Problems
109
Inductive:
If blood pressure acts on an elastic membrane attached to a magnet
near a coil of wire, then variations in the blood pressure will induce
a current in the coil, and that current can be measured. Note that this
will give dp/dt, i.e. the variation of pressure with time.
Resistive:
Blood pressure acting on a lever can cause a wire to elastically stretch.
This causes the resistance of the wire to increase, which can be
detected in a Wheatstone bridge circuit.
Blood flow can be monitored with small devices placed around an artery or vein:
US Doppler flow-meter: Ultrasonic waves generated by a small piezoelectric
crystal can be used to measure blood flow speed v by
detecting the Doppler shift of the sound back-scattered
off blood corpuscles. The sound frequency is shifted by
f = 2v cos θ/v sound , where θ is the angle between the
artery (or vein) and the sound-wave direction.
Hall-effect flow-meter:
The Hall effect is the production of an electric field E
transverse across a conductor and perpendicular to an
external magnetic field B made perpendicular to the
conduction direction. The electric field E = vB is
generated by the Lorentz force acting to shift charges to
one side as they move with speed v through the magnetic
field. As blood plasma contains ions, the Hall effect will
occur when a magnetic field is placed across a blood
vessel.
Problems
4.1 Suppose you hold your breath and dive down 5 m into the ocean. What will be
the pressure in your lungs?
4.2 If a nitrogen bubble of diameter 0.3 μm were to form in a diver’s bloodstream
when at a depth of 200 m under the ocean, what would the diameter of that bubble
be at the surface, assuming no more nitrogen diffuses into or out of that bubble?
4.3 An IV infuser bag is placed on a stand 1.5 m above the heart of a patient in
bed. When the IV is operating, what is the infuser fluid pressure in the patient’s
vein where the cannula has been inserted? Compare this pressure with the patient’s
systolic pressure of 120 mmHg.
4.4 A certain fish weighs 530 g in air and has a body density of 1.05 gm/cm 3 . How
large a swim bladder does that fish need to be near buoyancy at a depth of 25 m in
the ocean (with a density of 1.03 gm/cm 3 )?
109
Inductive:
If blood pressure acts on an elastic membrane attached to a magnet
near a coil of wire, then variations in the blood pressure will induce
a current in the coil, and that current can be measured. Note that this
will give dp/dt, i.e. the variation of pressure with time.
Resistive:
Blood pressure acting on a lever can cause a wire to elastically stretch.
This causes the resistance of the wire to increase, which can be
detected in a Wheatstone bridge circuit.
Blood flow can be monitored with small devices placed around an artery or vein:
US Doppler flow-meter: Ultrasonic waves generated by a small piezoelectric
crystal can be used to measure blood flow speed v by
detecting the Doppler shift of the sound back-scattered
off blood corpuscles. The sound frequency is shifted by
f = 2v cos θ/v sound , where θ is the angle between the
artery (or vein) and the sound-wave direction.
Hall-effect flow-meter:
The Hall effect is the production of an electric field E
transverse across a conductor and perpendicular to an
external magnetic field B made perpendicular to the
conduction direction. The electric field E = vB is
generated by the Lorentz force acting to shift charges to
one side as they move with speed v through the magnetic
field. As blood plasma contains ions, the Hall effect will
occur when a magnetic field is placed across a blood
vessel.
Problems
4.1 Suppose you hold your breath and dive down 5 m into the ocean. What will be
the pressure in your lungs?
4.2 If a nitrogen bubble of diameter 0.3 μm were to form in a diver’s bloodstream
when at a depth of 200 m under the ocean, what would the diameter of that bubble
be at the surface, assuming no more nitrogen diffuses into or out of that bubble?
4.3 An IV infuser bag is placed on a stand 1.5 m above the heart of a patient in
bed. When the IV is operating, what is the infuser fluid pressure in the patient’s
vein where the cannula has been inserted? Compare this pressure with the patient’s
systolic pressure of 120 mmHg.
4.4 A certain fish weighs 530 g in air and has a body density of 1.05 gm/cm 3 . How
large a swim bladder does that fish need to be near buoyancy at a depth of 25 m in
the ocean (with a density of 1.03 gm/cm 3 )?