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Objective growth monitoring of the maxilla in full term infants
Archives of Oral Biology (2006) 51, 222—235
www.intl.elsevierhealth.com/journals/arob
Objective growth monitoring of the maxilla in full term infants Ariane Hohoff a,*, Thomas Stamm a, Ulrich Meyer b, Dirk Wiechmann c, Ulrike Ehmer a a
Poliklinik fu ¨ r Kieferorthopa ¨die, Westfa ¨lische Wilhelms-Universita ¨t Mu ¨ nster, Waldeyer Str. 30, 48129 Mu ¨ nster, Germany b Klinik und Poliklinik fu ¨ r Mund-, Kiefer- und Gesichtschirurgie, Westfa ¨lische Wilhelms-Universita ¨t Mu ¨ nster, Waldeyer Str. 30, 48129 Mu ¨ nster, Germany c Poliklinik fu ¨ r Kieferorthopa ¨die, Medizinische Hochschule Hannover, Carl-Neuberg-Strasse 1, 30625 Hannover, Germany Accepted 22 July 2005
KEYWORDS Growth; Development; Maxilla; Volume; Normative data
Summary Objective: To develop a non-invasive method for longitudinal maxillary volume measurements and to provide first normative data. Design: Thirty-four healthy infants served as a gold standard for a growing population sample. Alginate impressions were taken of the upper jaw within the first week after birth, and consecutively at different stages of development. The plaster casts were digitised by an optical scanner generating a high resolution polygon mesh of each object. The digital models were aligned to a reference coordinate system with an iterative, landmark-independent procedure. Biometric linear and volume measurements were obtained by using feature-dependent calculations independent of landmark placements. Intra-investigator reproducibility was tested by repeated alignments and measurements of 30 randomly selected casts. To assess the effect of mesh resolution, the reproducibility test was repeated with low resolution models. The method was proved to be valid on the defined gold standard consisting of 96 consecutive edentulous casts. Results: Feature-dependent, linear distances are less error prone (0.56—2.66%) compared to subjectively determined measurements (0.88—3.65%). The same applies to feature-dependent volume calculations (4.34%) compared to subjectively determined volumes (4.95%). Mesh resolution shows an effect ( p 0.001) only on two linear measurements: palatal depth and palatal length. Growth of the individuals in
* Corresponding author. Tel.: +49 251 8347101; fax: +49 251 8347187. E-mail address: [email protected] (A. Hohoff). 0003–9969/$ — see front matter # 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.archoralbio.2005.07.007
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the population sample was evidently confirmed by the maxillary volume measurements (asymptotic pattern) and by comparisons of head circumference (proportional pattern). Conclusion: The described method is non-invasive, precise and without any risk for the infant. Maxillary volume calculation could serve as an important biometric measurement for bone growth evaluation. # 2005 Elsevier Ltd. All rights reserved.
Introduction The anatomic phenomenon ‘growth of the maxilla’ occurs by intramembraneous ossification without cartilaginous precursors. Intramembraneous bone is the first bone to begin ossification.29 Postnatally, the maxilla grows by apposition of bone at the sutures7,19 and by surface remodelling.14 Bone resorption8 and apposition areas of the maxilla are complex,3 but all processes result in an increase of the maxillary volume during the foreward and downward translation. This makes volume measurements of the maxilla interesting for monitoring bone growth at different stages of development. Growth failure in the nasomaxillary complex may be caused by a complex interplay of different internal factors, such as inadequate nutrition, morbidities affecting nutrient requirements, endocrine abnormalities, central nervous system damage, metabolic disturbances and drug administration that influences on nutrient metabolism.6 Disturbances of growth in the nasomaxillary complex may also be caused by clefts or syndromes. Furthermore, external factors, such as side-to-side flattening of the head1,22 or orotracheal intubation may lead to changes in palatal shape and size1,22 or to alterations of the whole nasomaxillary complex (Fig. 1), especially in preterm infants. The long-
term results for preterm children with a history of orotracheal intubation with respect to palatal symmetry,18,32 palatal depth and width9,15,26 as well as crossbite9,15 are contradictory. Therefore, the scientific evidence until today is too weak to answer the questions as to whether premature birth causes permanent alteration of palatal morphology; to answer these questions and obtain reliable scientific evidence as to whether premature children are at risk for malocclusions from possible alterations of palatal morphology, such as asymmetry and higharched palates, further well-designed controlled studies as well as longitudinal studies are needed.25 Normative, longitudinal, reliability-checked measurements of the palatal volume of healthy term infants, which could serve as control data for children born prematurely or with clefts or syndromes, are not available in the current literature. The aim of our study was therefore, first, to develop a reliable method for longitudinal volume measurements of the maxilla and, second, to provide useful control information for developmental evaluation of groups which are at risk for ‘untypical’ growth of the maxilla. The method should be noninvasive, precise, clinically easy to use, without interference with intensive care, sensitive for growth in terms of volume increase, and robust against deformation effects.
Figure 1 Ten-year old, preterm boy with a history of orotracheal intubation. Side-to-side flattening of the head. Maxilla and mandible are very narrow corresponding to the head shape. Lip closure at rest is difficult due to the vertical growth excess.
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Methods Patients Thirty-four healthy, caucasian, normal birthweight term infants (15 male, 19 female), i.e. infants born at 37 weeks of gestation and with a birthweight >2500 g, born at the tertiary-care university hospital of Mu ¨nster, Germany served as a gold standard for a population sample of in actual fact growing individuals. Children with clefts, syndromes, hydrocephalus, cerebral palsy or metabolic diseases were excluded. According to the study protocol, which was approved by the local ethics committee, informed consent of both parents was necessary prior to inclusion of a child in the study. Alginate impressions (Blueprint, Dentsply/Detray, Konstanz, Germany) of the upper jaw were taken by one investigator with specially designed, sterilisible, steel trays within the first week after birth, and consecutively as described in Section ‘‘Statistics’’. The plaster casts were made with class IV plaster (Silky Rock White, Whip Mix, Kentucky, USA).
Data acquisition Data acquisition was performed by one investigator. The plaster casts were digitised with the ATOS II system (GOM GmbH, Braunschweig, Germany), which is mainly used in reverse engineering. The digitising technology is based on the triangulation principle: a sensor projects different fringe patterns onto the object to be measured and observes them with two cameras. Based on the optical transformation equations the system determines the 3D coordinates of the cast. For the present study we used the ATOS SO system (Fig. 2), an optimised unit for measuring volumes down to 45 mm 36 mm 20 mm with point spacings of 0.03—0.15 mm. The casts were placed on a motorised rotation table and measurements of eight views were used to completely digitise the complex morphometry of the palate. The system calculated a point cloud up to four million surface points and all
Figure 3
Figure 2 The ATOS II SO digitising unit consists of a fringe projector (FP), two CCD cameras (CCD) and a motorised rotation table (RT). Different white light fringe patterns are projected on the rotating cast surface and captured by the cameras. The digitising progress (DP) and the camera views (CV) can be controlled on the monitor.
measurements were automatically transformed into a common object coordinate system. At the end of the digitising process, a high resolution polygon mesh described the object. In order to reduce data the system thinned out the mesh based on its curvature without losing accuracy and details. For further processing, the data were exported in different formats like STL, OBJ and ASCII.
Theoretical considerations about palatal volume measurements The 3D shape of a preterm or term edentulous palate could be described as a halved torus (alveolar ridge) connected to a halved hemisphere (palatal vault). Looking at two consecutive casts of a preterm palate at different stages of postnatal life (Fig. 3), the manually placed landmark Lm0 on the current, grown or deformed surface is larger than the corresponding landmark Lm on the previous cast. Lm0 is equal to a fuzzy description of an
An anatomical landmark (Lm) is difficult to relocate (Lm0 ) on a grown or deformed surface.
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Figure 4 Left: cross-section of the cast of Fig. 7. C and C0 are the maximum values and equal to the highest contour points of the alveolar ridge in this specific section. The mathematical determination of the contour maximum is highly reliable in normal (middle) and altered surfaces (right).
anatomic point of interest because the size and the shape of the palate varies considerably with gestation and postnatal age.26 The description of Lm0 varies between consecutive casts and different observers and this variation is responsible for the lack of reliability of assessment made by manual superimposition of landmarks.21 It is therefore necessary to find patterns of consistency. The crest of the alveolar ridge could be seen as one of these patterns. In the plane of a transverse section of the palate, a point of the crest could be defined as the largest overall value of the alveolar outline (Fig. 4). This maximum (C) is characterised by mathematical precision and anatomical fuzziness in the case of longitudinal measurements. That applies also to the sequence of maximum values fCi gni¼1 (where n is a finite number of cross-sections) which determines a contour line along the alveolar ridge. A further pattern of consistency is needed in the region of the transition between hard and soft palate to determine a dorsal border line. The point nearest to that region which could be described mathematically is the deepest point of the palatal groove. Before calculating this point it is necessary
to digitally remove the base of the scanned cast (Fig. 5). The deepest point (P) is then equal to the minimum of the whole set of surface points. A transverse plane perpendicular to the midline (raphe palatina mediana) through point P defines the dorsal border line of the palate. With the mathematical determination of the alveolar contour maximum and the calculation of the deepest point of the palatal groove, a volume of interest can be estimated (Fig. 6). Independent of flattening effects (Fig. 6, right) an increase of size, e.g. growth, can be measured. This method is robust against systematic and random errors due to manual measurements. As follows from Fig. 5 the precision of the measurement of casts taken at one individual’s different stages of development depends on the cast’s orientation within the used coordinate system. A clockwise rotation of the palate in the lateral view of Fig. 5 would shift point P to dorsal with the effect of a systematic measurement error (compare righthand part of Fig. 7). The same effect applies to the alveolar contour line. The total measurement error increases by the sum of the effects in each plane. It is therefore necessary to transform the
Figure 5 Frontal (left) and lateral (right) view of the inner surface of the palatal groove of a scanned cast. Vestibulum and base of the cast are digitally removed. P is the overall deepest point of the whole cast.
