
==== Front
Crit Care Med
Crit Care Med
CCM
Critical Care Medicine
0090-3493
1530-0293
Lippincott Williams & Wilkins Hagerstown, MD

38856519
CCMED-D-23-01009
00024
10.1097/CCM.0000000000006350
3
Online Clinical Investigations
Validation of Math Model Using Porous Media for Determining Alveolar CO2 in Ventilated Patients
https://orcid.org/0000-0001-7820-0959
Jiménez-Posada L. D. PhD 1
Palacio- Sánchez A. F. MD 12
Montagut-Ferizzola Y. J. PhD 1
Ardila-Villegas M. 1
Maya Juan C. PhD 3
1 Universidad EIA, Escuela de Ingeniería y Ciencias Básicas, Grupo de Investigación en Ingenieria Biomédica (GIBEC) Envigado, Antioquia, Colombia.
2 Hospital Alma Mater de Antioquia, Servicio de Cuidados Intensivos, Medellín, Antioquia, Colombia.
3 Departamento de Procesos y Energía—TAYEA, Facultad de Minas, Universidad Nacional de Colombia—Sede Medellín, Medellín, Colombia.
For information regarding this article, E-mail: jcmaya@unal.edu.co; jcmaya@unal.edu.co
20 8 2024
10 2024
52 10 e503e511
Copyright © 2024 The Author(s). Published by Wolters Kluwer Health, Inc. on behalf of the Society of Critical Care Medicine and Wolters Kluwer Health, Inc.
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License 4.0 (CCBY-NC-ND), where it is permissible to download and share the work provided it is properly cited. The work cannot be changed in any way or used commercially without permission from the journal.

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.

carbon dioxide transport
convective and diffusive gas transport
lung model simulations
mathematical model
pulmonary gas transport models
Fondo de InvestigaciÃ³n en Salud (FIS)contract 801-2018 Not ApplicableSTATUSONLINE-ONLY
OPEN-ACCESSTRUE
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pmcKEY POINTS

Question: What is the accuracy and reliability of a mathematical model based on porous media theory in predicting alveolar CO2 in mechanically ventilated patients with healthy pulmonary function?

Findings: In a prospective observational study involving 13 ventilated patients, the model’s outcomes correlated highly with patient data for end-tidal CO2, area under the CO2 curve, and PaCO2, indicating significant precision and predictive power.

Meaning: The validated mathematical model offers a promising approach for estimating CO2 transport in pulmonary critical care, with potential for broader clinical applications after further validation.

INTRODUCTION

Determining the PaCO2 is essential for managing patients in ICUs, especially those on mechanical ventilation. Research has led to various mathematical models aiming to accurately predict PaCO2 levels, incorporating complex gas transport dynamics within the respiratory system (1–7). The lung’s bifurcated airway structure, featuring around 8.4 million bifurcations over 23 generations, complicates these models due to the sheer volume of equations required for precise simulation. This computational challenge necessitates simplified or efficient approaches to model the respiratory gas transport effectively (8).

The airway’s structure is typically divided into regions responsible for conduction (both convective and diffusive) and gas exchange, with CO2 exchange occurring in the alveolar sacs to meet metabolic demands (9). To manage the high computational demands, one strategy conceptualizes the lung as a porous medium, facilitating a detailed examination of gas kinetics and diffusion through the lung’s complex network (10–14).

This approach not only offers a more granular understanding of pulmonary gas exchange but also addresses the limitations of simpler models, making it particularly useful for improving our understanding of respiratory pathophysiology in mechanically ventilated patients.

Owen and Lewis (15) introduced a porous medium model to analyze lung tissue mechanics under high-frequency oscillatory ventilation, focusing on macroscopic tissue behavior rather than specific gas transport dynamics.

Viewing part of the lung as a continuum allows for a more robust equation for gas movement from airway entrance to blood, overcoming the computational challenges of modeling each airway path individually (16).

This body of research, which includes a comparison of mathematical model predictions with actual measurements from 13 mechanically ventilated patients, supports the feasibility of using a comprehensive model that accounts for the entire lung structure. The model, implemented in MATLAB (MathWorks, Natick, MA) dynamically calculates CO2 levels from alveoli to airway entrance, offering a valuable tool for simulating patient conditions and enhancing ventilation management strategies.

