A virtual patient in interpretation of massive pleural effusion impact on hemidiaphragm work and an insignificant influence on blood oxygenation

A virtual patient in interpretation of massive pleural effusion impact on hemidiaphragm work and an insignificant influence on blood oxygenation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A virtual patient in interpretation of massive pleural effusion impact on hemidiaphragm work and an insignificant influence on blood oxygenation Anna Małgorzata Stecka, Elżbieta Magdalena Grabczak, Marcin Michnikowski, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3873696/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 09 Apr, 2025 Read the published version in Frontiers in Physiology → Version 1 posted You are reading this latest preprint version Abstract Computer modeling, particularly in the form of virtual patients, can be a useful tool for explaining complex phenomena associated with medical procedures. Based on interesting phenomena observed in 8 living patients undergoing large-volume therapeutic thoracentesis (TT) with pleural pressure (Ppl), transcutaneous oxygen and carbon dioxide pressures, and spirometric measurements, we formulated four questions regarding the impact of pleural effusion (PE) and TT on hemidiaphragm function and blood oxygenation. To answer these questions, we simulated right-sided PE in a virtual patient and studied changes in Ppl and lung volume during the respiratory cycle (exemplified by P-V loops, where P is Ppl in the ipsilateral hemithorax and V is the volume of both lungs), alveolar O2 (PAO2) and CO2 partial pressures and airflows in the main bronchi. The simulations suggest that: (a) the mediastinum compliance has a particular meaning for the work of both hemidiaphragms and explaining the 8-shape of P-V loops in hemidiaphragm inversion; (b) PAO2 is higher than normal before TT due to decreased ratio of the tidal volume to the volume of processed air at the end of expiration; and (c) in some patients, the Ppl amplitude related to breathing can be significantly greater before TT than later on. Physical sciences/Engineering/Biomedical engineering Biological sciences/Computational biology and bioinformatics/Computational models Biological sciences/Physiology/Respiration Health sciences/Signs and symptoms/Respiratory signs and symptoms Health sciences/Medical research/Translational research Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction 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 15% of all patients with malignant diseases 1 and almost half of those with heart failure 2 . Thus, PE is a relatively common condition with a rough incidence of 322 per 100000 3,4 . Moreover, with the increase in the world population and aging in developed countries, its incidence is expected to increase. 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, the increasing significance of computer modeling makes the use of virtual patients an important supplementary approach (e.g., 5 , 6 ) 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 7 , 8 . 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 9 . Additionally, paradoxical excursion of the inverted hemidiaphragm might result in pendulum breathing 10 . It may be expected that the above and decreased gas exchange surface lead to deterioration of blood oxygenation 11 , 12 . Elevated P pl also exerts pressure on systemic and pulmonary vessels, leading to impaired blood flow 13 . Therefore, arterial blood oxygenation is expected to decrease in such patients, particularly in those with massive PE, and therapeutic thoracentesis (TT) is expected to significantly increase this oxygenation. However, studies evaluating changes in blood gases associated with TT have shown contradictory results. Wang et al. observed a significant improvement in oxygenation after TT 14 , while Taylor et al. reported no statistically significant changes in saturation 15 . Zielińska-Krawczyk et al. showed that the partial pressure of oxygen in arterial blood (P a O 2 ) was greater 1 hour after TT than before TT, but it decreased nearly to the level before TT after 24 hours 16 . Surprisingly, patients with very large PE exhibited the least pronounced increase in P a O 2 after TT. Using a virtual (in silico) patient and data from living patients, Stecka et al. demonstrated that various changes in P a O 2 levels, including both a decrease and an increase, are possible 6 . The primary aim of this study was to use the abovementioned virtual patient to answer the following fundamental questions: when and why large-volume PE need not lead to hemidiaphragm inversion; why massive PE, whether with hemidiaphragm inversion or not, need not be related to a significant decrease in P a O 2 . To our knowledge, this study is one of few that concerns the use of computer modeling in interpretations and explanations of the phenomena, sometimes surprising, that were observed during TT in living patients with massive PE. Study design In the way previously described 5 , 6 , a general-purpose virtual patient was used to explain the variety of ipsilateral hemidiaphragm work and blood gas changes that were observed during TT in living patients with massive pleural effusion who participated in our previous clinical study. The ipsilateral hemidiaphragm work was characterized by P-V loops, 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. A functionally inverted hemidiaphragm is present if the P value for the maximal V (the end of inspiration) is greater than the P value for V = 0 (the inspiration beginning), i.e., if the P-V loop leans to the left (e.g., as the loop 1 for p1 in Fig. 1 ). Simulations performed for deviations of virtual patient parameters from their default values were used to establish (a) parameters crucial for the loop orientation, and (b) airflows in the main bronchi, including the possibility of pendulum breathing. The results of these simulations and those concerning changes in pulmonary blood flow during TT presented elsewhere 6 were subsequently used to explain changes in arterial blood gases during this procedure. Virtual Patient Presentation of models Our virtual patient serves as a versatile tool capable of simulating a broad spectrum of physiological and pathophysiological phenomena associated with ventilation, gas exchange, gas transport, and pulmonary circulation 17 , 18 . Its intricacies and instances of its application in diverse investigations have been extensively outlined in prior works 5 , 6 , 17 , 19 . In essence, the VP comprises models of respiratory system mechanics, pulmonary circulation, gas transfer in bronchi, gas exchange in the lungs and blood gas transport. Additionally, there is a possibility to connect external systemic circulation models of various complexities 6 , 17 , 18 . The models collaborate by exchanging calculated variable values, enabling interaction between them. For instance, the gas transfer model utilizes airflow data from respiratory system mechanics and gas exchange models, while the blood transport model incorporates blood flow data from the pulmonary circulation model 20 . The default values of the respiratory system model parameters were calibrated to match those of an average 50-year-old Polish woman, as per the Polish reference values 21 . Parameters in other models were set to correspond to the average adult. In the standard version of the virtual patient, each lung lobe is subdivided into 16 segments characterized by their volumes and the coordinates of their mass centers in the coordinate system with the origin at the pulmonary trunk 18 . This subdivision enables the investigation of ventilation-perfusion mismatches in different positions, such as supine, standing or lateral. This division is applied uniformly across all models, including both respiratory system mechanics and pulmonary circulation models. However, in PE simulations, another division had to be carried out. The hydrostatic pressure exerted by pleural fluid, which modifies local P pl , is crucial, e.g., it influences local airflow and causes the collapse of those lungs parts for which the alveolar pressure is lower than the surrounding local P pl . Therefore, the division of lungs into multiple horizontal layers was necessary since, in the sitting position, hydrostatic pressure progressively increases vertically from the apex to the diaphragm. Initial simulations showed that using more than 100 layers did not significantly alter the simulation outcomes; hence, 100 layers were deemed appropriate. The model of respiratory system mechanics consists of compartments related to the mouth and trachea, main bronchi, viscoelastic rib cage, elastic mediastinum, two compliant hemidiaphragms, viscoelastic abdomen, and compliance of dead space (separately for each lung) and, for each layer, viscoelastic parenchyma, compliance of the alveolar space (gas compressibility), collapsible bronchi of the middle orders, smallest bronchi and ducts 5 . For mathematical descriptions of the compartments that are crucial in this study, please refer to the Appendix. Simulation Procedures We replicated a scenario of right-sided PE. The simulations primarily focused on monitoring P pl and lung volume changes during the respiratory cycle, exemplified by the P-V loops. Additionally, we observed alveolar O 2 and CO 2 partial pressures as well as airflow in the main bronchi. To elucidate the variations in observed P-V loops in living patients, we examined the impact of mediastinal, rib cage and diaphragmatic compliances. The model coefficient related to one of these factors was initially reduced from its default value in the first series of simulations and then increased in the second series. A pleural fluid volume of only 3 liters was simulated, allowing for the maintenance of a small upper part of the ipsilateral lung to analyze possible pendulum breathing. Interpreted materials Presentation of cases A database was created within the framework of a previously conducted project related to TT. The protocol of that project, approved by the Institutional Review Board (KB 105/2012), was registered at ClinicalTrials.gov (NCT02192138). The project complied with the standards set out in the Declaration of Helsinki. Medical procedures were conducted with the participation of patients hospitalized in the Department of Internal Medicine, Pulmonary Diseases and Allergy. Patients signed an informed consent to participate in the study beforehand. Simulations were performed to explain the results obtained for all patients from this database with the functionally inverted hemidiaphragm (patients p1, p2 and p8 in Fig. 1 ). For comparison, three patients with the greatest volume of withdrawn pleural fluid but the P-V loops leaned to the right were also included (patients p5, p6 and p7 in Fig. 1 ). Additionally, all patients with a vertical P-V loop were included (patients p3 and p4 in Fig. 1 ). Table 1 presents the characteristics of these patients. Table 1 Characteristics of living patients. Patient Sex Age [yrs] Side of PE Dyspnea before TT (Borg scale) Dyspnea after TT (Borg scale) V wpf [L] p1 M 52 R 7 3 4.83 I p2 M 57 L 9 1 4.80 I p3 M 58 L 2 2 4.25 F p4 M 82 R 8 4 3.78 F p5 M 77 R 7 3 4.65 N p6 M 91 R NA NA 4.00 N p7 F 82 R 4 0 4.94 N p8 F 73 L NA NA 2.70 I M/F – Male/Female; R/L – the right/left side of pleural effusion (PE); V wpf – the total volume of withdrawn pleural fluid; I/F/N – functionally inverted/flattened/normal ipsilateral hemidiaphragm (based on P-V loops); in the case of p8, TT had to be stopped prematurely due to symptoms (hence, a smaller V wpf ). Management The TT procedure under the control of P pl measurements was performed as described elsewhere 16 , 22 . Briefly, P pl was measured intermittently after removal of defined fluid portions (200 mL up to 1 liter and then 100 mL) while the patient was in the sitting position. The following parameters were recorded: Instantaneous P pl (digital pleural manometer, IBBE PAS, Warsaw, Poland 23 ); Airflow at the level of the mouth (modified spirometer, LungTest 1000, MES, Cracow, Poland); Transcutaneous partial pressures of O 2 (P tc O 2 ) and CO 2 (P tc CO 2 ) (TCM4™ monitoring system, Radiometer, Copenhagen, Denmark) – due to technical problems, these parameters were not measured in the patient p8; Heart rate (HR), systolic and diastolic blood pressure (SBP and DBP, respectively) (IGEL ICARD M, IGEL, Gliwice, Poland). The instantaneous P pl and airflow were recorded at 1-minute intervals between the aspiration of the subsequent pleural fluid portions using the sampling frequency equal to 25 Hz. All signals were synchronized and recorded using Toracemon software (IBBE PAS, Warsaw, Poland). Airflow integration provides the volume of inhaled/exhaled air used for P-V loop creation. Dyspnea was assessed by the 10-point modified Borg scale immediately before and after termination of TT. Minute ventilation (V E ) was calculated as V⋅RR, where RR is the respiratory rate. Because the stroke volume was not accessible, changes in cardiac output were assessed by changes in the index ∼CO=(SBP−DBP)⋅HR. Data for interpretation The tendencies of changes in P tc O 2 , P tc CO 2 , V E and ∼CO in real patients are presented in Figs. 2 a-d. The tendency was characterized quantitatively by means of the slope of the linear regression line (red lines in Fig. 2 ). In massive PE, withdrawal up to approximately 1.9 L seems to have a different impact on respiratory system work than further withdrawal; e.g., the P-V loop in patients with the functionally inverted hemidiaphragm starts to lean to the right (p1, p2 and p8 in Fig. 1 ), and the amplitude of breathing-related P pl changes usually starts to grow steadily after withdrawal of 1.9 L, whereas earlier, it changes in a more diverse way (Fig. 2 e). Therefore, the slope was calculated separately for volumes < 1.9 L (the first TT stage) and for greater volumes (the second stage). Table 2 Tendencies for changes in selected parameters during TT. P tc O 2 P tc CO 2 V E ~ CO Slope [kPa/min] ([mmHg/min]) Slope [kPa/min] ([mmHg/min]) Slope [L/min 2 ] Slope [kPa/min 2 ] ([mmHg/min 2 ]) I II I II I II I II p1 0.006 (0.045) 0.006 (0.045) 0.000 (0.000) 0.000 (0.000) -0.0480 -0.0120 3.67 (27.5) -3.77 (-28.3) p2 -0.006 (-0.045) -0.024 (-0.180) 0.012 (0.090) 0.006 (0.045) -0.1380 -0.0480 -3.87 (29.0) -1.13 (-8.5) p3 0.006 (0.045) -0.006 (-0.045) 0.000 (0.000) -0.012 (-0.090) 0.1560 0.0000 0.84 (6.3) -1.29 (-9.7) p4 -0.036 (-0.270) 0.000 (0.000) 0.006 (0.045) 0.000 (0.000) -0.0180 -0.0420 -6.42 (-48.2) -1.05 (7.9) p5 -0.024 (-0.180) -0.012 (-0.090) 0.006 (0.045) -0.006 (-0.045) 0.0240 0.0120 0.51 (3.8) -0.46 (-3.4) p6 -0.012 (-0.090) 0.006 (0.045) 0.006 (0.045) 0.012 (0.090) 0.1440 0.0060 -0.85 (-6.4) -2.83 (-21.8) p7 -0.030 (-0.225) 0.006 (0.045) 0.000 (0.000) 0.018 (0.135) -0.0240 -0.0300 -0.90 (-6.8) 0.37 (2.7) p1 … p7 – living patients from Table 1 . Slope – the slope of the linear regression of a parameter on time. I - the first stage of TT: fluid withdrawal up to 1.9 L; II - the second stage; P tc O2 - transcutaneous oxygen pressure; P tc CO2 - transcutaneous carbon dioxide pressure; V E – minute ventilation; ~CO – estimation of cardiac output changes with changes in the pulse pressure and heart rate product. There was no uniform trend in P tc O 2 changes during TT (Fig. 2 a, Table 2 ), and different patterns were observed, i.e., slight increase (p1), decrease (p2) and biphasic alteration (p3). P tc CO 2 demonstrated overall greater stability and its variations were also not uniform (Fig. 2 b, Table 2 ). Table 3 Spearman correlations between slopes shown in Table 2 . V E (I) ∼CO (I) V E (II) ∼CO (II) P tc O 2 (I) 0.02 0.74 P tc CO 2 (I) -0.23 -0.62 P tc O 2 (II) 0.15 -0.26 P tc CO 2 (II) -0.36 0.18 (I) and (II) – slopes for the first and second stages of TT, respectively. Neither the changes in P tc CO 2 nor in P tc O 2 could be attributed to variations in V E, as indicated by the negligible correlation of V E with P tc O 2 and the weak correlation with P tc CO 2 (Table 3 ). The slopes of P tc O 2 and P tc CO 2 exhibited significant correlations only with ∼CO during the first stage of TT (Table 3 ). However, it is important to note that this observation may be an artifact, as the ∼CO decrease during this stage is mainly related to the arterial pressure decrease (perhaps due to the alleviation of the initial patient’s stress), which might have an impact on transcutaneous measurements: the arterial pressure rise increases the arterial component and decreases the venous component in microcirculation (hence, the positive correlation for P tc O 2 and the negative correlation for P tc CO 2 ). All P-V loops for the functionally inverted hemidiaphragm were 8-shaped (p1, p2 and p8 before TT, as shown in Fig. 1 ), and the P pl amplitude rapidly decreased in the first stage in some patients (p1, p2 and p7 in Fig. 2 e); these observations are other intriguing findings. Due to the small number of cases, conducting a reliable statistical analysis was not feasible. Nevertheless, four key issues were formulated to be explained by simulations: Why can the hemidiaphragm work normally despite massive PE? Why are some P-V loops 8-shaped? Why is there no significant and uniform impact on blood oxygenation during pleural fluid withdrawal, despite the notable disturbance in breathing mechanics caused by massive PE, particularly in patients with functionally inverted hemidiaphragms? Why may the P pl amplitude decrease with pleural fluid withdrawal in massive PE since it usually increases in the majority of patients 22 ? Results and discussion The First Question (hemidiaphragm inversion) As simulations have suggested, the rib cage and abdomen compliances are important for addressing this issue. In particular, a stiffer abdomen may protect the ipsilateral hemidiaphragm against significant deformation. However, simulations have shown that the impact of the mediastinum compliance seems to be most significant and much more intriguing. Figure 3 shows examples of the P-V loops from simulations with mediastinum compliance higher (a) and lower (b) than the default value. If this compliance is high, massive PE deforms the mediastinum more than the ipsilateral hemidiaphragm; consequently, this hemidiaphragm may not be inverted, and the P-V loop may lean to the right. If the ipsilateral hemidiaphragm is physically inverted (e.g., the inversion is evident in USG or RTG examination), despite the high mediastinum compliance, it need not be functionally inverted in the sense defined above; i.e., the P-V loop can lean to the right (Fig. 3 a shows such a case) because the contralateral hemidiaphragm affects also the ipsilateral lung through the compliant mediastinum. It might be enhanced in patients with contralateral hemidiaphragm hyperactivity 24 . The Second Question (8-shaped P-V loops) To our knowledge, 8-shaped P-V loops have not yet been noted or discussed in the literature. Simulations have suggested the following sequence can explain this shape in patients with a less compliant mediastinum, i.e., with the functionally inverted hemidiaphragm. 1. The inspiration beginning: Before inspiration begins, the contralateral hemidiaphragm, stretched by the negative P pl in the contralateral hemithorax, is longer than the ipsilateral hemidiaphragm (supported by abdominal organs). Therefore, according to the force‒length relationship of the muscles, initial diaphragm contraction means mainly contraction of the contralateral hemidiaphragm. A decrease in the P pl in the contralateral hemithorax propagates through the mediastinum to the ipsilateral hemithorax. Additionally, the activity of rib cage muscles decreases P pl in both hemithoraxes. The above causes: (a) flow of fresh air into both lungs (Fig. 4 a and the light green part in Fig. 5 a) like in case of not inverted hemidiaphragm (the light green part in Fig. 5 c), (b) the part of the P-V loop that is directed to the right, i.e., to the smaller P (the light green line in Fig. 4 e). 2. The second inspiration phase: Further diaphragm contraction causes upwards movement of the inverted ipsilateral hemidiaphragm, and this activity predominates over the influence of the contralateral hemidiaphragm that is propagated through the mediastinum. This increases P pl and, consequently: (a) processed air flows out from the ipsilateral lung and mixes with fresh air still flowing into the contralateral lung (Fig. 4 b and the dark green line in Fig. 5 a) unlike the case of not inverted hemidiaphragm (the light green part in Fig. 5 c), (b) the second part of the P-V loop is directed to the left, i.e., to the greater P (the dark green line in Fig. 4 e). 3. The beginning of expiration: The inverted hemidiaphragm starts to relax, i.e., it moves down, which decreases P pl . This causes that: (a) processed air exhaled from the contralateral lung flows into the ipsilateral lung (Fig. 4 c and the light red line in Fig. 5 a), (b) P decreases with decreasing V (the light red line in Fig. 4 e). 4. The second expiration phase: The influence of the inverted hemidiaphragm is insignificant in comparison with the influence of the contralateral hemidiaphragm; thus, the airflows in both lungs are similar, which gives: (a) exhalation of processed air from both lungs (Fig. 4 d and the dark red line in Fig. 5 a), (b) P increases with decreasing V (the dark red line in Fig. 4 e). The above subpoints 2a and 3a suggest that pendulum breathing may be present, if a part of the ipsilateral lung is not collapsed, whereas subpoints 1a and 4a show that there are two subperiods when pendulum breathing is not present. Since pendulum breathing may be present during only a part of inspiration, the mean P A O 2 in the contralateral lung can be almost normal. Thus, although pendulum breathing can occur in massive PE, it has an insignificant influence on blood gases. The above four subpoints 1b-4b explain the 8-shaped loops. Note also that although the ipsilateral hemidiaphragms of patients p3 and p4 were initially assumed to not be inverted, the 8-shaped P-V loops also suggested that in these patients, the hemidiaphragm was slightly inverted since the 8-shaped space requires points 2 and 3. The Third Question (blood gases) It could be expected that massive PE, which significantly disturbs ventilation, should worsen blood oxygenation, and consequently, pleural fluid withdrawal should be associated with significant improvement in blood oxygenation. This improvement, however, was not observed in living patients (Fig. 2 ). As the virtual patient is fully observable, the three following phenomena could be identified, which enabled us to answer this question. First, increased P pl in the ipsilateral hemithorax significantly suppresses blood flow (e.g., see corresponding simulations presented elsewhere 6 ); thus, almost all the blood flows through the ventilated contralateral lung. As pleural fluid is withdrawn, P pl in the ipsilateral hemithorax decreases, and blood also flows through the ipsilateral lung regardless of whether the collapsed lung parts are recruited and ventilated. Second, before TT the majority of blood flows through the contralateral lung, and therefore the rate of gas exchange in the alveoli of this lung is greater, which causes P A O 2 during expiration to be lower than normal. As pleural fluid is withdrawn, blood starts to flow through the ipsilateral lung, and this lung may also participate in gas exchange to an increasing extent; consequently, P A O 2 may not fall as much as during expiration. Third, fresh air is mixed during inspiration with the processed air that remains in the lungs and bronchi after preceding expiration, and the volume of this processed air is equal to the sum of the functional residual capacity (FRC) and anatomical dead space (V D ). The V T /(FRC + V D ) ratio, were V T is the tidal volume, determines the composition of the mixture of fresh and processed air (i.e., P A O 2 and P A CO 2 ) during inspiration; for example, a typical P A O 2 value is lower by approximately 8 kPa (60 mmHg) than the partial pressure of O 2 in atmospheric air. If the ipsilateral lung is collapsed, this ratio may even be two times greater because FRC + V D concerns only the contralateral lung; hence, the mean P A O 2 in this lung can be higher than normal, and P A CO 2 can be lower (Figs. 5 b and d). As pleural fluid is withdrawn, the ratio may decrease due to the requirement of collapsed parts of the ipsilateral lung; consequently, P A O 2 during inspiration also decreases. This may explain the intriguing observation that blood oxygenation changes the least after TT in patients with large PE 22 . Before TT, almost all the blood flows through the ventilated lung with P A O 2 during inspiration, which is higher than normal due to the big V T /(FRC + V D ) but P A O 2 may be lower than normal during expiration due to more intensive gas exchange. Consequently, the average P a O 2 in mixed blood in the systemic arterial system may be within the physiological range despite massive PE. These three phenomena have opposite influences on blood oxygenation, and the final effect related to pleural fluid withdrawal depends on which phenomenon suppresses the others; hence, there is no uniform reaction to the withdrawal. The Fourth Question (unusual P pl amplitude decrease) In all the cases analyzed by Zielińska et al., the P pl amplitude increased with pleural fluid withdrawal at the beginning of TT 22 , which is understandable from a physical point of view 5 . However, in some of the cases presented in Fig. 2 e, the amplitude initially decreases. This decrease may be easily explained, even without simulations, in patients with the functionally inverted hemidiaphragm. Indeed, during TT, the P-V loop in such patients leans to the left, then becomes vertical and, finally, leans to the right (p1 and p2 in Fig. 1 ). Since the P pl variations are smallest when the loop is vertical, the P pl amplitude is initially higher, then decreases according to the loop rotation, and finally increases. However, the decrease in the P pl amplitude in patient p7, who had a normally working hemidiaphragm, was surprising. The simulations suggested the following explanation. Since massive PE leads to the collapse of the whole or a significant part of the lung, the total lung compliance decreases because a smaller part of the lungs is involved in ventilation. Additionally, the same V T requires a greater expansion of the contralateral lung to the volume of smaller lung compliance due to its nonlinearity (e.g., see the Appendix for the mathematical equation that describes this nonlinearity). As a consequence, the amplitude of breathing-related P pl changes in the contralateral hemithorax must be much greater than normal to preserve the required V T . Thus, compensatory hyperactivity of this hemidiaphragm can be observed 24 . In addition, if the mediastinum is very compliant, then these large changes may propagate to the ipsilateral hemithorax, leading to the P-V loop that is leaned to the right but with great P pl variation. When the total compliance increases due to the recruitment of a collapsed lung part caused by pleural fluid withdrawal, the amplitude decreases. Note that the P pl amplitude did not change in the second stage of TT (Fig. 2 e), which additionally confirms the recruitment. Study limitations The main limitation is related to the lack of information about actual arterial blood gas data during TT in living patients. Such data could be obtained using only ethically unjustified invasive methods; therefore, we decided to analyze P tc O 2 and P tc CO 2 recorded throughout the whole procedure. Although transcutaneous measurement is a well-known technique for monitoring blood gases, some previous studies have not confirmed the significant correlation between P tc O 2 and P a O 2 measured in different subjects 25 . Therefore, although monitoring the trend of P tc O 2 can be useful, it should not be regarded as a perfect substitute for P a O 2 . Although this would be a significant obstacle in comparisons of results between different patients, the assumption that relative changes in P tc O 2 and P tc CO 2 imitate relative changes in P a O 2 and P a CO 2 in a particular patient seems to be reasonable if the influence of the arterial pressure is taken into account. Another limitation concerns the lack of direct measurements of CO. Instead, we had to rely on estimations based on SBP, DBP, and HR. This estimation could be disturbed by reactions to stress at the beginning of TT, which is an invasive procedure that is additionally supplemented by the connection of the patient to several measuring devices. The lack of a more precise representation of components in the virtual patient’s abdomen is a very important limitation. In particular, the liver as such is not modeled, whereas it supports the right hemidiaphragm, which is postulated to be the reason for the less frequent inversion of the right hemidiaphragm 10 , 26 , which is also our case (Table 1 ). The influence of the liver was simulated indirectly only as a decrease in the abdominal compliance. Nevertheless, our simulations seem to be reliable since the P-V loops from the simulations match well with the loops observed in patients, particularly those with the 8-shaped loop. On the other hand, by relying on these simulations, we were able to explain why TT changes blood oxygenation the least in massive PE. We also hypothesized that factors other than arterial blood gases are mainly responsible for the dyspnea frequently experienced by patients with massive PE since the oxygenation did not change significantly, whereas dyspnea substantially decreased after TT (Table 1 ). Conclusion Computer modeling, particularly in the form of virtual patients, can be a useful tool for explaining complex physiological and pathophysiological phenomena associated with medical procedures. It enabled to explain several interesting observations related to TT, such as the slight change in blood oxygenation in patients with massive PE compared with patients with less severe PE, the necessity of hyperactivity of the contralateral hemidiaphragm or the peculiar 8-shaped form of the P-V loop in patients with functional hemidiaphragm inversion. Declarations Acknowledgments: The authors thank Piotr Korczyński, PhD, MD, and Krzysztof Zieliński, PhD, Eng., for their assistance during therapeutic thoracentesis. This study was supported by the National Science Center, Poland (grant N 2019/35/B/NZ5/02531). Authors’ contributions: TG and AMS conceived and designed the study. TG and MM developed the measuring system and wrote computer programs. RK, EMG, MM, MZK, and AMS collected the clinical data. AMS and TG analyzed and interpreted the data, performed the simulations and drafted the manuscript. RK and EMG revised and critically reviewed the manuscript for important intellectual content. All the authors provided their approval on the final version. Data availability: Data are available from the corresponding author upon reasonable request. Competing interests: All the authors declare that they have no competing interests. References Management of malignant pleural effusions. Am. J. Respir. Crit. Care Med . 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Care Med. 156, 1205–1209 (1997). Wang, J. S. & Tseng, C. H. Changes in pulmonary mechanics and gas exchange after thoracentesis on patients with inversion of a hemidiaphragm secondary to large pleural effusion. Chest 107 (6) , 1610–1614 (1995). Taylor, T. M. et al. The impact of thoracentesis on postprocedure pulse oximetry. J. Bronchol. Interv. Pulmonol. 28 (3) , 192–200 (2021). Zielińska-Krawczyk, M. et al. Impact of therapeutic thoracentesis and pleural pressure changes on breathing pattern, dyspnea, lung function and arterial blood gases. Pol Arch Intern Med. 132(4), (2022). Zieliński, K., Stecka, A. & Gólczewski, T. VirRespir—an application for virtual pneumonological experimentation and clinical training. IFMBE Proceedings 697–701 (2018). VirRespir - user manual. Available at: https://virrespir.ibib.waw.pl/Docs/VirRespirUserManual.pdf. (Accessed: 16th January 2024) Gólczewski, T. & Darowski, M. Virtual respiratory system for education and research: Simulation of expiratory flow limitation for spirometry. Int. J. Artif. Organs. 29 (10) , 961–972 (2006). Gólczewski, T. Virtual respiratory system in research and education - principles and applications. IBBE PAS Works No. 74, Warsaw (2010). Lubiński, W. & Gólczewski, T. Physiologically interpretable prediction equations for spirometric indexes. J. Appl. Physiol. 108 (5) , 1440–1446 (2010). Zielińska-Krawczyk, M. et al. Patterns of pleural pressure amplitude and respiratory rate changes during therapeutic thoracentesis. BMC Pulm. Med. 18 (1) , (2018). Krenke, R. et al. Development of an electronic manometer for Intrapleural Pressure Monitoring. Respiration 82 (4) , 377–385 (2011). Fitzgerald, D. B., Muruganandan, S., Peddle‐McIntyre, C. J., Lee, Y. C. & Singh, B. Ipsilateral and contralateral hemidiaphragm dynamics in symptomatic pleural effusion: The 2nd pleural effusion and symptom evaluation (please‐2) study. Respirology 27 (10) , 882–889 (2022). Górska, K., Korczyński, P., Maskey-Warzęchowska, M., Chazan, R. & Krenke, R. Variability of transcutaneous oxygen and carbon dioxide pressure measurements associated with sensor location. Adv. Exp. Med. Biol. 39–46 (2015). Nason, L. K. et al. Imaging of the diaphragm: Anatomy and function. Radiographics 32 (2) , (2012). De Groote, A. et al. Ventilation asymmetry after transplantation for emphysema. Am. J. Respir. Crit. Care Med. 170 (11) , 1233–1238 (2004). Additional Declarations No competing interests reported. Supplementary Files Appendix.pdf Cite Share Download PDF Status: Published Journal Publication published 09 Apr, 2025 Read the published version in Frontiers in Physiology → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3873696","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":268995010,"identity":"69cd09da-034e-49d0-800a-155a48edbf83","order_by":0,"name":"Anna Małgorzata Stecka","email":"","orcid":"","institution":"Institute of Biocybernetics and Biomedical Engineering","correspondingAuthor":false,"prefix":"","firstName":"Anna","middleName":"Małgorzata","lastName":"Stecka","suffix":""},{"id":268995011,"identity":"28321f0a-e035-477b-bca4-8bb016622c24","order_by":1,"name":"Elżbieta Magdalena Grabczak","email":"","orcid":"","institution":"Medical University of Warsaw","correspondingAuthor":false,"prefix":"","firstName":"Elżbieta","middleName":"Magdalena","lastName":"Grabczak","suffix":""},{"id":268995012,"identity":"16284949-c1cf-4f60-aa3c-352bd2b9f767","order_by":2,"name":"Marcin Michnikowski","email":"","orcid":"","institution":"Institute of Biocybernetics and Biomedical Engineering","correspondingAuthor":false,"prefix":"","firstName":"Marcin","middleName":"","lastName":"Michnikowski","suffix":""},{"id":268995013,"identity":"456c1c91-7b85-4f6d-816b-251e1ba26981","order_by":3,"name":"Monika Zielińska-Krawczyk","email":"","orcid":"","institution":"Medical University of Warsaw","correspondingAuthor":false,"prefix":"","firstName":"Monika","middleName":"","lastName":"Zielińska-Krawczyk","suffix":""},{"id":268995014,"identity":"9f1bd91b-0593-481d-ab3f-cc480fb27148","order_by":4,"name":"Rafał Krenke","email":"","orcid":"","institution":"Medical University of Warsaw","correspondingAuthor":false,"prefix":"","firstName":"Rafał","middleName":"","lastName":"Krenke","suffix":""},{"id":268995015,"identity":"5c034eff-a8fb-4cf0-9518-9c24ced151b3","order_by":5,"name":"Tomasz Gólczewski","email":"data:image/png;base64,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","orcid":"","institution":"Institute of Biocybernetics and Biomedical Engineering","correspondingAuthor":true,"prefix":"","firstName":"Tomasz","middleName":"","lastName":"Gólczewski","suffix":""}],"badges":[],"createdAt":"2024-01-17 19:59:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3873696/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3873696/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.3389/fphys.2025.1539781","type":"published","date":"2025-04-10T00:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":50172809,"identity":"9dcbc90f-839e-4ba0-a5e8-c0f41cbd2a40","added_by":"auto","created_at":"2024-01-25 15:58:24","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1199504,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe P-V loops: living patients.