Startseite Inspiratory and expiratory elastance in a non-linear autoregressive model of pulmonary mechanics
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Inspiratory and expiratory elastance in a non-linear autoregressive model of pulmonary mechanics

  • Ruby Langdon EMAIL logo , Paul D. Docherty und Knut Möller
Veröffentlicht/Copyright: 30. September 2016
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Current Directions in Biomedical Engineering
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Abstract

For patients with acute respiratory distress syndrome (ARDS), the use of mathematical models to determine patient-specific ventilator settings can reduce ventilator induced lung injury and improve patient outcomes. A non-linear autoregressive model of pulmonary mechanics was used to identify inspiratory and expiratory pressure-dependent elastance (Ei and Ee) as independent variables. The analysis was implemented on 19 data sets of recruitment manoeuvres (RMs) that were performed on 10 mechanically ventilated patients. At pressures p = 15–20 cmH2O the agreement between Ei and Ee was low. However, Ei was a well-matched predictor of Ee for p = 25–40 cmH2O, with R2 ≥ 0.78, and there was no significant bias in the difference between Ei and Ee. Since many other models cannot uniquely identify Ei and Ee, the outcome may provide further insight into the characteristics of ARDS lungs in sedated patients.

Keywords: autoregressive models; parameter identification; pulmonary modelling

1 Introduction

Acute respiratory distress syndrome (ARDS) is a condition treated via mechanical ventilation in the intensive care unit (ICU). ARDS generally involves inflammation in the lungs and excess fluid in the airspaces, which increases elastance. While ventilation is necessary, it can sometimes cause ventilator induced lung injury (VILI) [1]. Excessively high airway pressure or high tidal volumes can cause distension and sometimes rupture of alveoli. Low pressures cause the cyclical opening and closing of alveoli with each breath that can damage healthy alveoli, known as atelectrauma [2].

The use of patient specific ventilator settings can help to avoid VILI [3]. As each patient and their disease state are unique, the optimal ventilator settings are patient specific. Mathematical models that describe the physiology of ARDS lungs can allow these optimal patient specific ventilator settings to be found. VILI is associated with a high mortality rate [4], thus a model that effectively describes lung behaviour and reduces the chances of VILI could significantly improve patient outcomes and reduce morbidity and mortality.

While there are a wide range of physiologically and clinically relevant models [5], [6], [7], in general these models are not able to uniquely identify inspiratory elastance Ei, and expiratory elastance Ee as independent variables. This is because the flow and volume both follow exponential decays during relaxed expiration of the sedated lung. As flow and volume are not linearly independent, single elastance and resistance terms are non-identifiable.

A nonlinear autoregressive (NARX) model of pulmonary mechanics has been described by Langdon et al. [8]. The NARX model uses basis functions to describe a pressure-dependent elastance, allowing it to describe recruitment and distension effects across recruitment manoeuvres (RMs). The model also uses time-dependent, flow-dependent terms to fit the passive lung relaxation during an inspiratory pause.

The aim of this paper is to determine the ability of the NARX model to identify independent inspiratory and expiratory elastances, and show the relationship between Ei and Ee. This will help to further validate the NARX model and its usefulness in accurately describing patient physiology.

2 Material and methods

2.1 Data

Data from a pilot clinical utilisation of respiratory elastance (CURE) software trial was used in this analysis. Airway pressure and flow data were collected from ten fully sedated ARDS patients, seven of which were ventilated in pressure controlled mode, and three of which were ventilated in volume controlled mode. Patient age ranged from 18 to 88 with a mean of 50.3 years. The breathing rate was approximately 18 breaths per minute. Pressure and flow were recorded from a Puritan Bennett 840 ventilator at a sampling rate of 50 Hz. Volume was calculated from continuous integration of the flow, with compensation for volume drift to maintain a volume of zero at PEEP.

As patients often underwent multiple RMs during the trial, 19 sets of data were obtained. PEEP at the beginning of the RM varied between 8 cmH2O and 16 cmH2O for different patients. During each RM, PEEP was increased in steps of 2 cmH2O. The RMs of different patients contained between four and nine PEEP step increases. The maximum pressure reached for each patient ranged between 36 cmH2O and 52 cmH2O.

Ethics approval for the study and use of collected data was granted by the New Zealand South Regional Ethics Committee. Informed consent was obatined from all individuals.

