Wolf MB. Whole body acid-base and fluid-electrolyte balance: a mathematical model. Am J Physiol Renal Physiol 305: F1118-F1131, 2013. First published July 24, 2013 doi:10.1152/ajprenal.00195.2013.-A cellular compartment was added to our previous mathematical model of steady-state acid-base and fluid-electrolyte chemistry to gain further understanding and aid diagnosis of complex disorders involving cellular involvement in critically ill patients. An important hypothesis to be validated was that the thermodynamic, standard free-energy of cellular H ϩ and Na ϩ pumps remained constant under all conditions. In addition, a hydrostatic-osmotic pressure balance was assumed to describe fluid exchange between plasma and interstitial fluid, including incorporation of compliance curves of vascular and interstitial spaces. The description of the cellular compartment was validated by close comparison of measured and model-predicted cellular pH and electrolyte changes in vitro and in vivo. The new description of plasma-interstitial fluid exchange was validated using measured changes in fluid volumes after isoosmotic and hyperosmotic fluid infusions of NaCl and NaHCO 3. The validated model was used to explain the role of cells in the mechanism of saline or dilutional acidosis and acid-base effects of acidic or basic fluid infusions and the acid-base disorder due to potassium depletion. A module was created that would allow users, who do not possess the software, to determine, for free, the results of fluid infusions and urinary losses of water and solutes to the whole body. mathematical model; acid-base balance; fluid and electrolyte balance; potassium depletion; saline acidosis A TRUE UNDERSTANDING OF THE physiological effects of disease processes and attendant fluid infusions and losses requires consideration of the distribution of water, protein, electrolytes, and electrically neutral solutes among all the body fluids. Many simple analytical solutions to subsets of this physicochemical problem have been used since the time of Henderson (22), but they have yielded only limited understanding.Recently, Wolf and DeLand (39) developed a model of the steady-state water and electrolyte exchanges between interstitial fluid (I), plasma (P), and erythrocytes (E). They showed (38) that their model could be used along with laboratory blood-chemistry values to predict both the abnormal fluid and electrolyte distribution and acid-base status in critically ill patients. However, the lack of a cellular compartment limited this tool to the study of disease processes lacking significant osmolarity changes. Another shortcoming was an incomplete description of the forces moving water between plasma and interstitial fluid.Hence, the aims of the present study were to expand and modify the previous IPE model (39) by 1) adding a parenchymal cell compartment, 2) incorporating a more explicit description of the forces leading to plasma-interstitial water distribution, 3) providing much more extensive validation of both water and electrolyte distrib...