Figure 6 Mathematical determination of the deepest point of the palatal groove (P, P0 ) is highly reliable in normal (left, middle) and grown or deformed surfaces (right). A transverse plane through P determines a border line between the ends of the alveolar contour line and defines thereby a volume of interest (dark grey). Volume measurements are independent of flattening effects (right).
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Figure 7 The measurement coordinate system (x0, y0, z0) was transformed into a pre-reference coordinate system (x, y, z) by defining a reference plane based on a set of five landmarks. Fine adjustment was performed in separate planes independent of the previously used landmarks. Upper right: symmetrical alignment of the alveolar ridge towards the reference plane (RF). A clockwise rotation of as little as two degrees leads to a visual impression of unsymmetrical orientation (lower right).
object coordinate system into a reference coordinate system which provides identical measurement conditions for all consecutive casts.
Theoretical considerations about cast registration Registration is the process of transforming different sets of data into one coordinate system. The aim is
the 3D superimposition of objects for nominal/ actual comparisons. This method is mainly used in the industry for quality control reasons to check tolerance limits in production processes. Using the ATOS software the alignment is based on characteristic features like holes, edge points or surface areas. Based on feature correspondence the software minimises the distance in space between the feature coordinates. After alignment, the deviation
Figure 8 Biometric calculations. Palatal width ( pw): the longest distance parallel to the x and perpendicular to the y plane between two maximum values of the alveolar ridge. Palatal length ( pl): the longest distance parallel to the y plane between two surface points. Palatal depth ( pd): the longest distance parallel to the z plane between the highest and the deepest point of the cast. Total volume: the volume of the whole trimmed palate, i.e. all light and dark grey parts of the cast, including the area distal to (P) and lateral to the crest of the alveolar ridge. Extremal volume (ve): the volume enclosed by the maximum contour line of the alveolar ridge and the dorsal border line determined by the minimum (P) of the palatal vault.
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of each 3D coordinate is calculated with respect to the nominal object. Taking into account the considerations of Section ‘‘Theoretical considerations about palatel volume measurements’’, the registration of palates is also feature-dependent, e.g. landmark-dependent, and would therefore limit the overall measurement accuracy to the level of factually inaccurate manual landmark placement. We therefore used a different method consisting of a coarse, landmark-dependent pre-transformation and a landmark-independent fine adjustment. In the first step five landmarks were placed on the cast surface with the ATOS 3-2-1-Registration tool: the right and left tuberosity points, the papilla incisiva point, and two raphe mediana points. With the first three points, a reference plane (RF) is aligned towards the surface of the alveolar ridge (Fig. 7, left). With the two raphe points, a new yaxis is adjusted along the raphe palatina. The object coordinate system is now transformed into a prereference coordinate system. The precise adjustment is performed stepwise in an iterative procedure for each separate plane in space. In the 2D view of a plane the observer minimises symmetrically the vectors that run perpendicular to the horizontal reference plane, from the plane to the surface of the alveolar ridge, by rotat-
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ing the cast (Fig. 7, right). The adjustment is finished if the alveolar ridge is aligned symmetrically to the reference plane in each individual plane. After 3D alignment the pre-reference coordinate system is transformed into the final reference coordinate system. The origin is set in the mid-sagittal plane in front of the frenulum whereby the upper right palate lies in the {x, y, z} quadrant and the upper left palate in the {x, y, z} quadrant. After removing the base of the digital cast, the palate is ready for volume measurements.
Experimental verification It follows from Sections ‘‘Theoretical considerations about palatal volume measurements’’ and ‘‘Theoretical considerations about cast registration’’ that a volume increase of actually growing maxillae could be measured reliably by the described method if the theoretical assumptions are correct. To validate the method we therefore used a population sample of healthy, term, newborn infants as a gold standard and measured the palatal volume of consecutive casts at different stages of growth. The sample size comprised 98 edentulous casts, obtained from a total of 34 individuals. The age of the patients at the respective examination timepoints was calculated from the first day of the
Figure 9 Flow diagram of the growth monitoring process. With the ATOS II system, the plaster model is digitised, processed, and registered to a reference coordinate system to ensure identical conditions for intra- and inter-individual measurements. A Java-based software application (JSA) was developed to obtain the biometric measurements from the digital models. The processes of ATOS and JSA were separated to ensure flexibility of the workflow. After two full cycles of analysis of an individual’s subsequent casts, the clinician is able to assess the growth increase by comparing the consecutive volume measurements. Inter-individual and consecutive measurements are used to collect normative data.
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mother’s last menstruation. The examination intervals were defined as follows, with the number of casts per quarter specified in parenthesis: quarter 0: 37 < 40 weeks of gestation (11 casts); quarter 1: 40 < 52 weeks of gestation (24 casts); quarter 2: 52 < 64 weeks of gestation (15 casts); quarter 3: 64 < 76 weeks of gestation (13 casts); quarter 4: 76 < 88 weeks of gestation (21 casts); quarter 5: 88 < 100 weeks of gestation (14 casts). All casts were digitised, digitally trimmed and aligned as described in randomised order by one investigator who was blinded as to the individual’s name, birth-date and date of the cast. For biometric calculations a Java-based software application (JSA) was developed to process the measurements as described in Fig. 8. The whole process of growth monitoring is summarised in Fig. 9. Assessment of measurement errors Measurement errors are represented with the following equation: g = h + x + d + e, where g is the measured value, h the true value, x the systematic error due to the particular investigator, d the systematic error due to the digitising device, and e the random error. h, d, and e are independent in this kind of study, whereas d was verified by the manufacturer before delivery according to the VDI Standard no. 2634, Sheet 1 (Verein Deutscher Ingenieure e.V., Du ¨ sseldorf, Germany). Based on this inspection sheet the measurement tolerance of the used device is 0.01 mm. Therefore, x is the main source of measurement error for the present method. To assess x, i.e. the intra-investigator reproducibility of cast alignment, a spot sample of 30 randomly selected plaster casts of the population sample was processed twice at different times (t1, t2, 2-months interval) by the same investigator. To assess the influence of polygon mesh resolution of the digital casts, the reproducibility test was also performed a third time with point spacing different from the first and second investigation. For this reason the digital casts were sectioned coronally (x, z plane) at time t1 and t2 with a slice spacing of 0.02 mm, which means the data sets have parallel point gaps of 0.02 mm perpendicular to the y-axis. These casts consist of five million coordinates on average. For the replication of the test at time t3 the original data sets were sectioned coronally with a slice spacing of 0.5 mm. These casts consist of 60,000 coordinates on average. The differences of the biometric measurements (Fig. 8) between the investigations were denoted as the measurement error. For additional detail of the analysis, two more distances were computed: the palatal length at the
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maximal palatal depth ( plpd) and the palatal length at the maximal palatal width ( plpw).
Statistics The descriptive statistic comprises mean (¯ x) and standard deviation (S.D.) of the differences of measurements. The relative measurement error e was determined by e ¼ ðjDmj=mt1 Þ 100, where jDmj is the absolute of the difference between measurements (m) at different times (t1t2; t1t3). Due to comparison reasons, the measurement error was also expressed as the technical error of measurements (tem), also known as Dahlberg’s formula, and the coefficient of variation of tem (cvtem): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P tem ðm1 m2 Þ2 ; cvtem ¼ tem ¼ 100 2 nr x¯ where nr is the number of repeated measurements. To assess differences between different alignments of casts, a one-way ANOVA was performed, followed by Bonferroni post testing, assuming equal variances. The Wilcoxon test was applied to check for significant differences between the measurements of different point spacing. The significance level was set at p < 0.05. To represent biometrical data of the sample population, time-adjusted means (nA) were chosen. This reduced variances resulting from different examination timepoints of different patients in the course of a quarter (quarter 0: 37 < 40 weeks of gestation, quarter 1: 40 < 52 weeks of gestation, etc.). Non-equidistant values arising through aggregation of age groups in quarters could be pooled by this procedure. By standardisation with the time that passed, the time-adjusted mean nA = A/tit0{i = 1, . . . n} is available at each timepoint, also for patients with examination at time t0 only, which in this case would be nAt0 ¼ ðmÞeasurementt0 . For patients with several examinations mi þ mi1 Ai ¼ ðti ti1 Þ 2
and
P A P nAi ¼ Dt
Results Measurement error The measurement error D expressed as the differences of the biometric calculations between the first and second alignment are shown in Table 1. For both alignments the polygon meshes of the digital casts consist of five million coordinates on
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Table 1 Differences D of the biometric calculations (Fig. 8) between first and second alignment of the digital casts with point gaps of 0.02 mm. Cast
Dpd
Dplpd
Dpw
Dplpw
Dpl
Dvt
Dve
0011 0021 0022 0023 0031 0041 0042 0043 0051 0052 0053 0061 0062 0071 0072 0073 0081 0082 0083 0091 0092 0093 0101 0102 0103 0112 0113 011a 0121 00a3
0.40 0.04 0.06 0.18 0.12 0.34 0.34 0.34 0.17 0.04 0.25 0.18 0.14 0.14 0.27 0.14 0.39 0.23 0.01 0.02 0.24 0.16 0.59 0.13 0.02 0.28 0.06 0.24 0.31 0.01
0.06 0.00 0.10 0.08 0.04 0.08 0.46 1.00 1.30 0.04 0.06 0.72 0.00 0.00 0.04 0.08 0.10 0.08 0.02 0.24 0.14 0.08 0.26 0.04 0.10 0.08 0.76 0.08 0.24 0.02
0.01 0.10 0.03 0.03 0.06 0.06 0.34 0.08 0.01 0.01 0.20 0.00 0.04 0.05 0.01 0.06 0.11 0.14 0.01 1.89 0.26 0.64 0.01 0.04 0.01 0.05 0.01 0.05 0.24 0.01
0.04 0.02 0.48 0.12 0.54 0.50 0.70 0.26 0.14 2.52 0.54 0.00 0.18 0.74 0.16 0.02 0.84 0.36 0.02 3.64 0.10 0.12 5.12 0.16 0.06 0.24 0.18 0.06 0.50 0.02
0.06 0.12 0.06 0.02 0.06 0.26 0.00 0.02 0.52 0.28 0.16 0.04 0.22 0.68 0.02 0.24 0.16 0.02 0.00 0.02 0.30 0.76 0.80 0.04 0.04 0.22 0.08 0.00 0.56 0.00
207.89 86.61 47.77 21.41 49.60 386.25 391.56 167.82 123.21 253.59 177.67 13.21 32.71 94.76 191.33 87.82 393.29 140.46 27.80 132.52 32.95 413.92 256.84 22.25 119.55 41.66 117.23 199.40 215.29 27.80
129.93 47.34 24.21 25.63 38.49 227.07 241.88 87.36 22.09 148.10 137.59 19.93 28.64 100.54 112.73 52.71 305.16 81.73 13.32 112.45 9.36 182.97 174.44 28.72 54.85 27.83 86.50 123.25 83.79 13.32
x¯ S.D.
