Measurement Protocols

A measurement protocol specifies which electrodes carry current (the drive or injection electrodes) and between which electrodes voltages are recorded (the measurement electrodes). The two sets need not be the same, and the choice decides which electrode model can describe the data.

Measuring on current-carrying electrodes

Integrating the boundary condition $u+z_{\ell }\sigma {\partial }_{\nu }u=U_{\ell }$ of the Complete Electrode Model over $e_{\ell }$ gives the exact identity

$$U_{\ell }=\frac{1}{|e_{\ell }|}{\int }_{e_{\ell }}u\mathrm{d}s+\frac{z_{\ell }}{|e_{\ell }|}{I}_{\ell }.$$

The voltage on an electrode is the mean potential under it plus the voltage drop over the contact layer. The contact impedance $z_{\ell }$ depends on skin, gel and pressure, so it is poorly known and changes over time.

• Current-carrying electrode ($I_{\ell }\ne 0$): the contact term $z_{\ell }{I}_{\ell }/|e_{\ell }|$ enters the measurement directly and is often larger than the signal from the interior. Only the CEM models it. The Gap Model predicts the mean potential without it, and the Point Electrode Model predicts an infinite voltage.
• Electrode without current ($I_{\ell }=0$): the contact term vanishes, and the voltage is essentially the mean potential under the electrode. Gap, point and complete models agree closely here.

This is the four-electrode (tetrapolar) principle: drive current through one pair of electrodes and measure the voltage with a high-impedance voltmeter on a different pair, so no current flows through the measuring contacts. Two-electrode measurements, with voltage taken on the driving pair, measure the contact impedances along with the object.

Common protocols

• Adjacent (neighbouring) protocol. Current between electrodes $\ell ,\ell +1$. Voltages between all other adjacent pairs, skipping the pairs that involve a driven electrode. With $L$ electrodes this gives $L(L-3)$ measurements, of which half are independent by reciprocity ($104$ for $L=16$). Only electrodes without current are measured, so a gap or point model suffices. Its sensitivity in the centre is poor.
• Opposite and skip-$k$ protocols. Current between electrodes a fixed distance apart. Larger separations reach deeper and distinguish interior changes better than the adjacent protocol.
• Trigonometric (optimal) patterns. All electrodes carry current at once, $I_{\ell }=\cos (k{\theta }_{\ell })$ or $\sin (k{\theta }_{\ell })$ (see Current Patterns). Voltages are then necessarily measured on current-carrying electrodes, so the data must be modelled with the CEM.
• Continuum data. In simulations, every boundary node can inject and measure. This is the idealised Neumann-to-Dirichlet Map without contact effects.

Which model for which protocol

protocol	voltages measured on	adequate models
adjacent, skip-$k$	electrodes without current	CEM, gap, point
all-electrode (trigonometric) patterns	current-carrying electrodes	CEM
idealised boundary data	every boundary point	continuum

With separate drive and measurement electrodes, the forward operator maps $L_{\mathrm{drive}}$ currents to $L_{\mathrm{meas}}$ voltages. In the discrete model this means different injection and measurement matrices (see Discrete Electrode Models).

References

1. B. H. Brown (2003). Electrical impedance tomography (EIT): a review. J. Med. Eng. Technol. 27(3), 97–108. doi:10.1080/0309190021000059687
2. K. Boone, D. Barber, B. Brown (1997). Imaging with electricity: Report of the European Concerted Action on Impedance Tomography. J. Med. Eng. Technol. 21(6), 201–232. doi:10.3109/03091909709070013
3. A. Adler, P. O. Gaggero, Y. Maimaitijiang (2011). Adjacent stimulation and measurement patterns considered harmful. Physiol. Meas. 32(7), 731–744. doi:10.1088/0967-3334/32/7/S01
4. K.-S. Cheng, D. Isaacson, J. C. Newell, D. G. Gisser (1989). Electrode models for electric current computed tomography. IEEE Trans. Biomed. Eng. 36(9), 918–924. doi:10.1109/10.35300
5. D. Isaacson (1986). Distinguishability of Conductivities by Electric Current Computed Tomography. IEEE Trans. Med. Imaging 5(2), 91–95. doi:10.1109/TMI.1986.4307752