Validation of a two-compartment model of ventilation/perfusion distribution

Pulmonary gas exchange evaluated by machine learning: a computer simulation

Using computer simulation we investigated whether machine learning (ML) analysis of selected ICU monitoring data can quantify pulmonary gas exchange in multi-compartment format. A 21 compartment ventilation/perfusion (V/Q) model of pulmonary blood flow processed 34,551 combinations of cardiac output, hemoglobin concentration, standard P50, base excess, VO₂ and VCO₂ plus three model-defining parameters: shunt, log SD and mean V/Q. From these inputs the model produced paired arterial blood gases, first with the inspired O₂ fraction (FiO₂) adjusted to arterial saturation (SaO₂) = 0.90, and second with FiO₂ increased by 0.1. 'Stacked regressor' ML ensembles were trained/validated on 90% of this dataset. The remainder with shunt, log SD, and mean 'held back' formed the test-set. 'Two-Point' ML estimates of shunt, log SD and mean utilized data from both FiO₂ settings. 'Single-Point' estimates used only data from SaO₂ = 0.90. From 3454 test gas exchange scenarios, two-point shunt, log SD and mean estimates produced linear regression models versus true values with slopes ~ 1.00, intercepts ~ 0.00 and R² ~ 1.00. Kernel density and Bland-Altman plots confirmed close agreement. Single-point estimates were less accurate: R² = 0.77-0.89, slope = 0.991-0.993, intercept = 0.009-0.334. ML applications using blood gas, indirect calorimetry, and cardiac output data can quantify pulmonary gas exchange in terms describing a 20 compartment V/Q model of pulmonary blood flow. High fidelity reports require data from two FiO₂ settings.

The effects of oxygen induced pulmonary vasoconstriction on bedside measurement of pulmonary gas exchange

In patients with respiratory failure measurements of pulmonary gas exchange are of importance. The bedside automatic lung parameter estimator (ALPE) of pulmonary gas exchange is based on changes in inspired oxygen (FiO2) assuming that these changes do not affect pulmonary circulation. This assumption is investigated in this study. Forty-two out of 65 patients undergoing coronary artery bypass grafting (CABG) had measurements of mean pulmonary arterial pressure (MPAP), cardiac output and pulmonary capillary wedge pressure thus enabling the calculation of pulmonary vascular resistance (PVR) at each FiO2 level. The research version of ALPE was used and FiO2 was step-wise reduced a median of 0.20 and ultimately returned towards baseline values, allowing 6-8 min' steady state period at each of 4-6 levels before recording the oxygen saturation (SpO2). FiO2 reduction led to median decrease in SpO2 from 99 to 92 %, an increase in MPAP of 4 mmHg and an increase in PVR of 36 dyn s cm(-5). Changes were immediately reversed on returning FiO2 towards baseline. In this study changes in MPAP and PVR are small and immediately reversible consistent with small changes in pulmonary gas exchange. This indicates that mild deoxygenation induced pulmonary vasoconstriction does not have significant influences on the ALPE parameters in patients after CABG.

On the practical identifiability of a two-parameter model of pulmonary gas exchange

Background

Successful application of mechanical ventilation as a life-saving therapy implies appropriate ventilator settings. Decision making is based on clinicians’ knowledge, but can be enhanced by mathematical models that determine the individual patient state by calculating parameters that are not directly measurable. Evaluation of models may support the clinician to reach a defined treatment goal. Bedside applicability of mathematical models for decision support requires a robust identification of the model parameters with a minimum of measuring effort. The influence of appropriate data selection on the identification of a two-parameter model of pulmonary gas exchange was analyzed.

Methods

The model considers a shunt as well as ventilation-perfusion-mismatch to simulate a variety of pathologic pulmonary gas exchange states, i.e. different severities of pulmonary impairment. Synthetic patient data were generated by model simulation. To incorporate more realistic effects of measurement errors, the simulated data were corrupted with additive noise. In addition, real patient data retrieved from a patient data management system were used retrospectively to confirm the obtained findings. The model was identified to a wide range of different FiO₂ settings. Just one single measurement was used for parameter identification. Subsequently prediction performance was obtained by comparing the identified model predicted oxygen level in arterial blood either to exact data taken from simulations or patients measurements.

Results

Structural identifiability of the model using one single measurement for the identification process could be demonstrated. Minimum prediction error of blood oxygenation depends on blood gas level at the time of system identification i.e. the measurement situation. For severe pulmonary impairment, higher FiO₂ settings were required to achieve a better prediction capability compared to less impaired pulmonary states. Plausibility analysis with real patient data could confirm this finding.

Discussion and conclusions

Dependent on patients’ pulmonary state, the influence of ventilator settings (here FiO₂) on model identification of the gas exchange model could be demonstrated. To maximize prediction accuracy i.e. to find the best individualized model with as few data as possible, best ranges of FiO₂-settings for parameter identification were obtained. A less effort identification process, which depends on the pulmonary state, can be deduced from the results of this identifiability analysis.