0.20 0.14
0.21 0.32
0.15 0.35
0.61 1.15
0.19 0.24
149.14 122.22
91.40 76.16
¯ e eS.D.
2.66 1.89
1.31 1.94
0.56 1.28
3.65 6.37
0.88 1.15
4.95 4.05
4.34 3.50
tem cvtem
0.17 2.28
0.27 1.69
0.27 1.01
0.91 5.84
0.21 0.91
135.43 4.92
83.55 3.90
¯ = mean of relative error (%); Mean (¯ x) and standard deviation (S.D.) of linear measurements in mm, volumes (vt, ve) in mm3. e e (%); tem = technical error of measurement (mm, mm3); cvtem = coefficient of variation of tem (%). eS.D. = standard deviation of ¯
average with point gaps of 0.02 mm. The mean differences of the linear measurements range from 0.1 9 mm to 0.61 mm. The error of the palatal length up to the maximal palatal width ( plpw) shows the highest relative error (3.6%) and the highest coefficient of variation of tem (5.8%). For this variable the largest outliers (cast 0052, 0091, and 0101) of all linear differences were observed. The volume error is higher in nature than linear values, because the error is raised to the third power. The mean difference for the mathematically calculated ve is significantly smaller (p < 0.001) ¯ and compared to the manually determined vt. e cvtem for both volume measurements are below 5%.
Table 2 summarises the measurement errors between the first and the third alignment. In the latter case the polygon meshes of the digital casts were thinned out to point gaps of 0.5 mm. The characteristics of the errors were comparable to those of the high resolution casts. Again, Dplpw showed the highest error of the linear measurements. The largest outliers could also be found for this variable (casts 0011, 0051, and 0101). The volume error of ve was also significantly smaller ¯ and tem exceeded than Dvt ( p < 0.001) but both e now 6%. The biometric measurements showed now significant differences between the different alignments.
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Table 2 Differences D of the biometric calculations (Fig. 8) between first and third alignment of the digital casts with point gaps of 0.5 mm. Cast
Dpd
Dplpd
Dpw
Dplpw
Dpl
Dvt
Dve
0011 0021 0022 0023 0031 0041 0042 0043 0051 0052 0053 0061 0062 0071 0072 0073 0081 0082 0083 0091 0092 0093 0101 0102 0103 0112 0113 011a 0121 00a3
0.00 0.03 0.01 0.01 0.02 0.05 0.01 0.02 0.01 0.00 0.03 0.00 0.00 0.00 0.01 0.01 0.03 0.01 0.01 0.01 0.03 0.00 0.01 0.03 0.00 0.00 0.02 0.01 0.01 0.01
0.10 0.08 0.08 0.10 0.02 0.14 0.18 0.58 0.04 0.20 1.40 0.00 0.42 0.12 0.00 0.44 0.40 0.04 0.54 0.20 0.16 0.50 0.10 0.36 0.10 0.24 0.08 0.30 0.30 0.54
0.06 0.39 0.02 0.15 0.04 0.08 0.00 0.06 0.07 0.06 0.21 0.14 0.08 0.00 0.06 0.01 0.01 0.10 0.29 0.04 0.04 0.10 0.16 0.11 0.09 1.12 0.00 0.10 0.03 0.29
3.18 0.36 0.50 0.14 0.76 0.50 0.22 0.86 1.24 0.00 0.22 0.16 0.74 0.04 0.36 0.02 0.50 0.02 0.74 0.18 0.16 0.62 2.46 0.36 0.02 0.08 0.12 0.34 0.34 0.74
0.40 0.20 0.56 0.14 0.28 0.58 0.64 0.82 0.26 0.28 0.22 0.20 0.78 0.20 0.36 0.52 0.44 0.48 0.64 0.60 0.30 0.68 0.58 0.60 0.52 0.04 0.16 0.72 0.46 0.64
221.60 20.88 190.01 119.03 689.91 446.10 183.13 43.18 46.77 99.40 167.66 17.64 21.26 24.98 77.79 9.92 15.33 53.71 17.60 366.11 67.00 355.27 74.88 485.28 714.77 41.66 85.26 724.11 567.76 17.60
152.31 20.61 135.51 100.24 421.56 312.71 121.11 11.79 31.43 87.09 121.36 16.11 21.01 34.66 54.88 4.14 17.75 35.25 12.33 252.69 36.29 220.92 54.55 340.87 491.84 0.00 76.91 484.01 431.55 12.33
x¯ S.D.
0.01 0.01
0.26 0.28
0.13 0.21
0.53 0.70
0.44 0.21
198.85 231.03
137.13 156.45
¯ e eS.D.
0.19 0.18
1.60 1.63
0.50 0.82
3.42 4.63
1.96 0.98
6.13 6.73
6.22 6.83
tem cvtem
0.01 0.13
0.27 1.69
0.17 0.64
0.61 3.89
0.35 1.53
213.47 6.88
145.71 6.92
¯ = mean of relative error (%); Mean (¯ x) and standard deviation (S.D.) of linear measurements in mm, volumes (vt, ve) in mm3. e e (%); tem = technical error of measurement (mm, mm3); cvtem = coefficient of variation of tem (%). eS.D. = standard deviation of ¯
In general all mean values of the low resolution casts were smaller compared to the high resolution casts, but this effect was not statistically significant. Concerning the measurement error only Dpd and Dpl ( p 0.001) show a significant effect of different polygon mesh resolution. Interestingly, Dpd between t1 and t3 showed the smallest error compared to all other linear measurements (Table 2).
Biometric data of a growing population sample The represented data refer to casts of 34 healthy term infants (15 male, 19 female). As no significant
differences for the respective palatal measurements between the sexes could be recorded, data for males and females were pooled in the respective quarters. Only such casts were included in the data analysis in which tooth eruption had not yet occurred, and in which palatal width, depth and volume were faultlessly identifiable resulting in different numbers of casts for the respective palatal measurements at comparable quarters. The time-adjusted means of the measurements are represented as boxplots by quarterly time intervals. The one-dimensional parameters palatal depth and palatal width are increasing with time (Fig. 10). The shape of the increase has an approximately
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Figure 10 The one-dimensional measurements palatal depth (left) and palatal width (right). All values in [mm] as timeadjusted means [nApd] and [nApw]. [N] = number of casts measured at each quarter. Both measurements increase with an approximately asymptotic pattern. The peak of palatal depth in quarter 1 differs significantly from quarter 0 ( p = 0.005). Palatal width shows a decline in quarter 3—5.
asymptotic pattern. There is a peak of palatal depth in quarter 1 which differs significantly ( p = 0.005) from quarter zero. Palatal width declines in quarter 3 and remains constant. The assessment of growth based on these one-dimensional parameters could lead to misinterpretations. There is no evidence that the peak of palatal depth could be interpreted as acceleration of vertical growth. On the other hand, there is no evidence either that the decline in palatal width in quarter 3—5 means stagnation of growth. The palatal index ( pi) is a dimensionless value and is defined as the ratio between palatal depth and palatal width. If depth and width are developing similarly, pi should be constant over time. The greater the value of pi the deeper the palate relative to its width.26 Palatal index shows also a peak in quarter 1 (Fig. 11) but with no significant effect ( p = 0.06). Excepting the peak, there is a slight increase of pi proportional to time which could be interpreted as a slight shape change in terms of palatal deepening or palatal narrowing. The increase of pi could be caused by a disproportional increase of pd in the quarters 0—2 followed by the decline of pw in the quarters 3—5. There is also no evidence that the ratio between pd and pw could confirm growth or any growth characteristics. The palatal volume ve, calculated as described in Figs. 6 and 8, increases over time with an approximately asymptotic pattern (Fig. 12, left). Compared to pd, pw and pi, the palatal volume is independent of palatal deepening or palatal narrowing and therefore robust to deformation effects. The increase of ve evidently confirms growth. The growth pattern of
ve also confirms that, unlike what may be suspected from pd and pw, there are no amplitudes like acceleration of palatal growth in quarter 1 or stagnation of palatal growth in quarters 3—5. The head circumference (hc) is an anthropometric measurement with a different pattern compared to pd, pw, pi and ve. In the observed time period, the growth of the head is affected by the
Figure 11 The dimensionless palatal index as the ratio between palatal depth and palatal width. All values dimensionless as time-adjusted means [nApi]. [N] = number of casts measured at each quarter. An increase of pi could be caused by deepening or narrowing of the palate.
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Figure 12 Left: the palatal volume (ve), presented in [mm3] as time-adjusted means [nAve], increases over time with an approximately asymptotic pattern. This three-dimensional measurement is independent of palatal deepening or palatal narrowing, effects that would be caused by deformation. The increase of ve evidently confirms palatal growth. [N] = number of casts measured at each quarter. Right: the head circumference (hc), presented in [mm] as time-adjusted means [nAhc], shows a proportional pattern of increase and confirms head growth in the population sample. [N] = number of measurements obtained at each quarter.
sum of different growth moduli and by different organs and tissues. In the absence of pathological alterations, hc is an evident indicator of growth and increases proportional to time (Fig. 12, right). Therefore, hc confirms growth in the observed population sample.