2.2 Respiratory models

The NARX model contains first order b-spline basis functions that describe a pressure dependent elastance, and time dependent terms that capture the pressure responses that occur due to changes in flow:

(1)Pa⁢w⁢(t)=⁢∑k=14ai⁢k⁢∅k⁢(Pa⁢wi⁢(t))⁢Vi⁢(t)+⁢∑k=14ae⁢k⁢∅k⁢(Pa⁢we⁢(t))⁢Ve⁢(t)+⁢∑j=1170bj⁢V˙⁢(t−j)+P0⁢(t)

where: Pawi and Pawe are the measured inspiratory and expiratory airway pressure (cmH2O), V˙ is the airway flow rate (l/s), Vi and Ve are the inspiratory and expiratory volume (l), and P0 is the end-expiratory pressure (cmH2O). There are four first order basis-functions to be used, k is the index of a particular basis function, ak is the coefficient for a given basis function (cmH2O/l), and ∅k⁢(Pa⁢w⁢(t)) is the basis function value for a given pressure measurement. The sum of the basis functions multiplied by their ak coefficients defines elastance. There are 170 bj coefficients (cmH2Os/l) that capture airway resistance, viscoelastic effects, and expiratory relaxation. The subscript –j in the third term refers to the previous time samples. Thus, each Paw(t) is calculated from information from the previous 170 data points.

The optimal number of basis functions and bj terms was determined in previous analyses of the NARX model fit for this data set [9].

To identify the NARX model coefficients, a linear system of equations must be generated and inverted to find:

(2)x=[ai⁢1…ai⁢4ae⁢1…ae⁢4b1⋯b170]T

where: ai1–ai4 are the inspiratory elastance coefficients, and ae1–ae4 are the expiratory elastance coefficients.

The inspiratory elastance coefficients are identified based on inspiratory data only, and the expiratory elastance coefficients are identified on expiratory data only. The b coefficients are identified on both inspiratory and expiratory data.

2.3 Analysis

The ai, ae, and b coefficients were identified for each data set. The basis functions multiplied by the a terms gives a continuous elastance across pressure between the minimum and maximum pressures present in each data set. The coefficient of determination (R2) was calculated for the linear relationship between Ee and Ei at different pressures. Bland-Altman analysis was performed to determine any bias in the difference between Ee and Ei as pressure increased. To further quantify intra-patient versus inter-patient variability, the variance of Ei, Ee, and (Ei–Ee) were calculated. All analysis was undertaken on an i7 quad core PC with 16GB RAM using MATLAB 2014a 64 bit functions and the statistical toolbox (Mathworks, Natick, MA, USA).

3 Results

The inspiratory and expiratory elastances were determined for each of the 19 data sets. The agreement between Ei and Ee was generally poor at low pressure, and good at pressures greater than the second basis function knot. The behaviour of a typical patient is shown in Figure 1.

Figure 1 Inspiratory and expiratory elastance across pressure for one patient.
Figure 1

Inspiratory and expiratory elastance across pressure for one patient.

The relationship between Ei and Ee at various pressures is shown in Figure 2. The plot at p = 15 cmH2O contains 18 data points because one data set did not contain pressures as low as 15 cmH2O. Similarly, two data sets did not contain pressures at 40 cmH2O or greater.

Figure 2 Expiratory elastance vs. inspiratory elastance for p = [15 20 25 30 35 40] cmH2O. R2 values are given for the linear relationship between Ee and Ei, plotted in red. The 1:1 line is plotted in black.
Figure 2

Expiratory elastance vs. inspiratory elastance for p = [15 20 25 30 35 40] cmH2O. R2 values are given for the linear relationship between Ee and Ei, plotted in red. The 1:1 line is plotted in black.

The R2 value for the Ei to Ee linear relationship describes how well the Ei value predicts the Ee value. Figure 2 shows the strength of prediction is weak at p = 15 cmH2O, but strong for p ≥ 25 cmH2O, with R2 ≥ 0.78. The 1:1 lines plotted plotted on Figure 2 show that there is a tendency for Ei to be > Ee at low pressures, and for Ee to be slightly higher than Ei at high pressures.

