Statistical estimation of resin composite polymerization sufficiency using microhardness

Mark E. Cohen, Daniel L. Leonard, David G. Charlton, Howard W. Roberts, James Ragain

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

With respect to determining sub-surface resin polymerization sufficiency, this study compared a traditional method of applying linear regression to bottom- to top-surface Knoop hardness ratios to an alternative method based on nonlinear regression. Inverse linear regression on ratios was used to estimate the exposure duration required for 80% bottom-surface hardness with respect to the top, in six light-by-material groups. Alternatively, a one-phase, two-parameter, exponential association of the form Y = Ymax(1-e -kt) (where Ymax is maximum hardness, k is a rate constant, and t is exposure duration), was used to model hardness. Inverse nonlinear regression estimated, for each condition, the exposure duration required for the bottom surface to achieve 80% of corresponding condition (light and material) top-surface Ymax. Mathematically, analysis of ratios was demonstrated to yield potentially less precise and biased estimates. Nonlinear regression yielded better statistical fit and provided easily accessible tests for differences in k across light-system groups. Another recently proposed nonlinear model for polymerization, Y = Ymaxkt n/(1+ktn), was also considered. While this new model has substantially greater phenomenological and mechanistic justification, we found that the model-fitting process was more sensitive to initial parameter values and sometimes yielded untenable results when applied to our data. However, we believe that these problems would not occur if sample points are well distributed across a wide range of exposure durations, and that the model, Y = Ymaxktn/(1+ktn), should be considered for such data sets. Published by Elsevier Ltd. on behalf of Academy of Dental Materials.

Original languageEnglish (US)
Pages (from-to)158-166
Number of pages9
JournalDental Materials
Volume20
Issue number2
DOIs
StatePublished - Feb 1 2004
Externally publishedYes

Fingerprint

Composite Resins
Hardness
Polymerization
Microhardness
Resins
Composite materials
Light
Linear Models
Linear regression
Dental Materials
Nonlinear Dynamics
Dental materials
Rate constants
Association reactions

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Dentistry(all)
  • Mechanics of Materials

Cite this

Statistical estimation of resin composite polymerization sufficiency using microhardness. / Cohen, Mark E.; Leonard, Daniel L.; Charlton, David G.; Roberts, Howard W.; Ragain, James.

In: Dental Materials, Vol. 20, No. 2, 01.02.2004, p. 158-166.

Research output: Contribution to journalArticle

Cohen, Mark E. ; Leonard, Daniel L. ; Charlton, David G. ; Roberts, Howard W. ; Ragain, James. / Statistical estimation of resin composite polymerization sufficiency using microhardness. In: Dental Materials. 2004 ; Vol. 20, No. 2. pp. 158-166.
@article{457ece47c7314c81b02504a97d486999,
title = "Statistical estimation of resin composite polymerization sufficiency using microhardness",
abstract = "With respect to determining sub-surface resin polymerization sufficiency, this study compared a traditional method of applying linear regression to bottom- to top-surface Knoop hardness ratios to an alternative method based on nonlinear regression. Inverse linear regression on ratios was used to estimate the exposure duration required for 80{\%} bottom-surface hardness with respect to the top, in six light-by-material groups. Alternatively, a one-phase, two-parameter, exponential association of the form Y = Ymax(1-e -kt) (where Ymax is maximum hardness, k is a rate constant, and t is exposure duration), was used to model hardness. Inverse nonlinear regression estimated, for each condition, the exposure duration required for the bottom surface to achieve 80{\%} of corresponding condition (light and material) top-surface Ymax. Mathematically, analysis of ratios was demonstrated to yield potentially less precise and biased estimates. Nonlinear regression yielded better statistical fit and provided easily accessible tests for differences in k across light-system groups. Another recently proposed nonlinear model for polymerization, Y = Ymaxkt n/(1+ktn), was also considered. While this new model has substantially greater phenomenological and mechanistic justification, we found that the model-fitting process was more sensitive to initial parameter values and sometimes yielded untenable results when applied to our data. However, we believe that these problems would not occur if sample points are well distributed across a wide range of exposure durations, and that the model, Y = Ymaxktn/(1+ktn), should be considered for such data sets. Published by Elsevier Ltd. on behalf of Academy of Dental Materials.",
author = "Cohen, {Mark E.} and Leonard, {Daniel L.} and Charlton, {David G.} and Roberts, {Howard W.} and James Ragain",
year = "2004",
month = "2",
day = "1",
doi = "10.1016/S0109-5641(03)00087-3",
language = "English (US)",
volume = "20",
pages = "158--166",
journal = "Dental Materials",
issn = "0109-5641",
publisher = "Elsevier Science",
number = "2",

