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Mathematical Biosciences and Engineering

A mathematical model of the four cardinal acid-base disorders.

Alhaji Cherif, Vaibhav Maheshwari, Doris Fuertinger, Gudrun Schappacher-Tilp, Priscila Preciado, David Bushinsky, Stephan Thijssen, Peter Kotanko

Precise maintenance of acid-base homeostasis is fundamental for optimal functioning of physiological and cellular processes. The presence of an acid-base disturbance can affect clinical outcomes and is usually caused by an underlying disease. It is, therefore, important to assess the acid-base status of patients, and the extent to which various therapeutic treatments are effective in controlling these acid-base alterations. In this paper, we develop a dynamic model of the physiological regulation of an HCO3-/CO2 buffering system, an abundant and powerful buffering system, using Henderson-Hasselbalch kinetics. We simulate the normal physiological state and four cardinal acidbase disorders: Metabolic acidosis and alkalosis and respiratory acidosis and alkalosis. We show that the model accurately predicts serum pH over a range of clinical conditions. In addition to qualitative validation, we compare the in silico results with clinical data on acid-base homeostasis and alterations, finding clear relationships between primary acid-base disturbances and the secondary adaptive compensatory responses. We also show that the predicted primary disturbances accurately resemble clinically observed compensatory responses. Furthermore, via sensitivity analysis, key parameters were identified which could be the most effective in regulating systemic pH in healthy individuals, and those with chronic kidney disease and distal and proximal renal tubular acidosis. The model presented here may provide pathophysiologic insights and can serve as a tool to assess the safety and efficacy of different therapeutic interventions to control or correct acid-base disorders.

About the Contributors

Dr. Peter Kotanko, MD

RRI Research Director

SVP, Corporate Research & Development

Peter Kotanko, MD is Research Director at the Renal Research Institute (RRI), New York. Prior to joining RRI, from 1997 to 2007 he served as Vice Chair of a department of internal medicine at an academic teaching hospital in Graz, Austria. Prior to moving to Graz in 1989, he worked 1982-89 at the Department of Physiology and the University Clinic of Internal Medicine, Innsbruck, Austria...

Alhaji Cherif, D. Phil.

Senior Mathematician

Alhaji Cherif, D.Phil., is Senior Mathematician at the RRI with over 10 years of multi- and transdisciplinary research experiences in nanotechnology (microfluidics), adaptive complex systems, and applied mathematical sciences and its application in life, physical and social sciences. He leads the mathematical modeling efforts relevant to pathophysiological mechanisms in dialysis patients, particularly, acid-base disturbance, bone and mineral disease, cardiovascular calcification and anemia...

Stephan Thijssen, M.D.

Vice President, Applied and Basic Research

Prior to coming to New York, Dr. Thijssen worked in the Nephrology Department at the University Hospital Homburg, Germany. He joined Renal Research Institute in 2005 and currently serves as VP of Applied and Basic Research. Dr. Thijssen brings more than one and a half decades of research experience to the RRI team, covering laboratory research, clinical research, epidemiology research and mathematical modeling...