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Human evaluation in association to the mathematical analysis of arch forms: Two-dimensional study

Zabidin N, Mohamed AM, Zaharim A, Marizan Nor M, Rosli TI

Int Orthod, 2018 03;16(1):133-143.
PMID: 29478934 DOI: 10.1016/j.ortho.2018.01.009

OBJECTIVES: To evaluate the relationship between human evaluation of the dental-arch form, to complete a mathematical analysis via two different methods in quantifying the arch form, and to establish agreement with the fourth-order polynomial equation.
MATERIALS AND METHODS: This study included 64 sets of digitised maxilla and mandible dental casts obtained from a sample of dental arch with normal occlusion. For human evaluation, a convenient sample of orthodontic practitioners ranked the photo images of dental cast from the most tapered to the less tapered (square). In the mathematical analysis, dental arches were interpolated using the fourth-order polynomial equation with millimetric acetate paper and AutoCAD software. Finally, the relations between human evaluation and mathematical objective analyses were evaluated.
RESULTS: Human evaluations were found to be generally in agreement, but only at the extremes of tapered and square arch forms; this indicated general human error and observer bias. The two methods used to plot the arch form were comparable.
CONCLUSION: The use of fourth-order polynomial equation may be facilitative in obtaining a smooth curve, which can produce a template for individual arch that represents all potential tooth positions for the dental arch.
Applications of the Box-Wilson design model for bio-hydrogen production using Clostridium saccharoperbutylacetonicum N1-4 (ATCC 13564)

Alalayah WM, Kalil MS, Kadhum AA, Jahim J, Zaharim A, Alauj NM, et al.

Pak J Biol Sci, 2010 Jul 15;13(14):674-82.
PMID: 21848059

Box-Wilson design (BWD) model was applied to determine the optimum values of influencing parameters in anaerobic fermentation to produce hydrogen using Clostridium saccharoperbutylacetonicum N1-4 (ATCC 13564). The main focus of the study was to find the optimal relationship between the hydrogen yield and three variables including initial substrate concentration, initial medium pH and reaction temperature. Microbial growth kinetic parameters for hydrogen production under anaerobic conditions were determined using the Monod model with incorporation of a substrate inhibition term. The values of micro(max) (maximum specific growth rate) and K, (saturation constant) were 0.398 h(-1) and 5.509 g L(-1), respectively, using glucose as the substrate. The experimental substrate and biomass-concentration profiles were in good agreement with those obtained by the kinetic-model predictions. By varying the conditions of the initial substrate concentration (1-40 g L(-1)), reaction temperature (25-40 degrees C) and initial medium pH (4-8), the model predicted a maximum hydrogen yield of 3.24 mol H2 (mol glucose)(-1). The experimental data collected utilising this design was successfully fitted to a second-order polynomial model. An optimum operating condition of 10 g L(-1) initial substrate concentration, 37 degrees C reaction temperature and 6.0 +/- 0.2 initial medium pH gave 80% of the predicted maximum yield of hydrogen where as the experimental yield obtained in this study was 77.75% exhibiting a close accuracy between estimated and experimental values. This is the first report to predict bio-hydrogen yield by applying Box-Wilson Design in anaerobic fermentation while optimizing the effects of environmental factors prevailing there by investigating the effects of environmental factors.

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