Diffusion capacity of the lung for carbon monoxide - A potential marker of impaired gas exchange or of systemic deconditioning in chronic obstructive lung disease?

Gas exchange impairment is primarily caused by ventilation-perfusion mismatch in chronic obstructive pulmonary disease (COPD), where diffusing capacity of the lungs for carbon monoxide (DLCO) remains the clinical measure. This study investigates whether DLCO: (1) can predict respiratory impairment in COPD, that is, changes in oxygen and carbon dioxide (CO2); (2) is associated with combined risk assessment score for COPD (Global Initiative for Chronic Obstructive Lung Disease (GOLD) score); and (3) is associated with blood glucose and body mass index (BMI). Fifty patients were included retrospectively. DLCO; arterial blood gas at inspired oxygen (FiO2) = 0.21; oxygen saturation (SpO2) at FiO2 = 0.21 (SpO2 (21)) and FiO2 = 0.15 (SpO2 (15)) were registered. Difference between arterial and end-tidal CO2 (ΔCO2) was calculated. COPD severity was stratified according to GOLD score. The association between DLCO, SpO2, ΔCO2, GOLD score, blood glucose, and BMI was investigated. Multiple regression showed association between DLCO and GOLD score, BMI, and glucose level (R (2) = 0.6, p < 0.0001). Linear and multiple regression showed an association between DLCO and SpO2 (21) (R (2) = 0.3, p = 0.001 and p = 0.03, respectively) without contribution from SpO2 (15) or ΔCO2. A stronger association between DLCO and GOLD score than between DLCO and SpO2 could indicate that DLCO is more descriptive of systemic deconditioning than gas exchange in COPD patients. However, further larger studies are needed. A weaker association is seen between DLCO and SpO2 (21) without contribution from SpO2 (15) and ΔCO2. This could indicate that DLCO is more descriptive of systemic deconditioning than gas exchange in COPD patients. However, further larger studies are needed.

Can computer simulators accurately represent the pathophysiology of individual COPD patients?

BACKGROUND

Computer simulation models could play a key role in developing novel therapeutic strategies for patients with chronic obstructive pulmonary disease (COPD) if they can be shown to accurately represent the pathophysiological characteristics of individual patients.

METHODS

We evaluated the capability of a computational simulator to reproduce the heterogeneous effects of COPD on alveolar mechanics as captured in a number of different patient datasets.

RESULTS

Our results show that accurately representing the pathophysiology of individual COPD patients necessitates the use of simulation models with large numbers (up to 200) of compartments for gas exchange. The tuning of such complex simulation models 'by hand' to match patient data is not feasible, and thus we present an automated approach based on the use of global optimization algorithms and high-performance computing. Using this approach, we are able to achieve extremely close matches between the simulator and a range of patient data including PaO2, PaCO2, pulmonary deadspace fraction, pulmonary shunt fraction, and ventilation/perfusion (/Q) curves. Using the simulator, we computed combinations of ventilator settings that optimally manage the trade-off between ensuring adequate gas exchange and minimizing the risk of ventilator-associated lung injury for an individual COPD patient.

CONCLUSIONS

Our results significantly strengthen the credibility of computer simulation models as research tools for the development of novel management protocols in COPD and other pulmonary disease states.

Minimal model quantification of pulmonary gas exchange in intensive care patients

Mathematical models are required to describe pulmonary gas exchange. The challenge remains to find models which are complex enough to describe physiology and simple enough for clinical practice. This study aimed at finding the necessary 'minimal' modeling complexity to represent the gas exchange of both oxygen and carbon dioxide. Three models of varying complexity were compared for their ability to fit measured data from intensive care patients and to provide adequate description of patients' gas exchange abnormalities. Pairwise F-tests showed that a two parameter model provided superior fit to patient data compared to a shunt only model (p<0.001), and that a three parameter model provided superior fit compared to the two parameter model (p<0.1). The three parameter model describes larger ranges of ventilation to perfusion ratios than the two parameter model, and is identifiable from data routinely available in clinical practice.

A computer model of the artificially ventilated human respiratory system in adult intensive care

A multi-technique approach to modelling artificially ventilated patients on the adult general intensive care unit (ICU) is proposed. Compartmental modelling techniques were used to describe the mechanical ventilator and the flexible hoses that connect it to the patient. 3D CFD techniques were used to model flow in the major airways and a Windkessel style balloon model was used to model the mechanical properties of the lungs. A multi-compartment model of the lung based on bifurcating tree structures representing the conducting airways and pulmonary circulation allowed lung disease to be modelled in terms of altered V/Q ratios within a lognormal distribution of values and it is from these that gas exchange was determined. A compartmental modelling tool, Bathfp, was used to integrate the different modelling techniques into a single model. The values of key parameters in the model could be obtained from measurements on patients in an ICU whilst a sensitivity analysis showed that the model was insensitive to the value of other parameters within it. Measured and modelled values for arterial blood gases and airflow parameters are compared for 46 ventilator settings obtained from 6 ventilator dependent patients. The results show correlation coefficients of 0.88 and 0.85 for the arterial partial pressures of the O(2) and CO(2), respectively (p<0.01) and of 0.99 and 0.96 for upper airway pressure and tidal volume, respectively (p<0.01). The difference between measured and modelled values was large in physiological terms, suggesting that some optimisation of the model is required.

