A physio-chemical mathematical model of the effects of blood analysis delay on acid-base, metabolite and electrolyte status: evaluation in blood from critical care patients

Abstract

Objectives: Measurements of acid-base status are performed quickly after blood sampling avoiding errors. This necessitates rapid sample transport which can be problematic. This study measures blood sampled in critically ill patients over 180 min and proposes a mathematical physio-chemical model to simulate changes.

Methods: Eleven blood samples were taken from 30 critically ill patients and measured at baseline (2 samples) and 36, 54, 72, 90, 108, 126, 144, 162, and 180 min. A mathematical model was proposed including red blood cell metabolism, carbon dioxide diffusion, electrolyte distribution and water transport. This model was used to simulate values of plasma pH, pCO₂, pO₂, SO₂, glucose, lactate, Na⁺ and Cl^- during analysis delay. Simulated and measured values were compared using Bland-Altman and correlation analysis, and goodness of model fits evaluated with chi-squared.

Results: The mathematical model provided a good fit to data in 29 of 30 patients with no significant differences (p>0.1) between simulated and measured plasma values. Differences were (bias±SD): pH 0.000 ± 0.012, pCO₂ 0.00 ± 0.24 kPa, lactate -0.10 ± 0.23 mmol/L, glucose 0.00 ± 0.34 mmol/L, Cl^- -0.2 ± 1.21 mmol/L, Na⁺ 0.0 ± 1.0 mmol/L, pO₂ 0.0 ± 0.44 kPa, SO₂ -0.6 ± 5.5 %, with these values close to manufacturers' measurement errors. All linear correlations had R²>0.86. Simulations of pH, PCO₂, glucose and lactate could be performed from baseline values without patient specific parameters.

Conclusions: This paper illustrates that analysis delay can be accurately simulated with a mathematical model of physio-chemistry. While further evaluation is necessary, this may indicate a role for this model in clinical practice to simulate analysis delay.

Keywords: acid-base; analysis delay; mathematical modelling.