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eP – the pleural pressure in the ipsilateral hemithorax, V – the change in the total lung volume during inspiration (green) and expiration (red). 1,2 and 3 - the loops from measurements before pleural fluid withdrawal, after a withdrawal of approximately 1.9 L and after withdrawal of approximately 3.8 L, respectively. p1 … p8 – living patients from Table 1.\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-3873696/v1/b4cb7b849cf32465fb397e42.png"},{"id":50174141,"identity":"cb1d68d8-4e06-43cb-8b02-a2a9cc522d09","added_by":"auto","created_at":"2024-01-25 16:06:24","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1043024,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eChanges in selected parameters during therapeutic thoracentesis in living patients.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eP\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e - transcutaneous oxygen pressure, P\u003csub\u003etc\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e - transcutaneous carbon dioxide pressure, V\u003csub\u003eE\u003c/sub\u003e – minute ventilation, \u003csub\u003e~\u003c/sub\u003eCO – the product of heart rate and pulse pressure (an estimation of cardiac output), P\u003csub\u003epl_ampl\u003c/sub\u003e – the median value of the pleural pressure amplitude form intervals recorded between aspiration of subsequent pleural fluid portions; red lines - linear regression of a parameter on time (a, b, c, d) or volume (e) calculated for the first and the second stages of therapeutic thoracentesis, respectively. p1 … p7 – living patients from Table 1 (P\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e and P\u003csub\u003etc\u003c/sub\u003eCO\u003csub\u003e2 \u003c/sub\u003ewere not measured in the patient p8 due to technical problems).\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-3873696/v1/14402c7e3638cbd474abe36d.png"},{"id":50172811,"identity":"bcd3ce50-e944-4520-b4c0-878b63a9e912","added_by":"auto","created_at":"2024-01-25 15:58:24","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":533375,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExamples of simulated P-V loops\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eP – the pleural pressure in the ipsilateral hemithorax, V – the change in the total lung volume during inspiration (green) and expiration (red).\u003c/p\u003e","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-3873696/v1/48d4e4bdb0e847a8b63602b3.png"},{"id":50174142,"identity":"59505b81-4e81-400f-9bc2-e37f0c7cef7e","added_by":"auto","created_at":"2024-01-25 16:06:24","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":3054368,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExplanation of the 8-shaped P-V loop\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea-d\u003c/strong\u003e - an illustration of hemidiaphragms, rib cage and mediastinum movements and flows in main bronchi during (a) the inspiration beginning, (b) the second inspiration phase, (c) the expiration beginning, and (d) the second expiration phase (green/red arrows – fresh/processed air; black arrows – movement of the structures; P¯/P­ – decrease/increase in P\u003csub\u003epl\u003c/sub\u003e and corresponding change in P\u003csub\u003eA\u003c/sub\u003e); \u003cstrong\u003ee\u003c/strong\u003e – the simulated 8-shaped P-V loop from Fig. 3b; the letters a-d correspond to Figs. 4a-d (see the text for details).\u003c/p\u003e","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-3873696/v1/9647827ed4dad5478d3fb14f.png"},{"id":50172812,"identity":"e0ab3dd2-6372-4469-adb4-5e909d1c4d6b","added_by":"auto","created_at":"2024-01-25 15:58:24","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":900156,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExamples of simulated airflows in the main bronchi and alveolar O\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e and CO\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e partial pressures: the virtual patient with PE in the right hemithorax.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e(a) and (c) inflow to the left bronchus (blue) and the right bronchus (black and in one respiratory cycle: light/dark green – inflow/outflow during inspiration, light/dark red – inflow/outflow during expiration; these colors correspond to the colors in Fig. 4e); (b) and (d) the mean values of the alveolar oxygen partial pressure (P\u003csub\u003eA\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e) and the alveolar carbon dioxide partial pressure (P\u003csub\u003eA\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e), respectively.\u003c/p\u003e","description":"","filename":"Figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-3873696/v1/55d1e84359af129766d4bc94.png"},{"id":80753808,"identity":"b288416b-6e87-4d84-8cbe-5a542114e52e","added_by":"auto","created_at":"2025-04-16 17:12:20","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":11886178,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3873696/v1/ee0c896c-6e8d-4982-89e6-bc224b2a2f4d.pdf"},{"id":50172813,"identity":"38fe53df-a85a-4948-b9cc-0a0609e08a73","added_by":"auto","created_at":"2024-01-25 15:58:24","extension":"pdf","order_by":7,"title":"","display":"","copyAsset":false,"role":"supplement","size":215213,"visible":true,"origin":"","legend":"","description":"","filename":"Appendix.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3873696/v1/e557bd0adac43b0536b5adc9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A virtual patient in interpretation of massive pleural effusion impact on hemidiaphragm work and an insignificant influence on blood oxygenation","fulltext":[{"header":"Introduction","content":"\u003cp\u003ePleural 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 15% of all patients with malignant diseases\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e and almost half of those with heart failure\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Thus, PE is a relatively common condition with a rough incidence of 322 per 100000\u003csup\u003e3,4\u003c/sup\u003e. Moreover, with the increase in the world population and aging in developed countries, its incidence is expected to increase. 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, the increasing significance of computer modeling makes the use of virtual patients an important supplementary approach (e.g., \u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e,\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e)\u003c/p\u003e \u003cp\u003eThe direct impact of PE on ventilation is associated with an increase in pleural pressure (P\u003csub\u003epl\u003c/sub\u003e). PE exerts pressure on the surrounding structures, i.e., the lungs, hemidiaphragm, mediastinum and rib cage\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. 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.\u003c/p\u003e \u003cp\u003eExpansion of the rib cage and deformation of the ipsilateral hemidiaphragm contribute to decreased efficiency of inspiratory muscles hindering ventilation\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. Additionally, paradoxical excursion of the inverted hemidiaphragm might result in pendulum breathing\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. It may be expected that the above and decreased gas exchange surface lead to deterioration of blood oxygenation\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. Elevated P\u003csub\u003epl\u003c/sub\u003e also exerts pressure on systemic and pulmonary vessels, leading to impaired blood flow\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. Therefore, arterial blood oxygenation is expected to decrease in such patients, particularly in those with massive PE, and therapeutic thoracentesis (TT) is expected to significantly increase this oxygenation. However, studies evaluating changes in blood gases associated with TT have shown contradictory results. Wang et al. observed a significant improvement in oxygenation after TT\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e, while Taylor et al. reported no statistically significant changes in saturation\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. Zielińska-Krawczyk et al. showed that the partial pressure of oxygen in arterial blood (P\u003csub\u003ea\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e) was greater 1 hour after TT than before TT, but it decreased nearly to the level before TT after 24 hours\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. Surprisingly, patients with very large PE exhibited the least pronounced increase in P\u003csub\u003ea\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e after TT. Using a virtual (in silico) patient and data from living patients, Stecka et al. demonstrated that various changes in P\u003csub\u003ea\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e levels, including both a decrease and an increase, are possible\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe primary aim of this study was to use the abovementioned virtual patient to answer the following fundamental questions:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003ewhen and why large-volume PE need not lead to hemidiaphragm inversion;\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ewhy massive PE, whether with hemidiaphragm inversion or not, need not be related to a significant decrease in P\u003csub\u003ea\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eTo our knowledge, this study is one of few that concerns the use of computer modeling in interpretations and explanations of the phenomena, sometimes surprising, that were observed during TT in living patients with massive PE.\u003c/p\u003e"},{"header":"Study design","content":"\u003cp\u003eIn the way previously described\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e, a general-purpose virtual patient was used to explain the variety of ipsilateral hemidiaphragm work and blood gas changes that were observed during TT in living patients with massive pleural effusion who participated in our previous clinical study.\u003c/p\u003e\n\u003cp\u003eThe ipsilateral hemidiaphragm work was characterized by P-V loops, where P is the P\u003csub\u003epl\u003c/sub\u003e measured in the ipsilateral hemithorax and V is the current volume of air inhaled to or exhaled from the whole respiratory system. A functionally inverted hemidiaphragm is present if the P value for the maximal V (the end of inspiration) is greater than the P value for V\u0026thinsp;=\u0026thinsp;0 (the inspiration beginning), i.e., if the P-V loop leans to the left (e.g., as the loop 1 for p1 in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eSimulations performed for deviations of virtual patient parameters from their default values were used to establish (a) parameters crucial for the loop orientation, and (b) airflows in the main bronchi, including the possibility of pendulum breathing.\u003c/p\u003e\n\u003cp\u003eThe results of these simulations and those concerning changes in pulmonary blood flow during TT presented elsewhere\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e were subsequently used to explain changes in arterial blood gases during this procedure.\u003c/p\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n\u003ch2\u003eVirtual Patient\u003c/h2\u003e\n\u003cdiv id=\"Sec4\" class=\"Section3\"\u003e\n\u003ch2\u003ePresentation of models\u003c/h2\u003e\n\u003cp\u003eOur virtual patient serves as a versatile tool capable of simulating a broad spectrum of physiological and pathophysiological phenomena associated with ventilation, gas exchange, gas transport, and pulmonary circulation\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Its intricacies and instances of its application in diverse investigations have been extensively outlined in prior works\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. In essence, the VP comprises models of respiratory system mechanics, pulmonary circulation, gas transfer in bronchi, gas exchange in the lungs and blood gas transport. Additionally, there is a possibility to connect external systemic circulation models of various complexities\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe models collaborate by exchanging calculated variable values, enabling interaction between them. For instance, the gas transfer model utilizes airflow data from respiratory system mechanics and gas exchange models, while the blood transport model incorporates blood flow data from the pulmonary circulation model\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. The default values of the respiratory system model parameters were calibrated to match those of an average 50-year-old Polish woman, as per the Polish reference values\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. Parameters in other models were set to correspond to the average adult.