Henning Vilmann

Finite element method modeling of craniofacial growth

The application of the concepts of continuum mechanics and of the numerical techniques of the finite element method permits the development of a new and potentially clinically useful method of describing craniofacial skeletal growth. This new method differs from those associated with customary roentgenographic cephalometry in that its descriptions and analyses are invariant; that is, they are independent of any method of registration and superimposition. Such invariance avoids the principal geometric constraint explicit in all analytical methods associated with conventional roentgenographic cephalometry. The conceptual and mathematical bases of the finite element method (FEM) are presented and illustrated by the numerical and graphic descriptions of the two-dimensional growth of the rat skull, for which two sets of longitudinal growth data are used. In practice, the FEM permits analysis of the skull at a scale significantly finer than previously possible, by considering cranial structure as consisting of a relatively large number of contiguous finite elements. For each such element, independently, it is then possible to describe and depict both the magnitude and the direction of temporal size and shape changes occurring in that element relative to itself at some initial time. It is emphasized that such descriptions are completely independent of any local reference frame.

Space, time, and space-time in craniofacial growth☆

Abstract Craniofacial growth is expressed as a patterned series of changes in size, shape, and location of cranial structure in space-time. The study of this growth is aided by the reduction of cranial structure to a series of points whose paths may be mathematically modeled. The conventions of roentgenographic cephalometry are demonstrated to be capable only of demonstrating spatial changes occurring during finite intervals of time and incapable of demonstrating point kinematics in space-time. The differences between anatomic and material points are emphasized. The location of any point is described by four coordinate values, three spatial and one temporal; hence, cranial growth occurs in a four-dimensional space-time. Models of space-time are depicted in which various projections of the point paths in space-time to space only are illustrated. Analyses of molluscan bivalve and of rat parietal bone growth suggest that the representation of time as an angular coordinate in a polar coordinate projection provides a growth model that closely simulates the biologic and physical realities of growth. It is noted that the point paths in this model are closely described by logarithmic spirals, a mathematical description that has additional biologic connotations. Since the conventional methods of cranial growth analysis, explicit in roentgenographic cephalometry, do not directly represent a time dimension, an expansion of these methods seems warranted.

Os penis of the Rat

The morphogenesis and morphology of the distally positioned cartilage of the os penis, the processus cartilagineus, are described in rats aged from 1 to 100 days. Based on observations of metachromacy

Studies on orthocephalization

In the period from 14 to 150 days, the zygomatic arch of the rat skull possesses a marked positional stability in relation to the parietal bone, the basisphenoid bone and the length axis of the skull.

Statistical testing of an allometric centered model of craniofacial growth

An allometric centered model of craniofacial growth was tested by several computer-assisted statistical methods on the pure longitudinal growth data of twenty-four close-bred female rats and on cross-sectional human cranial growth data. The study demonstrated that such a model was heuristic and, being incapable of exact definition, was deemed inappropriate for further use in modeling of craniofacial skeletal growth. The necessity for vigorous testing of any hypothesis concerning the modeling of craniofacial growth is stressed.

An allometric network model of craniofacial growth

This study of cranial skeletal growth kinematics details the conceptual principles underlying the development of an allometric network model of such growth. This model is tested by the analysis of longitudinal rat and cross-sectional human growth data and by comparison of this model with a previously described allometric centered model. It is shown that the network model is superior to the centered model in three ways: (1) The allometric network model permits growth prediction when allometric constants are known; (2) the network model has significantly smaller errors than the centered model; and (3) the network model is capable of displaying growth kinematics of both the neural and facial skulls while in time there are marked transformations, such as relative rotations of two sets of cranial anatomic points.

Os penis of the rat. IV: The proximal growth cartilage

Histomorphological and histochemical aspects of the proximal cartilage of os penis and its surrounding perichondrium in 60 rats aged between 1 and 100 days are described. Comparisons at 11-14 days with the mandibular condylar cartilage reveal a slight difference in their general morphological composition. The developmental changes which take place in the os penis cartilage reveal histomorphologic events, some of which may be brought into agreement with previous observations of patterns of transformations of the bone. Observations on an age-dependent morphological appearance of the area adjacent to the proximal surface of the cartilage suggest certain agreements between the mandibular angular cartilage and the os penis cartilage. The study of phosphomonoesterases in the os penis cartilage and its perichondrium reveals significant, unexplained differences in the distribution of alkaline phosphatase between this cartilage and the mandibular condylar cartilage.

Space-time presentations of the shell of the bivalved mollusk Cardium edule.

In a recent article the concept of studying craniofacial growth in space-time was introduced. The possibilities of carrying out such studies were demonstrated with the aid of some generalized shell of a bivalved mollusk. In this study presentations of space-time models of a real biologic model, the shell of the bivalved mollusk Cardium edule, have been constructed. Quantitative expressions of paths in space-time of anatomic and material points have been elaborated. A further analysis has shown that a number of the space-time presentations may represent biologic reality. They may be used for comparisons with presentations of skull models and may represent a tool for the better understanding of results from other studies.