Discussion Reliability of the method An important source of error in growth studies based on dental casts is the reliability of the common reference system. The hard palate and the alveolar process of a dental cast are delimited by parts of the vestibule mucosa, the soft palate, and the base of the cast. These structures can vary considerably between different impressions of the same object, and thus measurements based on a superimposition of landmarks on these structures can be misleading.21,38 Historically, the assessment of morphological changes of the maxilla is based on the analysis of anatomical landmarks on the palatal surface,16,31,34,36 but over time it was recognised that landmark reproducibility is insufficient. Therefore, in the present paper a landmark-independent approach was used. Two-dimensional measurements2,4,16,21,36 as well as three-dimensional observations limited to single reference points5 are insufficient to analyse morphological changes. Concerning the tolerable size of a measurement error there are different statements in the litera-
ture. Many authors consider linear errors up to 0.8 mm acceptable, which could be a relative error of 10% depending on the distance to be measured.31 Further indicators of measurement precision in anthropometry are the technical error of measurement (tem), which is also known as Dahlberg’s formula, and the coefficient of variation (cvtem) which should not exceed 5% for 2D analyses.39 Both were used for cast analysis of distances with error intervals of tem = {0.12—0.27 mm}35 and cvtem = {0.14— 2.06%},38 as well as for area measurements with cvtem = {1.38—5.53%}.38 The errors of the linear measurements in the present paper are equal or superior to that of the above cited references. There is a variety of current 3D measurement techniques for the palate, which have very low errors in each individual plane in space, but which are difficult to compare to the 3D measurements of the present paper because when calculating a volume the measurement errors are raised to the third power. We demonstrated that our method is able to measure palatal volumes with an error of ¯ e¼ 4:3% and cvtem = 3.9%, which fulfils the criteria for 2D measurements. The first and hitherto sole volume measurements were performed on cleft palates by Braumann et al.4 The authors used a feature and landmark-dependent approach to compare alveolar segments of 10 cleft palates at different stages of growth. The average error of the segment volumes ranged from 4% (dorsal segments) to 23% (anterior segments). The method, however, is not comparable to that of the present study, due to its subjective specification
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of the base plane: 3 mm below the highest alveolar point throughout all casts. The volume measurements of the edentulous palate as described in the present study are thus unique in the literature.
Invasiveness of the method The clinical procedure is limited to the impression of the upper jaw with a very short application time. Changes in head posture are not necessary if the baby is lying on the back. Orotracheal intubation is the only restricting factor. There is no evidence for contact sensitisation with alginate.10,28 A potential, but very low risk is the aspiration of impression material due to uncoordinated sucking and swallowing. There is no incident of alginate suction described in the literature, neither in normal patients nor in patients with disturbed swallowing reflex. Nevertheless, the risk could be eliminated by using (preferably latex-free) condom-covered impression trays.12
Impact on palatal growth monitoring and clinical implications The present study is the first to provide reliabilitychecked normative, three-dimensional data of healthy term infants’ maxillary growth pooled with other biometric features in the first year of life. The obtained measurements could serve to control growth of children that are at risk for growth disturbances. The maxilla is suited for growth measurements because it depends on intramembraneous bone during foetal development, which is the first bone to begin ossification.29 Any bone growth restriction must therefore also affect the maxillary configuration in terms of size and resistance to deformation. When looking at data of the observed subjects, in particular at the peak of the one-dimensional parameter palatal depth (Fig. 10) in combination with the peak of the two-dimensional parameter palatal index (Fig. 11) in the first quarter, it is impossible to determine if this is the result of either growth or only deformation of the palate, the latter occurring, e.g. due to side-to-side flattening of the head. As palatal volume (Fig. 12) increased, too, it seems more likely that growth independent of deformation occurred. With the combination of one-, two- and three-dimensional measurements it may be possible to distinguish between growth, deformation, and direction of both deformation and growth, but only volume measurements are sensitive to growth. This is what makes three-dimensional volume measurements important for growth monitoring as compared to the usage of one- and two-dimensional measure-
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ments only: it makes the method robust to unpredictable translation and distortion in space. The data could serve in the growth assessment of preterm infants, a patient group in which a current lack of information emphasises the need for more long-term and controlled research.25 Normative data on these patients are extremely limited6,17 and the development of non-invasive techniques to collect data is required.29 It was speculated that prenatal pressure on the developing face can lead to distortion of rapidly growing areas and therefore could cause growth disturbances.27 In vitro studies have shown that mechanical stress and strain have an influence on chondro- and osteogenesis and are an external stimulus responsible for phenotypic cell alterations.20 Mechanical stress and strain is exerted especially on the nasomaxillary structures of preterm infants, due to the need for early intubation, orogastric feeding, or distortion of the immature craniofacial bones. Longitudinal normative threedimensional data may clarify the contradictions of long-term results for preterm children with a history of orotracheal intubation with respect to palatal symmetry,18,32 palatal depth and width9,15,26 as well as crossbite.9,15 Three-dimensional volume measurements of the palate are also adequate to determine the effect of therapeutic measures. Patients with cleft lip and palate show more or less developmental disturbances in the nasomaxillary region. Evidence is still vague as to whether the disturbances are caused primarily by malfunction of the cleft or the effect of surgical or (infant) orthopaedic interventions.5 Current intercentre studies have shown that the amount of treatment does not correlate with the quality of clinical outcome.33 Therefore, longitudinal volume measurements could support the assessment of effects of different forms of clefts, different orthopaedic and different surgical procedures on further growth and development.13 Specifically patients with craniofacial syndromes, e.g. Apert, Crouzon or Goldenhar will benefit from normative data because of various early surgical interventions needed. Morphologic changes of the maxilla after palatal expansion are still assessed by two-dimensional measurements.23 Volume measurements could also clarify the final effects of different appliances independent of possible maxillary deformations. The development of the method was intended to reliably assess growth but it is not limited to growing infants. The opposite, evaluation of bone loss, is also possible and the method could be used to assess jaw atrophy,37 longitudinal effects of different prosthetic dentures24 and success rates of different bone graft procedures.11,30
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Conclusion The described method is the first technique for noninvasive volume measurements of the total edentulous palate. It is reliable, absolute feature-dependent, highly objective due to the mathematical approach, and virtually without any risk for the infant. Based on this reliable method, we could demonstrate that in healthy term infants palatal growth in terms of three-dimensional volume analysis proceeds asymptotically and puts linear, one-dimensional measurements into perspective. The obtained normative data could serve as a control tool for comparative studies monitoring, e.g. the palatal development of preterm infants, children with a history of orotracheal intubation and patients with clefts or syndromes.
References 1. Ash SP, Moss JP. An investigation of the features of the preterm infant palate and the effect of prolonged orotracheal intubation with and without protective appliances. Br J Orthod 1987;14:253—61. 2. Berkowitz S, Krischer J, Pruzansky S. Quantitative analysis of cleft palate casts. A geometric study. Cleft Palate J 1974;11: 134—61. 3. Bjo ¨rk A, Skieller V. Postnatal growth and development of the maxillary complex. In: McNamara Jr JA, editor. Factors affecting the growth of the midface. Ann Arbor: The University of Michigan; 1976. p. 61—99. Monograph No. 6. 4. Braumann B, Keilig L, Bourauel C, Ja ¨ger A. Three-dimensional analysis of morphological changes in the maxilla of patients with cleft lip palate. Cleft Palate Craniofac J 2002;39:1—11. 5. Braumann B, Keilig L, Stellzig-Eisenhauer A, Bourauel C, Berge S, Ja ¨ger A. Patterns of maxillary alveolar arch growth changes of infants with unilateral cleft lip and palate: preliminary findings. Cleft Palate Craniofac J 2003;40: 363—72. 6. De Curtis M, Rigo J. Extrauterine growth restriction in verylow-birthweight infants. Acta Paediatr 2004;93:1563—8. 7. Delaire J. Conside ´rations sur l’acroissement du pre ´-maxillaire chez l’homme. Rev Stomatol 1974;75:951—70. 8. Enlow DH, Bang S. Growth and remodeling of the human maxilla. Am J Orthod 1965;51:446—64. 9. Fadavi S, Adeni S, Dziedzic K, Punwani I, Vidyasagar D. The oral effects of orotracheal intubation in prematurely born preschoolers. ASDC J Dent Child 1992;59:420—4. 10. Gallenkemper G, Rabe E, Bauer R. Contact sensitization in chronic venous insufficiency: modern wound dressings. Contact Dermatitis 1998;38:274—8. 11. Jaquiery C, Rohner D, Kunz C, Bucher P, Peters F, Schenk RK, et al. Reconstruction of maxillary and mandibular defects using prefabricated microvascular fibular grafts and osseointegrated dental implants–—a prospective study. Clin Oral Implants Res 2004;15:598—606. 12. Jasmin JR, Muller-Giamarchi M, Dupont D, Velin P. Plaque palatine du nouveau-ne ´ pre ´mature ´. Actual Odontostomatol 1991;45:63—6.
