Comprehensive diagnosis of whole-body acid–base and fluid-electrolyte disorders using a mathematical model and whole-body base excess

Abstract

A mathematical model of whole-body acid-base and fluid-electrolyte balance was used to provide information leading to the diagnosis and fluid-therapy treatment in patients with complex acid-base disorders. Given a set of measured laboratory-chemistry values for a patient, a model of their unique, whole-body chemistry was created. This model predicted deficits or excesses in the masses of Na(+), K(+), Cl(-) and H2O as well as the plasma concentration of unknown or unmeasured species, such as ketoacids, in diabetes mellitus. The model further characterized the acid-base disorder by determining the patient's whole-body base excess and quantitatively partitioning it into ten components, each contributing to the overall disorder. The results of this study showed the importance of a complete set of laboratory measurements to obtain sufficient accuracy of the quantitative diagnosis; having only a minimal set, just pH and PCO2, led to a large scatter in the predicted results. A computer module was created that would allow a clinician to achieve this diagnosis at the bedside. This new diagnostic approach should prove to be valuable in the treatment of the critically ill.

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

“…Our implementation in Modelica language enables switching complexity of a particular compartment. That is, we can use three different models for formulation of the physicochemical plasma compartment with various complexity: the simplest model of Fencl [ 34 ], the Figge-Fencl model [ 14 ], updated to version 3.0 [ 20 ] to quantify albumin in detail, or Wolf’s plasma compartment from [ 35 ] in current version v3.51 to consider also effects of Mg 2+ and Ca 2+ binding on albumin). The trade-off is computational complexity.…”

“…Wolf model [ 35 ] is the most complete mechanistic description of whole body acidbase. The model is available as a VisSim simulator, which is however unsuitable for integration into other models.…”

Acid-Base Equilibrium Modeling Based on the Balance Concept

“…A number of rather complex acid-base equilibrium models have been published [25][26][27][28][29][30] However, they are actually too complex to find application in the clinical practice and are unable to serve as a guide for selecting the best treatment method against acid-base equilibrium disorders. Such complex models are sometimes only created as scientific outcomes to be cited in other papers.…”

Determining the appropriate model complexity for patient-specific advice on mechanical ventilation

“…The remaining equations account for the physico-chemical properties of blood, including the solubility of O 2 and CO 2 in plasma and red blood cells (18r-21r), the fractions of plasma and erythrocyte (22r, 23r), and a modified form [45] of the empirical relationship relating pH in the plasma and red blood cells, derived by Funder and Weith [13], to describe the link between plasma and red blood cell acid-base status without the need to represent electrolyte transport across cell membranes. This simplification means that the model cannot calculate values of electrolytes in the plasma and red blood cells, as can newer models by Wolf [54,55].…”

“…In doing so, excess concentration of buffer base is calculated for the combination of blood, interstitial fluid, and tissues, taking into account the buffer mass in each compartment. This system's base excess (BEs) is the patient-specific parameter, such that for changes in ventilation, BEs can exchange between the three compartments, but in the absence of anaerobic metabolism, total BEs is constant [54]. BEs is calculated as…”