MATERIALS AND METHODS

This section outlines a detail of the geometrical model, integrates segments, and introduces a transient state model. It explains boundary conditions, and the flow excitation function, develops a script for simulations, outlines patient data collection, and describes the analysis approach.

Geometric Model

The conceptualized geometric framework has been methodically synthesized to encapsulate a comprehensive representation of the pulmonary system involved in gaseous interchange. Depicted in Figure 1, generation 0 (pathway 0) is illustrative of the trachea where an endotracheal tube of standard length and an inner diameter of 8 mm has been positioned, serving as the conduit for the inflow of ambient gases and the egress of expired gases. This pathway structure subsequently bifurcates into the right and left main bronchi (generation 1), identified as pathway 1 and pathway 2, respectively. These bronchial subdivisions each interface with a porous medium, embodying generations 2–23, identified as pathway 3 for the right lung and pathway 4 for the left lung. Of note is the introduction of CO2 from generation 17 (respiratory bronchioles) to generation 23 (alveolar sacs), which is considered as anatomically described by Weibel (8).

Figure 1. Geometric model.

Ultimately, each of the porous media is interconnected with the pulmonary blood flow, from which the CO2 originates and is expelled externally via these porous routes (pathways 3 and 4). The lengths and diameters assigned to each generation have been ascertained in accordance with the research conducted by Wiggs et al (17).

Although the alveoli are not explicitly illustrated in the geometric model, their influence is integrated through a function that quantifies the alveolar contribution based on the relative distance from the second generation of the bronchial tree. This incorporation is mathematically represented in the model as the “alveolated fraction” (refer to Eq. [5], denoted as the variable Fa in the last term).

Formulated Mathematical Model

For the implementation of the mathematical model, the pathway was partitioned into two fundamental segments: an initial section encompassing generations 0 (trachea) and 1 (main bronchi), and a subsequent section comprising generations 2–23.

Transport in Pathways 0 and 1

Within these initial two pathways, mass transport occurs through convective (axially) and diffusive (axial and radial) mechanisms during both the inspiratory and expiratory phases. Consequently, the species balance within these pathways is governed by:

∂ρg∂t=DmAC∂∂x(Ac∂ρg∂x)⏟Axialdiffusiveflow+DmAs∂∂r(As∂ρg∂r)⏟Radialdiffusiveflow−1AC∂∂x(ρgvAC)⏟Convectiveflow (1)

where ρg is the concentration of CO2, Dm is the molecular diffusivity of the gas within the respiratory gas mixture (16), AC and As are the cross-sectional and surface areas of the analyzed pathway, r is the radius of the pathway, and v is the velocity occurring in each segment of the pathway according to the established flow. To solve equation (1), it is necessary to implement a 2D mesh, which significantly increases the computational cost. However, let us now consider the Pellet number for mass transfer, defined as the ratio of convective to molecular mass transport (Pe = vLc/Dm) (18). Thus, if Pe ≫ 1, the flux is primarily convective (19), and the diffusive term can be depreciated. This condition is satisfied for pathways 0, 1, and 2, as observed in Table 1 which displays the calculated Péclet number (Pe) for commonly used flow values during mechanical ventilation (40 and 75 L/m) in the three pathways of the model.

TABLE 1. Calculation of the Péclet Number

Airway	Cross-Sectional Area (m2) Wiggs et al (17)a	Average Linear Velocity Through Generation (m/s)	Reynolds Number	Péclet Numberb	
75 L/min	40 L/min	75 L/min	40 L/min	75 L/min	40 L/min	
0 (with endotracheal tube)	0.00005	24.87	13.26	11,884	6,338	11,908	6,351	
1	0.00010	6.19	3.30	4,199	2,240	4,208	2,244	
2	0.00010	6.19	3.30	4,199	2,240	4,208	2,244	
a The pathway data submitted by Weibel (8) and Wiggs et al (17) are used. The data by Wiggs et al (17) are used for area and speed calculation. Inspired gas density: 1138 kg/m3. Dynamic viscosity: 0.000019 kg/m2⋅s.

b The Péclet number presented is calculated with an average diffusivity value of CO2, O2, nitrogen, and H2O in the inspired gas mixture, according to data presented by Jiménez-Posada et al (16).

