Cardiac output estimation using pulmonary mechanics in mechanically ventilated patients
- Ashwath Sundaresan^{1}Email author,
- J Geoffrey Chase^{1},
- Christopher E Hann^{1} and
- Geoffrey M Shaw^{2}
https://doi.org/10.1186/1475-925X-9-80
© Sundaresan et al; licensee BioMed Central Ltd. 2010
Received: 27 July 2010
Accepted: 25 November 2010
Published: 25 November 2010
Abstract
The application of positive end expiratory pressure (PEEP) in mechanically ventilated (MV) patients with acute respiratory distress syndrome (ARDS) decreases cardiac output (CO). Accurate measurement of CO is highly invasive and is not ideal for all MV critically ill patients. However, the link between the PEEP used in MV, and CO provides an opportunity to assess CO via MV therapy and other existing measurements, creating a CO measure without further invasiveness.
This paper examines combining models of diffusion resistance and lung mechanics, to help predict CO changes due to PEEP. The CO estimator uses an initial measurement of pulmonary shunt, and estimations of shunt changes due to PEEP to predict CO at different levels of PEEP. Inputs to the cardiac model are the PV loops from the ventilator, as well as the oxygen saturation values using known respiratory inspired oxygen content. The outputs are estimates of pulmonary shunt and CO changes due to changes in applied PEEP. Data from two published studies are used to assess and initially validate this model.
The model shows the effect on oxygenation due to decreased CO and decreased shunt, resulting from increased PEEP. It concludes that there is a trade off on oxygenation parameters. More clinically importantly, the model also examines how the rate of CO drop with increased PEEP can be used as a method to determine optimal PEEP, which may be used to optimise MV therapy with respect to the gas exchange achieved, as well as accounting for the impact on the cardiovascular system and its management.
Introduction
Patients diagnosed with acute respiratory distress syndrome (ARDS) often experience pulmonary shunt or gas exchange abnormalities due to lack of recruited alveoli. Shunt also occurs when there is an increased thoracic pressure that restricts blood flow, thus reducing the gas exchange. The primary objective of mechanical ventilation (MV) is to improve the condition of the patient by increasing alveoli recruitment and thus also improving or optimising gas exchange.
A common MV parameter used to optimise recruitment is the positive end expiratory pressure (PEEP). PEEP is used to prevent alveoli derecruitment at the end of the expiration cycle [1] and to maintain a level of oxygenation. However, clinicians often debate the optimal level of PEEP required [2–4]. In particular, the application of PEEP poses some unique problems that need to be addressed.
First, the ranges of allowable PEEP for ventilation vary significantly between patients [5]. If PEEP is set too high, healthy, non-ARDS alveoli may over inflate, which can cause more harm to the patient [6]. However, if PEEP is too low, then cyclic derecruitment can occur during the breathing cycle, which can aggravate and further damage the alveoli [7]. This balance results from the heterogeneous nature of the ARDS lung with a mix of healthy and ARDS affected alveoli at all levels [8].
Second, the application of PEEP decreases cardiac output (CO) [9, 10]. The decrease in CO from high PEEP is due to the reduction in stroke volume (SV). As PEEP increases, the intrathoracic pressure increases, which restricts the venous flow into the thorax and thus lowers CO. Any decrease in CO lowers oxygen consumption, as determined by Fick's law, and describes the inability of the heart to pump enough blood to meet the metabolic requirements of the body. Reduced CO can also have an impact on circulation management and therapeutics used. Hence, PEEP may also have a negative spill over into cardiovascular therapy.
Current methods to measure CO, such as thermodilution and pulse pressure methods, are clinically invasive, requiring the use of catheters [11, 12]. These catheters carry some added risks of infection [13], and are thus used only in a subset of critically ill patients receiving MV. For critically ill patients, the benefits from CO measurements may not offset the dangers associated with invasive tools. In addition, these methods take time and effort, and are thus not performed regularly and cannot be monitored in clinical real time. Hence, strong motivations exist to develop non-invasive, real-time tools to measure CO.
