Testing an inverse modeling approach with gradient boosting regression for stroke volume estimation using patient thermodilution data

Abstract

Stroke volume (SV) is a major indicator of cardiovascular function, providing essential information about heart performance and blood flow adequacy. Accurate SV measurement is particularly important for assessing patients with heart failure, managing patients undergoing major surgeries, and delivering optimal care in critical settings. Traditional methods for estimating SV, such as thermodilution, are invasive and unsuitable for routine diagnostics. Non-invasive techniques, although safer and more accessible, often lack the precision and user-friendliness needed for continuous bedside monitoring. We developed a modified method for SV estimation that combines a validated 1-D model of the systemic circulation with machine learning. Our approach replaces the traditional optimization process developed in our previous work, with a regression method, utilizing an in silico-generated dataset of various hemodynamic profiles to create a gradient boosting regression-enabled SV estimator. This dataset accurately mimics the dynamic characteristics of the 1-D model, allowing for precise SV predictions without resource-intensive parameter adjustments. We evaluated our method against SV values derived from the gold standard thermodilution method in 24 patients. The results demonstrated that our approach provides a satisfactory agreement between the predicted and reference data, with a MAE of 16 mL, a normalized RMSE of 21%, a bias of -9.2 mL, and limits of agreement (LoA) of [-47, 28] mL. A correlation coefficient of r = 0.7 (p < 0.05) was reported, with the predicted SV slightly underestimated (68 ± 23 mL) in comparison to the reference SV (77 ± 26 mL). The significant reduction in computational time of our method for SV assessment should make it suitable for real-time clinical applications.

Keywords: blood pressure; cardiac output; gradient boosting; hemodynamics; non-invasive monitoring; supervised learning.

Figure 1

Estimation of cfPWV estimation. The calculation of cfPWV involves two key components: the estimation of L, the distance between these two arterial sites, and the measurement of the pulse transit time (Δt). The cfPWV is then calculated using the formula cfPWV = L/Δt.

Figure 2

Schematic representation of the model of systemic circulation developed by Reymond et al. (2009). (A) Main systemic arterial tree. (B) Detail of the aortic arch and the coronary network. (C) Detail of the principal abdominal aorta branches. (D) Blown-up schematic of the detailed cerebral arterial tree, which is connected via the carotids (segments 5 and 15) and the vertebrals (segments 6 and 20) to the main arterial tree shown in panel (A).

Figure 3

Main mathematical components describing the numerical modeling approach of the 1-D arterial tree computer solver. Adapted from https://infoscience.epfl.ch/entities/publication/79637d9b-89a0-4fc0-8649-50e00810a0b6, with permission.

Figure 4

Pressure and flow waveforms are generated at every arterial side of the arterial tree model with every simulation. Adapted from https://infoscience.epfl.ch/entities/publication/79637d9b-89a0-4fc0-8649-50e00810a0b6, with permission.

Figure 5

Schematic representation of the training (including hyperparameter tuning) and testing methodological approach.

Figure 6

Schematic representation of the measurement setup for the acquisition the input data (brSBP, brDBP, HR, and cfPWV). The animation was created using OpenAI’s GPT-4 model (OpenAI, 2023).

Figure 7

Schematic representation of the study procedures.

Figure 8

Comparison of the predicted and the reference stroke volume (SV) data for GB model. The left panel shows the scatter plot of predicted SV against reference SV with a line of equality (dashed black line) indicating perfect agreement. The right panel displays the Bland–Altman plot, showing the differences between reference and predicted SV against their mean, with dashed lines for mean difference and limits of agreement (mean ± 1.96 SD).