Building upon the previous discussion, equation (1) can be simplified by neglecting the diffusive transport. Additionally, due to the cartilaginous structure present in generations 0 and 1 (pathways 0, 1, and 2 in this case), the variability in the areas is also negligible at pressure values commonly used under mechanical ventilation (20). Ultimately, equation (1) is reduced to:

∂ρg∂t=−∂∂x(ρgv) (2)

Finally, it is necessary to establish how the various segments of the model are interconnected. Therefore, it is stipulated that at the junction between pathways 0, 1, and 2, the flow present in pathway 0 is equal to the sum of the flows present in pathways 1 and 2:

v¯0A0=v¯1A1+v¯2A2 (3)

where v¯iandA¯i are, respectively, the average flow velocity in, and the cross-sectional area of pathway i (I = 0, 1, 2 in Eq. [3]). On the other hand, for the coupling between pathways 1–3 and 2–4, it is considered that they, respectively, have the same flow.

Transport in Pathways 3 and 4

This will be treated as a porous medium, where the local mass balance is:

∂(ρgε)∂t=∂∂x(Deff∂ρg∂x)⏟Diffusiveinporousm.−∂∂x(ρgεv¯)⏟Convectiveinporousm.−FaK(ρg−ρS)a⏟Alveolar~-bloodexchange (4)

where Deff is the effective diffusivity of the analyzed gas in the mixture of respiratory gases, ρs is the gas concentration in blood, and a is the specific surface area defined as the ratio between the interfacial area of the pore and its volume (a=Astotal/totalvolume) (21).

The lung porosity, denoted as ε, is defined as the total volume of the pores (alveoli and airways) divided by the overall lung volume. This is a value that remains constant over time for each specific clinical condition (although it may vary according to the disease pathology), and therefore equation (4) can be reformulated as follows:

ε∂(ρg)∂t=∂∂x(Deff∂ρg∂x)−ε∂∂x(ρgv¯)−FaK(ρg−ρS)a (5)

Fa and v¯ are the alveolated fraction, and the average velocity, respectively, which are functions of the axial position of the airway from generations 2 to 23. The term on the left-hand side of equation (5) represents the mass accumulation in the porous media. The first term on the right-hand side (RHS) of equation (5) represents diffusive gas transport, the second RHS term refers to convective transport in the porous medium, and the third RHS term refers to the transport of CO2 between the alveoli and the blood, where K is the exchange constant or diffusive capacity of the lung and which depends on the permeability of the alveolar-capillary membrane, the geometry, and the solubility and diffusivity characteristics of each gas.

Considering that the effective diffusivity is expressed as Deff=εDpτ, where Dp is the diffusivity in the pore and τ is the tortuosity of the porous media. Dp is defined according to the following equation 1Dp=1Dm+1Dk (22), where Dk is Knudsen’s diffusivity. However, since Knudsen-type diffusion is only dominant for pores whose average diameter varies between 2 and 50 nm (23), Dp is fundamentally equal to Dm in this case. Additionally, the specific surface area for cylindrical pores can be expressed as a=2εrp, where rp is the pore radius. Based on the above and considering a constant porosity over time, upon division of equation (4) by ε, we ultimately derive the subsequent equation:

∂(ρg)∂t=Dmτ∂2ρg∂x2−∂∂x(ρgv¯)−FaK(ρg−ρS)2rp (6)

Given that the variables for specific surface area, alveolar fraction, and pore radius possess distinct values corresponding to their relative positioning within the porous medium, they need to be expressed through dedicated piecewise functions for each individual variable. Furthermore, the velocity (v¯=flow/Ac) is subject to variations throughout the porous medium due to fluctuations in the cross-sectional area, a factor that is consequently incorporated into this equation.

Development of Script to Process Each Simulation

A MATLAB script using equations (2) and (6) and piecewise functions was developed to solve differential equations with the ODE15S solver. It handles equations considering boundary conditions and generates an inlet velocity function for pressure control ventilation. The application includes ventilator data and displays waveforms and CO2 concentration. Both lungs were modeled as nearly identical.

