Mathematical modeling of whole-body electrolyte homeostasis

Abstract

Electrolyte balance is crucial for many physiological processes, including cellular signaling, muscle contractions, membrane potentials, hormonal secretion, and bone structure. Disruptions to electrolyte balance, arising from disease, diet, or drugs can have severe health consequences, such as muscle weakness, bone fragility, and life-threatening cardiac arrythmias. Therefore, a comprehensive understanding of these regulatory systems and how they may be disrupted is important for developing effective preventative and therapeutic strategies. Mathematical modeling provides a powerful tool for investigating these systems through simulations and analysis. In this thesis, we present the development and analysis of mathematical models focused on the regulation of key electrolytes, potassium and calcium.

For potassium homeostasis, we first developed a detailed, whole-body model incorporating known regulatory mechanisms. We conducted model simulations to quantify the individual contributions of these regulatory mechanisms on long-term potassium balance and responses to a meal. Additionally, we conducted sensitivity analyses to understand how parameter variations impact potassium levels in the extracellular and intracellular fluid. Furthermore, we integrated recent experimental data on renal adaptations to high potassium intake to analyze these findings from a whole-body perspective.

For calcium homeostasis, we developed mathematical models representing a male, female, late pregnant, and lactating rat to quantify sex-specific differences and maternal adaptations in calcium regulation. These models synthesized literature data to identify key mechanisms that enable females to meet the high calcium demands of pregnancy and lactation. Finally, we developed an integrated model that represents the renin-angiotensin system, calcium regulation, and bone remodeling to investigate the impact of estrogen deficiency in post-menopausal women and common antihypertensive treatments on bone density and calcium regulation.

The research provided in this thesis contributes frameworks for understanding electrolyte homeostasis and predicting the impacts of physiological changes and pharmacological interventions on electrolyte and bone homeostasis.