}

TY - JOUR

T1 - Statistical estimation of resin composite polymerization sufficiency using microhardness

AU - Cohen, Mark E.

AU - Leonard, Daniel L.

AU - Charlton, David G.

AU - Roberts, Howard W.

AU - Ragain, James

PY - 2004/2/1

Y1 - 2004/2/1

N2 - With respect to determining sub-surface resin polymerization sufficiency, this study compared a traditional method of applying linear regression to bottom- to top-surface Knoop hardness ratios to an alternative method based on nonlinear regression. Inverse linear regression on ratios was used to estimate the exposure duration required for 80% bottom-surface hardness with respect to the top, in six light-by-material groups. Alternatively, a one-phase, two-parameter, exponential association of the form Y = Ymax(1-e -kt) (where Ymax is maximum hardness, k is a rate constant, and t is exposure duration), was used to model hardness. Inverse nonlinear regression estimated, for each condition, the exposure duration required for the bottom surface to achieve 80% of corresponding condition (light and material) top-surface Ymax. Mathematically, analysis of ratios was demonstrated to yield potentially less precise and biased estimates. Nonlinear regression yielded better statistical fit and provided easily accessible tests for differences in k across light-system groups. Another recently proposed nonlinear model for polymerization, Y = Ymaxkt n/(1+ktn), was also considered. While this new model has substantially greater phenomenological and mechanistic justification, we found that the model-fitting process was more sensitive to initial parameter values and sometimes yielded untenable results when applied to our data. However, we believe that these problems would not occur if sample points are well distributed across a wide range of exposure durations, and that the model, Y = Ymaxktn/(1+ktn), should be considered for such data sets. Published by Elsevier Ltd. on behalf of Academy of Dental Materials.

AB - With respect to determining sub-surface resin polymerization sufficiency, this study compared a traditional method of applying linear regression to bottom- to top-surface Knoop hardness ratios to an alternative method based on nonlinear regression. Inverse linear regression on ratios was used to estimate the exposure duration required for 80% bottom-surface hardness with respect to the top, in six light-by-material groups. Alternatively, a one-phase, two-parameter, exponential association of the form Y = Ymax(1-e -kt) (where Ymax is maximum hardness, k is a rate constant, and t is exposure duration), was used to model hardness. Inverse nonlinear regression estimated, for each condition, the exposure duration required for the bottom surface to achieve 80% of corresponding condition (light and material) top-surface Ymax. Mathematically, analysis of ratios was demonstrated to yield potentially less precise and biased estimates. Nonlinear regression yielded better statistical fit and provided easily accessible tests for differences in k across light-system groups. Another recently proposed nonlinear model for polymerization, Y = Ymaxkt n/(1+ktn), was also considered. While this new model has substantially greater phenomenological and mechanistic justification, we found that the model-fitting process was more sensitive to initial parameter values and sometimes yielded untenable results when applied to our data. However, we believe that these problems would not occur if sample points are well distributed across a wide range of exposure durations, and that the model, Y = Ymaxktn/(1+ktn), should be considered for such data sets. Published by Elsevier Ltd. on behalf of Academy of Dental Materials.

UR - http://www.scopus.com/inward/record.url?scp=0348170753&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0348170753&partnerID=8YFLogxK

U2 - 10.1016/S0109-5641(03)00087-3

DO - 10.1016/S0109-5641(03)00087-3

M3 - Article

VL - 20

SP - 158

EP - 166

JO - Dental Materials

JF - Dental Materials

SN - 0109-5641

IS - 2

ER -