Thus, MV patients treated for ARDS may not have CO measurements readily available. However, the changes in CO due to changes in applied PEEP are important as it may also help indicate an optimal level of PEEP. In particular, if a change in PEEP causes a large drop in CO, it may more than offset its benefit on recruitment. Alternatively, if the drop in CO is minimal, then the benefits of PEEP induced recruitment may offset the detrimental effects of an insignificant drop in CO. Hence, the ability to model changes in CO due to PEEP may also prove beneficial for optimizing the setting of PEEP, which is itself controversial [4].
Simple mathematical models and parameter identification methods can provide the framework to quantify unknown physiological values using known clinical information. Mathematical models can also allow clinicians to assess the impact of various therapies without having to implement them. Finally, such model-based approaches can create a clinical, physiological picture of the patient to clearly illustrate tradeoffs between condition and treatment choices. Thus, there is potential to mitigate harmful effects that can occur with non-optimal clinical decisions.
Model Based Methods
This paper examines two separate mathematical models and aims to combine the effects of both to estimate changes in CO due to changes in PEEP. The first model, developed by Andreassen et al [14] looks at estimations of pulmonary shunt and oxygen diffusion resistance by measuring variations in the fraction of inspired oxygen (FIO_{2}) and arterial oxygen saturation (S_{a}O_{2}). The diffusion model takes inputs of CO, F_{I}O_{2} and other ventilation data, to estimate pulmonary shunt and diffusion resistance as outputs.
The second model was developed by Sundaresan et al [15, 16] and evaluates the effect of PEEP on alveolar recruitment. In particular, the model quantifies the level of alveolar recruitment as a function of PEEP by evaluating the threshold opening and closing pressures required to recruit and derecruit alveoli. It obtains these values based on clinically measured respiratory PV loops from MV patients.
Diffusion Model
Current methods of describing gas exchange abnormalities, such as arterial oxygen saturation, alveolar arterial oxygen pressure gradient or venous admixture [17, 18] are insufficient. In particular, these parameters lump the effects of oxygen diffusion and true pulmonary shunt into a single parameter. This single parameter is typically inadequate as it is difficult to interpret which mechanism causes the gas exchange abnormality.
Pulmonary shunt occurs when the alveoli in the lung are perfused with blood, as desired, but not adequately ventilated. In patients with ARDS, alveoli collapse occurs as a result of fluid build up, which results in the ARDS lung not being ventilated. Thus, as ARDS severity increases, pulmonary shunt also increases. Even if the alveoli is recruited or not collapsed, if gas exchange does not occur it is considered to be part of the shunt volume. Similar abnormality or failure of gas exchange can occur when CO and minute ventilation are mismatched [19].
In patients who are mechanically ventilated, the application of PEEP can increase alveolar recruitment. As more alveoli are recruited, there is an increase in alveolar ventilation and as a result, pulmonary shunt decreases. Using standard data, such as S_{a}O_{2} and arterial oxygen pressure (P_{a}O_{2}), curves of S_{a}O_{2} can be generated as a function of F_{I}O_{2}. These curves can then be used to estimate the pulmonary shunt and diffusion resistance [20, 21].
The ODC is a function of the capillary pH (pH^{c}), base excess (BE^{c}) and the temperature of the blood (T^{c}). Any other variables which influence the ODC are lumped into a correction factor (cf^{c}). The ODC is then calculated by multiplying these parameters with the P_{c}O_{2} and individual correction factors (f_{1}, f_{2} and f_{3}). The values of f_{1}, f_{2} and f_{3} are obtained from [22].
where αO_{2} is the solubility coefficient of oxygen in blood.
