- Open Access
Realistic human muscle pressure for driving a mechanical lung
© Fresnel et al.; licensee Springer. 2014
- Received: 9 December 2013
- Accepted: 1 June 2014
- Published: 19 August 2014
An important issue in noninvasive mechanical ventilation consists in understanding the origins of patient-ventilator asynchrony for reducing their incidence by adjusting ventilator settings to the intrinsic ventilatory dynamics of each patient. One of the possible ways for doing this is to evaluate the performances of the domiciliary mechanical ventilators using a test bench. Such a procedure requires to model the evolution of the pressure imposed by respiratory muscles, but for which there is no standard recommendations.
In this paper we propose a mathematical model for simulating the muscular pressure developed by the inspiratory muscles and corresponding to different patient ventilatory dynamics to drive the ASL 5000 mechanical lung. Our model is based on the charge and discharge of a capacitor through a resistor, simulating contraction and relaxation phases of the inspiratory muscles.
Our resulting equations were used to produce 420 time series of the muscle pressure with various contraction velocities, amplitudes and shapes, in order to represent the inter-patient variability clinically observed. All these dynamics depend on two parameters, the ventilatory frequency and the mouth occlusion pressure.
Based on the equation of the respiratory movement and its electrical analogy, the respiratory muscle pressure was simulated with more consistency in regards of physiological evidences than those provided by the ASL 5000 software. The great variability in the so-produced inspiratory efforts can cover most of realistic patho-physiological conditions.
- Respiratory muscle pressure
- Mechanical lung
- Mechanical ventilation
Issues in noninvasive mechanical ventilation
The main goal of mechanical ventilation is to assist the spontaneous breathing of a patient with acute or chronic respiratory failure. The ventilator improves the blood oxygenation and unloads the respiratory muscles by supplying a suitable level of pressure support . Typically, a ventilator delivers a high pressure (often named “Inspiratory Positive Airway Pressure”) during the inspiration and a low pressure (named “Expiratory Positive Airway Pressure”) during the expiration. Noninvasive mechanical ventilation is thus quite tricky since the pressure cycle delivered by the ventilator must be synchronized with the patient breathing cycle, that is, the pressure rise to reach the upper pressure level must be triggered at the onset of the patient inspiratory effort and the pressure release must be triggered when the patient ends his inspiration for breathing out. Such a good synchronization between the patient breathing cycle and the pressurization cycle delivered by the ventilator is important to ensure a better comfort and to reduce the patient work of breathing, although these points have not yet been clearly validated . Patient-ventilator asynchrony is defined as a phase shift between the patient ventilatory cycle and the pressurization cycle delivered by the ventilator. There are various types of asynchrony events , which can be detected using noninvasive measurements : reducing their incidence allows to decrease the duration for which a patient needs mechanical ventilatory assistance . The quality of the synchronization between the patient ventilatory cycle and the pressurization cycle delivered by the ventilator depends on patient physiological characteristics and on ventilator settings. Some parameters are considered as being critical for synchronizing the ventilator pressure cycle to the patient breathing dynamics: the sensitivity of the high pressure trigger , the low pressure value , the level of pressure support (the difference between the high and low pressure values) , or the time during which the high pressure is delivered . However, the way according which the pressure cycle is governed by patient inspiratory demand depends on the considered ventilators. Moreover, the terminology as well as the units of the settings present strong heterogeneities among the available ventilators .
Our objective is therefore to construct time series of the respiratory muscle pressure in agreement with physiological evidences for investigating ventilator performances under quite realistic conditions. For that purpose, we started from the equation of motion for the respiratory system, used to determine the muscle pressure Pmus. Based on an electrical analogy, the resulting mathematical model is then presented and some examples of inspiratory efforts are discussed.
Mechanics of the respiratory system: historical aspects
Equation of motion for the respiratory system
A fitted quadratic model for Pmus
A flexible dynamical model from an electrical analogy
where Urm(0)=Umax as expected at the end of the inspiration (and so at the beginning of the expiration). From the mechanical point of view, the positive muscular contraction induces a negative pressure Pmus in the respiratory system. Thus, Pmus=−Urm.
When simulating an inspiratory effort, the charge corresponds to the inspiratory phase whose duration must be chosen, and the discharge is associated with the expiratory phase. The duration of the breathing cycle is directly related to the patient ventilatory frequency f v that we choose to vary from 10 to 30 cpm (cycles per minute) in order to simulate “normal” ventilatory dynamics corresponding to stable health conditions and faster dynamics observed in acute situations or during physical efforts.
Parameter Umax appearing in solutions (13) and (15) corresponds to the amplitude of the pressure delivered by the respiratory muscles. Solutions (13) and (15) are negative, that is, they are consistent with Mecklenburg and co-workers as well as with the definitions used in the ASL 5000.
Inspiratory and expiratory durations
The transition between inspiration and expiration is assumed to correspond to the onset of the relaxation of the ventilatory muscles. Solution (13) retained for the contraction is valid between t=0 and t=TI, and solution (15) for relaxation is used between t=TI and t=Ttot, where Ttot is the duration of the breathing cycle. It has been shown that is not constant when the ventilatory frequency is varied . When f v is increased, the expiratory time decreases faster than the inspiratory duration and, consequently, increases. Physiologically, the inspiratory duration cannot be shorter than 0.5 s and longer than 1.5 s. From the data provided in , is measured in healthy subjects within the range [0.4;0.6] when f v is varied within [16;51] cpm using various levels of exercise. The ratio for resting subjects is commonly between 0.3 and 0.4 .
