Algebraic formulas characterizing an alternative to Guyton's graphical analysis relevant for heart failure.

Although Guyton's graphical analysis of cardiac output-venous return has become a ubiquitous tool for explaining how circulatory equilibrium emerges from heart-vascular interactions, this classical model relies on a formula for venous return that contains unphysiological assumptions. Furthermore, Guyton's graphical analysis does not predict pulmonary venous pressure, which is a critical variable for evaluating heart failure patients' risk of pulmonary edema. Therefore, the purpose of the present work was to use a minimal closed-loop mathematical model to develop an alternative to Guyton's analysis. Limitations inherent in Guyton's model were addressed by 1) partitioning the cardiovascular system differently to isolate left ventricular function and lump all blood volumes together, 2) linearizing end-diastolic pressure-volume relationships to obtain algebraic solutions, and 3) treating arterial pressures as constants. This approach yielded three advances. First, variables related to morbidities associated with left ventricular failure were predicted. Second, an algebraic formula predicting left ventricular function was derived in terms of ventricular properties. Third, an algebraic formula predicting flow through the portion of the system isolated from the left ventricle was derived in terms of mechanical properties without neglecting redistribution of blood between systemic and pulmonary circulations. Although complexities were neglected, approximations necessary to obtain algebraic formulas resulted in minimal error, and predicted variables were consistent with reported values.

Integrating research and education at research-extensive universities with research-intensive communities.

Although the Boyer Commission (1998) lamented the lack of research opportunities for all undergraduates at research-extensive universities, it did not provide a feasible solution consistent with the mandate for faculty to maintain sustainable physiology research programs. The costs associated with one-on-one mentoring, and the lack of a sufficient number of faculty members to give intensive attention to undergraduate researchers, make one-on-one mentoring impractical. We therefore developed and implemented the "research-intensive community" model with the aim of aligning diverse goals of participants while simultaneously optimizing research productivity. The fundamental organizational unit is a team consisting of one graduate student and three undergraduates from different majors, supervised by a faculty member. Undergraduate workshops, Graduate Leadership Forums, and computer-mediated communication provide an infrastructure to optimize programmatic efficiency and sustain a multilevel, interdisciplinary community of scholars dedicated to research. While the model radically increases the number of undergraduates that can be supported by a single faculty member, the inherent resilience and scalability of the resulting complex adaptive system enables a research-intensive community program to evolve and grow.