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Revista chilena de anatomía
versión impresa ISSN 07169868
Rev. chil. anat. v.17 n.2 Temuco
http://dx.doi.org/10.4067/S071698681999000200002
PRINCIPAL COMPONENT ANALYSIS OF THE HUMAN FETAL METATARSAL
GROWTH IN THE SECOND GESTATIONAL TRIMESTER
ANALISIS DEL PRINCIPAL COMPONENTE DEL CRECIMIENTO METATARSAL
FETAL HUMANO EN EL SEGUNDO TRIMESTRE GESTIONAL
^{*}  Henrique Ayres de Vasconcellos 
^{**}  Carlos Alberto MandarimdeLacerda 
This research was partially supported by Brazilian agencies CNPq (Proc. 52.41.14/970) and Faperj (Proc. 151.495/99).
SUMMARY: We carried out a study with 800 metatarsal bones retired from 80 pairs of feet of human fetuses from single gestation. Fetuses aged from 13 to 24 gestational weeks (45 men and 35 women), were fixed in 10% formaldehyde during 30 days, conception. The total length, the length of the ossified shaft and the diameter of the shaft were measured. The covariance matrix was calculated and the relative growth of the measurements was computed through of the principal component analysis (PCA). Considering both sexes together the first principal component accounted 82.7% of the total variance and all the characters were positively correlated with this component. No measurement was considered isometric (p<0.01). PCA suggested the total length and the diameter of the shaft grew with negative allometry and the length of the ossified shaft grew with positive allometry. The differences between sexes were not significant (p>0.05). These results are useful in prenatal assessment of the gestational age using metatarsal length as the anatomical landmark.
KEY WORDS: 1. Fetal foot; 2. Metatarsal growth; 3. Principal component analysis.
INTRODUCTION
Metatarsals are long bones that grow even in length as well as in width. During the human fetal period the growth of the metatarsal has specific equations to each metatarsal bone, that is, with different growth rates than the growth of the body (VASCONCELLOS & MANDARIMDELACERDA, 1988; VASCONCELLOS & MORAES, 1989; VASCONCELLOS et al., 1992 b; VASCONCELLOS & FERREIRA, 1998). This is important to detect precociously some congenital malformations of the foot and also to the assessment of the prenatal age (CHERVENAK & ISSACSON, 1989; MANDARIMDELACERDA, 1990; SANTUCCI et al., 1993; VASCONCELLOS et al., 1992a).
Bivariate allometric coefficients estimated from mensural data, as these ratios are independent of the absolute rates, are considered to provide complete information about growth related changes (BLACKSTONE, 1987). On the other hand, multivariate allometries are rates of growth estimated with respect to overall body size, which is a different estimate of biological age than chronological time, but one more directly tied to growth (STRAUSS, 1987).
In principal components analysis (PCA), morphometric data are interpreted as patterns of covariation in size and shape. JOLICOEUR (1963a) demonstrated that the eigenvector in PCA, extracted from the covariance matrix of logarithmic values, describes relative changes in the measured characters during growth. The first principal component is usually interpreted as a multivariate approximation of general size, often with near equal contributions from each character. Generally, researchers assume that the first component represents overall size, since all characters are positively correlated with this component (JOLICOEUR, 1963ab; HOPKINS, 1966; TAKAI & AKIYOSHI, 1979; SHEA, 1985; SOMERS, 1986; MANLY, 1994).
Figure 1. Schematic drawing of the metatarsal and the anatomical points where measurements were taken. OL: ossified length; TL: total length; WB: width breadth. 
MATERIAL AND METHOD
Our material consisted of 800 metatarsal bones taken from 80 feet's pairs of spontaneously aborted human Brazilian fetuses of single pregnancy (45 males and 35 females). None of the fetuses presented any external anomaly. The gestational age ranged from 13 to 24 weeks post conception, estimated according to the foot length criterion (STREETER, 1920; MANDARIMDELACERDA, 1990; VASCONCELLOS et al. 1992 b).
