Explicit Residence Time Distribution of a Generalised Cascade of Continuous Stirred Tank Reactors for a Description of Short Recirculation Time (Bypassing)

The tanks-in-series model (TIS) is a popular model to describe the residence time distribution (RTD) of non-ideal continuously stirred tank reactors (CSTRs) with limited back-mixing. In this work, the TIS model was generalised to a cascade of n CSTRs with non-integer non-negative n. The resulting model describes non-ideal back-mixing with n > 1. However, the most interesting feature of the n-CSTR model is the ability to describe short recirculation times (bypassing) with n < 1 without the need of complex reactor networks. The n-CSTR model is the only model that connects the three fundamental RTDs occurring in reactor modelling by variation of a single shape parameter n: The unit impulse at n→0, the exponential RTD of an ideal CSTR at n = 1, and the delayed impulse of an ideal plug flow reactor at n→∞. The n-CSTR model can be used as a stand-alone model or as part of a reactor network. The bypassing material fraction for the regime n < 1 was analysed. Finally, a Fourier analysis of the n-CSTR was performed to predict the ability of a unit operation to filter out upstream fluctuations and to model the response to upstream set point changes.

Bifurcation Analysis and Application for Impulsive Systems with Delayed Impulses

In this article, we present a systematic approach to bifurcation analysis of impulsive systems with autonomous or periodic right-hand sides that may exhibit delayed impulse terms. Methods include Lyapunov–Schmidt reduction and center manifold reduction. Both methods are presented abstractly in the context of the stroboscopic map associated to a given impulsive system, and are illustrated by way of two in-depth examples: the analysis of a SIR model of disease transmission with seasonality and unevenly distributed moments of treatment, and a scalar logistic differential equation with a delayed census impulsive harvesting effort. It is proven that in some special cases, the logistic equation can exhibit a codimension two bifurcation at a 1:1 resonance point.

Abstract 15288: Conductive Polymer Hydrogel for Enhancement of Electrical Propagation in Border Zone Myocardium after Myocardial Infarction

Introduction: After myocardial infarction (MI), cardiomyocyte death results in a non-contractile fibrotic scar and altered electrical properties, including delayed impulse propagation across the scar region which may contribute to ventricular dysfunction. Hydrogels such as chitosan have been used clinically to stabilize the LV free wall and prevent dilation. We chemically modified chitosan with the charge-carrying conductive polymer polypyrrole (PPy), yielding a biomaterial with more than 100X the conductivity of chitosan alone. Chitosan-PPy is capable of carrying electrical impulses and may enhance synchronous contraction. Methods: Biomaterials were synthesized under sterile conditions and were thoroughly characterized in vitro . Myocardial infarction was created by coronary artery ligation in Sprague-Dawley rats (n = 36), and 1 week later chitosan, chitosan-PPy or saline were injected into the border zone regions. Animals were followed for 8 or 16 weeks (n = 6/treatment/time-point) and cardiac conduction and function were assessed with ECG, echocardiography, impedance catheter analysis and finally Langendorff-perfused epicardial optical mapping. Results: Eight weeks post-injection, QRS duration was increased in saline and chitosan treated hearts, but was maintained in chitosan-PPy hearts until 16 weeks ( p < 0.01), suggesting less maladaptive ventricular remodeling associated with slowing of depolarizing conduction in the chitosan-PPy group. Echocardiography revealed that fractional shortening was enhanced in chitosan-PPy treated hearts at both 8 and 16 weeks ( p < 0.01). At 16 weeks, chitosan-PPy hearts had increased stroke work capacity, and better maintained (lower) end systolic volume ( p < 0.05). Optical mapping demonstrated that chitosan-PPy-treated hearts had faster transverse conduction velocities measured along the border zone epicardial surface ( p < 0.01). Conclusions: We synthesized and characterized a novel conductive polymer hydrogel that may be used therapeutically to enhance favorable cardiac recovery at the LV border zone following an MI. Chitosan-PPy enhanced heart function by augmenting synchronized contraction.