Tter person TERM PAPER BM 600 Nuruddin Bahar Date: 30/4/2012 09002040 MEDICAL VENTILATOR It is an artificial ventilating device which is used to mechanically move breathable air in and out of lungs at times of lung malfunctioning or breathing insufficiency. It basically works on the principle of pressure difference created within the lungs upon alveolar expansion and contraction. The model assumed here is an isothermal environment, where the net temperature change is zero between the body and its surroundings.
A typical Medical Ventilator consists of the following settings: 1. Respiration Rate : RR = (number of breaths delivered by the ventilator)/(specified Time) = f 2. Tidal Volume : Vf = Volume of the gas delivered by the ventilator in each breath. The typical range lies between 5-15 cc/kg. 3. Oxygen Concentration : Amount of oxygen delivered to the patient. Its range will lie between 21% (ambient oxygen concentration) and 100%. Vo = Cardiac Output (amount of blood flow in L) * (Hb volume per L of blood) * (Oxygen volume per L Hb) = CO * ɣh * ɣo 4. IE(Inspiratory to Expiratory Ratio) : It is the ratio of duration of gas inhalation to the duration of gas exhalation. Typically, for normal breathing, this range lies between 1:2 and 1:1.5. 5. Pressure Limit : It is the amount of pressure generated to preset the tidal volume. Its typical value lies between 10-20 mm water more than the respiratory pressure. 6. Flow Rate : It is the speed of gas flow from the ventilator to the mouth via a constant area of cross-section. Typical value lies between 40-100 LPM. 7. Sensitivity : Ratio of Pressure required initiating inspiration to the actual alveolar pressure. 8. SIGH : (ɳo) A pulse of larger tidal volume in order to prevent alveolar collapse due to uniform alveolar expansion and contraction.
Modelling Based on Isothermal Assumption: Ventilator: RR = f (#/s) Tidal Volume = Vf (m3/#) Hence the Volume Flow Rate (dv/dt) = RR * Vf Now, for a constant area of cross section of the ventilator, AS, dv/dt = AS*v Where v = speed of gas flow from the ventilator v = (RR * Vf)/AS System 1: Ambient Air Atmospheric pressure > Po = 760 mm Hg At constant ambient temperature, Ta and constant volume packet of air PO2 = 0.21 Po (Air contains 21% Oxygen) = 0.21*760 mm Hg = 159.6 mm Hg (Here we assume negligible water content in atmosphere, else we will be having PO2 = 0.21 (Po SPsat), where SPsat = Vapor Pressure of Water at relative saturation S) System 2: Trachea We have S saturation, i.e. S < 1 Hence Pwater vapor = SPsat ~ 47 mm Hg at Ta = 37 C PO2tr = 0.21 * (Po S Psat) = 150 mm Hg System 3: Alveoli and Pulmonary Capillaries We still assume ambient conditions with 100% saturation, i.e. S = 1 Here Pwater vapor = Psat ~ 284 mm Hg PAO2 = 0.21(Po Psat) = 100 mm Hg
For pulmonary capillaries, PHbO2 = 40 mm Hg (when oxygen has been used at its optimum by the cells and the blood is returned to the lungs) PAO2 being greater than PHbO2, oxygen will start flowing from the alveoli to the pulmonary capillaries until the Hb molecule reaches the optimum level of saturation(>95%). When due to a respiratory problem, a breathing insufficiency is created, the alveoli pressure becomes insufficient in providing the Hb molecules with sufficient oxygen. Here Let, PAO2 = μ PAO2, where (<1) is the fraction of O2 delivered in comparison to 100% O2 delivery. Thus, the work of a medical ventilator is to provide enough thrust of air / oxygen to maintain normal conditions for a patient suffering from breathing insufficiency. At isothermal condition, if one wants to deliver same no of moles of oxygen (PAO2 * VAO2 ) = (PAO2 * VAO2) VAO2 = μ VAO2 Thus the volume of lungs will increase by a factor of (1/ μ 1) But the lung has to operate on Functional Residual Capacity (FRC) and the amount of oxygen to be delivered to Hb must be VAO2. If CO is the total volumetric flow rate of the blood capillaries around all the alveoli VAO2 = CO *ɣh * ɣo Hence an extra amount of pressure ΔP = PAO2(1 μ) is required. This extra pressure is compensated by the medical ventilator, as net pressure required in alveoli for normal breathing = PAO2 and Ambient pressure = Po For isothermal conditions, assuming negligible height difference, Amount of Work done by the Ventilator in case the patient has lost all his capacity to inspire,
W = ( ) ( ) = ZnRTa ln(v(lung)/v(ventilator)) Power Delivered = dw / dt = (-ZnRTa/V(ventilator) )* dv(ventilator)/dt = (-ZnRTa * RR * Vf)/V(ventilator) Again assuming Isothermal Condition, Po * V(ventilator) = PAO2 * CO *ɣh * ɣo V (ventilator) = (PAO2 * CO *ɣh * ɣo)/po Power Delivered = I * V = (-ZnRTa * RR * Vf * Po)/ (PAO2 * CO *ɣh * ɣo) A typical ventilating device works within the above limits of air pressure with a predefined efficiency factor.