: A dilemma! Or is it? Amer. J. Orthodont. dentofacial Orthop. 1999, 115, s. 628-33. 15. Zachrisson, B.: Mandibular third molars and late lower arch crowding - the evidence base, World J. Orthodont. 2005, 6, s.180-186.

16. Sable, D. L.; Woods, M. G.: Growth and treatment changes distal to the mandibular first molar: A lateral cephalometric study. Angle Orthodont. 2004, 74, cÏ. 3, s. 367-374. 17. RichterovaÂ, L.: Vliv meziaÂlnõÂho posunu molaÂruÊ

naverti-kaÂlnõ skeletaÂlnõ parametry. Odborna praÂce ke speciali-zacÏnõ zkousÏce z ortodoncie. PlzenÏ 2008.

18. Dibbets, J. M.: Mandibular rotation and enlargement, Amer. J. Orthodont. dentofacial Orthop. 1990, 98, cÏ. 1, s. 29-32.

19. Forsberg, C. M.: Tooth size, spacing, and crowding in re-lation to eruption or impaction of third molars. Amer. J. Orthodont. dentofacial Orthop. 1988, 94, cÏ. 1, s. 57-62.

MUDr. Bc. ZdeneÏk Haken Ortodonticke oddeÏlenõÂ

Stomatologicka klinika 1. LF UK KaterÏinska 32, 120 00 Praha 2 CÏlensky poplatek pro rok 2010 cÏinõ 1500,- KcÏ nebo 45,- EUR.

CÏlenove v zameÏstnaneckeÂm vztahu 800,- KcÏ nebo 25,- EUR.

Postgraduanti, duÊchodci a zÏeny na materÏske dovolene 300,- KcÏ nebo 10,- EUR. RegistracÏnõ polatek cÏinõ 500,- KcÏ.

PrÏedplatne cÏasopisu Ortodoncie pro necÏleny CÏOSje 1000,- KcÏ za rok nebo 35,- EUR. UÂhrada poplatku do 28. 2. 2010,

cÏ. uÂ.: 32932021/0100, konst. symbol: 0558, variab. symbol: rodne cÏõÂslo.

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