Data Collection in Patients

The research was conducted at the Hospital Alma Mater de Antioquia following approval by the Technical Research Committee, under record number 207, code IN09-2023, dated February 14, 2023, with final approval on April 12, 2023. The title of the research was “Validation of a Mathematical Model Using Artificial Intelligence for Determining Alveolar CO2 Concentration in Mechanically Ventilated Patients.” The committee mandated informed consent, which was duly obtained from each patient, adhering to all the recommendations of the Helsinki Declaration of 1975.

The exclusion criteria were: presence of tracheostomy, postsurgical patients from thoracic surgery, postsurgical patients from laparoscopic surgery, patients with thoracic trauma, presence of pneumothorax, presence of chest tubes, preexisting cardiac or pulmonary disease, presence of atelectasis or pneumonia, suspected pulmonary embolism, and body mass index (BMI) greater than 35 kg/m2.

All patients were hospitalized in the various ICUs at the Alma Mater Hospital of Antioquia (Medellín, Colombia) and were ventilated in pressure-controlled ventilation mode (two on Galileo Hamilton Medical ventilators (Hamilton Medical AG., Bonaduz, Switzerland), eight on Dragger Savina 300 Select ventilators (Drägerwerk AG & Co. KGaA, Lübeck, Germany), two on Leisgtung ventilators (Leistung Argentina, Cordoba, Argentina), and one on a Newport medical e-360 ventilator (Newport Medical Instruments, Costa Mesa, CA). Concurrently, side stream capnography was used (Mindray BeneView T5; Henzhen Mindray Bio-Medical Electronics Co., Ltd., Shenzhen, China), from which the end-tidal CO2 (EtCO2), data were collected. The area under the CO2 curve (AeCO2) derived from each patient was quantified using a mathematical process.

Once the ventilator data were collected, an arterial blood sample was then taken for arterial gas analysis using an arterial gas analyzer (I-STAT-CG4+; Abbott Laboratories, Lake, IL).

Analysis of the Results

By using the Minitab software (, the error for each of the 13 samples is analyzed for the variables PaCO2, EtCO2, and AeCO2. Additionally, the correlation (r) and determination (R2) factors are calculated for these variables. Subsequently, Bland-Altman plots will be used to evaluate the agreement between the mathematical model and the obtained data.

RESULTS

Table 2 shows the clinical data for each of the patients, recording their age, height, sex, weight, comorbidities, primary diagnosis, and the ventilator used. Additionally, the ideal body weight, the BMI, and the verification that the time elapsed since the start of mechanical ventilation is less than 24 hours are performed.

TABLE 2. Patient Data Acquisition

No.	Age (yr)	Sex	Height (m)	Weight (kg)	Comorbidities	Primary Diagnosis	Ventilator	
1	70	Female	1.45	52	Diabetes, hypertension, dyslipidemia	Urinary sepsis, acute kidney injury	Drager Savina 300 (Drägerwerk AG & Co KGaA, Lübeck, Germany)	
2	66	Female	1.52	60	Diabetes mellitus, hypertension, chronic kidney disease	Septic arthritis, dialysis emergency	Drager Savina 300	
3	73	Male	1.68	62	Hypertension, chronic obstructive pulmonary disease, CVA	Septic shock, acute cholangitis	Leistung Luf3 AP (Leistung Argentina, Cordoba, Argentina)	
4	64	Male	1.52	70	Hypertension, atrial fibrillation	CVA, convulsive status	Drager Savina 300	
5	64	Female	1.65	70	Hypertension, diabetes, diabetic nephropathy, dyslipidemia	CVA	Hamilton Galileo (Hamilton Medical AG, Bonaduz, Switzerland)	
6	66	Female	1.8	100	Obesity, hypertension, diabetes mellitus	Septic shock, CVA	Hamilton Galileo	
7	40	Male	1.6	70	None	Severe traumatic brain injury, postoperative hematoma, drainage	Drager Savina 300	
8	70	Male	1.72	75	Liver cirrhosis, Child B, systemic lupus, erythematosus	Intraparenchymal cerebral hemorrhage	Hamilton Galileo	
9	58	Male	1.68	50	None	Abdominal septic shock, postoperative hematoma, drainage	Drager Savina 300	
10	61	Male	1.71	60	Peptic acid disease	Postoperative abdominal surgery, acute pancreatitis	Drager Savina 300	
11	70	Male	1.64	65	None	Right subdural hemorrhage, postoperative hematoma	Drager Savina 300	
12	62	Male	1.67	70	Hypertension, appendectomy, splenectomy, tobacco use disorder	Abdominal septic shock	Leistung Luf3 AP	
CVA = cerebrovascular accident.

