Pleural effusion (PE) may be a sequela of various diseases, including acute and chronic heart failure, pulmonary and pleural infections and malignancies. It is estimated that PE may appear in as many as 20% of all patients with malignant diseases (Gonnelli et al., 2024) and almost half of those with heart failure (Morales-Rull et al., 2018). Thus, PE was a relatively common condition with the annual incidence of 350 per 100,000 in US and, with the increase in the world population and aging in developed countries, its incidence is expected to increase (Piggott et al., 2023; Bodtger and Hallifax, 2020). Therefore, understanding all the phenomena associated with PE and with pleural fluid withdrawal is crucial. While patient-based research remains the primary means to expand knowledge, development of computer modeling can make the use of virtual patients an important supplementary approach.

The direct impact of PE on ventilation is associated with an increase in pleural pressure (P_pl). PE exerts pressure on the surrounding structures, i.e., the lungs, hemidiaphragm, mediastinum and rib cage (Karkhanis and Joshi, 2012). This results in lung compression with the collapse of ipsilateral lung dependent regions, leading to a decrease in the gas exchange surface area and deformation of other structures. If PE is large, deformation of the ipsilateral hemidiaphragm can be so significant that this hemidiaphragm may become flattened without any meaningful movement during breathing or even inverted with a paradoxical excursion.

Expansion of the rib cage and deformation of the ipsilateral hemidiaphragm contribute to decreased efficiency of inspiratory muscles hindering ventilation (DeBiasi and Feller-Kopman, 2019). Additionally, paradoxical excursion of the inverted hemidiaphragm might result in “pendulum breathing” (Mulvey, 1965). It may be expected that the above and a decrease in gas exchange surface lead to deterioration of blood oxygenation (Thomas et al., 2020). Elevated P_pl also exerts pressure on systemic and pulmonary vessels, leading to impaired blood flow (Stecka et al., 2018). Therefore, arterial blood oxygenation is expected to decrease in such patients, particularly in those with large PE, and therapeutic thoracentesis (TT) is expected to significantly increase this oxygenation. However, Taylor et al. reported no statistically significant changes in saturation (Taylor et al., 2021). Zielińska-Krawczyk et al. showed that the partial pressure of oxygen in arterial blood (P_aO₂) was greater 1 h after TT than before TT but patients with very large PE exhibited the least pronounced increase (Zielińska-Krawczyk et al., 2022). Surprisingly, the median P_aO₂ before TT was slightly higher in patients with very large PE than in the other patients and the median P_aCO₂ was slightly lower (Zielińska-Krawczyk et al., 2022). Using a virtual (in silico) patient and data from living patients, Stecka et al. demonstrated that various changes in P_aO₂ levels, including both a decrease and an increase, are possible (Stecka et al., 2018).

Our medical-engineering team pursues both clinical and theoretical research to evaluate respiratory mechanics during large and very large PE, and its changes during TT. In particular: (a) we utilized changes in transcutaneous partial pressures of O₂ (P_tcO₂) and CO₂ (P_tcCO₂) to evaluate changes in P_aO₂ and P_aCO₂, (b) to evaluate whether the ipsilateral hemidiaphragm is functionally inverted, i.e., whether P_pl in the ipsilateral hemithorax increases during inspiration (which leads to “pendulum breathing”), we analyzed the shape and orientation of the P-V loop (where P is the P_pl measured in the ipsilateral hemithorax and V is the current volume of air inhaled to or exhaled from the whole respiratory system): if P at the end of inspiration is greater than at the end of expiration, the loop leans to the left and the ipsilateral hemidiaphragm is treated as functionally inverted.

On the other hand, a large part of our theoretical research bases on virtual experiments with the use of VirRespir (Zieliński et al., 2018), i.e., a versatile virtual cardiopulmonary patient being a set of models working together (Zieliński et al., 2022); however, the respiratory mechanics model was modified to enable simulation of pleural effusion and TT (Gólczewski et al., 2017; Stecka et al., 2018).

Based on seemingly contradictory results presented in the literature and the interesting cases from our database that are presented below, the following four key questions were formulated to be explained by computer simulations:

1. Why can the hemidiaphragm be not functionally inverted despite very large PE?

To our knowledge, this study is the first one that analyzes the P-V loop defined above, and, in general, it is one of few works that concern the use of computer modeling to find possible explanations of the phenomena, sometimes surprising, that were observed during TT in living patients, particularly in those with large PE. It should be stressed, however, that computer models enable investigators to formulate only sufficient conditions of the phenomena, which also concerns our study.

Knowledge of pleural space physiology is not complete (Hu et al., 2020). This is due in part to difficulties in measurement of key physiological parameters. In particular, studies of ipsilateral hemidiaphragm activity and its influence on airflows, P_AO₂ and P_ACO₂ in individual bronchi are impossible in living patients because measurements of these parameters are unfeasible. The same concerns analyses of mediastinum behaviour during TT. Therefore, experiments in silico seem to be the only way to gain understanding of pleural space physiology. To our knowledge, this study is the first one that presents simulations of diaphragm and mediastinum functions in large PE. As our virtual patient made it possible to observe factors inaccessible in the case of living patients, it enabled us to propose sufficient conditions for the interesting phenomena that are presented above.

