Using this information, one can deduce the area enclosed by the inductor, hence the thoracic and abdominal cross sectional area. Basic inductance plethysmography setup. In a circular loop, symmetry holds true only for the center of the loop, but not for any other point within the loop. Finally the inductance can be found using the equation 3. Even for a simple shape like a circle, the above equations are difficult to calculate.
Engineers usually utilize numerical techniques to calculate such integrals.
Figure 4 below shows the results from numerical evaluation of inductor values as a function of the radius of the circular loop. As it can be seen from the figure below, inductance increases linearly with the radius, or by the square root of the area of the circle. Inductance values calculated from numerical simulations. Inductance plethysmograph instruments measure the inductance of the two coils as seen in Figure 3. From this measurement, instrument estimates the cross sectional area of the chest and the abdominal coil.