Table 3 displays the summary of data obtained from each patient through the ventilator, capnograph, and arterial gas equipment. Special care was taken to ensure confidentiality and a strict procedure for repeatability was followed with each patient.

TABLE 3. Data Acquisition From Mechanical Ventilators and Arterial Blood Gas Analyzers

No.	Control Pressure/Positive End-Expiratory Pressure (cm H2O)	Rate (Beats/min)/(Inspiration:Expiration)	Tidal Volume (mL)	Compliance (mL/cm H2O)	Airway Resistance (cm H2O/s/L)	End-Tidal CO2 (mm Hg)	PaCO2 (mm Hg)	
1	17/8	17/(1:2.5)	324	40	21	31	39.6	
2	22/6	17/(1:2.1)	349	77	17	19	32.5	
3	17/8	17/(1:2.5)	410	32	26	35	35.7	
4	15/6	16/(1:2.1)	475	39	21	23	24.2	
5	17/7	17/(1:2.1)	503	39	5	36	50.4	
6	16/8	18/(1:2)	492	35	13	35	35.4	
7	15/5	19/(1:2)	512	45	11	28	33.8	
8	15/5	16/(1:2.4)	505	63	11	32	36.9	
9	12/5	16/(1:2.4)	461	46	12	39	43.3	
10	17/5	17/(1:2.4)	485	45	10	59	57.7	
11	11/6	16/(1:2.7)	410	48	19	27	30.4	
12	13/6	18/(1:2.3)	440	43	19	34	37.3	
13	8/6	18/(1:2.3)	520	38	5	43	44.4	
Average	15/6	17	453	45	14	33	39	

The mathematical model for each patient was simulated using the MATLAB application. The model’s compliance and resistance values were calibrated based on the ventilator’s metrics to ensure that tidal volume and inspiratory and expiratory flows matched patient measurements. The simulation results for each patient were consistent with the data typically found in such studies. For details on PaCO2 values, refer to the discussion section.

To rigorously validate the proposed model, we extended our analysis beyond PaCO2 to encompass both EtCO2 and AeCO2. Upon juxtaposing observed values with those simulated by the mathematical model for each patient, we discerned the following discrepancies in terms of error:

For EtCO2, the mean error registered at 11.61% with a sd of the error at 6.14%, spanning an error range from 3.30% to 23.68%.

For AeCO2, the mean error was 11.45% with a sd of the error at 7.04%, and an error range between 1.41% and 24.31%.

For PaCO2, the mean error stood at 4.27% with a sd of the error at 1.88%, and an error range from 1.10% to 7.0%.

These findings underscore the mathematical model’s precision in estimating CO2 values in ventilated patients.

Pearson’s correlation coefficients (r) and determination coefficients (R2) for the variables PaCO2 by model, EtCO2, AeCO2, and PaCO2 were calculated using Minitab software (Minitab LLC, State College, PA). The results obtained are presented in Table 4.

TABLE 4. Correlation (r) and Determination (R2) Coefficients for PaCO2, End-Tidal CO2, and Area Under the CO2 Curve

Sample 1	Sample 2	n	Pearson Correlation Coefficient (r)	Pearson Determination Coefficient (R2)	5% CI	p	
Model EtCO2	Patient EtCO2	13	0.918	0.843	0.742–0.975	0.000	
Model AeCO2	Patient AeCO2	13	0.954	0.910	0.849–0.986	0.000	
Model PaCO2	Patient PaCO2	13	0.995	0.990	0.984–0.999	0.000	
AeCO2 = area under the CO2 curve, EtCO2 = end-tidal CO2.

Figure 2 presents the results of the Bland-Altman plots (24) for the variables: EtCO2, AeCO2, and PaCO2.

Figure 2. Bland-Altman plots evaluate the concordance between the patient-measured data (EtCO2_P, AeCO2_P, PACO2_P) and the results generated by the model (EtCO2_M, AeCO2_M, PACO2_M) for the variables end-tidal CO2 (EtCO2), area under the CO2 curve (AeCO2), and PaCO2.