Our simulations primarily enable insight into influence of the mediastinum on the breathing mechanics in large PE; the mediastinal compliance appeared as a key parameter. To our knowledge, this influence has not been discussed yet despite that a number of authors recognized and discussed mediastinal shift towards the contralateral hemithorax [e.g. (Muruganandan et al., 2020; Cho et al., 2022; Polski et al., 2023)] or even towards the ipsilateral hemithorax when PE is accompanied by bronchial obstruction leading to ipsilateral lung atelectasis (Khajotia, 2012).

First of all, the mediastinum can transmit or not the P_pl changes that are related to breathing, which depends on the value of its compliance. If the mediastinum is compliant then decrease of P_pl during inspiration in the contralateral hemithorax is transmitted to the ipsilateral hemithorax, which can balance paradoxical ipsilateral hemidiaphragm movement giving normal P-V loop (Figure 4A) despite that RTG or USG shows ipsilateral hemidiaphragm inversion. If, however, mediastinum is stiff, and thus it separates both hemithoraxes, then the ipsilateral hemidiaphragm may be both anatomically and functionally inverted, which is a worse case (Figure 4B). For example, two results (i.e., the P-V loop leaned to the right and the great P_pl amplitude before TT; Figure 1) suggest that the patient p7 has a high mediastinal compliance; therefore, although she had the greatest PE volume despite the smallest height, she reported less severe dyspnea before TT than most others (Table 1). As thoracic radiation therapy may lead to fibrosis also involving the mediastinum making it stiff (Lin et al., 2004; Zhao et al., 2017), we hypothesize that if a patient suffers from malignant PE and is treated with this therapy, he/she may be in a worse condition before TT than others.

Mediastinum compliance can also help explain other unresolved issues. For example, there is controversy about whether pleural manometry is useful to protect against complications caused by excessive P_pl fall during large-volume TT or not (Hassaballa et al., 2023; Lentz et al., 2019). On the other hand, Chopra et al. showed discrepancy in the detection of incomplete lung expansion between post-TT pleural manometry and radiographic examination (Chopra et al., 2020). In our opinion, these controversy and discrepancy would disappear if both P_pl and the P_pl amplitude were analyzed. In particular, the role of the mediastinum cannot be adequately assessed without such an analysis. Unfortunately, even if P_pl is monitored during TT by other authors, the P_pl amplitude seems to be completely absent in studies concerning problems related to PE and effects of TT [e.g. (Hu et al., 2020; Hassaballa et al., 2023)]. For example, if the mediastinum is very compliant, then even if the ipsilateral lung is not expanded completely, P_pl at FRC may not fall extensively because the contralateral lung takes the place of withdrawn pleural fluid. On the other hand, if the ipsilateral lung is not expanded completely, the total lung compliance is still decreased and thus the P_pl amplitude has to be greater to provide the required tidal volume. Figure 3 presents the P-V loops obtained for a patient with such a moderate fall of P_pl at FRC and the very great increase in the P_pl amplitude (TT was terminated in this patient just due to symptoms caused by this amplitude).

Simulations have suggested the following sequence explaining small influence of large PE on arterial blood gases. Before TT, almost all the blood flows through the ventilated (contralateral) lung with P_AO₂ higher than normal during inspiration due to the big value of the ratio VT/(FRC+VD) and lower than normal during expiration due to more intensive gas exchange in this lung. Consequently, before TT, the average P_aO₂ in mixed blood in the systemic arterial system may be either lower or higher or within the physiological range despite large PE. Additionally during and after TT the pulmonary shunt may be present or not. As these three phenomena have opposite influences on blood oxygenation, the final effect related to pleural fluid withdrawal depends on which phenomenon suppresses the others; hence, there is no uniform reaction to the withdrawal (Stecka et al., 2018; Taylor et al., 2021; Muruganandan et al., 2020).

Although the problem related to possible pendulum breathing in patients with hemidiaphragm inversion and its adverse influence on P_AO₂ and gas exchange in lungs was raised decades ago [e.g. (Mulvey, 1965)], it has not yet been finally resolved as neither airflows in bronchi nor partial pressures in particular regions of lung are observable in living patients. Therefore, only conjectural consideration has been possible [e.g. (Thomas et al., 2020)]. Our simulation showed that “pendulum breathing” may be present only at the end of inspiration and beginning of expiration. This is supported by the 8-shaped form of the P-V loop observed in both the virtual patient and living ones. And since the “pendulum breathing” may be present during only a part of inspiration, the mean P_AO₂ in the contralateral lung need not be low. Thus, in conclusion, whether pendulum breathing exists or not, large PE has an insignificant influence on blood gases.

Finally, note that the oxygenation did change significantly during TT in neither the virtual patient nor living ones, whereas dyspnea substantially decreased after TT (Table 1); therefore, we support opinion that factors other than arterial blood gases are mainly responsible for the dyspnea frequently experienced by patients with large PE (Muruganandan et al., 2020; Skaarup et al., 2020; Fjaellegaard et al., 2024). However, since dyspnea is a subjective symptom, it cannot be simulated by computer models. However, our work shows that computer simulations of objective physiological phenomena can be very helpful in both research and education (Tomalak et al., 2008; Zieliński et al., 2022).

Computer simulations offered a new insight into mechanisms of respiration in large PE. It enabled to propose possible explanations of such interesting observations related to TT as the slight change in blood oxygenation in patients with large PE compared with patients with less severe PE, the necessity of hyperactivity of the contralateral hemidiaphragm, the peculiar 8-shaped form of the P-V loop, and insignificant influence of ‘pendulum breathing’ on arterial gas tensions in patients with hemidiaphragm inversion.