The bones were immersed in a formalin solution for at least 30 days. The fixation makes dissection easier, especially when removing the periosteum and pericondrium (HATTORI, 1986). We measured bone lengths both before and after fixation and no significant difference was found (VASCONCELLOS et al., 1992 a; VASCONCELLOS & FERREIRA). Lengths were measured on the dorsal surface of the bones, by the same observer, with a caliper of 0.01cm of accuracy in a straight line analyzing welldefined anatomical marks: Total length (TL), ossified length (OL) and width breadth (WB) (Figure 1).
Statistical Analysis: Multivariate analysis was performed in order to determine the different growth rates. A covariance matrix was calculated from natural logarithms of the measurements. The relative growth rates of these variables were computed by multivariate analysis using a principal components analysis (PCA) (JOLICOEUR, 1963a; SOMERS and MANLY). PCA is a statistical method of data reduction. A set of correlated variable is transformed into a smaller set of uncorrelated variables (named principal components) that account for most of the variability among subjects. The principal components are linear combinations (weighted averages) of the original variables. The first principal component (cp 1) has the largest variance of any such linear combination. . Successive principal components are meaningful and if they include most of the variability of the original variables, these new variables can efficiently substitute the original, larger set of variables in subsequent analysis (MANDARIMDELACERDA, 1993; NELSON et al., 1991). In the present study, PCA was based on the covariance matrix. Multivariate isometry exists when all z dimensions increase at the same rate; this implies that all z loadings are equal, that is, .^{ }A loading greater than indicates positive allometry, whereas one less than signifies negative allometry (JOLICOEUR, 1963a; JUNGERS & GERMAN, 1981; MANDARIMDELACERDA, 1995.
The covariance matrix and the relative growth of bony measurements were computed by multivariate allometry, using the principal components analysis (PCA). Using the software Excel and Statgraphics in an IBM PC Computer eigen values and eigen vectors of the matrix were determined.
RESULTS
Results are set out in Table 1 and Figure 2. Considering female and male fetuses together the eigen values for a PCA shown the variance that accounts for out of the total variance of the sample. In this study the first component accounted for 82.7% of the total variance and all characters were positively correlated with this component, therefore the first component was far more important than the other.
Figure 2. Plot of first component weight (growth rates) for the growth of the fetal body. Crosses  metatarsal width breadth, triangles  metatarsal total length, circles  metatarsal ossified length. 
Considering the different parameters in the sequence of the increasing eigen value no measurement was considered to growth in isometric relationship.
PCA showed that the TL and WB grew with negative allometry while the OL grew with positive allometry (Table I and Figure 2). The analysis was not significant analyzing feminine and masculine fetuses independently (X^{2} values 24.9 and 34.7 with p>0.05, respectively) as well as the analysis demonstrated no differences between sexes.
Table I  Component weight (growth rates) for the first principal component of the principal component analysis studying the increase of the metatarsals in early fetal life. Metatarsals are indicated by roman numerals where r is the right side and l is the left side.  
 
Width breadth  Component weight  Total Length  Component weight  Ossified Length  Component weight 
V r  0.1277  I l  0.1570  II l  0.2178 
IV r  0.1285  IV l  0.1593  II r  0.2184 
III r  0.1342  V r  0.1596  V r  0.2210 
III l  0.1405  I r  0.1602  I l  0.2258 
II r  0.1407  III r  0.1616  IV r  0.2287 
V l  0.1427  IV r  0.1636  III r  0.2306 
IV l  0.1491  II l  0.1640  IV l  0.2312 
I r  0.1538  V l  0.1660  I r  0.2371 
I l  0.1560  II r  0.1664  V l  0.2397 
II l  0.1561  II l  0.1729  III l  0.2469 

DISCUSSION
JOLICOEUR (1963a) demonstrated that the eigenvector in PCA, extracted from the covariance matrix of logarithmic values, describes relative changes in the measured characters during growth. This agrees with a study of mandibular growth (MANDARINDELACERDA & ALVES, 1992) that found similar growth rates using bivariate and multivariate analyses.
