Serena Y. Kuang ^1* Besjana Ahmetaj ¹ Xianggui Qu ²

• ¹ Oakland University William Beaumont School of Medicine, Rochester, United States
• ² Department of Mathematics and Statistics, College of Arts and Sciences, Oakland University, Rochester, Michigan, United States

Glomerular filtration rate (GFR) is the outcome of glomerular hemodynamics. It is influenced by a series of parameters: renal plasma flow, resistances of afferent arterioles and efferent arterioles (EA), hydrostatic pressures in the glomerular capillary and Bowman's capsule, and plasma colloid osmotic pressure in the glomerular capillary. Although mathematical models have been proposed to predict GFR at both the single-nephron level and the two-kidney system level using these parameters, mathematical equations governing glomerular filtration have not been well established because of two major problems. First, the two-kidney system-level models are simply extended from the equations at the single-nephron level, which is inappropriate in epistemology and methodology. Second, the role of EA in maintaining the normal GFR is underappreciated. In this article, a section is dedicated to concretely elaborating these two problems, which collectively show the need for a shift in epistemology toward a more holistic and evolving way of thinking as reflected in the concept of complex adaptive system (CAS). After this elaboration, we illustrate eight fundamental mathematical equations and four hypotheses governing glomerular hemodynamics at both the single-nephron and two-kidney levels as the theoretical foundation of glomerular hemodynamics. This illustration takes two steps. The first step is to modify the existing equations in the literature and establish a new equation within the conventional paradigm of epistemology. The second step is to formulate four hypotheses through logical reasoning from the perspective of CAS (beyond the conventional paradigm). Finally, we apply the new equation and hypotheses to comprehensively analyze glomerular hemodynamics in different conditions and predict GFR. In so doing, some concrete issues are eliminated. Unresolved issues are discussed from the perspective of CAS plus a designer's view. In summary, this article advances the theoretical study of glomerular dynamics by: 1) clarifying the necessity of shifting to the CAS paradigm; 2) adding new knowledge/insights into the significant role of EA in maintaining the normal GFR; 3) bridging the significant gap between research findings and physiology education; and 4) establishing a new and advanced foundation for physiology education.