The pressure in the aorta changes throughout the cardiac cycle. During systole, as the heart contracts, the outflux of blood into the aorta causes an increase in pressure, whereas during diastole the pressure decreases as the heart relaxes. A simple model for the aortic pressure waveform is given by the Windkessel effect described by the image below. In this model, the heart is considered a pressure generating pump which is directly connected to an elastic compartment (the aorta), which in turn is connected to a rigid set of peripheral vessels (the hose of the firefighter). ● Pump ● Heart Air Windkessel In order to find the aortic pressure waveform from the Windkessel model, a mass balance formulation around the aorta must be formulated. Coming into the aorta from the heart we have the flowrate Q(t). According to conservation of mass, this inflow rate Q(t) must be equal to the outflow rate into the peripheral vessels and the change in volume of the aorta. To find these two relationships, the following assumptions must be made: Elastic arteries Assume the blood pressure in the aorta is given by p Assume that the change in volume (and therefore mass) in the aorta with respect to time is proportional to the change in pressure, p, with respect to time up to a proportionality constant K Assume that the outflow rate into the peripheral vessels is dependent on the resistance of those vessels R and the blood pressure in the aorta p. This outflow relationship follows a form like Ohm's Law, where the pressure is similar to the voltage and the flow similar to the current. Based on the assumptions described before, write the first order differential equation that describes the mass balance of the Windkessel model.
The pressure in the aorta changes throughout the cardiac cycle. During systole, as the heart contracts, the outflux of blood into the aorta causes an increase in pressure, whereas during diastole the pressure decreases as the heart relaxes. A simple model for the aortic pressure waveform is given by the Windkessel effect described by the image below. In this model, the heart is considered a pressure generating pump which is directly connected to an elastic compartment (the aorta), which in turn is connected to a rigid set of peripheral vessels (the hose of the firefighter). ● Pump ● Heart Air Windkessel In order to find the aortic pressure waveform from the Windkessel model, a mass balance formulation around the aorta must be formulated. Coming into the aorta from the heart we have the flowrate Q(t). According to conservation of mass, this inflow rate Q(t) must be equal to the outflow rate into the peripheral vessels and the change in volume of the aorta. To find these two relationships, the following assumptions must be made: Elastic arteries Assume the blood pressure in the aorta is given by p Assume that the change in volume (and therefore mass) in the aorta with respect to time is proportional to the change in pressure, p, with respect to time up to a proportionality constant K Assume that the outflow rate into the peripheral vessels is dependent on the resistance of those vessels R and the blood pressure in the aorta p. This outflow relationship follows a form like Ohm's Law, where the pressure is similar to the voltage and the flow similar to the current. Based on the assumptions described before, write the first order differential equation that describes the mass balance of the Windkessel model.
Human Physiology: From Cells to Systems (MindTap Course List)
9th Edition
ISBN:9781285866932
Author:Lauralee Sherwood
Publisher:Lauralee Sherwood
Chapter9: Cardiac Physiology
Section: Chapter Questions
Problem 4TAHL
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Transcribed Image Text:The pressure in the aorta changes throughout the cardiac cycle. During systole, as the heart contracts, the outflux
of blood into the aorta causes an increase in pressure,
whereas during diastole the pressure decreases as the
heart relaxes. A simple model for the aortic pressure
waveform is given by the Windkessel effect described by
the image below. In this model, the heart is considered a
pressure generating pump which is directly connected to
an elastic compartment (the aorta), which in turn is
connected to a rigid set of peripheral vessels (the hose of
the firefighter).
5
Pump
Heart
Air
Windkessel
Elastic arteries
In order to find the aortic pressure waveform from the Windkessel model, a mass balance formulation around the aorta
must be formulated. Coming into the aorta from the heart we have the flowrate Q(t). According to conservation of mass,
this inflow rate Q(t) must be equal to the outflow rate into the peripheral vessels and the change in volume of the aorta. To
find these two relationships, the following assumptions must be made:
Assume the blood pressure in the aorta is given by p
Assume that the change in volume (and therefore mass) in the aorta with respect to time is proportional to the
change in pressure, p, with respect to time up to a proportionality constant K
Assume that the outflow rate into the peripheral vessels is dependent on the resistance of those vessels R and the
blood pressure in the aorta p. This outflow relationship follows a form like Ohm's Law, where the pressure is
similar to the voltage and the flow similar to the current.
Based on the assumptions described before, write the first order differential equation that describes the
mass balance of the Windkessel model.
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