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Year : 2018  |  Volume : 9  |  Issue : 3  |  Page : 75-76

Novel Approach to Dental Reconstruction by Means of Monomer/Polymer Gaussian Chain Statistics

1 Research Center for Traditional Medicine and History of Medicine, Phytopharmaceutical Technology and Traditional Medicine Incubator, Shiraz University of Medical Sciences, Shiraz, Iran
2 Student Research Committee, Phytopharmaceutical Technology and Traditional Medicine Incubator, Shiraz University of Medical Sciences, Shiraz; Essence of Parsiyan Wisdom Institute, Phytopharmaceutical Technology and Traditional Medicine Incubator, Shiraz University of Medical Sciences, Shiraz, Iran
3 Department of Oral and Maxillofacial Radiology, School of Dentistry, Isfahan University of Medical Sciences, Isfahan, Iran

Date of Web Publication31-Oct-2018

Correspondence Address:
Parisa Soltani
School of Dentistry, Isfahan University of Medical Sciences, Hezar-Jarib St., Isfahan
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/denthyp.denthyp_70_17

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How to cite this article:
Sanaye MR, Daneshfard B, Soltani P. Novel Approach to Dental Reconstruction by Means of Monomer/Polymer Gaussian Chain Statistics. Dent Hypotheses 2018;9:75-6

How to cite this URL:
Sanaye MR, Daneshfard B, Soltani P. Novel Approach to Dental Reconstruction by Means of Monomer/Polymer Gaussian Chain Statistics. Dent Hypotheses [serial online] 2018 [cited 2023 Jun 5];9:75-6. Available from:


In dental regenerating material researches, particularly those that are regarded to be bioactive (or more likely, nondegradable), the specificity of biocompatibility and/or polymeric composition are the most pivotal characteristics whereby monomer model systems go from monomeric state to some sort of photochemical or chemical polymerization.[1]

This brings about a whole array of conspecific possibilities, which are generally governed either directly by the thermodynamic laws of common physical chemistry or by systems that could possibly be involved with tensile forces along displacement sheets.[2] Subsequently, the forces of tension generally turn out to be of the nature of Helmholtz energy, whereby normal unstressed states are themselves minimally free to show free forces within their own reach.

If and when such biomaterials are overly cohesive, then they are not ideally suited to function for the purposes that they are purported for. Thence, there comes the need for assistance by a complex hierarchical structure. Such structuration might well be made up both of mineral and of organic polymer co-chains, by means of which neo-structures are prone to be ossified.

In any simulation modeling, chain force conjoinment, that is to say, Gaussian chain joined vertexes, is the pre-assumption. The scenario would be that there are no interactions or forces in between polymeric molecules.[3] This means that ideal chains are mostly made up of segments that are not exactly linearly connected. Quasi-nonlinear connections lead to considerations of probability of those topologies that are propounded by the nuances of Bernoulli’s inequality.

Such usage of the aforementioned inequality could be applied in conjunction with arithmetic mean-geometric mean (AM-GM) inequality to determine the level of regeneration that simply arises from either tensors or vectors that are at work as individual monomers. The situation becomes even more complex, but again calculable, when the end-to-end tensors of the same polymeric chain fall in between a number of monomers, which bear the central responsibilities of regional regeneration based on Gaussian probability density functions for a chain of rigid-oriented rods.[4]

That the majority of dental tissue culturing, pulp regenerating, and ossification regeneration authorities have ignored such three-dimensional Gaussian chain statistics simply arises from the fact that biologists and medical personnel and dentists (specifically) are not conversant with polymer solvent tensor interacted induction chain expansions, whereby conformational characteristics do not stand down to a level of just one single monomer.[5],[6] Polymers are, thus, exhibited to be under the conditions that simply correspond to particular temperatures where polymer–solvent combinations work, and then, they return back to normal body temperature just only to make their conformation again end-to-end so that really joined chains can be exhibited to have no bond angles or valance cone vertices. This spells that, not only is there a possibility of a conspecific (that is to say, human to human) regeneration of the dental/bone tissue chain end-to-end metamorphosis reconstruction, but also such restoration could be initiated according to temperature, volume, adjacent tissue type, and those Gaussian distribution tensors/vectors that had originally created them.

As and when it comes to the question of providing/applying the organic matrix for hydroxyapatite (re-)integration and crystalline organismic growth, a mention could be made regarding the acceptor–donor role played specifically among the side branches of semi-disparate polymers. Of peculiar significance here are the dihedral angles that possess the capacity to either radicalize a polymer side chain (which is absolutely harmful to dental micro-environment) or ionize them into cross-linked elastomers, whereby the interactions of the extensible matrices of fairly heterogeneous tissues could well occur.

Local spaces (Hilbert vectorian subspaces) have the capability to bring off symmetry-braking events into the Euclidian space of all normal dental and periodontal tissues. Thus, translation from the extremely complex quantum chemistry and physical chemistry space-filling into metrizable homeomorphic space-filling can be conducted by means of collagen-based organic matrices that do not violate the biochemistry of noncollagenous proteins and other organic components thereabout from the point of view of bonding topology. The in-vitro morphomechanical characteristics are, thence, self-consistent with the maximum level of likelihood for the multiplicities of manifolds to emanate all throughout the “reduplication” adjacent continuity.[7]

In cases of pH deregulations that have the potential to decelerate concentration-dependent side-polymerization, recourse should be sought from symmetry-stretching Ca/Al nuclei as the centers of pH homeostasizing. Hereafter come the whole series of dynamic axial, torsional, manifolding, stiffening, and loading construct-inducing Gaussian-calculated sheet displacement of both mineral and organic rod-orienting. Mention ought to be made of the fact that—due to dental microtubule specificities—some amendments have to be made to the (re-normalized) AM-GM inequality so that more precise calculations might be made of the regeneration rate of side monomers into both dental enamel and dental pulp.

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Conflicts of interest

There are no conflicts of interest.

  References Top

Skrtic D, Antonucci JM. Bioactive polymeric composites for tooth mineral regeneration: Physicochemical and cellular aspects. J Funct Biomater 2011;2:271-307.  Back to cited text no. 1
Wojnar R. Bone and cartilage—Its structure and physical properties. Biomechanics of Hard Tissues: Modeling, Testing, and Materials. Weinheim: Wiley 2010. p. 1-75.  Back to cited text no. 2
Nitta K-h. On the orientation-induced crystallization of polymers. Polymers 2016;8:229.  Back to cited text no. 3
Belfiore LA. Gaussian statistics of linear chain molecules and crosslinked elastomers. Physical Properties of Macromolecules. Weinheim: Wiley 2010. p. 547-607.  Back to cited text no. 4
Nair AJ. Introduction to Biotechnology and Genetic Engineering. Laxmi Publications, Ltd.; 2008.  Back to cited text no. 5
Lever WE, Kane VE, Scott DS, Shepherd DE. Mathematics and Statistics Research Department. Progress Report, Period Ending June 30, 1981. TN, USA: Oak Ridge National Lab.; 1981.  Back to cited text no. 6
Wang X, Nyman JS, Reyes M. Fundamental Biomechanics in Bone Tissue Engineering. Morgan & Claypool Publishers; 2010.  Back to cited text no. 7


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