Validation of Math Model Using Porous Media for Determining Alveolar co2 in Ventilated Patients.

OBJECTIVES: To validate a mathematical model using porous media theory for alveolar CO2 determination in ventilated patients. DESIGN: Mathematical modeling study with prospective clinical validation to simulate CO2 exchange from bloodstream to airway entrance. SETTING: ICU. PATIENTS: Thirteen critically ill patients without chronic or acute lung disease. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: Model outcomes compared with patient data showed correlations for end-tidal CO2 (EtCO2), area under the CO2 curve, and PaCO2 of 0.918, 0.954, and 0.995. Determination coefficients (R2) were 0.843, 0.910, and 0.990, indicating precision and predictive power. CONCLUSIONS: The mathematical model shows potential in pulmonary critical care. Although promising, practical application demands further validation, clinician training, and patient-specific adjustments. The path to clinical use will be iterative, involving validation and education.

Nonlinear N - Compartments model of respiratory mechanics considering viscoelasticity, inertia and surface tension properties.

Respiratory biomechanics constitutes an important topic in clinical practice. Different strategies like mathematical models have been implemented to understand and replicate scenarios allowing deeper analysis. In this paper, a nonlinear N - compartments model is presented, allowing to represent the lung in a heterogeneous way. It considers the resistance of each generation of the airway and each alveolar compartment characterized independently. Includes properties of nonlinear elastance, viscoelasticity, inertia, and surface tension. In this work, to show the functionality of the model, a simulation of four alveolar units coupled to the airway model is presented using pressure as input signal simulating mechanical ventilation. However, the model can be used to simulate any desired number of alveolar units. Values at airway output were compared to the linear model, obtaining a correlation close to 1. Also, was compared to a physical test lung using Hamilton - S1 mechanical ventilator obtaining a positive correlation. The model makes it possible to evaluate the effects of different properties during spontaneous respiration or mechanical ventilation, both at the airway opening and alveolar. These properties include viscoelasticity, surface tension, inertia, among others.

Computational model of trachea-alveoli gas movement during spontaneous breathing.

A computational model of the transport of gases involved in spontaneous breathing, from the trachea inlet to the alveoli was developed for healthy patients. Convective and diffusive transport mechanisms were considered simultaneously, using a diffusion coefficient (D) that has considered the four main species of gases present in the exchange carried out by the human lung, nitrogen (N2), oxygen (O2), carbon dioxide (CO2) and water vapor (H2O). A Matlab® script was programmed to simulate the trachea-alveolus gas exchange model under three respiratory frequencies: 12, 24 and 40 breaths per minute (BPM), each with three diaphragmatic movements of 2 cm, 4 cm, and 6 cm. During the simulations, the CO2 inlet concentrations in the alveoli and the O2 concentration at the inlet of the trachea were kept constant. A simplified but stable model of mass transport between the trachea and alveoli was obtained, allowing the concentrations to be determined dynamically at the selected test points in the airway.