Measured, estimate and calculated parameters in the diffusion resistance model
Directly Measured Parameters | Estimated Parameters | Calculated Parameters |
---|---|---|
Respiratory Frequency (f) | Dead Space (V_{d}) | Shunt (f_{s}) |
Inspired Oxygen Content (F_{i}O_{2}) | Diffusion Resistance (R) | |
Expired Oxygen Content (F_{e}O_{2}) | ||
Tidal Volume (V_{t}) | ||
Atmospheric Pressure (P_{B}) | ||
Pulse or Arterial Oxygen Saturation (S_{a}O_{2}) | ||
Cardiac Output (CO) | ||
Haemoglobin (cHb) | ||
Methaemoglobin (cMetHb) | ||
Carboxyhaemoglobin (cCOHb) |
In the model developed by Andreassen et al [14], CO was estimated, but it can also be measured using thermodilution techniques. Using all these measurements, and an estimate of dead space, it is then possible to calculate shunt and diffusion resistance by solving Equations (1) - (7).
Lung Mechanics
The lung mechanics model developed by Sundaresan et al [15, 16] considers the lung as a collection of lung units, each representing a set of distal airways and alveoli. The model assumes that any volume change is predominantly due to alveoli recruitment and derecruitment in the ARDS lung.
The recruitability of the lung units is determined by the threshold opening pressure (TOP) and threshold closing pressure (TCP). The TOP is the critical pressure required to recruit an alveolus, while the TCP is the pressure where alveoli collapse, and both are assumed to take on a normal distribution [1]. The TCP and TOP distributions fitted to the data capture the continuous recruitment and derecruitment across a wide range of pressures and are described by a mean and standard deviation. In practice, TOP and TCP distributions are experimentally obtained, but the model allows these distributions to be estimated.
Model Development and Method
Diffusion Model Reproduction and Impact of Co
Diffusion model parameters from Andreassen et al 14
Respiratory frequency | f | 14 min^{-1} |
---|---|---|
Tidal volume | V_{t} | 0.5 L |
Dead space volume | V_{d} | 0.15 L |
Cardiac output | CO | 5 L/min |
Oxygen consumption | VO_{2} | 11.5 mmol/min |
Haemoglobin | cHb | 9 mmol/L |
Methaemoglobin | cMetHb | 0 mmol/L |
Carboxyhaemoglobin | cCOHb | 0 mmol/L |
Oxygen solubility coefficient | αO_{2} | 0.0102 mmol/(L kPa) |
Arterial pH status | pH^{a} | 7.4 |
Capillary pH status | pH^{c} | 7.4 |
Arterial base excess | BE^{a} | 0 mmol/L |
Capillary base excess | BE^{c} | 1 mmol/L |
Arterial blood temperature | T^{a} | 37 C |
Capillary blood temperature | T^{c} | 37 C |
Barometric pressure | P_{B} | 101.3 kPa |
Theoretically, if two different F_{I}O_{2} measurements were taken and the corresponding S_{a}O_{2} values measured and plotted, it is possible to evaluate the shunt and diffusion resistance (R) by plotting the best fit S_{a}O_{2} curve. However, in Figure 4 and 5, the cardiac output is held at a constant value of 5 L/min. Unless measured, the value of CO is assumed to be 5 L/min [14, 23]. However, in patients with ARDS where PEEP is titrated based on clinical choice, the assumption of using a constant CO is not valid. In addition, as a result of MV therapy and other aspects of their condition, CO is much more variable within a typical range of 2-7 L/min [24–26].
In Figure4-F the lines of constant shunt, diffusion resistance and cardiac output are analogous to principles in thermodynamics, such as isotherms (lines of constant temperature), isobars (lines of constant pressure) and isochors (lines of constant volume). In particular, if two states are known, then it is possible to determine the third state of a gas as all variables are interrelated. Similarly, the lines of constant shunt, diffusion resistance and cardiac output are all interrelated.
Estimating Shunt Changes Due to Peep - Linking the Two Models
Because the current diffusion models use CO as an input, it is possible to estimate the shunt and diffusion resistance if a few measurements such S_{a}O_{2} and F_{I}O_{2} are taken. However, as PEEP increases, the level of alveoli recruitment also increases at the cost of decreased CO. Thus, unless the patient has a continuous measurement of CO, then an alternative method must be developed to generate the S_{a}O_{2} curves and predict shunt.
