Linear System Modeling of a Mechanical Ventilator
BE 3317
12/13/2018
Malik Ibrahim, Tom Overman, Barsha Bogati, Joselyne White
Group 7
Introduction
A mechanical ventilator is an automated machine which provides assistance in breathing, primarily used by the patients having difficulty in breathing, unstable health condition, recovery from illness and other various health issues. As the device name suggests, its primary function is to ventilate the air inside and outside of the lungs and maintain homeostasis between gas concentration until the patients can breathe on their own effectively. It is usually connected to the patient’s body through an Endotracheal tube inserted in to the mouth or nose extending all the way to trachea by the process of intubation and inflating a small tube to snugly keep in place.
With the advancement of technology, the basic structure and function of mechanical ventilation has expanded bit the underlying working principle of the mechanical ventilation remains the same i.e., pumping air in to our lungs and allow for the escape passively. However the basic working principle of the ventilator system gets modified on the basis of different modes of the ventilator system that is set up as per the condition of the patient.
Assist Control (AC) is the most common form of ventilation and is also called continuous mandatory ventilation. In this type of ventilation, the vent is triggered by the patient (e.g.: patient takes breath) which creates a negative pressure which is sensed by the ventilator. This negative pressure delivers specific tidal volume of gas set from the ventilator system to the body. During the process various which modification in the parameter takes place and the homeostatic circulation of gas is possible. A backup mode or rate can also be set up in the system which will deliver certain volume of gas after certain interval of time only if the patient doesn’t take breath at required rate. Overall, we are setting the volume and our output to study and analyze is our pressure.
· Pressure Controlled Ventilation: Also known as PCV ventilator is one of the basic approach of ventilation used worldwide which use pressure as a primary controlled parameter and a the required tidal volume of air delivery is signified by the time signal. As we are setting the pressure the lungs will receive specific compliance. And as per the pressure supplies if the compliance is very low, the ventilator will detect lower volume and vice versa.
There are additional various modes of mechanical ventilation such as Pressure Controlled Inverse Ratio Ventilation, Airway Pressure Release Ventilation, Pressure Regulated Volume Control Ventilation and so on.
The essential parameters of a mechanical ventilation are described as follows:
Trigger: It is the starter point of any mechanical ventilation. The trigger can be general pressure or flow and when these trigger variable are set to a preset value, the inspiration is initiated.
Pressure Triggered: In the pressure triggered breathe, the ventilator senses the negative pressure deflection caused by the patient’s effort to initiate a breath. This drop-in pressure to trigger the ventilator.
Flow Triggered: In the flow triggered the ventilator sense the changes in inspiratory flow caused by the patient effort to initiate a breath.
The essential parameters of a mechanical ventilation are described as follows:
Tidal Volume: Tidal volume can be defined as an amount of hair inhaled by a person in a normal breath. As per research, the approximate tidal volume of healthy adult is 7 ml/kg of body mass. Meanwhile, the initial tidal volume preset for a mechanical ventilation depends upon the condition of the person and their disease.
Respiratory Rate: Respiratory Rate is total number of breaths per minute. The normal respiratory rate provided to patients is 12 to 16 breaths per minute as the best possible method for determining respiration rate is yet to be found.
Positive End Expiratory Pressure: It is defined as positive pressure that remains oin the airways at the end of exhalation. This important to prevent from expiratory alveolar collapse and to improve oxygenation in the body.
Flow Rate: As its name suggest flow rate is the pace of flow provided by the ventilator during inspiration. In most of the patient 60 L/min IFR is considered an optimal value
Inspiratory and Expiratory time ratio: The ratio between the inhalation and the exhalation time whose optimal value is 1:2. Since inspiration is an active process while expiration is passive process , expiration usually take a longer time period. Change in the ratio may cause respective disadvantage such as longer exhalation results stacking of carbon dioxide resulting an increases in expiratory PEEP while increase in inspiratory may increase chances of collapsing.