\u003c/p\u003e\n\u003cp\u003eIn the standard version of the virtual patient, each lung lobe is subdivided into 16 segments characterized by their volumes and the coordinates of their mass centers in the coordinate system with the origin at the pulmonary trunk\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. This subdivision enables the investigation of ventilation-perfusion mismatches in different positions, such as supine, standing or lateral. This division is applied uniformly across all models, including both respiratory system mechanics and pulmonary circulation models. However, in PE simulations, another division had to be carried out. The hydrostatic pressure exerted by pleural fluid, which modifies local P\u003csub\u003epl\u003c/sub\u003e, is crucial, e.g., it influences local airflow and causes the collapse of those lungs parts for which the alveolar pressure is lower than the surrounding local P\u003csub\u003epl\u003c/sub\u003e. Therefore, the division of lungs into multiple horizontal layers was necessary since, in the sitting position, hydrostatic pressure progressively increases vertically from the apex to the diaphragm. Initial simulations showed that using more than 100 layers did not significantly alter the simulation outcomes; hence, 100 layers were deemed appropriate.\u003c/p\u003e\n\u003cp\u003eThe model of respiratory system mechanics consists of compartments related to the mouth and trachea, main bronchi, viscoelastic rib cage, elastic mediastinum, two compliant hemidiaphragms, viscoelastic abdomen, and compliance of dead space (separately for each lung) and, for each layer, viscoelastic parenchyma, compliance of the alveolar space (gas compressibility), collapsible bronchi of the middle orders, smallest bronchi and ducts\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. For mathematical descriptions of the compartments that are crucial in this study, please refer to the Appendix.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n\u003ch2\u003eSimulation Procedures\u003c/h2\u003e\n\u003cp\u003eWe replicated a scenario of right-sided PE. The simulations primarily focused on monitoring P\u003csub\u003epl\u003c/sub\u003e and lung volume changes during the respiratory cycle, exemplified by the P-V loops. Additionally, we observed alveolar O\u003csub\u003e2\u003c/sub\u003e and CO\u003csub\u003e2\u003c/sub\u003e partial pressures as well as airflow in the main bronchi. To elucidate the variations in observed P-V loops in living patients, we examined the impact of mediastinal, rib cage and diaphragmatic compliances. The model coefficient related to one of these factors was initially reduced from its default value in the first series of simulations and then increased in the second series. A pleural fluid volume of only 3 liters was simulated, allowing for the maintenance of a small upper part of the ipsilateral lung to analyze possible pendulum breathing.\u003c/p\u003e\n\u003c/div\u003e\n\u003ch2\u003eInterpreted materials\u003c/h2\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n\u003ch2\u003ePresentation of cases\u003c/h2\u003e\n\u003cp\u003eA database was created within the framework of a previously conducted project related to TT. The protocol of that project, approved by the Institutional Review Board (KB 105/2012), was registered at ClinicalTrials.gov (NCT02192138). The project complied with the standards set out in the Declaration of Helsinki. Medical procedures were conducted with the participation of patients hospitalized in the Department of Internal Medicine, Pulmonary Diseases and Allergy. Patients signed an informed consent to participate in the study beforehand.\u003c/p\u003e\n\u003cp\u003eSimulations were performed to explain the results obtained for all patients from this database with the functionally inverted hemidiaphragm (patients p1, p2 and p8 in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). For comparison, three patients with the greatest volume of withdrawn pleural fluid but the P-V loops leaned to the right were also included (patients p5, p6 and p7 in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Additionally, all patients with a vertical P-V loop were included (patients p3 and p4 in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e presents the characteristics of these patients.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eCharacteristics of living patients.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ePatient\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eSex\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eAge\u003c/p\u003e\n\u003cp\u003e[yrs]\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eSide of PE\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eDyspnea before TT (Borg scale)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eDyspnea after TT (Borg scale)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eV\u003csub\u003ewpf\u003c/sub\u003e [L]\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ep1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eM\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e52\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eR\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e4.83\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eI\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ep2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eM\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e57\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e4.80\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eI\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ep3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eM\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e58\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e4.25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eF\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ep4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eM\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e82\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eR\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3.78\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eF\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ep5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eM\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e77\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eR\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e4.65\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eN\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ep6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eM\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e91\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eR\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eNA\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eNA\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e4.00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eN\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ep7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e82\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eR\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e4.94\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eN\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ep8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e73\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eL\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eNA\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eNA\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2.70\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eI\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003ctfoot\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"8\"\u003eM/F \u0026ndash; Male/Female; R/L \u0026ndash; the right/left side of pleural effusion (PE); V\u003csub\u003ewpf\u003c/sub\u003e \u0026ndash; the total volume of withdrawn pleural fluid; I/F/N \u0026ndash; functionally inverted/flattened/normal ipsilateral hemidiaphragm (based on P-V loops); in the case of p8, TT had to be stopped prematurely due to symptoms (hence, a smaller V\u003csub\u003ewpf\u003c/sub\u003e).\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tfoot\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n\u003ch2\u003eManagement\u003c/h2\u003e\n\u003cp\u003eThe TT procedure under the control of P\u003csub\u003epl\u003c/sub\u003e measurements was performed as described elsewhere\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e. Briefly, P\u003csub\u003epl\u003c/sub\u003e was measured intermittently after removal of defined fluid portions (200 mL up to 1 liter and then 100 mL) while the patient was in the sitting position. The following parameters were recorded:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eInstantaneous P\u003csub\u003epl\u003c/sub\u003e (digital pleural manometer, IBBE PAS, Warsaw, Poland \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e);\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eAirflow at the level of the mouth (modified spirometer, LungTest 1000, MES, Cracow, Poland);\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eTranscutaneous partial pressures of O\u003csub\u003e2\u003c/sub\u003e (P\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e) and CO\u003csub\u003e2\u003c/sub\u003e (P\u003csub\u003etc\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e) (TCM4\u0026trade; monitoring system, Radiometer, Copenhagen, Denmark) \u0026ndash; due to technical problems, these parameters were not measured in the patient p8;\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eHeart rate (HR), systolic and diastolic blood pressure (SBP and DBP, respectively) (IGEL ICARD M, IGEL, Gliwice, Poland).\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe instantaneous P\u003csub\u003epl\u003c/sub\u003e and airflow were recorded at 1-minute intervals between the aspiration of the subsequent pleural fluid portions using the sampling frequency equal to 25 Hz. All signals were synchronized and recorded using Toracemon software (IBBE PAS, Warsaw, Poland). Airflow integration provides the volume of inhaled/exhaled air used for P-V loop creation. Dyspnea was assessed by the 10-point modified Borg scale immediately before and after termination of TT. Minute ventilation (V\u003csub\u003eE\u003c/sub\u003e) was calculated as V\u0026sdot;RR, where RR is the respiratory rate. Because the stroke volume was not accessible, changes in cardiac output were assessed by changes in the index \u0026sim;CO=(SBP\u0026minus;DBP)\u0026sdot;HR.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n\u003ch2\u003eData for interpretation\u003c/h2\u003e\n\u003cp\u003eThe tendencies of changes in P\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e, P\u003csub\u003etc\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e, V\u003csub\u003eE\u003c/sub\u003e and \u0026sim;CO in real patients are presented in Figs.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea-d. The tendency was characterized quantitatively by means of the slope of the linear regression line (red lines in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). In massive PE, withdrawal up to approximately 1.9 L seems to have a different impact on respiratory system work than further withdrawal; e.g., the P-V loop in patients with the functionally inverted hemidiaphragm starts to lean to the right (p1, p2 and p8 in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e), and the amplitude of breathing-related P\u003csub\u003epl\u003c/sub\u003e changes usually starts to grow steadily after withdrawal of 1.9 L, whereas earlier, it changes in a more diverse way (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ee). Therefore, the slope was calculated separately for volumes\u0026thinsp;\u0026lt;\u0026thinsp;1.9 L (the first TT stage) and for greater volumes (the second stage).