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13. Joos U. Skeletal growth after muscular reconstruction for cleft lip, alveolus and palate. Br J Oral Maxillofac Surg 1995; 33:139—44. 14. Kurihara S, Enlow DH, Rangel RD. Remodeling reversals in anterior parts of the human mandible and maxilla. Angle Orthod 1980;50:98—106. 15. Kopra DE, Davis EL. Prevalence of oral defects among neonatally intubated 3- to 5- and 7- to 10-year old children. Pediatr Dent 1991;13:349—55. 16. Kriens O. Data-objective diagnosis of infant cleft lip alveolus and palate. Morphologic data guiding understanding and treatment concepts. Cleft Palate Craniofac J 1991;28: 157—68. 17. Lapillonne A, Braillon P, Claris O, Chatelain PG, Delmas PD, Salle BL. Body composition in appropriate and in small for gestational age infants. Acta Paediatr 1997;86:196— 200. 18. Macey-Dare LV, Moles DR, Evans RD, Nixon F. Long-term effect of neonatal endo-tracheal intubation on palatal form and symmetry in 8—11-year-old children. Eur J Orthod 1999;21: 703—10. 19. Melsen B. Palatal growth studied on human autopsy material. A histologic microra-diographic study. Am J Orthod 1975;68: 42—54. 20. Meyer U, Meyer T, Wiesmann HP, Kruse-Lo ¨sler B, Vollmer D, Stratmann U, et al. Mechanical tension in distraction osteogenesis regulates chondrocytic differentiation. Int J Oral Maxillofac Surg 2001;30:522—30. 21. Mishima K, Sugahara T, Mori Y, Sakuda M. Three-dimensional comparison between the palatal forms in complete unilateral cleft lip and palate with and without Hotz plate from cheiloplasty to palatoplasty. Cleft Palate Craniofac J 1996;33: 312—7. 22. Morris KM, Burns YR. Reduction of craniofacial and palatal narrowing in very low birthweight infants. J Paediatr Child Health 1994;30:518—22. 23. Oliveira NL, Da Silveira AC, Kusnoto B, Viana G. Threedimensional assessment of morphologic changes of the maxilla: a comparison of 2 kinds of palatal expanders. Am J Orthod Dentofacial Orthop 2004;126:354—62. 24. O’Sullivan M, Hansen N, Cronin RJ, Cagna DR. The hollow maxillary complete denture: a modified technique. J Prosthet Dent 2004;91:591—4. 25. Paulsson L, Bondemark L, Soderfeldt B. A systematic review of the consequences of premature birth on palatal morphology, dental occlusion, tooth-crown dimensions, and tooth maturity and eruption. Angle Orthod 2004;74: 269—79. 26. Procter AM, Lether D, Oliver RG, Cartlidge PH. Deformation of the palate in preterm infants. Arch Dis Child Fetal Neonatal 1998;78:F29—32. 27. Proffit WR, Fields Jr HW. Contemporary orthodontics. 2nd ed. St. Louis: Mosby; 1993. 106—7. 28. Rice CD, Barker BF, Kestenbaum T, Dykstra MA, Lumpkin D. Intraoral vesicles occurring after alginate impressions. Oral Surg Oral Med Oral Pathol 1992;74:698—704. 29. Rigo J, de Curtis M, Pieltain C, Picaud JC, Salle BL, Senterre J. Bone mineral metabolism in the micropremie. Clin Perinatol 2000;27:147—70. 30. Schwartz-Arad D, Levin L. Intraoral autogenous block onlay bone grafting for extensive reconstruction of atrophic maxillary alveolar ridges. J Periodontol 2005;76:636—41. 31. Seckel NG, van der Tweel I, Elema GA, Specken TFJM. Landmark positioning on maxilla of cleft lip and palate infant–—a reality? Cleft Palate Craniofac J 1995;32:434—41. 32. Seow WK, Brown JP, Tudehope DI, OCallaghan M. Effect of neonatal laryngoscopy and endotracheal intubation on pala-
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tal symmetry in two- to five-year-old children. Pediatr Dent 1985;7:30—7. 33. Shaw WC, Brattstrom V, Molsted K, Prahl-Andersen B, Roberts CT, Semb G. The eurocleft study: intercenter study of treatment outcome in patients with complete cleft lip and palate. Part 5: discussion and conclusions. Cleft Palate Craniofac J 2005;42:93—8. 34. Sillmann JH. Dimensional changes of the dental arches: longitudinal study from birth to 25 years. Am J Orthod 1964; 50:824—42. 35. Stellzig A, Basdra EK, Hauser C, Hassfeld S, Komposch G. Factors influencing changes in maxillary arch dimensions in unilateral cleft lip and palate patients until six months of age. Cleft Palate Craniofac J 1999;36:304—9.
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36. Sto ¨ckli PW. Application of a quantitative method for arch form evaluation in complete unilateral cleft lip and palate. Cleft Palate J 1971;8:322—41. 37. Sutton DN, Lewis BR, Patel M, Cawood JI. Changes in facial form relative to progressive atrophy of the edentulous jaws. Int J Oral Maxillofac Surg 2004;33:676—82. 38. Trefny P, Smahel Z, Formanek P, Peterka M. Three-dimensional analysis of maxillary dental casts using Fourier transform profilometry: precision and reliability of the measurement. Cleft Palate Craniofac J 2004;41:20—6. 39. Ward RE, Jamison PL. Measurement precision and reliability in craniofacial anthropometry: implications and suggestions for clinical applications. J Craniofac Genet Dev Biol 1991; 11:156—64.
www.intl.elsevierhealth.com/journals/arob
Objective growth monitoring of the maxilla in full term infants Ariane Hohoff a,*, Thomas Stamm a, Ulrich Meyer b, Dirk Wiechmann c, Ulrike Ehmer a a
Poliklinik fu ¨ r Kieferorthopa ¨die, Westfa ¨lische Wilhelms-Universita ¨t Mu ¨ nster, Waldeyer Str. 30, 48129 Mu ¨ nster, Germany b Klinik und Poliklinik fu ¨ r Mund-, Kiefer- und Gesichtschirurgie, Westfa ¨lische Wilhelms-Universita ¨t Mu ¨ nster, Waldeyer Str. 30, 48129 Mu ¨ nster, Germany c Poliklinik fu ¨ r Kieferorthopa ¨die, Medizinische Hochschule Hannover, Carl-Neuberg-Strasse 1, 30625 Hannover, Germany Accepted 22 July 2005
KEYWORDS Growth; Development; Maxilla; Volume; Normative data
Summary Objective: To develop a non-invasive method for longitudinal maxillary volume measurements and to provide first normative data. Design: Thirty-four healthy infants served as a gold standard for a growing population sample. Alginate impressions were taken of the upper jaw within the first week after birth, and consecutively at different stages of development. The plaster casts were digitised by an optical scanner generating a high resolution polygon mesh of each object. The digital models were aligned to a reference coordinate system with an iterative, landmark-independent procedure. Biometric linear and volume measurements were obtained by using feature-dependent calculations independent of landmark placements. Intra-investigator reproducibility was tested by repeated alignments and measurements of 30 randomly selected casts. To assess the effect of mesh resolution, the reproducibility test was repeated with low resolution models. The method was proved to be valid on the defined gold standard consisting of 96 consecutive edentulous casts. Results: Feature-dependent, linear distances are less error prone (0.56—2.66%) compared to subjectively determined measurements (0.88—3.65%). The same applies to feature-dependent volume calculations (4.34%) compared to subjectively determined volumes (4.95%). Mesh resolution shows an effect ( p 0.001) only on two linear measurements: palatal depth and palatal length. Growth of the individuals in
* Corresponding author. Tel.: +49 251 8347101; fax: +49 251 8347187. E-mail address: [email protected] (A. Hohoff). 0003–9969/$ — see front matter # 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.archoralbio.2005.07.007
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the population sample was evidently confirmed by the maxillary volume measurements (asymptotic pattern) and by comparisons of head circumference (proportional pattern). Conclusion: The described method is non-invasive, precise and without any risk for the infant. Maxillary volume calculation could serve as an important biometric measurement for bone growth evaluation. # 2005 Elsevier Ltd. All rights reserved.
Introduction The anatomic phenomenon ‘growth of the maxilla’ occurs by intramembraneous ossification without cartilaginous precursors. Intramembraneous bone is the first bone to begin ossification.29 Postnatally, the maxilla grows by apposition of bone at the sutures7,19 and by surface remodelling.14 Bone resorption8 and apposition areas of the maxilla are complex,3 but all processes result in an increase of the maxillary volume during the foreward and downward translation. This makes volume measurements of the maxilla interesting for monitoring bone growth at different stages of development. Growth failure in the nasomaxillary complex may be caused by a complex interplay of different internal factors, such as inadequate nutrition, morbidities affecting nutrient requirements, endocrine abnormalities, central nervous system damage, metabolic disturbances and drug administration that influences on nutrient metabolism.6 Disturbances of growth in the nasomaxillary complex may also be caused by clefts or syndromes. Furthermore, external factors, such as side-to-side flattening of the head1,22 or orotracheal intubation may lead to changes in palatal shape and size1,22 or to alterations of the whole nasomaxillary complex (Fig. 1), especially in preterm infants. The long-
term results for preterm children with a history of orotracheal intubation with respect to palatal symmetry,18,32 palatal depth and width9,15,26 as well as crossbite9,15 are contradictory. Therefore, the scientific evidence until today is too weak to answer the questions as to whether premature birth causes permanent alteration of palatal morphology; to answer these questions and obtain reliable scientific evidence as to whether premature children are at risk for malocclusions from possible alterations of palatal morphology, such as asymmetry and higharched palates, further well-designed controlled studies as well as longitudinal studies are needed.25 Normative, longitudinal, reliability-checked measurements of the palatal volume of healthy term infants, which could serve as control data for children born prematurely or with clefts or syndromes, are not available in the current literature. The aim of our study was therefore, first, to develop a reliable method for longitudinal volume measurements of the maxilla and, second, to provide useful control information for developmental evaluation of groups which are at risk for ‘untypical’ growth of the maxilla. The method should be noninvasive, precise, clinically easy to use, without interference with intensive care, sensitive for growth in terms of volume increase, and robust against deformation effects.
Figure 1 Ten-year old, preterm boy with a history of orotracheal intubation. Side-to-side flattening of the head. Maxilla and mandible are very narrow corresponding to the head shape. Lip closure at rest is difficult due to the vertical growth excess.
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Methods Patients Thirty-four healthy, caucasian, normal birthweight term infants (15 male, 19 female), i.e. infants born at 37 weeks of gestation and with a birthweight >2500 g, born at the tertiary-care university hospital of Mu ¨nster, Germany served as a gold standard for a population sample of in actual fact growing individuals. Children with clefts, syndromes, hydrocephalus, cerebral palsy or metabolic diseases were excluded. According to the study protocol, which was approved by the local ethics committee, informed consent of both parents was necessary prior to inclusion of a child in the study. Alginate impressions (Blueprint, Dentsply/Detray, Konstanz, Germany) of the upper jaw were taken by one investigator with specially designed, sterilisible, steel trays within the first week after birth, and consecutively as described in Section ‘‘Statistics’’. The plaster casts were made with class IV plaster (Silky Rock White, Whip Mix, Kentucky, USA).