Fraction of Inspired Oxygen: It can be defined as percentage of oxygen inhaled by an individual. Usually 100% FIO2 is provided to the patient after ventilation intubation in order to prevent the patient from hypoxemia. Late the value is changed as per the documentation of the person condition and arterial oxygenation report.
Compliance: It is defined as a measure of the stiffness of the lungs. In other words it is absorption of the applied force by the lung tissue produce from the change in intrathoracic pressure. It can be calculated by divide change in volume(l) by the change in pressure (cm H2O).
After analyzing the basic definition, function, principle of mechanical ventilation we are doing a research on Advance Lung dual Controlled Ventilation System . The system is an effort to improve the conventional dual controlled ventilation system by the use Pressure-controlled Ventilation with defined tidal and minute volume as a primary parameter. The main feature of ALVS is the use of linear respiratory mechanics for waveform optimization of the Demand Controlled Ventilation.
Dual Control Ventilation System
Dual control ventilation components: the solution to the limitations caused by traditional ventilation systems is the dual controlled ventilation system. Where the constant air pressure for the inspiration is not set at a constant value. The goal being to optimize a waveform to get a good airway flow going. Some functional properties of the DCV is the ability is to apply any pressure waveform of choice. For the ventilator to be insensitive to waveform shape and load due to fluctuations or variations. It needs to be capable of monitoring pressure waveform with respect to time. Also needs to have compatibility with spontaneous behavior due to patient by using some pressure support ventilation. Its split up into three parts the Time-varying Pressure Stabilizer ( TVAPS), The Stationary and Transient Flow Generator Stabilizer (STFGS), and The Dynamic Respiratory System Simulator (DRSS).
The Stationary and Transient Flow Generator Stabilizer (STFGS) is the start of the dual controlled ventations system. It consists of a variable pressure generator (Pg) and a time varying resistance (Rg). Its goal is to provide to the subject an airway pressure waveform of choice during the actions of inspiration and expiration.It starts at ground which is the atmospheric level running it through the pressure generator where the input square waveform is implemented. Then it goes to a time varying resistance which we treat as a constant. The STFGS is designed for independent stabilization of the flow crossing the Time-varying airways pressure stabilizer both in stationary and transient conditions.
Time-varying Airways Pressure Stabilizer (TVAPS) is a component of the dual-control ventilator which utilizes pressure controlled ventilation but with an ensured volume. His section of the mechanical ventilator uses feedback control to supply the proper tidal volume. Varying the pressure rather than keeping it constant like in most pressure controlled ventilators. TVAPS responsible for regulation of fluidodynamic resistance modeled in a circuit as a potentiometer. Time-varying resistance between airways and ground which is just the normal atmospheric pressure outside of a lung.
The Dynamic Respiratory System Simulator (DRSS) is a lung simulator used to simulate specific lung pathologies. It is also used to test lung-function equipment. The system consisting of a variable resistance Rp (airway resistance), the pressure of the endoalveolar, and variable elastic compliance Cp (lung compliance). The system as a whole represents a artificial lung. With the variable elastic compliance represents the lung compliance and airway resistance of the subject.
Analysis of System
In order to more easily characterize the system and find output responses to given biologically-relevant inputs, the system was translated into the equivalent electrical circuit. This allows the use of Kirchhoff’s laws and other circuit analysis methods to more easily arrive at results. The following electro-fluidic analogues were used:
Resistance of lung: electrical resistance
Compliance of lung: electrical capacitance
Volumetric flow rate: electrical current
Volume: charge
Pressure: voltage potential
The equivalent circuit is shown below in the figure.
The next step is to transform the circuit into a useful set of equations. As the circuit is much easier to handle in the Laplace domain, we will convert all of the circuit components to their Laplace equivalents and then use Kirchhoff’s laws to derive a system of equations.
For inspiratory flow:
From this set of three equations we are able to algebraically manipulate and use the inverse Laplace transform to determine useful expressions in the time domain for our target parameter. The output parameters of interest in this system are the volume of the lung, airways pressure, alveolar pressure, and respiratory volume flow versus time.