Bland-Altman plots allow any fixed bias between Ei and Ee to be more easily observed. Figure 3 shows the Bland-Altman plots for pressures 15–40 cmH2O. The mean and corresponding p value are specified on each plot. A p value > 0.05 indicates that the mean difference is not significantly different from zero, based on a one sample t-test, thus there is no significant difference between Ei and Ee for this pressure. The analysis found that there is a significant difference between Ei and Ee for p = 15 cmH2O and p = 20 cmH2O only. The bias is towards Ei being larger than Ee.

Figure 3 Bland-Altman plots for p = [15 20 25 30 35 40] cmH2O. Solid line = the mean of the difference. Dotted lines = standard error of the mean difference.
Figure 3

Bland-Altman plots for p = [15 20 25 30 35 40] cmH2O. Solid line = the mean of the difference. Dotted lines = standard error of the mean difference.

Variances of Ei, Ee, and (Ei–Ee) were calcualted to determine intra-patient versus inter-patient variability. For pressures of 20 cmH2O and above, the variance of (Ee–Ei) was smaller than the variance of both Ei and Ee at each measured pressure. Based on the t-test, the variance of Ei and Ee were not significantly different. The variance of (Ee–Ei) was significantly smaller than the variance of Ei (t-test, p = 0.0007) and significantly smaller than the variance of Ee (t-test, p = 0.03).

4 Discussion

This analysis shows that the NARX model is capable of identifying unique inspiratory and expiratory elastance profiles. Ei was a well-matched predictor of Ee for p = 25–40 cmH2O (Figure 2). There was no significant bias in the difference between Ei and Ee for p = 25–40 cmH2O (Figure 3). The intra-patient variability was significantly lower than the inter-patient variablility for p = 20–40 cmH2O. Overall, this indicates that for this cohort, Ei and Ee were comparable for 25 ≤ p ≤ 40 cmH2O, and thus may be equally valuable as an indicator of patient condition.

There was low agreement between Ei and Ee at low pressures (Figure 1). Ei was a bad predictor of Ee at p = 15 cmH2O. There was a significant positive bias in (Ei–Ee) at p = 15 cmH2O and p = 20 cmH2O. In addition, the variance of (Ei–Ee) was larger than the variance of Ee at p = 15 cmH2O. The cause of this behaviour relates to the use of distinct basis functions used to define elastance. With M = 4, the first basis function (∅1) is non-zero for only the lowest third of the pressures present in the data set. Therefore ∅1 is identified using only the volume data that exists when these low pressures are present in inspiration.

At the beginning of inspiration, the pressure rises very rapidly. There are relatively few data points here, as the gradient of the pressure increase is so steep. Thus there are relatively few data points used to identify ∅1, compared to ∅2, ∅3, and ∅4. There is not enough useful information for determining the elastance in this small portion of inspiratory data. Since the gradient of the pressure drop during expiration is shallower at lower pressures, there is more data available to identify expiratory elastance, and the issue does not occur. Therefore Ee is likely to be more reliable than Ei at low pressure using the method presented in this paper.

A similar problem with inspiratory elastance would be likely to occur if the NARX model was identified using this method on any single PEEP level, where a recruitment manoeuvre was not carried out. In this scenario, either the Ei and Ee should not be identified separately, or the Ei should not be relied on for diagnostic use.

While a strong agreement between Ei and Ee was found for 25 ≤ p ≤ 40 cmH2O, the sample size of 19 data sets is relatively small. Also, due to the limited size of the RMs for some patients, the p = 15 cmH2O analysis was based on 18 data sets, and the analysis at p = 40 cmH2O was based on only 17 data sets. The methods should be tested on a larger patient cohort to verify the results. A larger number of patients with RMs that reached pressures of greater than 40 cmH2O would also allow an assessment of any possible variability in Ei and Ee at very high pressures.

Separate inspiratory and expiratory elastances may not be currently used as a diagnostic aid by clinicians. However, this analysis has shown that unique Ei and Ee values can be obtained using the NARX model. The outcomes of this type of analysis may provide further insight into sedated ARDS patient conditions that other models cannot accomplish.

Author’s Statement

Research funding: The author state no funding involved. Conflict of interest: Authors state no conflict of interest. Informed consent: Informed consent has been obtained from all individuals included in this study. Ethical approval: Ethics approval for the study and use of collected data was granted by the New Zealand South Regional Ethics Committee.