Data acquisition Data acquisition was performed by one investigator. The plaster casts were digitised with the ATOS II system (GOM GmbH, Braunschweig, Germany), which is mainly used in reverse engineering. The digitising technology is based on the triangulation principle: a sensor projects different fringe patterns onto the object to be measured and observes them with two cameras. Based on the optical transformation equations the system determines the 3D coordinates of the cast. For the present study we used the ATOS SO system (Fig. 2), an optimised unit for measuring volumes down to 45 mm 36 mm 20 mm with point spacings of 0.03—0.15 mm. The casts were placed on a motorised rotation table and measurements of eight views were used to completely digitise the complex morphometry of the palate. The system calculated a point cloud up to four million surface points and all
Figure 3
Figure 2 The ATOS II SO digitising unit consists of a fringe projector (FP), two CCD cameras (CCD) and a motorised rotation table (RT). Different white light fringe patterns are projected on the rotating cast surface and captured by the cameras. The digitising progress (DP) and the camera views (CV) can be controlled on the monitor.
measurements were automatically transformed into a common object coordinate system. At the end of the digitising process, a high resolution polygon mesh described the object. In order to reduce data the system thinned out the mesh based on its curvature without losing accuracy and details. For further processing, the data were exported in different formats like STL, OBJ and ASCII.
Theoretical considerations about palatal volume measurements The 3D shape of a preterm or term edentulous palate could be described as a halved torus (alveolar ridge) connected to a halved hemisphere (palatal vault). Looking at two consecutive casts of a preterm palate at different stages of postnatal life (Fig. 3), the manually placed landmark Lm0 on the current, grown or deformed surface is larger than the corresponding landmark Lm on the previous cast. Lm0 is equal to a fuzzy description of an
An anatomical landmark (Lm) is difficult to relocate (Lm0 ) on a grown or deformed surface.
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Figure 4 Left: cross-section of the cast of Fig. 7. C and C0 are the maximum values and equal to the highest contour points of the alveolar ridge in this specific section. The mathematical determination of the contour maximum is highly reliable in normal (middle) and altered surfaces (right).
anatomic point of interest because the size and the shape of the palate varies considerably with gestation and postnatal age.26 The description of Lm0 varies between consecutive casts and different observers and this variation is responsible for the lack of reliability of assessment made by manual superimposition of landmarks.21 It is therefore necessary to find patterns of consistency. The crest of the alveolar ridge could be seen as one of these patterns. In the plane of a transverse section of the palate, a point of the crest could be defined as the largest overall value of the alveolar outline (Fig. 4). This maximum (C) is characterised by mathematical precision and anatomical fuzziness in the case of longitudinal measurements. That applies also to the sequence of maximum values fCi gni¼1 (where n is a finite number of cross-sections) which determines a contour line along the alveolar ridge. A further pattern of consistency is needed in the region of the transition between hard and soft palate to determine a dorsal border line. The point nearest to that region which could be described mathematically is the deepest point of the palatal groove. Before calculating this point it is necessary
to digitally remove the base of the scanned cast (Fig. 5). The deepest point (P) is then equal to the minimum of the whole set of surface points. A transverse plane perpendicular to the midline (raphe palatina mediana) through point P defines the dorsal border line of the palate. With the mathematical determination of the alveolar contour maximum and the calculation of the deepest point of the palatal groove, a volume of interest can be estimated (Fig. 6). Independent of flattening effects (Fig. 6, right) an increase of size, e.g. growth, can be measured. This method is robust against systematic and random errors due to manual measurements. As follows from Fig. 5 the precision of the measurement of casts taken at one individual’s different stages of development depends on the cast’s orientation within the used coordinate system. A clockwise rotation of the palate in the lateral view of Fig. 5 would shift point P to dorsal with the effect of a systematic measurement error (compare righthand part of Fig. 7). The same effect applies to the alveolar contour line. The total measurement error increases by the sum of the effects in each plane. It is therefore necessary to transform the
Figure 5 Frontal (left) and lateral (right) view of the inner surface of the palatal groove of a scanned cast. Vestibulum and base of the cast are digitally removed. P is the overall deepest point of the whole cast.
Figure 6 Mathematical determination of the deepest point of the palatal groove (P, P0 ) is highly reliable in normal (left, middle) and grown or deformed surfaces (right). A transverse plane through P determines a border line between the ends of the alveolar contour line and defines thereby a volume of interest (dark grey). Volume measurements are independent of flattening effects (right).
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Figure 7 The measurement coordinate system (x0, y0, z0) was transformed into a pre-reference coordinate system (x, y, z) by defining a reference plane based on a set of five landmarks. Fine adjustment was performed in separate planes independent of the previously used landmarks. Upper right: symmetrical alignment of the alveolar ridge towards the reference plane (RF). A clockwise rotation of as little as two degrees leads to a visual impression of unsymmetrical orientation (lower right).
object coordinate system into a reference coordinate system which provides identical measurement conditions for all consecutive casts.
Theoretical considerations about cast registration Registration is the process of transforming different sets of data into one coordinate system. The aim is
the 3D superimposition of objects for nominal/ actual comparisons. This method is mainly used in the industry for quality control reasons to check tolerance limits in production processes. Using the ATOS software the alignment is based on characteristic features like holes, edge points or surface areas. Based on feature correspondence the software minimises the distance in space between the feature coordinates. After alignment, the deviation
Figure 8 Biometric calculations. Palatal width ( pw): the longest distance parallel to the x and perpendicular to the y plane between two maximum values of the alveolar ridge. Palatal length ( pl): the longest distance parallel to the y plane between two surface points. Palatal depth ( pd): the longest distance parallel to the z plane between the highest and the deepest point of the cast. Total volume: the volume of the whole trimmed palate, i.e. all light and dark grey parts of the cast, including the area distal to (P) and lateral to the crest of the alveolar ridge. Extremal volume (ve): the volume enclosed by the maximum contour line of the alveolar ridge and the dorsal border line determined by the minimum (P) of the palatal vault.
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of each 3D coordinate is calculated with respect to the nominal object. Taking into account the considerations of Section ‘‘Theoretical considerations about palatel volume measurements’’, the registration of palates is also feature-dependent, e.g. landmark-dependent, and would therefore limit the overall measurement accuracy to the level of factually inaccurate manual landmark placement. We therefore used a different method consisting of a coarse, landmark-dependent pre-transformation and a landmark-independent fine adjustment. In the first step five landmarks were placed on the cast surface with the ATOS 3-2-1-Registration tool: the right and left tuberosity points, the papilla incisiva point, and two raphe mediana points. With the first three points, a reference plane (RF) is aligned towards the surface of the alveolar ridge (Fig. 7, left). With the two raphe points, a new yaxis is adjusted along the raphe palatina. The object coordinate system is now transformed into a prereference coordinate system. The precise adjustment is performed stepwise in an iterative procedure for each separate plane in space. In the 2D view of a plane the observer minimises symmetrically the vectors that run perpendicular to the horizontal reference plane, from the plane to the surface of the alveolar ridge, by rotat-
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ing the cast (Fig. 7, right). The adjustment is finished if the alveolar ridge is aligned symmetrically to the reference plane in each individual plane. After 3D alignment the pre-reference coordinate system is transformed into the final reference coordinate system. The origin is set in the mid-sagittal plane in front of the frenulum whereby the upper right palate lies in the {x, y, z} quadrant and the upper left palate in the {x, y, z} quadrant. After removing the base of the digital cast, the palate is ready for volume measurements.
Experimental verification It follows from Sections ‘‘Theoretical considerations about palatal volume measurements’’ and ‘‘Theoretical considerations about cast registration’’ that a volume increase of actually growing maxillae could be measured reliably by the described method if the theoretical assumptions are correct. To validate the method we therefore used a population sample of healthy, term, newborn infants as a gold standard and measured the palatal volume of consecutive casts at different stages of growth. The sample size comprised 98 edentulous casts, obtained from a total of 34 individuals. The age of the patients at the respective examination timepoints was calculated from the first day of the
Figure 9 Flow diagram of the growth monitoring process. With the ATOS II system, the plaster model is digitised, processed, and registered to a reference coordinate system to ensure identical conditions for intra- and inter-individual measurements. A Java-based software application (JSA) was developed to obtain the biometric measurements from the digital models. The processes of ATOS and JSA were separated to ensure flexibility of the workflow. After two full cycles of analysis of an individual’s subsequent casts, the clinician is able to assess the growth increase by comparing the consecutive volume measurements. Inter-individual and consecutive measurements are used to collect normative data.
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mother’s last menstruation. The examination intervals were defined as follows, with the number of casts per quarter specified in parenthesis: quarter 0: 37 < 40 weeks of gestation (11 casts); quarter 1: 40 < 52 weeks of gestation (24 casts); quarter 2: 52 < 64 weeks of gestation (15 casts); quarter 3: 64 < 76 weeks of gestation (13 casts); quarter 4: 76 < 88 weeks of gestation (21 casts); quarter 5: 88 < 100 weeks of gestation (14 casts). All casts were digitised, digitally trimmed and aligned as described in randomised order by one investigator who was blinded as to the individual’s name, birth-date and date of the cast. For biometric calculations a Java-based software application (JSA) was developed to process the measurements as described in Fig. 8. The whole process of growth monitoring is summarised in Fig. 9. Assessment of measurement errors Measurement errors are represented with the following equation: g = h + x + d + e, where g is the measured value, h the true value, x the systematic error due to the particular investigator, d the systematic error due to the digitising device, and e the random error. h, d, and e are independent in this kind of study, whereas d was verified by the manufacturer before delivery according to the VDI Standard no. 2634, Sheet 1 (Verein Deutscher Ingenieure e.V., Du ¨ sseldorf, Germany). Based on this inspection sheet the measurement tolerance of the used device is 0.01 mm. Therefore, x is the main source of measurement error for the present method. To assess x, i.e. the intra-investigator reproducibility of cast alignment, a spot sample of 30 randomly selected plaster casts of the population sample was processed twice at different times (t1, t2, 2-months interval) by the same investigator. To assess the influence of polygon mesh resolution of the digital casts, the reproducibility test was also performed a third time with point spacing different from the first and second investigation. For this reason the digital casts were sectioned coronally (x, z plane) at time t1 and t2 with a slice spacing of 0.02 mm, which means the data sets have parallel point gaps of 0.02 mm perpendicular to the y-axis. These casts consist of five million coordinates on average. For the replication of the test at time t3 the original data sets were sectioned coronally with a slice spacing of 0.5 mm. These casts consist of 60,000 coordinates on average. The differences of the biometric measurements (Fig. 8) between the investigations were denoted as the measurement error. For additional detail of the analysis, two more distances were computed: the palatal length at the
A. Hohoff et al.
maximal palatal depth ( plpd) and the palatal length at the maximal palatal width ( plpw).
