1. Bayesian Estimation of Toluene and Trichloroethylene Biodegradation Kinetic Parameters
Feng Yu and Breda Munoz
RTI International

2. Introduction
Trichloroethylene (TCE) is mainly used as a solvent or degreasing agent found in industries and household products.
Improper treatment/disposal leads to groundwater pollution.
Toxic and possible carcinogenic
TCE can be treated under aerobic condition via Cometabolic Biodegradation, a process by which microbial organisms transform the toxic compound in the environment into non-toxic ingredients in the presence of another compound.
e.g. TCE can be biodegraded by Pseudomonas putida F1, in the presence of toluene
The rate of compound transformation is the Biological Kinetics, usually expressed using non-linear differential equations:
− 𝑑𝑿 𝑑𝑡 =𝑓 𝑿 𝑡 ,𝜽 + 𝝎(𝑡)
Several parameters (𝜽) are involved in the toluene and TCE biodegradation kinetics. They are important for modeling, prediction, and bioreactor design.

3. Methods for Parameter Estimation
Options to Obtain the Parameter Values:
Literature
Solving the reverse problem
Issues:
Values reported in literature vary substantially
Solving the reverse problem is not an easy job
Traditional Approach for Parameter Estimation usually cannot handle high dimensional parameter space problems and one has to simplify the model before applying it.
Maximum likelihood estimation methods are not well suited for small-scale experimental data (e.g. significant bias).
A Bayesian estimation approach was considered for estimating 5 model parameters using kinetic data from replicated batch experiments for toluene and TCE biodegradation.

4. Bayesian Estimation
Markov Chain Monte Carlo (MCMC) simulations were used to generate samples from the desired posterior distributions and then these simulated samples were used to approximate the parameter distributions.
Means and 95% Credible Intervals (C.I.) of parameters estimated from the Bayesian approach were calculated and compared to the estimations obtained from the traditional method.
Goodness of Fit:
Deviance Information Criterion(DIC)
Mean Absolute Errors(MAE)
Mean Square Errors(MSE)
SAS STAT14.1 was used to perform the simulations.

5. Conclusions
This Bayesian estimation approach produced relatively accurate biodegradation parameter estimates for toluene and TCE cometabolism on three different models:
DIC range (0.01, 62.44);
MAE range (0.04, 1.13);
MSE range (0.002, 3.21)
It is a useful tool for bioreaction kinetic determination and can be applied for parameter estimation in the complex biological systems especially in the presence of small experimental data.

6. More Information Feng Yu Breda Munoz 919.248.8543 919.990.8304