\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab2\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eTendencies for changes in selected parameters during TT.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n\u003cth colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eP\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eP\u003csub\u003etc\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eV\u003csub\u003eE\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e~ CO\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eSlope [kPa/min] ([mmHg/min])\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eSlope [kPa/min]\u003c/p\u003e\n\u003cp\u003e([mmHg/min])\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eSlope [L/min\u003csup\u003e2\u003c/sup\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eSlope [kPa/min\u003csup\u003e2\u003c/sup\u003e]\u003c/p\u003e\n\u003cp\u003e([mmHg/min\u003csup\u003e2\u003c/sup\u003e])\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eI\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eII\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eI\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eII\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eI\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eII\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eI\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eII\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ep1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.006\u003c/p\u003e\n\u003cp\u003e(0.045)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.006\u003c/p\u003e\n\u003cp\u003e(0.045)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.000\u003c/p\u003e\n\u003cp\u003e(0.000)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.000\u003c/p\u003e\n\u003cp\u003e(0.000)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.0480\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.0120\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.67\u003c/p\u003e\n\u003cp\u003e(27.5)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-3.77\u003c/p\u003e\n\u003cp\u003e(-28.3)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ep2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.006\u003c/p\u003e\n\u003cp\u003e(-0.045)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.024\u003c/p\u003e\n\u003cp\u003e(-0.180)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.012\u003c/p\u003e\n\u003cp\u003e(0.090)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.006\u003c/p\u003e\n\u003cp\u003e(0.045)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.1380\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.0480\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-3.87\u003c/p\u003e\n\u003cp\u003e(29.0)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.13\u003c/p\u003e\n\u003cp\u003e(-8.5)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ep3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.006\u003c/p\u003e\n\u003cp\u003e(0.045)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.006\u003c/p\u003e\n\u003cp\u003e(-0.045)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.000\u003c/p\u003e\n\u003cp\u003e(0.000)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.012\u003c/p\u003e\n\u003cp\u003e(-0.090)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.1560\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0000\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.84\u003c/p\u003e\n\u003cp\u003e(6.3)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.29\u003c/p\u003e\n\u003cp\u003e(-9.7)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ep4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.036\u003c/p\u003e\n\u003cp\u003e(-0.270)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.000\u003c/p\u003e\n\u003cp\u003e(0.000)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.006\u003c/p\u003e\n\u003cp\u003e(0.045)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.000\u003c/p\u003e\n\u003cp\u003e(0.000)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.0180\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.0420\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-6.42\u003c/p\u003e\n\u003cp\u003e(-48.2)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.05\u003c/p\u003e\n\u003cp\u003e(7.9)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ep5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.024\u003c/p\u003e\n\u003cp\u003e(-0.180)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.012\u003c/p\u003e\n\u003cp\u003e(-0.090)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.006\u003c/p\u003e\n\u003cp\u003e(0.045)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.006\u003c/p\u003e\n\u003cp\u003e(-0.045)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0240\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0120\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.51\u003c/p\u003e\n\u003cp\u003e(3.8)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.46\u003c/p\u003e\n\u003cp\u003e(-3.4)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ep6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.012\u003c/p\u003e\n\u003cp\u003e(-0.090)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.006\u003c/p\u003e\n\u003cp\u003e(0.045)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.006\u003c/p\u003e\n\u003cp\u003e(0.045)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.012\u003c/p\u003e\n\u003cp\u003e(0.090)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.1440\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0060\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.85\u003c/p\u003e\n\u003cp\u003e(-6.4)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2.83\u003c/p\u003e\n\u003cp\u003e(-21.8)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ep7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.030\u003c/p\u003e\n\u003cp\u003e(-0.225)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.006\u003c/p\u003e\n\u003cp\u003e(0.045)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.000\u003c/p\u003e\n\u003cp\u003e(0.000)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.018\u003c/p\u003e\n\u003cp\u003e(0.135)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.0240\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.90\u003c/p\u003e\n\u003cp\u003e(-6.8)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.37\u003c/p\u003e\n\u003cp\u003e(2.7)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003ctfoot\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"9\"\u003ep1 \u0026hellip; p7 \u0026ndash; living patients from Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. Slope \u0026ndash; the slope of the linear regression of a parameter on time. I - the first stage of TT: fluid withdrawal up to 1.9 L; II - the second stage; P\u003csub\u003etc\u003c/sub\u003eO2 - transcutaneous oxygen pressure; P\u003csub\u003etc\u003c/sub\u003eCO2 - transcutaneous carbon dioxide pressure; V\u003csub\u003eE\u003c/sub\u003e \u0026ndash; minute ventilation; ~CO \u0026ndash; estimation of cardiac output changes with changes in the pulse pressure and heart rate product.\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tfoot\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThere was no uniform trend in P\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e changes during TT (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea, Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e), and different patterns were observed, i.e., slight increase (p1), decrease (p2) and biphasic alteration (p3). P\u003csub\u003etc\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e demonstrated overall greater stability and its variations were also not uniform (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb, Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab3\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eSpearman correlations between slopes shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eV\u003csub\u003eE\u003c/sub\u003e (I)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u0026sim;CO (I)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eV\u003csub\u003eE\u003c/sub\u003e (II)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u0026sim;CO (II)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eP\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e (I)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.02\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.74\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eP\u003csub\u003etc\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e (I)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-0.23\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-0.62\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eP\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e (II)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.15\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-0.26\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eP\u003csub\u003etc\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e (II)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-0.36\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.18\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003ctfoot\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"5\"\u003e(I) and (II) \u0026ndash; slopes for the first and second stages of TT, respectively.\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tfoot\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eNeither the changes in P\u003csub\u003etc\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e nor in P\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e could be attributed to variations in V\u003csub\u003eE,\u003c/sub\u003e as indicated by the negligible correlation of V\u003csub\u003eE\u003c/sub\u003e with P\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e and the weak correlation with P\u003csub\u003etc\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). The slopes of P\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e and P\u003csub\u003etc\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e exhibited significant correlations only with \u0026sim;CO during the first stage of TT (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). However, it is important to note that this observation may be an artifact, as the \u0026sim;CO decrease during this stage is mainly related to the arterial pressure decrease (perhaps due to the alleviation of the initial patient\u0026rsquo;s stress), which might have an impact on transcutaneous measurements: the arterial pressure rise increases the arterial component and decreases the venous component in microcirculation (hence, the positive correlation for P\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e and the negative correlation for P\u003csub\u003etc\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e).\u003c/p\u003e\n\u003cp\u003eAll P-V loops for the functionally inverted hemidiaphragm were 8-shaped (p1, p2 and p8 before TT, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e), and the P\u003csub\u003epl\u003c/sub\u003e amplitude rapidly decreased in the first stage in some patients (p1, p2 and p7 in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ee); these observations are other intriguing findings.\u003c/p\u003e\n\u003cp\u003eDue to the small number of cases, conducting a reliable statistical analysis was not feasible. Nevertheless, four key issues were formulated to be explained by simulations:\u003c/p\u003e\n\u003col\u003e\n\u003cli\u003e\n\u003cp\u003eWhy can the hemidiaphragm work normally despite massive PE?\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eWhy are some P-V loops 8-shaped?