The hypothesis that this research suggests is that any increase in PEEP directly causes a decrease in shunt. In ARDS affected lungs, collapsed alveoli do not contribute to the ventilation process. Although collapsed alveoli may be properly perfused they contribute to pulmonary shunt because they do not contribute to ventilation. As PEEP is applied, more alveoli are recruited, which means there is more aerated surface area for gas exchange, which causes a decrease in shunt [27, 28]. Thus, if it is possible to estimate changes in shunt, then the question is whether the diffusion model can work backwards to predict changes in CO?
If shunt decreases with increased recruitment, then it is possible to estimate shunt changes using the lung mechanics model shown. Because the lung mechanics model has the ability to estimate changes in recruitment [15, 16], it is hypothesised here that the increase in recruited volume due to PEEP is directly related to the decrease in shunt. More specifically, changes in recruited volume are assumed equal to reductions in shunt.
Although the lung mechanics model cannot predict absolute shunt volumes, it does have the ability to predict changes in shunt volume. Thus, for the first PEEP setting, a shunt value/volume is measured using the diffusion model with a known or estimated CO. Once an initial shunt measurement is obtained, lung mechanics can be used to estimate the shunt at a new level of PEEP by calculating the percentage change in shunt from that initial value.
In particular, Figure 7 shows the need for an initial measurement of CO. Once an initial measurement or estimate is obtained, it is then possible to track changes in CO with changes to PEEP. Thus, over a given time period, the changes in CO are calibrated to the initial CO measurement obtained through thermodilution.
Model Validation and Analysis Results
Proof of Concept
To test the concept of tracking changes in CO, a proof of concept (POC) model has been evaluated based on a mixture of simulated parameters and clinical data. The data used in the study uses one set of data containing PV loops obtained from Bersten et al [29] and arterial blood gas measurements from Andreassen et al [14]. Although these measurements do not correspond to the same data set, the aim is to evaluate the utility of the POC model prior to further clinical validation.
Measured PV data from Bersten et al fitted with Yuta lung mechanics model
PEEP[cm H _{2} O] | EEV[L] | F _{ H } [L] | Δf _{ s } |
---|---|---|---|
5 | 0.4410 | ||
7 | 0.6740 | 1.98 | -15% |
12 | 1.1125 | -34% |
Measured values of varying FiO2 and SaO2 from Andreassen et al.
Time t _{1} | Time t _{2} | |
---|---|---|
F _{ I } O _{ 2 } [%] | 25 | 35 |
S _{ a } O _{ 2 } [%] | 90.9 | 95.1 |
Modified shunt and cardiac output as a function of PEEP.
PEEP [cm H _{2} O] | F _{ I } O _{ 2 } [%] | S _{ a } O _{ 2 } [%] | Shunt [%] | R [kPa/L/min] | CO [L/min] |
---|---|---|---|---|---|
5 | [25 35]* | [0.909 0.951]* | 16* | 45 | 5* |
7 | [25 35]* | [0.91 0.96]* | 13^{+} | 45 | 4.7^{+} |
12 | [25 35]* | [0.91 0.97]* | 9^{+} | 45 | 4.3^{+} |
Optimisation
In the POC model, the cardiac output was shown to drop from 5 to 4.3 L/min as PEEP increased from 5 to 12 cmH_{2}O. This drop agrees with current data showing that CO drops with increased PEEP [9, 10]. The POC model showed that the application of PEEP improved oxygenation (S_{a}O_{2}). However, Figure 6 shows that any decrease in CO should reduce oxygenation with all else equal and shunt at a constant value.
Figure 10 shows that if the drop in CO is too high, it can have a detrimental effect on oxygenation even with decreased shunt. The decrease in CO offsets the positive effects of PEEP application and causes decreased oxygenation. More importantly, the ability to capture this effect in this analysis suggests that this model can be used to evaluate oxygenation based on changes in cardiac output due to PEEP.