Within the scope of this study, meticulous attention was devoted to the selection of patients exhibiting healthy pulmonary conditions. This approach facilitated the utilization of the well-established premise that the pulmonary shunt typically approximates around 5% (20). Consequently, this resulted in comparatively lower PaCO2 values than those measured for PaCO2. Considering that PaCO2 is deemed normal with values ranging between 33 and 45 mm Hg (25), alveolar values (PaCO2) will be between 1.6 and 2.5 mm Hg lower than the PaCO2 according to the parameters set for normal pulmonary shunt. In this research, a value of 2 mm Hg below the PaCO2 measurements was used as the representative PaCO2 value for each patient. Although this approach may raise questions about the model’s validation, it is essential to recognize that the alveolar gas values identified by the developed model do not derive from this methodology. Instead, they come from a differential equation of mass transport, which considers the arterial gases and the inflow and outflow of the airway with its true geometry as input conditions. Furthermore, the model mirrors the conditions of a patient under mechanical ventilation concerning volumes, pressures, and flows.

This study uniquely addresses the alveolar and bronchial structures of the lungs from the perspective of porous media theory, uncovering details about the complexity and organization of gas diffusion processes in the lungs. By modeling the lungs as porous media, aligns with advanced research in computational fluid dynamics and pulmonary physiology, offering a novel perspective that complements current methods of mechanical ventilation and gas exchange analysis.

The analysis of EtCO2 and the evaluation of the AeCO2 were included in the results, given the availability of additional data such as the patient’s capnography. This strategy of incorporating more data from the model supports its validation with enhanced rigor.

As displayed in Table 4, the correlation for the variables EtCO2, AeCO2, and PaCO2 (0.918, 0.954, and 0.995, respectively) and the determination factor for the same variables (0.843, 0.910, and 0.990, respectively) show that the mathematical model performs well in the direction and determination of the variables EtCO2, AeCO2, and PaCO2.

Overall, the evidence suggests that the mathematical model developed here is notably proficient in predicting the gas concentrations in pulmonary healthy patients undergoing mechanical ventilation. Despite this, given that the study was conducted with a relatively small group of only 13 patients, it would be beneficial to widen the research scope to include a larger population of patients with varying pulmonary pathologies, enabling a more comprehensive validation of the model.

It is noteworthy that the EtCO2 can be impacted by various factors, such as lung ventilation/perfusion, cardiac output, and CO2 metabolic production. Although the model has shown promising performance with pulmonary healthy patients, it would be interesting to ascertain whether it maintains its accuracy in patients with pulmonary pathologies that can alter these parameters.

In reference to the Bland-Altman plots, for both EtCO2 and PaCO2, most measurements (12/13) fall within the established boundaries. For AeCO2, all measurements adhere to the set limits, indicating a strong concordance between the model’s estimations and the real data in most instances. This consistency bolsters the overall validity of the mathematical model concerning the estimation of lung gas transport. It is important to note, however, that the model’s validity is primarily applicable to patients with healthy pulmonary function.

CONCLUSIONS

The results obtained with this sample of 13 healthy, mechanically ventilated patients allow us to conclude that the developed mathematical model presents interesting strides toward the integration of advanced mathematical models into the pulmonary aspects of critical care medicine. Clinically, this model has the potential to revolutionize the optimization of mechanical ventilation, adapting to the specific needs of each patient and thereby reducing complications associated with ventilation. The future of this research involves a series of clinical trials and the development of integrated monitoring systems for mechanical ventilators, which could significantly improve decision-making in intensive care settings.

The final step will be to bring this model into the clinical environment, in collaboration with biomedical engineers, to develop technologies that seamlessly integrate into the current landscape of respiratory care, with the goal of enhancing patient care and outcomes.

Nevertheless, the practical implementation of these models will require additional validation, clinician training, and potentially, adjustments based on each patient’s pathophysiologic conditions and characteristics. These findings are promising, yet the journey toward clinical implementation will be an iterative process of validation, refinement, and education.

Drs. Jiménez-Posada, Palacio Sánchez, Montagut Ferizzola, and Maya López received support for article research from Fondo de Investigación en Salud, convocatoria 807-2018 Colciencias, Colombia (project 133380764110, contract 801-2018). Dr. Ardila Villegas has disclosed that he does not have any potential conflicts of interest.
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