\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eWhy is there no significant and uniform impact on blood oxygenation during pleural fluid withdrawal, despite the notable disturbance in breathing mechanics caused by massive PE, particularly in patients with functionally inverted hemidiaphragms?\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eWhy may the P\u003csub\u003epl\u003c/sub\u003e amplitude decrease with pleural fluid withdrawal in massive PE since it usually increases in the majority of patients\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e?\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003c/div\u003e"},{"header":"Results and discussion","content":"\u003cp\u003e\u003cstrong\u003eThe First Question\u003c/strong\u003e (hemidiaphragm inversion)\u003c/p\u003e\n\u003cp\u003eAs simulations have suggested, the rib cage and abdomen compliances are important for addressing this issue. In particular, a stiffer abdomen may protect the ipsilateral hemidiaphragm against significant deformation. However, simulations have shown that the impact of the mediastinum compliance seems to be most significant and much more intriguing. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e shows examples of the P-V loops from simulations with mediastinum compliance higher (a) and lower (b) than the default value. If this compliance is high, massive PE deforms the mediastinum more than the ipsilateral hemidiaphragm; consequently, this hemidiaphragm may not be inverted, and the P-V loop may lean to the right. If the ipsilateral hemidiaphragm is physically inverted (e.g., the inversion is evident in USG or RTG examination), despite the high mediastinum compliance, it need not be functionally inverted in the sense defined above; i.e., the P-V loop can lean to the right (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea shows such a case) because the contralateral hemidiaphragm affects also the ipsilateral lung through the compliant mediastinum. It might be enhanced in patients with contralateral hemidiaphragm hyperactivity\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe Second Question\u003c/strong\u003e (8-shaped P-V loops)\u003c/p\u003e\n\u003cp\u003eTo our knowledge, 8-shaped P-V loops have not yet been noted or discussed in the literature. Simulations have suggested the following sequence can explain this shape in patients with a less compliant mediastinum, i.e., with the functionally inverted hemidiaphragm.\u003c/p\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n\u003ch2\u003e1. The inspiration beginning:\u003c/h2\u003e\n\u003cp\u003eBefore inspiration begins, the contralateral hemidiaphragm, stretched by the negative P\u003csub\u003epl\u003c/sub\u003e in the contralateral hemithorax, is longer than the ipsilateral hemidiaphragm (supported by abdominal organs). Therefore, according to the force‒length relationship of the muscles, initial diaphragm contraction means mainly contraction of the contralateral hemidiaphragm. A decrease in the P\u003csub\u003epl\u003c/sub\u003e in the contralateral hemithorax propagates through the mediastinum to the ipsilateral hemithorax. Additionally, the activity of rib cage muscles decreases P\u003csub\u003epl\u003c/sub\u003e in both hemithoraxes. The above causes:\u003c/p\u003e\n\u003cp\u003e(a) flow of fresh air into both lungs (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea and the light green part in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea) like in case of not inverted hemidiaphragm (the light green part in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ec),\u003c/p\u003e\n\u003cp\u003e(b) the part of the P-V loop that is directed to the right, i.e., to the smaller P (the light green line in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ee).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n\u003ch2\u003e2. The second inspiration phase:\u003c/h2\u003e\n\u003cp\u003eFurther diaphragm contraction causes upwards movement of the inverted ipsilateral hemidiaphragm, and this activity predominates over the influence of the contralateral hemidiaphragm that is propagated through the mediastinum. This increases P\u003csub\u003epl\u003c/sub\u003e and, consequently:\u003c/p\u003e\n\u003cp\u003e(a) processed air flows out from the ipsilateral lung and mixes with fresh air still flowing into the contralateral lung (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb and the dark green line in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea) unlike the case of not inverted hemidiaphragm (the light green part in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ec),\u003c/p\u003e\n\u003cp\u003e(b) the second part of the P-V loop is directed to the left, i.e., to the greater P (the dark green line in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ee).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n\u003ch2\u003e3. The beginning of expiration:\u003c/h2\u003e\n\u003cp\u003eThe inverted hemidiaphragm starts to relax, i.e., it moves down, which decreases P\u003csub\u003epl\u003c/sub\u003e. This causes that:\u003c/p\u003e\n\u003cp\u003e(a) processed air exhaled from the contralateral lung flows into the ipsilateral lung (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec and the light red line in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea),\u003c/p\u003e\n\u003cp\u003e(b) P decreases with decreasing V (the light red line in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ee).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n\u003ch2\u003e4. The second expiration phase:\u003c/h2\u003e\n\u003cp\u003eThe influence of the inverted hemidiaphragm is insignificant in comparison with the influence of the contralateral hemidiaphragm; thus, the airflows in both lungs are similar, which gives:\u003c/p\u003e\n\u003cp\u003e(a) exhalation of processed air from both lungs (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ed and the dark red line in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea),\u003c/p\u003e\n\u003cp\u003e(b) P increases with decreasing V (the dark red line in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ee).\u003c/p\u003e\n\u003cp\u003eThe above subpoints 2a and 3a suggest that pendulum breathing may be present, if a part of the ipsilateral lung is not collapsed, whereas subpoints 1a and 4a show that there are two subperiods when pendulum breathing is not present. Since pendulum breathing may be present during only a part of inspiration, the mean P\u003csub\u003eA\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e in the contralateral lung can be almost normal. Thus, although pendulum breathing can occur in massive PE, it has an insignificant influence on blood gases.\u003c/p\u003e\n\u003cp\u003eThe above four subpoints 1b-4b explain the 8-shaped loops. Note also that although the ipsilateral hemidiaphragms of patients p3 and p4 were initially assumed to not be inverted, the 8-shaped P-V loops also suggested that in these patients, the hemidiaphragm was slightly inverted since the 8-shaped space requires points 2 and 3.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe Third Question\u003c/strong\u003e (blood gases)\u003c/p\u003e\n\u003cp\u003eIt could be expected that massive PE, which significantly disturbs ventilation, should worsen blood oxygenation, and consequently, pleural fluid withdrawal should be associated with significant improvement in blood oxygenation. This improvement, however, was not observed in living patients (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). As the virtual patient is fully observable, the three following phenomena could be identified, which enabled us to answer this question.\u003c/p\u003e\n\u003cp\u003eFirst, increased P\u003csub\u003epl\u003c/sub\u003e in the ipsilateral hemithorax significantly suppresses blood flow (e.g., see corresponding simulations presented elsewhere\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e); thus, almost all the blood flows through the ventilated contralateral lung. As pleural fluid is withdrawn, P\u003csub\u003epl\u003c/sub\u003e in the ipsilateral hemithorax decreases, and blood also flows through the ipsilateral lung regardless of whether the collapsed lung parts are recruited and ventilated.\u003c/p\u003e\n\u003cp\u003eSecond, before TT the majority of blood flows through the contralateral lung, and therefore the rate of gas exchange in the alveoli of this lung is greater, which causes P\u003csub\u003eA\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e during expiration to be lower than normal. As pleural fluid is withdrawn, blood starts to flow through the ipsilateral lung, and this lung may also participate in gas exchange to an increasing extent; consequently, P\u003csub\u003eA\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e may not fall as much as during expiration.\u003c/p\u003e\n\u003cp\u003eThird, fresh air is mixed during inspiration with the processed air that remains in the lungs and bronchi after preceding expiration, and the volume of this processed air is equal to the sum of the functional residual capacity (FRC) and anatomical dead space (V\u003csub\u003eD\u003c/sub\u003e). The V\u003csub\u003eT\u003c/sub\u003e/(FRC\u0026thinsp;+\u0026thinsp;V\u003csub\u003eD\u003c/sub\u003e) ratio, were V\u003csub\u003eT\u003c/sub\u003e is the tidal volume, determines the composition of the mixture of fresh and processed air (i.e., P\u003csub\u003eA\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e and P\u003csub\u003eA\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e) during inspiration; for example, a typical P\u003csub\u003eA\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e value is lower by approximately 8 kPa (60 mmHg) than the partial pressure of O\u003csub\u003e2\u003c/sub\u003e in atmospheric air. If the ipsilateral lung is collapsed, this ratio may even be two times greater because FRC\u0026thinsp;+\u0026thinsp;V\u003csub\u003eD\u003c/sub\u003e concerns only the contralateral lung; hence, the mean P\u003csub\u003eA\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e in this lung can be higher than normal, and P\u003csub\u003eA\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e can be lower (Figs.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003eb and d). As pleural fluid is withdrawn, the ratio may decrease due to the requirement of collapsed parts of the ipsilateral lung; consequently, P\u003csub\u003eA\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e during inspiration also decreases. This may explain the intriguing observation that blood oxygenation changes the least after TT in patients with large PE\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eBefore TT, almost all the blood flows through the ventilated lung with P\u003csub\u003eA\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e during inspiration, which is higher than normal due to the big V\u003csub\u003eT\u003c/sub\u003e/(FRC\u0026thinsp;+\u0026thinsp;V\u003csub\u003eD\u003c/sub\u003e) but P\u003csub\u003eA\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e may be lower than normal during expiration due to more intensive gas exchange. Consequently, the average P\u003csub\u003ea\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e in mixed blood in the systemic arterial system may be within the physiological range despite massive PE. These three phenomena have opposite influences on blood oxygenation, and the final effect related to pleural fluid withdrawal depends on which phenomenon suppresses the others; hence, there is no uniform reaction to the withdrawal.