Study of oral lactobacillus towards developing a comprehensive structured for integrated exponential regression model

Introduction: Probiotics are well-defined as live microorganisms that usefully affect the host and probiotic bacteria have been used intensely. For years to target gastrointestinal disease by rebalancing the compound microflora. Besides the gastrointestinal tract also the oral cavity is highly colonized by bacteria and many different bacterial species are part of the microbiota in the mouth, as it offers ideal conditions for bacteria with a stable temperature, moist surface with a relatively stable pH and regular supply of nutrients. Probiotic bacteria like Lactobacillus are a promising treatment strategy for oral disease with a microbiological etiology. To gain better results, many researchers that study and emphasize specific methods been tried to build a new or improved methodology. Objectives: The aimed of this study is to improve the performance of exponential growth by adding bootstrap and fuzzy techniques (Integrated exponential regression method). The aim of the research work is to develop a comprehensive framework for an integrated exponential regression model. Material and Methods: The data were taken from the present data available from the recently done by a researcher for nurturing selected microorganisms. The gathered data will be used for the exponential modeling and the efficiency of the model will be compared accordingly due to the predicted interval from the exponential regression method and an integrated exponential regression method. This paper also provides the algorithm for the prediction of cell growth and inferences. Results: The result shows that the average width for the exponential regression model was 19.2228 while an integrated exponential regression method was 0.0075. The average width of integrated exponential regression was smaller than the exponential regression. This clearly shows that the integrated exponential regression method is more efficient than exponential regression technique. Conclusion: This proposed method can be applied to small sample size data, especially when limited data is obtained.


Bacteria in Dental Caries
The prevailing ecological view of the etiology of dental caries is more attuned to the polymicrobial nature of the dental plaque biofilm. However, only a limited number of bacteria are consistently recovered from caries lesions and have thus been recognized to be specifically associated with dental caries 1 . The association between Lactobacilli was the leading candidate in the causation of dental caries prior to the 1950s, when the mutans Streptococci(MS) started to dominate the literature 2 . Despite numerous studies linking Lactobacilli to caries in both adults and children, our understanding of their role in this disease remains incomplete. Some of the major gaps in knowledge span the transmission and colonization of the oral cavity, as well as the genetic basis for the adaptation to this niche. Probiotics are well-defined as live microorganisms that usefully affect the host. Probiotic bacteria have been used intensely. For years to target gastrointestinal disease by rebalancing the compound microflora. Besides the gastrointestinal tract also, the oral cavity is highly colonized by bacteria, and many different bacterial species are part of the microbiota in the mouth, as it offers ideal conditions for bacteria with a stable temperature, moist surface with a relatively stable pH and regular supply of nutrients 3 .
Probiotic bacteria like Lactobacillus are a promising treatment strategy for oral disease with a microbiological etiology. Those include plaqueassociated diseases like dental caries, which is an infectious disease with microbial processes eroding and destroying the hard dental tissue or inflammation of periodontal tissue, namely gingivitis and the more severe periodontitis 4 . In the oral cavity, Lactobacilli comprise about 1% of the cultivable microbiota. Commonly isolated strains include L. Casei,L. Paracasei, L.Lantarum, L.Rhamnosus, L.Fermentum, L. Acidophilus, and L.Salivarius. In contrast to MS, lactobacilli have poor adherence properties and have traditionally been considered as having an opportunistic role in the caries disease 5 . High levels of lactobacilli have been linked with high caries activity and high carbohydrate consumption. Simark-Mattsson and colleagues isolated lactobacilli from subjects with different levels of dental caries 6 . They demonstrated that naturally occurring lactobacilli inhibited the growth of MS; the effect of lactobacilli was most pronounced in subjects without dental caries, who were lacking S. Mutans.

Fuzzy Linear Regression
Fuzzy linear regression analysis was first introduced by 7 in which two factors namely the degree of fitness and the fuzziness of data sets, are considered 8 . Inthe Fuzzy method, regression plays a crucial role when dealing with imprecise data. A simple regression equation involving a single independent fuzzy variable can be used for such situation. The result from studies 9 , showed that fuzzy regression can be a better replacement for statistical regression when the data are vaque with poor model specification. According 10 , the regression problem in form of gradient descent optimization was used to show the effectiveness of an iterative algorithm for multiple regressions with fuzzy data. A fuzzy linear regression model iscommonlypresented ( ) is a vector of fuzzy parameters of the fuzzy linear regression model. j Ã is presented in the form of symmetric triangular fuzzy numbers denoted by a is the central value of the fuzzy number and j c is the spread. Therefore the fuzzy linear regression model can be rewritten as shown However, the interaction between variables and higher-order terms are not included in the fuzzy linear regression defined in 1 .
In fact, the interaction between variables and higher order terms often exist in physical systems. A simple procedure is commonly used to solve the linear programming problem 11 . Linear regression is used to study the linear relationship between a dependent variable Y and one or more independent variables X. The dependent variable Y must be continuous, while the independent variables may be either continuous, binary, or categorical. The initial judgment of a possible relationship between two continuous variables should always be made on the basis of a scatter plot 12 . Bootstrap Proposed by Efron (1979), the bootstrap is a simulation technique to evaluate the standard error of the estimation of a parameter 13 . The idea is to perform various resampling with the replacement of the dataset.

Let
) This way the bootstrapestimatorofthevarianceof θˆi s g i v e n b y ( ) where z a corresponds to the α -the quantile of standard normal distribution. We can estimate the empiric density F as a normal approximation of real F.
As such, we can estimate the confidence interval using F quantiles, so the interval is given by .

Data Collection
The data composed of two variables which are the days of the culture (x), bacterial growth (y), and the rate of the exponential growth of bacterial culture (lny). The data were taken from the present data available from the recently done by a researcher for nurturing selected microorganisms (Lactobacillus) in School of Dental Sciences, UniversitiSains Malaysia. Then, the data were recorded in a SAS Program to evaluate microorganism growth before analyzing by using the new proposed statistical methodology. The selected microorganisms were kept in storage accordingly (Table 1 and Figure 1). And so, all microorganisms were disposed of carefully in the clinical waste bin. .

Ethical Approval
This study was approved for ethical permission by the Human Research Ethics Committee of Universiti Sains Malaysia (USM/JEPeM/18080391).

Result
The result shows that the graph of Lactobacillus Salivarius.

(A)
Exponential Regression Model    Table 2 above shows that the results of exponential regression model and integrated exponential regression model. Therefore, the results show that the average width for the exponential regression model was 19.2228 while an integrated exponential regression method was 0.0075. The average width of integrated exponential regression was smaller than the exponential regression. According to the R-Square results obtained, the model is good and appropriate. This is because the value close to 1 is the best fit. For the nonlinear function (exponential) used here, the growth data was fitted to determine mathematical parameters with curve estimation. The model fitted by nonlinear regression gave reliable estimates of the correlation coefficient (R 2 values at p<0.01) for the functions used. They also assess the degree of fit of the model to each of the experimental data sets, which fell close to 1.

Summary And Discussion
From the result obtained, the integrated exponential regression method is more efficient than the exponential regression technique. This proposed method can be applied to small sample size data especially when limited data is obtained. We showed that the model can be used to find the potential biological parameters which may be able to predict the treatment outcome. We have demonstrated that the use of an exponential regression model along with the use of SAS software that can be a very precise and useful tool to study the exponential growth of Lactobacillus Salivarius.Paperwork gives the explanation of exponential growth by adding improvement method which adding bootstrap and the fuzzy technique SAS software.