Time parameters defining the phases of the breathing cycles: total duration T tot , ratio calculated from equation ( 16 ), and the associated inspiratory and expiratory times
f v (cpm)
f v (cpm)
f v (cpm)
Amplitude and stiffness of the muscular pressure
The respiratory muscle function is commonly assessed in clinical works by using the so-called mouth occlusion pressure P0.1, measured 100 ms after the onset of inspiration during quiet breathing. P0.1 is representative of the central unconscious control of breathing  and of the strength of the inspiratory demand. In healthy adults at rest, P0.1 equals about 1 cmH 2O  with an unavoidable inter-subject variability ,. The value for quiet breathing in healthy adults is P0.1=0.93±0.48 cmH 2O in  and, 0.75±0.32 cmH 2O in . In this latter work, the occlusion pressure is found to be 2.83±1.27 cmH 2O in patients with chronic obstructive pulmonary diseases (COPD) and 2.41±1.01 cmH 2O in patients with restrictive lung disease. In a large cohort of 464 patients with chronic hypercapnic respiratory failure , the occlusion pressure is P0.1=4.69 (3.57;6.63) cmH 2O for patients with COPD, P0.1=3.67 (2.45;5.51) cmH 2O for patients with an obesity hypoventilation syndrome (OHS) and, P0.1=2.55 (1.43;3.77) cmH 2O for patients with other various diseases. The main value is the median and values in parenthesis are quantile values. The occlusion pressure in patients with acute respiratory failure under mechanical ventilation assistance can be found within the range [ 6;10] cmH 2O - when the pressure support level is quite low.
that is, 420 different ventilatory dynamics, each pair (f v ,P0.1) corresponding to a given lung model (or a patient in a clinical equivalent). Our simulations then represent 420 lung models, thus taking into account the inter-patient variability.
Parameters defining the inspiratory effort
Examples of the time constant τ c for contraction and τ c for relaxation for few values of the ventilatory frequency f v and of the occlusion pressure P 0 . 1
f v =10 cpm
f v =20 cpm
f v =30 cpm
Some simulations using the mechanical lung
To validate our model, we chose to compare the airflow time series obtained from some simulations with the ASL 5000 to time series measured during a protocol which was conducted by Rabarimanantsoa-Jamous at the Rouen University Hospital during her Ph.D. thesis , in which written approval was obtained from the patients. In order to investigate how asynchrony events could affect the quality of noninvasive mechanical ventilation and sleep quality, airflow and airway pressure were measured during one night. The database consists of a cohort of 35 patients with respiratory diseases and daily assisted using a mechanical ventilator (VPAP III STA, ResMed, Australia). Some patients (n=20) were affected by obesity hypoventilation syndrome (OHS) and some other (n=15) by chronic obstructive pulmonary disease (COPD), associated or not with sleep apnea. Mean body index (BMI) for these patients is 42±10.5 and their mean age is 62±11.7. We selected three airflow time series in this database, our aim being, first, to exemplify how different the dynamics underlying airflow time series can be different and, second, to show that we are able to reproduce these different dynamics with our model for the muscle pressure.
For the three simulated time series, the amplitude of the expiratory airflow is always less than the expiratory airflow measured with patients. This is due to the fact that the airflow in ventilatory circuit with true patients was measured after the mask which contains intentional leaks to send the carbon dioxide out of the ventilatory circuit, thus avoiding carbon dioxide rebreathing. Contrary to this, the airflow in ventilatory circuit with the mechanical lung is measured within the piston chamber (the artificial lung), before any intentional leak. The presence of intentional leak has also an effect on the inspiratory airflow: the measured airflow with patient is overestimated because it takes into account the part flowing through the intentional leak and, consequently, not provided to the patient.
The transitions between inspiration and expiration in our simulations are stiffer than in the measured airflow. This could be also an effect induced by the location of the airflow sensor which differs in the two circuits. Such a stiffness is perhaps also induced by the fact that in our model the parameters used to simulate the patho-physiological conditions (the airway resistance R and the thoracopulmonary compliance C) are kept constant during the simulations whereas they could change during inspiration and expiration . As exemplified with the simulated time series shown in Figures 10, 11 and 12, such approximation did not prevent us to obtain airflow time series with characteristics close to those measured in ventilatory circuit with patient. We have therefore now a realistic mechanical lung model to assess performances of ventilators.
In this paper we designed a realistic respiratory muscle pressure to drive a mechanical lung such as the ASL 5000. In order to do that, we started from the scarce data available in the literature to define the main properties of the dynamics underlying the pressure driven by the respiratory muscles. Using an electrical analogy, we used two exponential functions, one for inspiration and one for expiration. In order to have a muscular dynamics only depending on the ventilatory frequency and the mouth occlusion pressure — two clinical parameters commonly measured —, we introduced a linear dependency between the ratio of the inspiratory duration to the breathing cycle duration and the ventilatory frequency as suggested by clinical evidences. The resulting model was validated by comparing simulated airflow time series measured in the mechanical lung driven by our model with those measured in ventilatory circuits with patients. By varying the ventilatory frequency and the mouth occlusion pressure we are now able to reproduce the inter-patient variability and, consequently, to investigate performances of ventilators on a “cohort” of realistic lung models.
Written informed consent was obtained from the patients for the publication of this report and any accompanying images.
We would like to thank Jean-Christophe Richard, Jean-Paul Janssens and Antoine Cuvelier for stimulating discussions at the origin of this work.
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