The main interest of this multivariate study is to compare the growth of the different metatarsals simultaneously. So, we observed that only the OL of the metatarsals grew with positive allometry in early fetal foot. The both metatarsals TL and WB grew with negative multivariate allometry. The results have not equivalent in the literature because studies about long bone growth have compared a limited sample of bones by using bivariate analyses: humerus and femur (MEHTA & SINGH, 1972); metacarpals (HATTORI; BARROS & MANDARIMDELACERDA, 1989); humerus, ulna and radius (BAREGGI et al., 1994). In previous bivariate studies on metatarsals TL and OL were correlated to fetal CrownRump length,
TL growing with isometry while OL growing with positive allometry (VASCONCELLOS & MANDARIMDELACERDA, 1988; VASCONCELLOS & MORAES; VASCONCELLOS et al., 1992 b). These results agree with this multivariate analysis and suggest a limited fetal growth of the metatarsal epiphyses relative to the growth in length of the shaft.
The periostium grows interstitially increasing the bone thickness by deposition of subperiosteal bone on the external surface of the shaft (JOSEPH, 1976). In metatarsals this subperiosteal growth occurred and presented smaller component weights in PCA (negative multivariate allometry) In PCA, each factor or "component" is viewed as a weighted combination of the input variables, with as many components derived, as there are variables (KACHIGAN, 1991). In our study this was measured as the WB and presented the lowest growth rate in metatarsal growth. Certainly, these differences in the rate of growth in metatarsals are responsible for the slight curvature of these bones since prenatal life.
The accuracy of the data should not be affected by the fixation of the fetuses. STREETER and SCHULTZ (1929) demonstrated that external measurements recorded in formalinimmersed fetuses are identical to those recorded in fresh specimens. The measurements of the bones were taken before and after the 30 days of fixation and no significant differences were observed (VASCONCELLOS et al., 1992 b).
Present study was performed analyzing fetuses from a mixed ethnic population. This sample is not large enough to verify a possible sexual dimorphism in fetal growth. The expression of sexual dimorphism in human groups remains a significant issue in anthropological study (VAN VARK et al., 1989). Frequently, however, the proper interpretation of the sexual dimorphism remains a difficult and rather speculative matter (CORRUCCINI, 1984). The findings of this work refer to the fetal growth the metatarsals. During the second trimester of prenatal life the growth of the metatarsals was allometrical. Although it may be considered a relative approach for the study of size changes in human fetuses, it does not necessarily, if at all, represent the rates of normal prenatal growth in living individuals. Nevertheless, the analysis preformed in this study provides an approximation of the biological phenomenon of growth that may be useful to the interpretation of the human growth.
RESUMEN: Se realizó un estudio de 800 huesos metatarsales retirados de 80 pares de pies de fetos humanos de gestación única. Los fetos con edades de 13 a 24 semanas post concepción (45 hombres y 35 mujeres), fueron fijados en formol al 10%, por 30 días. Fueron medidos la longitud total del hueso y la longitud y el diámetro de la diáfisis osificada. La matriz de covarianza fue calculada y el crecimiento relativo de las medidas fueron computados a través del análisis del componente principal (ACP). Para ambos sexos, el primer componente fue 82.7% de la varianza total y todos los caracteres fueron positivamente correlacionados con este componente. Ninguna medida fue considerada de crecimiento isométrico (p<0.01). La ACP indicó que la longitud total y el diámetro de la diáfisis crecieron con alometría negativa y la longitud de la diáfisis osificada con alometría positiva. Las diferencias entre ambos sexos no fueron significativas (p>0.05). Estos resultados son útiles en la valoración prenatal de la edad gestacional que usa la longitud metatarsal como referencia anatómico.
PALABRAS CLAVE: 1. Pie; 2. Feto; 3. Crecimiento metatarsal; 4. Análisis del componente principal.
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Address for correspondence:
Prof. Dr. Henrique Ayres de Vasconcellos
Caixa Postal 46523
20562970 _ Rio de Janeiro _ RJ
BRAZIL
Email: havasc@uerj.br.
Recibido : 09101999
Aceptado: 14111999