Algebraic Models in Physiology & Undergraduate Research

Abstract

Algebraic models are developed to provide qualitative insights and novel tools for experimentalists and clinicians to investigate processes involved in heart failure and renal fluid balance. The models employed graphical analysis to conceptualize how equilibrium behaviors in complex systems emerge from the interactions between mechanical processes. In contrast to numerical modeling methods, the models yielded explicit and general algebraic formulas for clinically relevant variables. Algebraic formulas were obtained by (1) characterizing the functional behavior of the most salient elements of the system, (2) constraining the scope of the model by assuming all global and local feedback acts through the physical properties of the system, and (3) assuming the relationships that characterize the functional elements of the system are linear. Because these models were developed through joint team research with undergraduate research scholars, a third study was conducted to identify the vocational identities and team attributes that predict undergraduate career goal change. Findings regarding the interactions between participant traits and team attributes inform the design of undergraduate research programs that seek to amplify and diversify the nation’s workforce of knowledge-producers.