Clinton R. Kennedy

Localized bacterial infection in a distributed model for tissue inflammation

Phagocyte motility and chemotaxis are included in a distributed mathematical model for the inflammatory response to bacterial invasion of tissue. Both uniform and non-uniform steady state solutions may occur for the model equations governing bacteria and phagocyte densities in a macroscopic tissue region. The non-uniform states appear to be more dangerous because they allow large bacteria densities concentrated in local foci, and in some cases greater total bacteria and phagocyte populations. Using a linear stability analysis, it is shown that a phagocyte chemotactic response smaller than a critical value can lead to a non-uniform state, while a chemotactic response greater than this critical value stabilizes the uniform state. This result is the opposite of that found for the role of chemotaxis in aggregation of slimemold amoebae because, in the inflammatory response, the chemotactic population serves as an inhibitor rather than an activator. We speculate that these non-uniform steady states could be related to the localized cell aggregation seen in chronic granulomatous inflammation. The formation of non-uniform states is not necessarily a consequence of defective phagocyte chemotaxis, however. Rather, certain values of the kinetic parameters can yield values for the critical chemotactic response which are greater than the normal response.Numerical computations of the transient inflammatory response to bacterial challenge are presented, using parameter values estimated from the experimental literature wherever possible.

Analysis of a lumped model for tissue inflammation dynamics.

The inflammatory response to bacterial invasion of tissue is a complex combination of chemical and physical events, and the outcome of a particular challenge is dependent upon the interaction of these. Thus a wide variety of behavior can be observed for the operation of this response. In this paper we develop and analyze a mathematical model for a generalized inflammatory response to bacterial invasion of a tissue region assumed to be homogeneous on a macroscopic scale, in order to study the dynamical behavior of the system. Our analysis allows interpretation of the outcome of a challenge in terms of key parameters representing the rate processes involved. It demonstrates how abnormalities in these processes can lead to pathological behavior. Numerical values for the parameters are estimated from experimental literature sources, and used in example computations to illustrate the predictions of the model under physiological conditions.

High Temperature Sensitivity of Paraffin Hydrocracking

Publisher Summary A viable route toward meeting the increased demand for clean diesel fuels is the conventional hydroprocessing of waxy feeds, such as those found along the Pacific Rim or, in the extreme, those produced from the Fischer–Tropsch technology. In addition to having an extremely high cetane number (> 70), the diesel fuel produced via this route is low in both aromatics and sulfur. An important consideration in the design of a commercial reactor for such operation is the apparent activation energy, E app , of the dominant heat-release reaction, which is cracking. Studies have shown that the value of E app for n-paraffin hydrocracking in the presence of basic-nitrogen poisons can be unusually high, being on the order of 200 kcal/gmole. Such a high E app has significant implications for the control of commercial reactors. The chapter presents a simplified model development for n-paraffin cracking that explains the way by which such poisoned reaction pathways can lead to such high E app values.