Differential Equations in Clinical Medicine Courtesy of Philip Crooke, Vanderbilt University In medicine, mechanical ventilation is a procedure that assists….
Differential Equations in Clinical Medicine Courtesy of Philip Crooke, Vanderbilt University In medicine, mechanical ventilation is a procedure that assists or replaces spontaneous breath- ing for critically ill patients, using a medical device called a ventilator Some people attribute the first mechanical ventilation to Andreas Vesalius in 1555. Negative pressure ventilators (iron lungs) came into use in the response to Drinker and Louis Shaw are credited with its invention. Modern ventilators use positive pressure to inflate the lungs of the patient. In the ICU (intensive care unit), common indications for the ini- tiation of mechanical ventilation are acute respiratory failure, acute exacerbation of chronic obstructive pulmonary disease, coma, and neuromuscular disorders. The goals of mechanical ventilation are to provide oxygen to the lungs and to remove carbon dioxide. 1950s in response to poliomyelitis (polio) epidemics. Philijp In this project, we model the mechanical process performed by the ventilator. We make the following assumptions about this process of filling the lungs with air and then letting them deflate to some rest volume (see Figure 2.13) (i) The length (in seconds) of each breath is fixed (o) and is set by the clinician, with each breath being identical to the previous breath. Each breath is divided into two parts: inspiration (air flowing into the patient) and expiration (air flowing out of the patient). We assume that inspiration takes place over the interval [0. tl and expiration over the time interval [t]. The time t, is called the inspliratory time. (ii) Ppp during inspiration airway-resistance pressure drop, P lung clastic and residual pressure, Pe Figure 2.13 Lung ventilation pressures http://www.mps.gov/missriverfacts htm
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