Point A represents the maximum allowable drop in cardiac output (approximately 0.43 L/min/cmH_{2}O) at which application of PEEP 7 cmH_{2}O will still yield beneficial oxygenation. However, at point A, if the PEEP is then raised to 12 cmH_{2}O, the oxygenation is worse off. Thus, point B is the maximum allowable CO drop if a PEEP of 12 cmH_{2}O is to be applied (approximately 0.33 L/min/cmH_{2}O). Between points B and C, an applied PEEP of 12 cmH_{2}O will provide better oxygenation than the initial PEEP, but still not as good as provided by PEEP of 7 cmH_{2}O. Only if the drop in CO is less than 0.3 L/min/cmH_{2}O (Point C), then a PEEP of 12 cmH_{2}O is more beneficial than 7 cmH_{2}O.
Optimum level of PEEP depending on rate of cardiac output change
PEEP [cmH _{2} O] | Drop in cardiac output [L/min/cmH2O] |
---|---|
5 | >0.43 |
7 | >0.30 and <0.43 |
12 | <0.30 |
Robustness Testing
In clinical practice, the need to initially measure the CO may not be viable due to the severity of the patient's condition, and an estimate for the CO at the base PEEP may be required. To test the validity of the initial CO estimate, a robustness test was conducted.
Initial estimate of CO at PEEP = 5 cmH2O (bold italicised cells).
PEEP | Drop in CO [L/Min] | Percentage Drop in CO [%] | |||||
---|---|---|---|---|---|---|---|
5 | 7 | 12 | PEEP 5 & 7 | PEEP 7 & 12 | PEEP 5 & 7 | PEEP 7 & 12 | |
Cardiac Output | 2 | 1.8 | 1.7 | 0.2 | 0.1 | 10 | 6 |
2.5 | 2.4 | 2.2 | 0.1 | 0.2 | 4 | 8 | |
3 | 2.7 | 2.5 | 0.3 | 0.2 | 10 | 7 | |
3.5 | 3.3 | 3 | 0.2 | 0.3 | 6 | 9 | |
4 | 3.6 | 3.3 | 0.4 | 0.3 | 10 | 8 | |
4.5 | 4.2 | 3.8 | 0.3 | 0.4 | 7 | 10 | |
5 | 4.5 | 4.1 | 0.5 | 0.4 | 10 | 9 | |
5.5 | 4.9 | 4.4 | 0.6 | 0.5 | 11 | 10 | |
6 | 5.2 | 4.7 | 0.8 | 0.5 | 13 | 10 | |
6.5 | 5.9 | 5.3 | 0.6 | 0.6 | 9 | 10 | |
7 | 6.2 | 5.6 | 0.8 | 0.6 | 11 | 10 | |
7.5 | 6.6 | 5.9 | 0.9 | 0.7 | 12 | 11 | |
8 | 7 | 6.2 | 1 | 0.8 | 13 | 11 | |
Median | 0.5 | 0.4 | 10 | 9.5 | |||
Max | 1.0 | 0.8 | 13.3 | 11.4 | |||
Minimum | 0.1 | 0.1 | 4.0 | 5.6 |
Figure 12 shows the effect of different initial estimates of CO on the absolute drop in CO at higher PEEP values. The graph illustrates the absolute drop on CO to be highly dependent on the initial estimate. As the initial estimate of CO becomes higher, the drop in CO also increases, and Figure 12 shows significant differences from the median CO drop.
However, from a percentage drop perspective, Figure 13 indicates that the percentage drop does not vary too much. The percentage drop of CO with the application of PEEP is approximately constant and does not drop by more than 15%. It is also clear that all points are within close proximity to the median. Thus, given an arbitrary initial estimate, it is possible to track percentage changes as a function of PEEP application.
Sensitivity to Lung Mechanics
The estimation of percentage change in shunt is calculated using Equation (8), and is dependent on the maximum theoretical lung capacity, as determined by the lung mechanics model. However, the theoretical lung capacity is a value derived from the model fit and is not the exact value of true lung capacity. Thus, the estimation of shunt changes according to Equation (8) may not be clinically accurate.
