A quantum biological hypothesis of human secondary dentinogenesis.

It is hypothesized that human coronal secondary dentin (SD) is a final classical mechanical (CM) response to a chain of prior quantum mechanical (QM) transductions of the information of initial CM occlusal loadings of enamel. Such CM energy is transduced into QM quanta (as protons) that are translocated centripetally via clustered water (CW), (as "proton wires"), that is structurally related to both enamel prism sheath and hydroxyapatite crystal hydration shells. These quanta pass into odontoblastic cell processes (OP), lying within dentinal tubules (DT). OP's contain abundant parallel arrays of cylindrical microtubules (MT). These are the sites of two further CW-related QM events: (i) proton translocation associated with conformal changes of MT tubulin protein dimers; and (ii) coherent energetic oscillations within the CW filling the MT's hollow cores. Finally, these quanta pass into the odontoblastic soma, where QM wave function collapse transduces this information into a final CM state that initiates the processes of SD formation. A critical portion of this hypothesis may be experimentally tested.

Anatomical macroelements in the study of craniofacial rat growth.

In order to avoid the arbitrary division of biological structures, rational polynomial interpolants are utilized to study growth. The major advantage of this method is the elimination of artificial internal element boundaries through anatomical structures. Since the boundary element methodology is employed in the finite element setting, other benefits, without additional computer coding, include the ability to use elements with any number of sides and reference frame invariance. Longitudinal landmark coordinates from midsagittal X-ray tracings of 22 albino female rat skulls of various ages were averaged. The skull was partitioned into three macroelements: a neural skull and two functionally distinct portions of the facial skull--olfactory and respiratory. The digital computer programming was carried out in the computer mathematics environment of Mathematica. Maximum elongation ratios were calculated for approximately 400 interior points. The elongation ratios in the neural skull compared well with previously documented growth behavior of internal brain structures. The calculated ratios from the facial skull were used to analyze the behavior of macroelement interpolation close to common anatomical boundaries.

Candidates for the mechanosensory system in bone.

Some potential mechanisms by which bone cells sense mechanical loads are described and hypotheses concerning the functioning of these mechanisms are explored. It is well known that bone tissue adapts its structure to its mechanical load environment. Recent research has illuminated the biological response of bone to mechanical loading at the cellular level, but the precise mechanosensory system that signals bone cells to deposit or resorb tissue has not been identified. The purpose of this paper is to describe the current status of this research and to suggest some possible mechanosensory systems by which bone cells might sense environmental loads.

Computer simulations of chondrocytic clone behaviour in rabbit growth plates.

The growth behaviour of chondrocytic clones in the cell columns of the proximal tibial growth plates of young rabbits was modelled in computer simulations. Simulations were performed, modelling either clones in large groups of columns or clones in one single column. The former were based on morphological data and measurements of cell columns from an earlier study while the latter utilised previous findings of cellular kinetics in rabbit growth plates. Simulation results that resembled most closely the actual observations on rabbit growth plates were those in which a distribution of values was assumed both for clone length (ranging from 1000 to 2000 microns) and for the lengths of the discontinuities between clones. When the assumption was made in the models that the disappearing (metaphyseal) end of an 'old' clone moved more rapidly than the developing (epiphyseal) end of a 'new' clone, replacing the former, the length of the discontinuity between these two clones increased with time. This assumption, which could be modelled in the simulations of clones in a single column based on cell growth behaviour, was found to provide an explanation for an earlier finding that there are more short columns at the epiphyseal side than at the metaphyseal side of a growth plate.

Numerical simulation of the crown of an incisiform tooth by conformal and polynomial regression mapping of a simple model.

We present a simple bowl-shaped model in the complex plane for the enamel and dentin structure of a tooth. Isochronous mode lines, and path lines representing the paths followed by individual ameloblasts and odontoblasts, form a simple regular mesh in the model. After the conformal map W = Z2, the transformed model is remarkably tooth like. To further improve the simulation of the crown of an incisiform tooth in particular, we compare our results to our own data from actual teeth and data from the literature. This leads us (a) to adjust the initial model so that the mesh of mode and path lines intersects the boundary of the tooth in a realistic way, and (b) to refine the mapping using least-squares regression to fit polynomial functions of Z and W to the available data.

A bilateral, superficial location of human sublingual glands: report of a case.

During a routine dissection of a cadaver, the unusual, completely superficial position of both sublingual glandular masses was noticed. Histologically, the glandular masses consisted of a group of minor sublingual glands. It is suggested that the existence of a wide gap between the anterior and posterior parts of the mylohyoid muscle, which was revealed during further dissection, was the primary embryologic anomaly that was responsible for the unusual location of the glands.

Morphological analysis and computer-aided, three dimensional reconstruction of chondrocytic columns in rabbit growth plates.