Statistics The descriptive statistic comprises mean (¯ x) and standard deviation (S.D.) of the differences of measurements. The relative measurement error e was determined by e ¼ ðjDmj=mt1 Þ 100, where jDmj is the absolute of the difference between measurements (m) at different times (t1t2; t1t3). Due to comparison reasons, the measurement error was also expressed as the technical error of measurements (tem), also known as Dahlberg’s formula, and the coefficient of variation of tem (cvtem): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P tem ðm1 m2 Þ2 ; cvtem ¼ tem ¼ 100 2 nr x¯ where nr is the number of repeated measurements. To assess differences between different alignments of casts, a one-way ANOVA was performed, followed by Bonferroni post testing, assuming equal variances. The Wilcoxon test was applied to check for significant differences between the measurements of different point spacing. The significance level was set at p < 0.05. To represent biometrical data of the sample population, time-adjusted means (nA) were chosen. This reduced variances resulting from different examination timepoints of different patients in the course of a quarter (quarter 0: 37 < 40 weeks of gestation, quarter 1: 40 < 52 weeks of gestation, etc.). Non-equidistant values arising through aggregation of age groups in quarters could be pooled by this procedure. By standardisation with the time that passed, the time-adjusted mean nA = A/tit0{i = 1, . . . n} is available at each timepoint, also for patients with examination at time t0 only, which in this case would be nAt0 ¼ ðmÞeasurementt0 . For patients with several examinations mi þ mi1 Ai ¼ ðti ti1 Þ 2
and
P A P nAi ¼ Dt
Results Measurement error The measurement error D expressed as the differences of the biometric calculations between the first and second alignment are shown in Table 1. For both alignments the polygon meshes of the digital casts consist of five million coordinates on
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Table 1 Differences D of the biometric calculations (Fig. 8) between first and second alignment of the digital casts with point gaps of 0.02 mm. Cast
Dpd
Dplpd
Dpw
Dplpw
Dpl
Dvt
Dve
0011 0021 0022 0023 0031 0041 0042 0043 0051 0052 0053 0061 0062 0071 0072 0073 0081 0082 0083 0091 0092 0093 0101 0102 0103 0112 0113 011a 0121 00a3
0.40 0.04 0.06 0.18 0.12 0.34 0.34 0.34 0.17 0.04 0.25 0.18 0.14 0.14 0.27 0.14 0.39 0.23 0.01 0.02 0.24 0.16 0.59 0.13 0.02 0.28 0.06 0.24 0.31 0.01
0.06 0.00 0.10 0.08 0.04 0.08 0.46 1.00 1.30 0.04 0.06 0.72 0.00 0.00 0.04 0.08 0.10 0.08 0.02 0.24 0.14 0.08 0.26 0.04 0.10 0.08 0.76 0.08 0.24 0.02
0.01 0.10 0.03 0.03 0.06 0.06 0.34 0.08 0.01 0.01 0.20 0.00 0.04 0.05 0.01 0.06 0.11 0.14 0.01 1.89 0.26 0.64 0.01 0.04 0.01 0.05 0.01 0.05 0.24 0.01
0.04 0.02 0.48 0.12 0.54 0.50 0.70 0.26 0.14 2.52 0.54 0.00 0.18 0.74 0.16 0.02 0.84 0.36 0.02 3.64 0.10 0.12 5.12 0.16 0.06 0.24 0.18 0.06 0.50 0.02
0.06 0.12 0.06 0.02 0.06 0.26 0.00 0.02 0.52 0.28 0.16 0.04 0.22 0.68 0.02 0.24 0.16 0.02 0.00 0.02 0.30 0.76 0.80 0.04 0.04 0.22 0.08 0.00 0.56 0.00
207.89 86.61 47.77 21.41 49.60 386.25 391.56 167.82 123.21 253.59 177.67 13.21 32.71 94.76 191.33 87.82 393.29 140.46 27.80 132.52 32.95 413.92 256.84 22.25 119.55 41.66 117.23 199.40 215.29 27.80
129.93 47.34 24.21 25.63 38.49 227.07 241.88 87.36 22.09 148.10 137.59 19.93 28.64 100.54 112.73 52.71 305.16 81.73 13.32 112.45 9.36 182.97 174.44 28.72 54.85 27.83 86.50 123.25 83.79 13.32
x¯ S.D.
0.20 0.14
0.21 0.32
0.15 0.35
0.61 1.15
0.19 0.24
149.14 122.22
91.40 76.16
¯ e eS.D.
2.66 1.89
1.31 1.94
0.56 1.28
3.65 6.37
0.88 1.15
4.95 4.05
4.34 3.50
tem cvtem
0.17 2.28
0.27 1.69
0.27 1.01
0.91 5.84
0.21 0.91
135.43 4.92
83.55 3.90
¯ = mean of relative error (%); Mean (¯ x) and standard deviation (S.D.) of linear measurements in mm, volumes (vt, ve) in mm3. e e (%); tem = technical error of measurement (mm, mm3); cvtem = coefficient of variation of tem (%). eS.D. = standard deviation of ¯
average with point gaps of 0.02 mm. The mean differences of the linear measurements range from 0.1 9 mm to 0.61 mm. The error of the palatal length up to the maximal palatal width ( plpw) shows the highest relative error (3.6%) and the highest coefficient of variation of tem (5.8%). For this variable the largest outliers (cast 0052, 0091, and 0101) of all linear differences were observed. The volume error is higher in nature than linear values, because the error is raised to the third power. The mean difference for the mathematically calculated ve is significantly smaller (p < 0.001) ¯ and compared to the manually determined vt. e cvtem for both volume measurements are below 5%.
Table 2 summarises the measurement errors between the first and the third alignment. In the latter case the polygon meshes of the digital casts were thinned out to point gaps of 0.5 mm. The characteristics of the errors were comparable to those of the high resolution casts. Again, Dplpw showed the highest error of the linear measurements. The largest outliers could also be found for this variable (casts 0011, 0051, and 0101). The volume error of ve was also significantly smaller ¯ and tem exceeded than Dvt ( p < 0.001) but both e now 6%. The biometric measurements showed now significant differences between the different alignments.
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Table 2 Differences D of the biometric calculations (Fig. 8) between first and third alignment of the digital casts with point gaps of 0.5 mm. Cast
Dpd
Dplpd
Dpw
Dplpw
Dpl
Dvt
Dve
0011 0021 0022 0023 0031 0041 0042 0043 0051 0052 0053 0061 0062 0071 0072 0073 0081 0082 0083 0091 0092 0093 0101 0102 0103 0112 0113 011a 0121 00a3
0.00 0.03 0.01 0.01 0.02 0.05 0.01 0.02 0.01 0.00 0.03 0.00 0.00 0.00 0.01 0.01 0.03 0.01 0.01 0.01 0.03 0.00 0.01 0.03 0.00 0.00 0.02 0.01 0.01 0.01
0.10 0.08 0.08 0.10 0.02 0.14 0.18 0.58 0.04 0.20 1.40 0.00 0.42 0.12 0.00 0.44 0.40 0.04 0.54 0.20 0.16 0.50 0.10 0.36 0.10 0.24 0.08 0.30 0.30 0.54
0.06 0.39 0.02 0.15 0.04 0.08 0.00 0.06 0.07 0.06 0.21 0.14 0.08 0.00 0.06 0.01 0.01 0.10 0.29 0.04 0.04 0.10 0.16 0.11 0.09 1.12 0.00 0.10 0.03 0.29
3.18 0.36 0.50 0.14 0.76 0.50 0.22 0.86 1.24 0.00 0.22 0.16 0.74 0.04 0.36 0.02 0.50 0.02 0.74 0.18 0.16 0.62 2.46 0.36 0.02 0.08 0.12 0.34 0.34 0.74
0.40 0.20 0.56 0.14 0.28 0.58 0.64 0.82 0.26 0.28 0.22 0.20 0.78 0.20 0.36 0.52 0.44 0.48 0.64 0.60 0.30 0.68 0.58 0.60 0.52 0.04 0.16 0.72 0.46 0.64
221.60 20.88 190.01 119.03 689.91 446.10 183.13 43.18 46.77 99.40 167.66 17.64 21.26 24.98 77.79 9.92 15.33 53.71 17.60 366.11 67.00 355.27 74.88 485.28 714.77 41.66 85.26 724.11 567.76 17.60
152.31 20.61 135.51 100.24 421.56 312.71 121.11 11.79 31.43 87.09 121.36 16.11 21.01 34.66 54.88 4.14 17.75 35.25 12.33 252.69 36.29 220.92 54.55 340.87 491.84 0.00 76.91 484.01 431.55 12.33
x¯ S.D.
0.01 0.01
0.26 0.28
0.13 0.21
0.53 0.70
0.44 0.21
198.85 231.03
137.13 156.45
¯ e eS.D.
0.19 0.18
1.60 1.63
0.50 0.82
3.42 4.63
1.96 0.98
6.13 6.73
6.22 6.83
tem cvtem
0.01 0.13
0.27 1.69
0.17 0.64
0.61 3.89
0.35 1.53
213.47 6.88
145.71 6.92
¯ = mean of relative error (%); Mean (¯ x) and standard deviation (S.D.) of linear measurements in mm, volumes (vt, ve) in mm3. e e (%); tem = technical error of measurement (mm, mm3); cvtem = coefficient of variation of tem (%). eS.D. = standard deviation of ¯
In general all mean values of the low resolution casts were smaller compared to the high resolution casts, but this effect was not statistically significant. Concerning the measurement error only Dpd and Dpl ( p 0.001) show a significant effect of different polygon mesh resolution. Interestingly, Dpd between t1 and t3 showed the smallest error compared to all other linear measurements (Table 2).