Hypoxemia and acute mountain sickness: which comes first?

Hypoxemia is usually associated with acute mountain sickness (AMS), but most studies have varied in time and magnitude of altitude exposure, exercise, diet, environmental conditions, and severity of pulmonary edema. We wished to determine whether hypoxemia occurred early in subjects who developed subsequent AMS while resting at a simulated altitude of 426 mmHg (approximately 16,000 ft or 4880 m). Exposures of 51 men and women were carried out for 8 to 12 h. AMS was determined by Lake Louise (LL) and AMS-C scores near the end of exposure, with spirometry and gas exchange measured the day before (C) and after 1 (A1), 6 (A6), and last (A12) h at simulated altitude and arterial blood at C, A1, and A12. Responses of 16 subjects having the lowest AMS scores (nonAMS: mean LL=1.0, range=0-2.5) were compared with the 16 having the highest scores (+AMS: mean LL=7.4, range=5-11). Total and alveolar ventilation responses to altitude were not different between groups. +AMS had significantly lower PaO2 (4.6 mmHg) and SaO2 (4.8%) at A1 and 3.3 mmHg and 3.1% at A12. Spirometry changes were similar at A1, but at A6 and A12 reduced vital capacity (VC) and increased breathing frequency suggested interstitial pulmonary edema in +AMS. The early hypoxemia in +AMS appears to be the result of diffusion impairment or venous admixture, perhaps due to a unique autonomic response affecting pulmonary perfusion. Early hypoxemia may be useful to predict AMS susceptibility.

A tidally breathing model of ventilation, perfusion and volume in normal and diseased lungs †

BACKGROUND

To simulate the short-term dynamics of soluble gas exchange (e.g. CO2 rebreathing), model structure, ventilation-perfusion (VA/Q) and ventilation-volume (VA/VA) parameters must be selected correctly. Some diseases affect mainly the VA/Q distribution while others affect both VA/Q and VA/VA distributions. Results from the multiple inert gas elimination technique (MIGET) and multiple breath nitrogen washout (MBNW) can be used to select VA/Q and VA/VA parameters, but no method exists for combining VA/Q and VA/VA parameters in a multicompartment lung model.

METHODS

We define a tidally breathing lung model containing shunt and up to eight alveolar compartments. Quantitative and qualitative understanding of the diseases is used to reduce the number of model compartments to achieve a unique solution. The reduced model is fitted simultaneously to inert gas retentions calculated from published VA/Q distributions and normalized MBNWs obtained from similar subjects. Normal lungs and representative cases of emphysema and embolism are studied.

RESULTS

The normal, emphysematous and embolism models simplify to one, three and two alveolar compartments, respectively.

CONCLUSIONS

The models reproduce their respective MIGET and MBNW patient results well, and predict disease-specific steady-state and dynamic soluble and insoluble gas responses.

CO2 rebreathing model in COPD: blood-to-gas equilibration

Rebreathing in a closed system can be used to estimate mixed venous PCO2 (PvCO2) and cardiac output, but these estimates are affected by VA/Q heterogeneity. The purpose of this study was to validate a mathematical model of CO2 exchange during CO2 rebreathing in 29 patients with chronic obstructive pulmonary disease (COPD), with baseline arterial PCO2 (PaCO2) ranging from 28 to 60 mmHg. Rebreathing increased end-tidal PCO2 (PETCO2) by 20 mmHg over 2.2 min. This model employed baseline values for inspired (bag) PCO2, estimated PvCO2, distribution of ventilation and blood flow in one high VA/Q and one low VA/Q compartment, the ventilation increase and conservation of mass equations to simulate time courses of PICO2, PETCO2, PvCO2, and PaCO2. Measured PICO2 and PETCO2 during rebreathing differed by an average (SEM) of 1.4 (0.4) mmHg from simulated values. By end of rebreathing, predicted PvCO2 was lower than measured and predicted PaCO2, indicating gas to blood CO2 flux. Estimates of the ventilatory response to CO2, quantified as the slope (S) of the ventilation increase versus PETCO2, were inversely related to gas-to-blood PCO2 disequilibria due to VA/Q heterogeneity and buffer capacity (BC), but not airflow limitation. S may be corrected for these artifacts to restore S as a more valid noninvasive index of central CO2 responsiveness. We conclude that a rebreathing model incorporating baseline VA/Q heterogeneity and BC can simulate gas and blood PCO2 in patients with COPD, where VA/Q variations are large and variable.