Question

Impedance plethysmography is a technique that can be used to detect thrombosis--the presence of clots in a blood vessel--by measuring the electrical resistance of a limb, such as the calf of the leg. In a typical clinical setting, a current of 200 μA is passed through the leg from the upper thigh to the foot. The voltage is measured at two points along the calf separated by 13 cm. Part A:
If the voltage measured is 17 mV, what is the resistance of the calf between the electrodes?

Part B:

If the average calf diameter between the electrodes is 12 cm, what is the average resistivity of this part of the leg?

Answer 1

Answer:

a) The resistance of the calf between the electrodes is $85\Omega$

b) The average resistivity of this part of the leg is $57.81m\Omega/cm^{3}$

Explanation:

Hi

a) Using Ohm's law $V=IR$, solving for $R$, we obtain $R=\frac{V}{I}=\frac{17mV}{200uA}=85\Omega$

b) The volume of the calf is like a cylinder, so $Vol=\pi r^{2}h$, with $h=13cm$ and $r=d/2=6cm$, therefore $Vol=\pi (6cm)^{2}(13cm)=468\pi cm^{3}$. Then we can use $R_{av}=\frac{R}{Vol} =\frac{85\Omega}{468\pi cm^{3}} =0.05781\Omega /cm^{3}=57.81m\Omega/cm^{3}$, this is the average resistivity of this part of the leg.