Proximal tibial growth plates of New Zealand white rabbits were serially sectioned in parasagittal and horizontal planes for three dimensional, light microscopic analysis of the chondrocytic columns. A total of 431 columns was analysed. Of these, 258 columns extended through the full height of the growth plate. The remaining columns were considerably shorter, being located either predominantly in the epiphyseal half of the growth plate (100) or in the metaphyseal half of the growth plate (73). The epiphyseal and metaphyseal columns were found in clusters in the plate. Some columns in all three groups had interruptions along their length, while others had duplications. Computer-aided, three dimensional graphic reconstructions were prepared of a selected group of columns. The reconstructions illustrated the variability in the morphology and the dimensions of the neighbouring chondrocytic columns. The observations suggest that chondrocytic columns in rabbit growth plates are replaced regularly and that the small cell zone may play an important role as the cellular source for column renewal.

Studies on orthocephalization: growth behavior of the rat skull in the period 13-49 days as described by the finite element method.

Rat cranial skeletal growth was studied, using a cross-sectional data set, for the period 13-49 days by the application of the concepts of continuum mechanics and the numerical techniques of the finite element method (FEM). In contrast to the methods of conventional craniometry (CM) and roentgenographic cephalometry (RCM) the FEM permits fine scale, reference frame invariant descriptions and analysis of growth behavior. This advantage was demonstrated by a numerical example of the use of FEM. The skull was discretized into a number of two-dimensional, triangular elements, whose enclosed areas corresponded closely to both specific skeletal structures and to related functional matrices. Since it was assumed presently that the growth behavior of all of the points enclosed within a given element was similar, the application of the functional matrix hypothesis permitted an integrated description of the growth of the skeletal structure and functional matrix related to each element. The principal locus of rotation of the facial skull, relative to the cranial base, is the inferior frontoethmoidal articulation, a motion that includes a rigid body rotation. Other active and passive skeletal and visceral growth events associated with orthocephalization were located and described. Finally it was shown that the morphogenetically important growth behavior of other portions of the rat head were not directly involved in orthocephalization.

Effects of pre-weaning undernutrition on 21 day-old male rat skull form as described by the finite element method.

Conventional Roentgenographic Cephalometric Methods (RCM) have certain conceptual and geometric constraints that ensure that their descriptions of cephalic growth and comparisons of cephalic form are reference-frame-dependent; and it is impossible to determine which, if any, RCM reference frame provides a biologically more correct description or comparison. The use of the concepts of continuum mechanics and of the numerical techniques of the Finite Element Method (FEM) overcomes these constraints and provides reference-frame-independent (invariant) growth descriptions and form comparisons. In the FEM, the structure of the head is subdivided (discretized) into a number of smaller, finite, elements. The FEM then describes the growth behavior, or compares the form, of the entire continuum of points enclosed with each element independently; in RCM only the behaviors, or comparisons, of the landmark points are described. The FEM is described and its use illustrated by a comparison of the cephalic forms of 4 groups of weanling (21 d old) rats. The 1st (control) group is derived from normally nourished dams, while the other 3 groups are derived from dams who were malnourished throughout the weaning period in 3 group specific manners. The FEM permitted reference-frame-independent comparisons of the 4 different, and group specific, head forms. These differences were reflected in the forms of each of the finite elements. The differences in element forms between the 4 groups were shown to be related primarily to nutritionally produced alterations of either neurocranial or splanchocranial viscera. These differences were expressed in the alterations of the forms of the continua enclosed within the boundaries of the several finite elements, and secondarily in the form of the cranial skeleton.

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.

A stochastic-mechanical model of longitudinal long bone growth.

A typical mammalian long bone will increase in length during the growth phase of the individual. This increase in length does not occur uniformly throughout the bone, since bone tissue is incapable of internal expansion after formation. The growth occurs at two, disc-shaped, regions near either end of the long bone. These regions are called growth plates. These plates are located between the osseous shaft (diaphysis) and osseous tip (epiphysis) whose bone tissues are discontinuous. The present study develops a stochastic-mechanical model for such a bone growth and demonstrates the capability of the model to reproduce the observed overall behavior of longitudinal long bone growth based on realistic information of cellular mitosis, growth and ossification. A numerical analysis was performed on the model under the assumption that the number of cells in the proliferation zone remains constant throughout the growth period. The growth curves thus obtained compare favorably with those growth curves proposed elsewhere essentially on the basis of phenomenological observation. The present model can demonstrate the effects of such parameters as the proliferation rate, initial age distribution and compressive stress on the growth. More importantly, the stochastic-mechanical model so developed permits one to incorporate further experimental evidence and statistical observation at the cellular level into the analysis to improve the solutions.

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.

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.

Neuro-skeletal topology of the primate basicranium: its implications for the "fetalization hypothesis".

The data above, and the literature reviewed, demonstrate that in 4 significant morphological characteristics the neuro-skeletal topology of the human basicranial regions is unique, and does not resemble that of any extant non-human primate at any fetal or postnatal age. These characteristics are: 1. the shape of the cranial base; 2. the composition of the anterior and posterior portions of that base; 3. the extent, or degree, of basicranial flexion; and 4. the extent, or degree, of brain flexion. On these bases, the craniological implications of Bolk's fetalization hypothesis cannot be supported.