The morphogenetic triangle: A new conceptual tool for application to problems in dental morphogenesis

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Abstract
A hypothetical mathematical model of human dental crown height attainment during morphogenesis was developed. The model is based on well‐known histologic stages of tooth development from initiation to crown completion, with special emphasis on the dynamics and life‐cycle of the cells of the inner enamel epithelium. From three temporal events (P, initiation of proliferation; D, initiation of differentiation; C, crown completion), and crown height (H) measured at the dentino‐enamel junction, a morphogenetic triangle PDZ can be constructed where Z = coordinates of H and C at the time of crown completion. The slope of lines PZ and DZ represent average proliferation rate (Rp) and average differentiation rate (Rd) of the inner enamel epithelium, respectively, during crown formation. From data available in the literature, and based on morphogenetic triangle principles, Rp and Rd were calculated for the deciduous and succedaneous dentitions. A strong positive correlation between Rp and Rd was observed throughout the 20‐tooth series (r = 0.996); however, Rp and Rd showed moderately strong negative associations with H, P, D, C, and the intervals between PD, PC, and DC. The smaller deciduous tooth in each deciduous:permanent pair was associated with faster Rp and Rd, and shorter intervals between initiation of proliferation, initiation of differentiation, and crown completion. The data generated in this analysis of a hypothetical dentition, while not definitive, provide new insights and a theoretical basis for a broader understanding of the basic mechanisms involved in the attainment of certain tooth dimensions during morphogenesis.

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