## 2 Materials and Methods  
To achieve these goals, a cross-sectional study was conducted at the Orthodontic Department of \"Carol Davila\" University of Medicine and Pharmacy, Bucharest, Romania. A sample of 100 dental casts of orthodontic patients were selected. As a routine procedure, a signed informed consent for releasing diagnostic records for scientific purposes is always obtained from the patients or legal guardians of the patients prior to the beginning of treatment. The present study did not need ethic approval, as our research just used measurements performed on dental casts, not involving clinical activities on patients. The selection of dental casts was performed by authors [PERSON] and M.-A.B. and met the following criteria:  
* Patient's age between 7 and 10 years;
* Class I malocclusions;
* No prior history of orthodontic treatment;* Mixed dentitions with all incisors and permanent first molars fully erupted;
* Dentitions without caries lesions, large coronal restorations, significant attrition, and dental anomalies (congenitally missing teeth, supernumerary teeth, tooth developmental disorders). The exclusion criteria were related to: patient's age (less than 7 years or more than 10 years), class II and class III malocclusions, previous history of orthodontic treatment, type of dentition (other than mixed dentition with all incisors and permanent first molars fully erupted), the presence of caries lesions, large coronal restorations, significant attrition, and dental anomalies. The space analysis was performed for all 200 dental arches (100 maxilla dental arches and 100 mandible dental arches), comparing the amount of space available for the alignment of the teeth and the amount of space required to properly align them [5]. The available space (arch perimeter) was measured from the mesial contact point of one first permanent molar to the other, over the contact points of posterior teeth and incisal edge of anterior teeth. The dental arch was divided into four segments, measured as straight-line approximations of the arch; the measurements were performed with a digital caliper with an accuracy of 0.01 mm (Figures 1 and 2). Figure 1: Measurement of the available space on maxillary cast: e = length between the mesial contact point of the upper right first permanent molar and the mesial contact point of the upper right canine, f = length between mesial contact point of the upper right canine and the midline; g = length between the midline and the mesial contact point of the upper left canine; h = length between the mesial contact point of the upper left canine and the mesial contact point of the upper left first permanent molar. Figure 2: Measurement of the available space on mandibular cast: a = length between the mesial contact point of the lower right first permanent molar and the mesial contact point of the lower right canine, b = length between mesial contact point of the lower right canine and the midline; c = length between the midline and the mesial contact point of the lower left canine; d = length between the mesial contact point of the lower left canine and the mesial contact point of the lower left first permanent molar. The amount of space required for alignment of the teeth was assessed by measuring the meso-distal (MD) width of incisors and first permanent molars from contact point to contact point (Figure 3) by estimating the size of permanent canines and premolars according to Tanaka and Johnston prediction formulas and then by summing all these values [18]. The Tanaka and [PERSON] prediction formulas applied in this study are included in Table 1. The difference between the sum of the meso-distal teeth dimensions and the arch perimeters value represents the space discrepancy.