References

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Published Online: 2016-9-30
Published in Print: 2016-9-1

©2016 Ruby Langdon et al., licensee De Gruyter.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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https://doi.org/10.1515/cdbme-2016-0138
Schlagwörter für diesen Artikel
autoregressive models; parameter identification; pulmonary modelling
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  51. Derivation of the respiratory rate from directly and indirectly measured respiratory signals using autocorrelation
  52. Left cardiac atrioventricular delay and inter-ventricular delay in cardiac resynchronization therapy responder and non-responder
  53. An automatic systolic peak detector of blood pressure waveforms using 4th order cumulants
  54. Real-time QRS detection using integrated variance for ECG gated cardiac MRI
  55. Preprocessing of unipolar signals acquired by a novel intracardiac mapping system
  56. In-vitro experiments to characterize ventricular electromechanics
  57. Continuous non-invasive monitoring of blood pressure in the operating room: a cuffless optical technology at the fingertip
  58. Application of microwave sensor technology in cardiovascular disease for plaque detection
  59. Artificial blood circulatory and special Ultrasound Doppler probes for detecting and sizing gaseous embolism
  60. Detection of microsleep events in a car driving simulation study using electrocardiographic features
  61. A method to determine the kink resistance of stents and stent delivery systems according to international standards
  62. Comparison of stented bifurcation and straight vessel 3D-simulation with a prior simulated velocity profile inlet
  63. Transient Euler-Lagrange/DEM simulation of stent thrombosis
  64. Automated control of the laser welding process of heart valve scaffolds
  65. Automation of a test bench for accessing the bendability of electrospun vascular grafts
  66. Influence of storage conditions on the release of growth factors in platelet-rich blood derivatives
  67. Cryopreservation of cells using defined serum-free cryoprotective agents
  68. New bioreactor vessel for tissue engineering of human nasal septal chondrocytes
  69. Determination of the membrane hydraulic permeability of MSCs
  70. Climate retainment in carbon dioxide incubators
  71. Multiple factors influencing OR ventilation system effectiveness
  72. Evaluation of an app-based stress protocol
  73. Medication process in Styrian hospitals
  74. Control tower to surgical theater
  75. Development of a skull phantom for the assessment of implant X-ray visibility
  76. Surgical navigation with QR codes
  77. Investigation of the pressure gradient of embolic protection devices
  78. Computer assistance in femoral derotation osteotomy: a bottom-up approach
  79. Automatic depth scanning system for 3D infrared thermography
  80. A service for monitoring the quality of intraoperative cone beam CT images
  81. Resectoscope with an easy to use twist mechanism for improved handling
  82. In vitro simulation of distribution processes following intramuscular injection
  83. Adjusting inkjet printhead parameters to deposit drugs into micro-sized reservoirs
  84. A flexible standalone system with integrated sensor feedback for multi-pad electrode FES of the hand
  85. Smart control for functional electrical stimulation with optimal pulse intensity
  86. Tactile display on the remaining hand for unilateral hand amputees
  87. Effects of sustained electrical stimulation on spasticity assessed by the pendulum test
  88. An improved tracking framework for ultrasound probe localization in image-guided radiosurgery
  89. Improvement of a subviral particle tracker by the use of a LAP-Kalman-algorithm
  90. Learning discriminative classification models for grading anal intraepithelial neoplasia
  91. Regularization of EIT reconstruction based on multi-scales wavelet transforms
  92. Assessing MRI susceptibility artefact through an indicator of image distortion
  93. EyeGuidance – a computer controlled system to guide eye movements
  94. A framework for feedback-based segmentation of 3D image stacks
  95. Doppler optical coherence tomography as a promising tool for detecting fluid in the human middle ear
  96. 3D Local in vivo Environment (LivE) imaging for single cell protein analysis of bone tissue
  97. Inside-Out access strategy using new trans-vascular catheter approach
  98. US/MRI fusion with new optical tracking and marker approach for interventional procedures inside the MRI suite
  99. Impact of different registration methods in MEG source analysis
  100. 3D segmentation of thyroid ultrasound images using active contours
  101. Designing a compact MRI motion phantom
  102. Cerebral cortex classification by conditional random fields applied to intraoperative thermal imaging
  103. Classification of indirect immunofluorescence images using thresholded local binary count features
  104. Analysis of muscle fatigue conditions using time-frequency images and GLCM features