Now we analyze the circuit for expiratory flow, use the inverse laplace transform to retrieve our desired output expressions, then we graph the waveforms as functions of time with two different inputs to demonstrate how the system responds to various inputs. The three equations derived from Kirchhoff’s for expiratory flow is below:
The above equations were algebraically manipulated then inverted with the Inverse Laplace transform back to the time domain.
Now that the proper expressions have been determined, proper input waveforms must be determined to achieve biologically-relevant volume and pressure measurements in the lung. The pressure generator will be the input source in this system. The first input will be a standard rect waveform. However, as this is not physically realizable, this will be compensated for in the second signal with a ramp/rect combination representing a gradual increase to a peak pressure value.
Several variables in the expressions above are constant values. The following constants will be used based on experimental data: RINS= 10cmH2Osl-1, REXP=20 cmH2Osl-1, Cp=25 ml/cmH2O, PEEPEXT=2.1 cmH2O, PGI=22.2 cmH2O
With a standard rect waveform input for the pressure generator, the corresponding output expressions were found. The following graphs were plotted in matlab to help visualize the system response. The plots created in Matlab are for an entire inhalation-exhalation cycle. The second input signal is a positive ramp function connected to a rect function with a negative ramp function going back to zero. This is a physically realizable input because the pressure does not immediately climb to a peak value in zero time.
Input Signal 1:
PG=u(t)-u(t-3)
Output signals 2:
INS(t) =2(u(t) – u(t-3))-10.556e-5t1400
Vpi(t)=25[.175-13INS(t)]
Input Signal 2:
PG=tu(t) – (t-0.5)u(t-0.5)-(t-2.5)u(t-2.5) + (t-3)u(t-3)
Output signals 2:
INS(t) =2(tu(t) – (t-0.5)u(t-0.5)-(t-2.5)u(t-2.5) + (t-3)u(t-3))-10.556e-5t1400
Vpi(t)=25[.175-13INS(t)]
Conclusion
The dual controlled ventilation model, while not widespread in medical communities yet, offers much versatility in providing proper volume and pressure to the lungs. A proper mechanical ventilation system is vital in the medical community, and optimizing the system to create the best output is critical for patient health. The ventilation system described was converted to an electrical system which is much easier to analyze. Then using standard Laplace techniques the system was solved and then converted back into the time domain.
For the first input signal which consisted of a single rect waveform, the output respiratory volume flow was an exponential decrease as the lung filled up and then a positive increase from a negative value during expiration as the flow was opposite to that during inspiration. The volume of the lung increased to a max value such as a capacitor would, then decreased exponentially during expiration.
The second input signal, which consisted of a positive ramp function leading to a rect waveform leading to a negative ramp function back to zero, had outputs similar to the first, but the volume flow did not start at a max and gradually increased to a maximum value before decreasing exponentially during the inspiration cycle. The volume of the lung increased similarly to input one but had a slower initial increase.
These output responses are biologically relevant and sound as they consist of a volume increase to a peak value during inspiration and decrease during expiration. The rect waveform was optimal but is unrealizable in real systems so the compensated ramp function input was employed and has an output response very similar to the first. Thus, the ventilation system described with the proper input signals should, in theory, function as a good ventilation system in practice.
References
“Advanced Lung Ventilation System (ALVS) with Linear Respiratory Mechanics Assumption for Waveform Optimization of Dual-Controlled Ventilation.” NeuroImage, Academic Press, 6 May 2006, www.sciencedirect.com/science/article/pii/S1350453306000646?via=ihub.
Case Chronic Bronchitis, www.meddean.luc.edu/lumen/meded/MEDICINE/PULMONAR/lecture/vent_f.htm.
Júnior, Victor, et al. “Parameter Estimation of an Artificial Respiratory System under Mechanical Ventilation Following a Noisy Regime.” Química Nova, SBQ, www.scielo.br/scielo.php?script=sci_arttext&pid=S2446-47402015000400343.