Mathematical description of the four-points measurement technique to be used to detect distributed micromotions

A MicroMotion Detection technique has been developed to detect small local motions in the walls of hollow organs, particularly the bladder. The four-points impedance measurement method has been applied for detecting small distance variations between electrodes mounted at the inner surface of a latex balloon filled with saline. Measurements in the bladder of patients have shown the clinical feasibility and relevance of this technique. This paper deals with the "crosstalk" problem, caused by the movement of current electrodes and giving an unwanted contribution to the potential difference between the voltage electrodes. A mathematical model is presented that is used to calculate the distance variations from the voltage variations despite the influence of crosstalk. Moreover, the relations between measured voltages and the interelectrode distances can be used to optimize the electrode configuration to reduce the crosstalk factor beforehand. The relations presented in this paper are verified with measurements and with simulations using a Boundary Element Model. The relations can be useful to interpret signals recorded with the four-points impedance measurement technique and to design probes for other applications.