  105. Numerical evaluation of image parameters of ETR-1
  106. Fabrication of a compliant phantom of the human aortic arch for use in Particle Image Velocimetry (PIV) experimentation
  107. Effect of the number of electrodes on the reconstructed lung shape in electrical impedance tomography
  108. Hardware dependencies of GPU-accelerated beamformer performances for microwave breast cancer detection
  109. Computer assisted assessment of progressing osteoradionecrosis of the jaw for clinical diagnosis and treatment
  110. Evaluation of reconstruction parameters of electrical impedance tomography on aorta detection during saline bolus injection
  111. Evaluation of open-source software for the lung segmentation
  112. Automatic determination of lung features of CF patients in CT scans
  113. Image analysis of self-organized multicellular patterns
  114. Effect of key parameters on synthesis of superparamagnetic nanoparticles (SPIONs)
  115. Radiopacity assessment of neurovascular implants
  116. Development of a desiccant based dielectric for monitoring humidity conditions in miniaturized hermetic implantable packages
  117. Development of an artifact-free aneurysm clip
  118. Enhancing the regeneration of bone defects by alkalizing the peri-implant zone – an in vitro approach
  119. Rapid prototyping of replica knee implants for in vitro testing
  120. Protecting ultra- and hyperhydrophilic implant surfaces in dry state from loss of wettability
  121. Advanced wettability analysis of implant surfaces
  122. Patient-specific hip prostheses designed by surgeons
  123. Plasma treatment on novel carbon fiber reinforced PEEK cages to enhance bioactivity
  124. Wear of a total intervertebral disc prosthesis
  125. Digital health and digital biomarkers – enabling value chains on health data
  126. Usability in the lifecycle of medical software development
  127. Influence of different test gases in a non-destructive 100% quality control system for medical devices
  128. Device development guided by user satisfaction survey on auricular vagus nerve stimulation
  129. Empirical assessment of the time course of innovation in biomedical engineering: first results of a comparative approach
  130. Effect of left atrial hypertrophy on P-wave morphology in a computational model
  131. Simulation of intracardiac electrograms around acute ablation lesions
  132. Parametrization of activation based cardiac electrophysiology models using bidomain model simulations
  133. Assessment of nasal resistance using computational fluid dynamics
  134. Resistance in a non-linear autoregressive model of pulmonary mechanics
  135. Inspiratory and expiratory elastance in a non-linear autoregressive model of pulmonary mechanics
  136. Determination of regional lung function in cystic fibrosis using electrical impedance tomography
  137. Development of parietal bone surrogates for parietal graft lift training
  138. Numerical simulation of mechanically stimulated bone remodelling
  139. Conversion of engineering stresses to Cauchy stresses in tensile and compression tests of thermoplastic polymers
  140. Numerical examinations of simplified spondylodesis models concerning energy absorption in magnetic resonance imaging
  141. Principle study on the signal connection at transabdominal fetal pulse oximetry
  142. Influence of Siluron® insertion on model drug distribution in the simulated vitreous body
  143. Evaluating different approaches to identify a three parameter gas exchange model
  144. Effects of fibrosis on the extracellular potential based on 3D reconstructions from histological sections of heart tissue
  145. From imaging to hemodynamics – how reconstruction kernels influence the blood flow predictions in intracranial aneurysms
  146. Flow optimised design of a novel point-of-care diagnostic device for the detection of disease specific biomarkers
  147. Improved FPGA controlled artificial vascular system for plethysmographic measurements
  148. Minimally spaced electrode positions for multi-functional chest sensors: ECG and respiratory signal estimation
  149. Automated detection of alveolar arches for nasoalveolar molding in cleft lip and palate treatment
  150. Control scheme selection in human-machine- interfaces by analysis of activity signals
  151. Event-based sampling for reducing communication load in realtime human motion analysis by wireless inertial sensor networks
  152. Automatic pairing of inertial sensors to lower limb segments – a plug-and-play approach
  153. Contactless respiratory monitoring system for magnetic resonance imaging applications using a laser range sensor
  154. Interactive monitoring system for visual respiratory biofeedback
  155. Development of a low-cost senor based aid for visually impaired people
  156. Patient assistive system for the shoulder joint
  157. A passive beating heart setup for interventional cardiology training
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Heruntergeladen am 12.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/cdbme-2016-0138/html
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