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe Fourth Question\u003c/strong\u003e (unusual P\u003csub\u003epl\u003c/sub\u003e amplitude decrease)\u003c/p\u003e\n\u003cp\u003eIn all the cases analyzed by Zielińska et al., the P\u003csub\u003epl\u003c/sub\u003e amplitude increased with pleural fluid withdrawal at the beginning of TT\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e, which is understandable from a physical point of view\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. However, in some of the cases presented in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ee, the amplitude initially decreases. This decrease may be easily explained, even without simulations, in patients with the functionally inverted hemidiaphragm. Indeed, during TT, the P-V loop in such patients leans to the left, then becomes vertical and, finally, leans to the right (p1 and p2 in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Since the P\u003csub\u003epl\u003c/sub\u003e variations are smallest when the loop is vertical, the P\u003csub\u003epl\u003c/sub\u003e amplitude is initially higher, then decreases according to the loop rotation, and finally increases.\u003c/p\u003e\n\u003cp\u003eHowever, the decrease in the P\u003csub\u003epl\u003c/sub\u003e amplitude in patient p7, who had a normally working hemidiaphragm, was surprising. The simulations suggested the following explanation. Since massive PE leads to the collapse of the whole or a significant part of the lung, the total lung compliance decreases because a smaller part of the lungs is involved in ventilation. Additionally, the same V\u003csub\u003eT\u003c/sub\u003e requires a greater expansion of the contralateral lung to the volume of smaller lung compliance due to its nonlinearity (e.g., see the Appendix for the mathematical equation that describes this nonlinearity). As a consequence, the amplitude of breathing-related P\u003csub\u003epl\u003c/sub\u003e changes in the contralateral hemithorax must be much greater than normal to preserve the required V\u003csub\u003eT\u003c/sub\u003e. Thus, compensatory hyperactivity of this hemidiaphragm can be observed\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. In addition, if the mediastinum is very compliant, then these large changes may propagate to the ipsilateral hemithorax, leading to the P-V loop that is leaned to the right but with great P\u003csub\u003epl\u003c/sub\u003e variation. When the total compliance increases due to the recruitment of a collapsed lung part caused by pleural fluid withdrawal, the amplitude decreases. Note that the P\u003csub\u003epl\u003c/sub\u003e amplitude did not change in the second stage of TT (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ee), which additionally confirms the recruitment.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\n\u003ch2\u003eStudy limitations\u003c/h2\u003e\n\u003cp\u003eThe main limitation is related to the lack of information about actual arterial blood gas data during TT in living patients. Such data could be obtained using only ethically unjustified invasive methods; therefore, we decided to analyze P\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e and P\u003csub\u003etc\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e recorded throughout the whole procedure. Although transcutaneous measurement is a well-known technique for monitoring blood gases, some previous studies have not confirmed the significant correlation between P\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e and P\u003csub\u003ea\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e measured in different subjects\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. Therefore, although monitoring the trend of P\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e can be useful, it should not be regarded as a perfect substitute for P\u003csub\u003ea\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e. Although this would be a significant obstacle in comparisons of results between different patients, the assumption that relative changes in P\u003csub\u003etc\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e and P\u003csub\u003etc\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e imitate relative changes in P\u003csub\u003ea\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e and P\u003csub\u003ea\u003c/sub\u003eCO\u003csub\u003e2\u003c/sub\u003e in a particular patient seems to be reasonable if the influence of the arterial pressure is taken into account.\u003c/p\u003e\n\u003cp\u003eAnother limitation concerns the lack of direct measurements of CO. Instead, we had to rely on estimations based on SBP, DBP, and HR. This estimation could be disturbed by reactions to stress at the beginning of TT, which is an invasive procedure that is additionally supplemented by the connection of the patient to several measuring devices.\u003c/p\u003e\n\u003cp\u003eThe lack of a more precise representation of components in the virtual patient\u0026rsquo;s abdomen is a very important limitation. In particular, the liver as such is not modeled, whereas it supports the right hemidiaphragm, which is postulated to be the reason for the less frequent inversion of the right hemidiaphragm\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e, which is also our case (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). The influence of the liver was simulated indirectly only as a decrease in the abdominal compliance. Nevertheless, our simulations seem to be reliable since the P-V loops from the simulations match well with the loops observed in patients, particularly those with the 8-shaped loop. On the other hand, by relying on these simulations, we were able to explain why TT changes blood oxygenation the least in massive PE. We also hypothesized that factors other than arterial blood gases are mainly responsible for the dyspnea frequently experienced by patients with massive PE since the oxygenation did not change significantly, whereas dyspnea substantially decreased after TT (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eComputer modeling, particularly in the form of virtual patients, can be a useful tool for explaining complex physiological and pathophysiological phenomena associated with medical procedures. It enabled to explain several interesting observations related to TT, such as the slight change in blood oxygenation in patients with massive PE compared with patients with less severe PE, the necessity of hyperactivity of the contralateral hemidiaphragm or the peculiar 8-shaped form of the P-V loop in patients with functional hemidiaphragm inversion.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments:\u0026nbsp;\u003c/strong\u003eThe authors thank Piotr Korczyński, PhD, MD, and Krzysztof Zieliński, PhD, Eng., for their assistance during therapeutic thoracentesis. This study was supported by the National Science Center, Poland (grant N 2019/35/B/NZ5/02531).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026rsquo; contributions:\u003c/strong\u003e TG and AMS conceived and designed the study. TG and MM developed the measuring system and wrote computer programs. RK, EMG, MM, MZK, and AMS collected the clinical data. AMS and TG analyzed and interpreted the data, performed the simulations and drafted the manuscript. RK and EMG revised and critically reviewed the manuscript for important intellectual content. All the authors provided their approval on the final version.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability:\u003c/strong\u003e Data are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests:\u0026nbsp;\u003c/strong\u003eAll the authors declare that they have no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eManagement of malignant pleural effusions. \u003cem\u003eAm. J. Respir. Crit. Care Med\u003c/em\u003e. Available at: https://pubmed.ncbi.nlm.nih.gov/11069845/. (Accessed: 15th January 2024)\u003c/li\u003e\n\u003cli\u003eMorales-Rull, J. L. et al. 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Med. \u003c/em\u003e\u003cstrong\u003e18\u003c/strong\u003e(1)\u003cstrong\u003e,\u003c/strong\u003e (2018).\u003c/li\u003e\n\u003cli\u003eKrenke, R. \u003cem\u003eet al.\u003c/em\u003e Development of an electronic manometer for Intrapleural Pressure Monitoring. \u003cem\u003eRespiration\u003c/em\u003e \u003cstrong\u003e82\u003c/strong\u003e(4)\u003cstrong\u003e,\u003c/strong\u003e 377\u0026ndash;385 (2011).\u003c/li\u003e\n\u003cli\u003eFitzgerald, D. B., Muruganandan, S., Peddle‐McIntyre, C. J., Lee, Y. C. \u0026amp; Singh, B. Ipsilateral and contralateral hemidiaphragm dynamics in symptomatic pleural effusion: The 2nd pleural effusion and symptom evaluation (please‐2) study. \u003cem\u003eRespirology\u003c/em\u003e \u003cstrong\u003e27\u003c/strong\u003e(10)\u003cstrong\u003e,\u003c/strong\u003e 882\u0026ndash;889 (2022).\u003c/li\u003e\n\u003cli\u003eG\u0026oacute;rska, K., Korczyński, P., Maskey-Warzęchowska, M., Chazan, R. \u0026amp; Krenke, R. Variability of transcutaneous oxygen and carbon dioxide pressure measurements associated with sensor location. \u003cem\u003eAdv. Exp. Med. Biol. \u003c/em\u003e39\u0026ndash;46 (2015).\u003c/li\u003e\n\u003cli\u003eNason, L. K. \u003cem\u003eet al.\u003c/em\u003e Imaging of the diaphragm: Anatomy and function. \u003cem\u003eRadiographics\u003c/em\u003e \u003cstrong\u003e32\u003c/strong\u003e(2)\u003cstrong\u003e,\u003c/strong\u003e (2012).\u003c/li\u003e\n\u003cli\u003eDe Groote, A. \u003cem\u003eet al.\u003c/em\u003e Ventilation asymmetry after transplantation for emphysema. \u003cem\u003eAm. J. Respir. Crit. Care Med.\u003c/em\u003e \u003cstrong\u003e170\u003c/strong\u003e(11)\u003cstrong\u003e,\u003c/strong\u003e 1233\u0026ndash;1238 (2004).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3873696/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3873696/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eComputer modeling, particularly in the form of virtual patients, can be a useful tool for explaining complex phenomena associated with medical procedures. Based on interesting phenomena observed in 8 living patients undergoing large-volume therapeutic thoracentesis (TT) with pleural pressure (Ppl), transcutaneous oxygen and carbon dioxide pressures, and spirometric measurements, we formulated four questions regarding the impact of pleural effusion (PE) and TT on hemidiaphragm function and blood oxygenation. To answer these questions, we simulated right-sided PE in a virtual patient and studied changes in Ppl and lung volume during the respiratory cycle (exemplified by P-V loops, where P is Ppl in the ipsilateral hemithorax and V is the volume of both lungs), alveolar O2 (PAO2) and CO2 partial pressures and airflows in the main bronchi. The simulations suggest that: (a) the mediastinum compliance has a particular meaning for the work of both hemidiaphragms and explaining the 8-shape of P-V loops in hemidiaphragm inversion; (b) PAO2 is higher than normal before TT due to decreased ratio of the tidal volume to the volume of processed air at the end of expiration; and (c) in some patients, the Ppl amplitude related to breathing can be significantly greater before TT than later on.\u003c/p\u003e","manuscriptTitle":"A virtual patient in interpretation of massive pleural effusion impact on hemidiaphragm work and an insignificant influence on blood oxygenation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-25 15:58:19","doi":"10.21203/rs.3.rs-3873696/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"51b903da-cb82-4e01-bda6-c4def6078543","owner":[],"postedDate":"January 25th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":28340980,"name":"Physical sciences/Engineering/Biomedical engineering"},{"id":28340981,"name":"Biological sciences/Computational biology and bioinformatics/Computational models"},{"id":28340982,"name":"Biological sciences/Physiology/Respiration"},{"id":28340983,"name":"Health sciences/Signs and symptoms/Respiratory signs and symptoms"},{"id":28340984,"name":"Health sciences/Medical research/Translational research"}],"tags":[],"updatedAt":"2025-04-16T17:11:57+00:00","versionOfRecord":{"articleIdentity":"rs-3873696","link":"https://doi.org/10.3389/fphys.2025.1539781","journal":{"identity":"frontiers-in-physiology","isVorOnly":true,"title":"Frontiers in Physiology"},"publishedOn":"2025-04-10 00:00:00","publishedOnDateReadable":"April 10th, 2025"},"versionCreatedAt":"2024-01-25 15:58:19","video":"","vorDoi":"10.3389/fphys.2025.1539781","vorDoiUrl":"https://doi.org/10.3389/fphys.2025.1539781","workflowStages":[]},"version":"v1","identity":"rs-3873696","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3873696","identity":"rs-3873696","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}