Biometric data of a growing population sample The represented data refer to casts of 34 healthy term infants (15 male, 19 female). As no significant
differences for the respective palatal measurements between the sexes could be recorded, data for males and females were pooled in the respective quarters. Only such casts were included in the data analysis in which tooth eruption had not yet occurred, and in which palatal width, depth and volume were faultlessly identifiable resulting in different numbers of casts for the respective palatal measurements at comparable quarters. The time-adjusted means of the measurements are represented as boxplots by quarterly time intervals. The one-dimensional parameters palatal depth and palatal width are increasing with time (Fig. 10). The shape of the increase has an approximately
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Figure 10 The one-dimensional measurements palatal depth (left) and palatal width (right). All values in [mm] as timeadjusted means [nApd] and [nApw]. [N] = number of casts measured at each quarter. Both measurements increase with an approximately asymptotic pattern. The peak of palatal depth in quarter 1 differs significantly from quarter 0 ( p = 0.005). Palatal width shows a decline in quarter 3—5.
asymptotic pattern. There is a peak of palatal depth in quarter 1 which differs significantly ( p = 0.005) from quarter zero. Palatal width declines in quarter 3 and remains constant. The assessment of growth based on these one-dimensional parameters could lead to misinterpretations. There is no evidence that the peak of palatal depth could be interpreted as acceleration of vertical growth. On the other hand, there is no evidence either that the decline in palatal width in quarter 3—5 means stagnation of growth. The palatal index ( pi) is a dimensionless value and is defined as the ratio between palatal depth and palatal width. If depth and width are developing similarly, pi should be constant over time. The greater the value of pi the deeper the palate relative to its width.26 Palatal index shows also a peak in quarter 1 (Fig. 11) but with no significant effect ( p = 0.06). Excepting the peak, there is a slight increase of pi proportional to time which could be interpreted as a slight shape change in terms of palatal deepening or palatal narrowing. The increase of pi could be caused by a disproportional increase of pd in the quarters 0—2 followed by the decline of pw in the quarters 3—5. There is also no evidence that the ratio between pd and pw could confirm growth or any growth characteristics. The palatal volume ve, calculated as described in Figs. 6 and 8, increases over time with an approximately asymptotic pattern (Fig. 12, left). Compared to pd, pw and pi, the palatal volume is independent of palatal deepening or palatal narrowing and therefore robust to deformation effects. The increase of ve evidently confirms growth. The growth pattern of
ve also confirms that, unlike what may be suspected from pd and pw, there are no amplitudes like acceleration of palatal growth in quarter 1 or stagnation of palatal growth in quarters 3—5. The head circumference (hc) is an anthropometric measurement with a different pattern compared to pd, pw, pi and ve. In the observed time period, the growth of the head is affected by the
Figure 11 The dimensionless palatal index as the ratio between palatal depth and palatal width. All values dimensionless as time-adjusted means [nApi]. [N] = number of casts measured at each quarter. An increase of pi could be caused by deepening or narrowing of the palate.
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A. Hohoff et al.
Figure 12 Left: the palatal volume (ve), presented in [mm3] as time-adjusted means [nAve], increases over time with an approximately asymptotic pattern. This three-dimensional measurement is independent of palatal deepening or palatal narrowing, effects that would be caused by deformation. The increase of ve evidently confirms palatal growth. [N] = number of casts measured at each quarter. Right: the head circumference (hc), presented in [mm] as time-adjusted means [nAhc], shows a proportional pattern of increase and confirms head growth in the population sample. [N] = number of measurements obtained at each quarter.
sum of different growth moduli and by different organs and tissues. In the absence of pathological alterations, hc is an evident indicator of growth and increases proportional to time (Fig. 12, right). Therefore, hc confirms growth in the observed population sample.
Discussion Reliability of the method An important source of error in growth studies based on dental casts is the reliability of the common reference system. The hard palate and the alveolar process of a dental cast are delimited by parts of the vestibule mucosa, the soft palate, and the base of the cast. These structures can vary considerably between different impressions of the same object, and thus measurements based on a superimposition of landmarks on these structures can be misleading.21,38 Historically, the assessment of morphological changes of the maxilla is based on the analysis of anatomical landmarks on the palatal surface,16,31,34,36 but over time it was recognised that landmark reproducibility is insufficient. Therefore, in the present paper a landmark-independent approach was used. Two-dimensional measurements2,4,16,21,36 as well as three-dimensional observations limited to single reference points5 are insufficient to analyse morphological changes. Concerning the tolerable size of a measurement error there are different statements in the litera-
ture. Many authors consider linear errors up to 0.8 mm acceptable, which could be a relative error of 10% depending on the distance to be measured.31 Further indicators of measurement precision in anthropometry are the technical error of measurement (tem), which is also known as Dahlberg’s formula, and the coefficient of variation (cvtem) which should not exceed 5% for 2D analyses.39 Both were used for cast analysis of distances with error intervals of tem = {0.12—0.27 mm}35 and cvtem = {0.14— 2.06%},38 as well as for area measurements with cvtem = {1.38—5.53%}.38 The errors of the linear measurements in the present paper are equal or superior to that of the above cited references. There is a variety of current 3D measurement techniques for the palate, which have very low errors in each individual plane in space, but which are difficult to compare to the 3D measurements of the present paper because when calculating a volume the measurement errors are raised to the third power. We demonstrated that our method is able to measure palatal volumes with an error of ¯ e¼ 4:3% and cvtem = 3.9%, which fulfils the criteria for 2D measurements. The first and hitherto sole volume measurements were performed on cleft palates by Braumann et al.4 The authors used a feature and landmark-dependent approach to compare alveolar segments of 10 cleft palates at different stages of growth. The average error of the segment volumes ranged from 4% (dorsal segments) to 23% (anterior segments). The method, however, is not comparable to that of the present study, due to its subjective specification
Growth monitoring of the maxillary complex
of the base plane: 3 mm below the highest alveolar point throughout all casts. The volume measurements of the edentulous palate as described in the present study are thus unique in the literature.
Invasiveness of the method The clinical procedure is limited to the impression of the upper jaw with a very short application time. Changes in head posture are not necessary if the baby is lying on the back. Orotracheal intubation is the only restricting factor. There is no evidence for contact sensitisation with alginate.10,28 A potential, but very low risk is the aspiration of impression material due to uncoordinated sucking and swallowing. There is no incident of alginate suction described in the literature, neither in normal patients nor in patients with disturbed swallowing reflex. Nevertheless, the risk could be eliminated by using (preferably latex-free) condom-covered impression trays.12
Impact on palatal growth monitoring and clinical implications The present study is the first to provide reliabilitychecked normative, three-dimensional data of healthy term infants’ maxillary growth pooled with other biometric features in the first year of life. The obtained measurements could serve to control growth of children that are at risk for growth disturbances. The maxilla is suited for growth measurements because it depends on intramembraneous bone during foetal development, which is the first bone to begin ossification.29 Any bone growth restriction must therefore also affect the maxillary configuration in terms of size and resistance to deformation. When looking at data of the observed subjects, in particular at the peak of the one-dimensional parameter palatal depth (Fig. 10) in combination with the peak of the two-dimensional parameter palatal index (Fig. 11) in the first quarter, it is impossible to determine if this is the result of either growth or only deformation of the palate, the latter occurring, e.g. due to side-to-side flattening of the head. As palatal volume (Fig. 12) increased, too, it seems more likely that growth independent of deformation occurred. With the combination of one-, two- and three-dimensional measurements it may be possible to distinguish between growth, deformation, and direction of both deformation and growth, but only volume measurements are sensitive to growth. This is what makes three-dimensional volume measurements important for growth monitoring as compared to the usage of one- and two-dimensional measure-
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ments only: it makes the method robust to unpredictable translation and distortion in space. The data could serve in the growth assessment of preterm infants, a patient group in which a current lack of information emphasises the need for more long-term and controlled research.25 Normative data on these patients are extremely limited6,17 and the development of non-invasive techniques to collect data is required.29 It was speculated that prenatal pressure on the developing face can lead to distortion of rapidly growing areas and therefore could cause growth disturbances.27 In vitro studies have shown that mechanical stress and strain have an influence on chondro- and osteogenesis and are an external stimulus responsible for phenotypic cell alterations.20 Mechanical stress and strain is exerted especially on the nasomaxillary structures of preterm infants, due to the need for early intubation, orogastric feeding, or distortion of the immature craniofacial bones. Longitudinal normative threedimensional data may clarify the contradictions of long-term results for preterm children with a history of orotracheal intubation with respect to palatal symmetry,18,32 palatal depth and width9,15,26 as well as crossbite.9,15 Three-dimensional volume measurements of the palate are also adequate to determine the effect of therapeutic measures. Patients with cleft lip and palate show more or less developmental disturbances in the nasomaxillary region. Evidence is still vague as to whether the disturbances are caused primarily by malfunction of the cleft or the effect of surgical or (infant) orthopaedic interventions.5 Current intercentre studies have shown that the amount of treatment does not correlate with the quality of clinical outcome.33 Therefore, longitudinal volume measurements could support the assessment of effects of different forms of clefts, different orthopaedic and different surgical procedures on further growth and development.13 Specifically patients with craniofacial syndromes, e.g. Apert, Crouzon or Goldenhar will benefit from normative data because of various early surgical interventions needed. Morphologic changes of the maxilla after palatal expansion are still assessed by two-dimensional measurements.23 Volume measurements could also clarify the final effects of different appliances independent of possible maxillary deformations. The development of the method was intended to reliably assess growth but it is not limited to growing infants. The opposite, evaluation of bone loss, is also possible and the method could be used to assess jaw atrophy,37 longitudinal effects of different prosthetic dentures24 and success rates of different bone graft procedures.11,30
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Conclusion The described method is the first technique for noninvasive volume measurements of the total edentulous palate. It is reliable, absolute feature-dependent, highly objective due to the mathematical approach, and virtually without any risk for the infant. Based on this reliable method, we could demonstrate that in healthy term infants palatal growth in terms of three-dimensional volume analysis proceeds asymptotically and puts linear, one-dimensional measurements into perspective. The obtained normative data could serve as a control tool for comparative studies monitoring, e.g. the palatal development of preterm infants, children with a history of orotracheal intubation and patients with clefts or syndromes.
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