To test how the change in shunt is affected by different values of theoretical lung capacity, a sensitivity test was performed. By varying the theoretical lung capacity by 10%, the effect on the shunt at a PEEP of 7 cmH_{2}O and the percentage decrease in shunt between 5 and 7 cmH_{2}O was modelled to measure the sensitivity of these two parameters.
Model Limitations and Discussion
According to the diffusion model, as CO drops, the S_{a}O_{2} should also drop given no other parameters change. However, an application of PEEP is generally used to improve oxygenation and cause an increase in S_{a}O_{2,} even when PEEP causes CO to drop. The POC model highlights the tradeoff that can occur when PEEP increases and CO drops. When PEEP is applied in the POC model, S_{a}O_{2} can increase. Although increasing PEEP causes a drop in CO, the S_{a}O_{2} can still increase if the beneficial effect of PEEP on oxygenation offsets the detrimental effect of a CO drop on oxygenation.
The model this paper presents has some limitations that must also be discussed. The first major limitation is the lack of complete clinical data in validating this model. Although the aim of this paper was to describe the proof of concept, the combination of two different data sets does not give an accurate representation of true lung mechanics. However, this model will be tested on real clinical haemodynamic and lung mechanics data, which will be obtained in recently approved trials. Equally importantly, as noted, the values obtained are still well within reported ranges lending some added credibility to the analysis presented.
Although the application of PEEP causes a decrease in CO, CO itself is affected by different factors [25]. In reality, it is difficult to know what effect various combinations of ventilation parameters and lung mechanics have on CO without any further clinical data. The work by Crotti et al [1] indicated that CO did change significantly as PEEP increased. However, in that paper, tidal volume was not kept constant across PEEP. The model presented here used PV data with constant tidal volume. Thus, it is reasonable to assume that with all other parameters constant, the sole application of PEEP will lower CO. However, the model is limited as it does not examine the effect on CO when other parameters are varied and more clinical data is required.
The paper uses the diffusion model of Andreassen et al [14]. When evaluating the changes in shunt due to PEEP application, the model assumes that diffusion resistance does not change for the purpose of simplicity. It also considers and treats shunt as being homogeneous and responsive to PEEP, which is not always the case. These assumptions may or may not be accurate and will be tested with further clinical data.
The estimations of shunt changes according to Equation (8) are dependent on the total lung capacity as modelled by the lung mechanics model. In reality, this theoretical lung capacity could take on any value and thus, the estimation of shunt changes may not be entirely accurate. However, the lung mechanics model is currently being validated in clinical trials. If the lung mechanics model accurately predicts recruitment as compared to computed tomography scans, then this assumption of shunt change should be accurate enough.
Finally, the initial measurement of shunt requires a known value of cardiac output. In this study, the initial cardiac output for the PEEP of 5 cmH_{2}O was assumed to be 5 L/min. This measurement may require some invasive measurement that may not be ideal for all MV patients. Furthermore, without the use of clinical data, it is difficult to see how frequently the CO needs to be re-calibrated to the initial measurement from thermodilution. However, even if the initial cardiac output is estimated, the changes in CO are still tracked, which is the more important parameter. Thus, the initial measurement of the initial CO can be avoided if the changes in CO is all that is needed, provided that a reasonably accurate estimate is available.
Conclusions
This article has developed a model of lung mechanics and gas exchange. It has two primary applications. First, it can be used to monitor CO and assess the impact of changes in PEEP on the resulting CO. Hence, it can, secondly, potentially be used to optimise PEEP with respect to gas exchange and oxygenation, as well as its impact on circulation and its management.
More specifically, two models are presented and linked through a hypothesis that a change in shunt can be approximated by a change in lung volumes as PEEP changes. A proof of concept case study based on clinical data is used to show the model's capability and validity. Finally, sensitivity studies are used to illustrate the models potential robustness.
Such linked physiological models offer the opportunity to move beyond simple clinical, model-based decision support to more complex cases including physiological interactions between systems. The results presented show promise and justify further clinical validation in upcoming clinical trials.
Declarations
Ackknowledgements
N/A
Authors’ Affiliations
References
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