Professor Ramkrishna's research group is motivated by ideas in the application of mathematics to solving problems in chemical and biochemical reaction engineering, biotechnology and biomedical engineering. Their research ideas arise from linear (operator methods) and nonlinear analysis of ordinary and partial differential equations, stochastic processes, and population balance modeling involving integro-partial differential equations.

The current focus in chemical reaction engineering is in the application of multidimensional population balance modeling in the area of precipitation and crystallization processes with the objective of controlling crystal morphology and polymorphs (Borchert et al., 2008). We are also interested in high performance computing applications for the study of first order phase transitions. We use novel algorithms, parallelization schemes, and physics to answer related to crystal structure prediction. On another front, joint work with Professor Joshi of Mumbai University Institute of Chemical Technology is in progress involving investigation of bubble columns with computational fluid dynamics and population balance models.

Recent developments in cybernetic modeling (Young, 2005; Young and Ramkrishna, 2007; Young et al., 2008) are being used to investigate hybrid models by synthesizing cybernetic models with the flux balance approach for intracellular fluxes for bioreaction engineering applications. Currently, bacterial systems are under investigation in batch, fed-batch and continuous bioreactors for nonlinear behavior with respect to multiplicity, stability, and periodic behavior using multi-substrate feeds (Kim, 2008).

In biotechnology, Professor Ramkrishna, in collaboration with Professor Morgan, is investigating dynamic, cybernetic models of large metabolic networks developed by his group along with experimental measurements of numerous intracellular metabolites and fluxes for parameter identification. Cybernetic models are also under investigation for application to metabolic engineering. Of particular interest is its application to metabolic engineering of yeast for the development of new strains to maximize productivity of bioethanol. This investigation is in collaboration with Professor Morgan and Dr. Nancy Ho.

Other recent work in the field of cybernetic modeling seeks to establish the relationship between cybernetic control and data for cellular control. Enabled by collaboration with Professor Subramaniam’s group at UCSD, preliminary results demonstrate that cybernetic variables determined from metabolite data predict the time-dependent behavior of gene expression data. An active research program in collaboration with Professors Hannemann (ChE), Rundell, and Leary of (BME) is under way in the application of population balance models for cancer chemotherapy (leukemia). This work involves clinical data from the Riley Children's Hospital at Indianapolis through collaboration with Dr. Vik. Stochastic models are being investigated for quantitative design of complete cancer cure.

A new project has just been initiated in collaboration with Prof. Wei-Shou Hu at the University of Minnesota. The primary objective of this research project is to construct mathematical models for signal transduction processes connected with transferring drug resistance between different cells. We aim to develop a better understanding of this mechanism in various ways for both Planktonic cells and biofilms. This can be done from a simple approach such as average single cell models to more advanced stochastic single cell models to even more advance models in which we can capture fully both the effects coming from population interaction and stochasticity.

Professor Ramkrishna is also associated with recently instituted research in Cancer Care Engineering at Purdue for mathematical modeling of the development of Colorectal Cancer based on information gleaned from clinical and biological data obtained from patients.

"Equation Chapter 1 Section 1Population Balance Modeling. Current Status and Future Prospects," D. Ramkrishna, and M. R. Singh, (Invited Review): Annual Reviews in Chemical and Biomolecular Engineering, 2014.

"Lipase-Catalyzed Process for Biodiesel Production: Protein engineering and lipase production," H. Hwang, F. Qi, C. Yuan, X. Zhao, D. Ramkrishna, D. Liu, and A. Varma, Biotech. & Bioeng., 111, (4), 639-653, 2014.

"Revitalizing Personalized Medicine: Respecting Biomolecular Complexities beyond Gene Expression," D. Jayachandran, U. Ramkrishna, J. Skiles, J. Renbarger and D. Ramkrishna, CPT: Pharmacometrics & Systems Pharmacology, 3 (4), e110, 2014.

"A New Rational 'Tau-Leap' Strategy for Accelerated Stochastic Simulation," D. Ramkrishna and C. Shu, Industrial & Engineering Chemistry Research, in press.

"Optimal Chemotherapy for Leukemia: A Model-based Strategy for Individualized Treatment," J. Devaraj, A. E. Rundell, R. E. Hannemann, T. A Vik, and D. Ramkrishna, PLoS ONE, in press.

"Effect of Impeller Design and Power Consumption on Crystal Size Distribution," C. V. Rane, K. Ekambara, J. B. Joshi and D. Ramkrishna, AIChE J., 60 (10), 3596-3613, 2014

"Measurement of Polar Plots of Crystal Dissolution Rates using Hot-Stage Microscopy. Some Further Insights on Dissolution Morphologies," M. Singh, N. Nere, H. Tung, S. Mukherjee, S. Bordawekar and D. Ramkrishna, Crystal Growth and Design, in press.

"CFD Simulation and Comparison of Industrial Crystallizers," C. V. Rane, K. Ekambara, J. B. Joshi and D. Ramkrishna, Can. J. Chem. Eng., in press.