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Short-term microfiltration (MF) fouling is commonly abated by periodically reversing the flow to remove foulants that weakly adhered to the membrane. Strong oxidants (i.e., chlorine) can be added to hydraulic backwash water to augment its efficacy—a process called chemically enhanced backwashing (CEB). Herein, we report a rigorous mathematical model for constant flux MF incorporating hydraulic backwashing and CEB, and validate it with laboratory data obtained using untreated and alum-coagulated water from the Foss Reservoir in Oklahoma, USA. We implemented an optimal control procedure and used it to predict MF behavior long past experimental timescales. We identified a frequency threshold beyond which the necessary transmembrane pressure (TMP) reached an asymptotic value, indicating a pseudo steady-state, periodic solution to the model when coupling hydraulic backwashing with CEB. We report differences in TMP saturation values and timescales by simulating transient MF of untreated and pretreated water. Numerical simulations revealed that the operating flux could be increased 10-fold after pretreatment (compared with raw water) before reaching the maximum manufacturer-recommended pressure for the hollow-fibers. The predicted higher flux and extended duration between cleaning-in-place demonstrated advantages of coagulation pretreatment under hydraulic backwashing and CEB. Model observations could guide decision making for CEB timing and frequency. 

Abstract The goal of patient-specific treatment of diseases requires a connection between clinical observations with models that are able to accurately predict the disease progression. Even when realistic models are available, it is very difficult to parameterize them and often parameter estimates that are made using early time course data prove to be highly inaccurate. Inaccuracies can cause different predictions, especially when the progression depends sensitively on the parameters. In this study, we apply a Bayesian data assimilation method, where the data are incorporated sequentially, to a model of the autoimmune disease alopecia areata that is characterized by distinct spatial patterns of hair loss. Using synthetic data as simulated clinical observations, we show that our method is relatively robust with respect to variations in parameter estimates. Moreover, we compare convergence rates for parameters with different sensitivities, varying observational times and varying levels of noise. We find that this method works better for sparse observations, sensitive parameters and noisy observations. Taken together, we find that our data assimilation, in conjunction with our biologically inspired model, provides directions for individualized diagnosis and treatments.