Whole body acid-base and fluid-electrolyte balance: a mathematical model

Abstract

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...

Simple accurate mathematical models of blood HbO2 and HbCO2 dissociation curves at varied physiological conditions: evaluation and comparison with other models

“…The resulting S HbO2 and S HbCO2 models are also tested using diverse experimental data available in the literature on the HbO 2 and HbCO 2 dissociation curves for a wide range of physiological conditions (Joels & Pugh, 1958; Naeraa et al , 1963; Bauer & Schroder, 1972; Hlastala et al , 1977; Matthew et al , 1977; Reeves, 1980). This study does not include the buffering of CO 2 in blood as that is covered in our previous work on blood-tissue gas exchange (Dash & Bassingthwaighte, 2006) and by Wolf (2013) for whole-body acid-base and electrolyte balance. Interested readers are referred to our previous article (Dash & Bassingthwaighte, 2010) for a historical perspective and details of the mathematical models of S HbO2 not covered in this paper.…”

Modern and traditional approaches combined into an effective gray-box mathematical model of full-blood acid-base

“…We validate the combined model by comparison with the Siggaard-Andersen’s nomogram [ 8 ], later Siggaard-Andersen’s updated albumin-sensitive Van Slyke formalization [ 19 ], Figge-Fencl’s physicochemical model (FF) [ 14 ], updated to version 3.0 [ 20 ]) and the recent full blood model by Wolf [ 6 ] (reduced to the plasma-erythrocyte compartments). A graphic comparison (Fig.…”

“…2 Results of Combined model in the pH-pCO 2 diagram. a Comparison of our Combined model with the formalised SA nomogram reflecting full blood, with the Figge-Fencl (FF) model of plasma and with the recent full blood model by Wolf [ 6 ] reduced to the erythrocyte-plasma compartments. b Sensitivity analysis for albumin of our combined model, the updated Van Slyke Eq.…”

“…Rees and Andreasen shown the extension to full blood and enhanced it by circulation, blood gases, interstitium and cellular compartments [ 4 ]. Wooten later presented an extension to the extracellular compartment [ 5 ] and most recently, Wolf [ 6 ] proposed a profound steady-state physicochemical model of erythrocyte-plasma-interstitium-cell compartments, including detailed ion and water balance. It has been built with the purpose to mechanistically describe complex physicochemical processes, which is, however, computationally demanding and hard to solve due to a large system of non-linear equations.…”

“…Described approaches [ 1 – 6 ] are, however, designed for steady-state situations. To extend the whole-body acid-base assessment by bodily regulatory loops and to show pathogenesis of developing disorders in time, one needs to construct even larger integrative model, including important bodily compartments (interstitial fluid, cells) and regulations (kidney, liver, respiratory regulation) interconnected by a circulation of full-blood, the core component of our approach [ 7 ].…”