Electrical Impedance Tomography

Electrical Impedance Tomography (EIT) is non-destructive detection of electrical impedance inside a body, by just doing measurements on the surface of the body. EIT and other electrical property sensing techniques have many applications, in geophysics, industrial process monitoring and non-destructive testing, and most spectacularly, in modern medical imaging.

Oneirix Labs has proved an exciting new mathematical result, that advances the field of EIT. But we stand on the shoulders of giants, and a brief historical acknowledgement is in order.

In 1861, Lord Kelvin first invented the 4-terminal sensing technique. His work was extended by the Schlumberger brothers; founders of Schlumberger Limited. They used multiple 4-terminal sensings, to detect underground electrical impedances, hoping to find metal ores. Many more 4-terminal sensing inventions followed over the next many decades.

Yet, the mathematics advanced slowly, and nearly a century passed until the next breakthrough.

It was not until the late 1900s, that, mathematicians Calderon, Faddeev, Sylvester, Uhlman and others proved that by taking all possible 4-terminal measurements of a body, one could recreate a complete electrical map of the body's interior. This reopened the field to many new possibilities.

We showed that 4-terminal measurements are mathematically equivalent to 2-terminal measurements

In 2015, we were able to further show, for the first time, that 4-terminal measurements are mathematically equivalent to 2-terminal measurements. This important and surprising improvement, has tremendous practical implications! An illustrative example follows.

4-terminal sensing, essentially unchanged from Lord Kelvin's time, uses two electrodes to introduce a precise current across two points, and two other electrodes to sense voltage across two other points. 2-terminal sensing measures voltage across the same two points across which current is introduced. (If you have ever used a multimeter to measure electrical resistance, you have performed 2-terminal sensing!)

Now, say we have to measure 31 points on a person's body. Then, there are over 200,000 possible 4-terminal measurements, but only 465 distinct 2-terminal measurements. Our theorem proves that the 465 measurements will have all the same data as the 200,000 measurements. A remarkable reduction of measurement effort!

For a more formal depiction, see the patent application Impedance methods and apparatuses using arrays of bipolar electrodes.


2-terminal measurements mean faster, more accurate, richer, lower-cost diagnostics, and also, far better patient experience.

Faster sensing directly yields accuracy, by reducing the chance of the patient moving, while readings are being taken; a pervasive problem in all tomography methods.

Fewer measurements mean less exposure to electric current for the patient.

The method also enables new ways of measuring across more frequencies, to further enrich the imagery.

2-terminal readings also require far less current than 4-terminal readings. This would further

• reduce patient exposure
• increase signal-to-noise ratio
• improve battery life
• allow for smaller electrode size, thus improving tomography resolution


Geological Surveys

Applications of geophysical impedance testing, detection, imaging and monitoring include archeological detection via geophysical arrays, as well as industrial uses such as finding ore, water, rock type, oil & gas.

Medical Tomography

Arrays of 2-terminal electrodes can perform bio-impedance imaging, detection, monitoring and sensing, such as tumor detection (e.g., breast tumor, skin tumor), biological monitoring (e.g., lung/ventilation monitoring, cardiac detection (e.g., stroke detection) and so forth.

Industrial Non-destructive Testing

Multi-electrode arrays find use in microfluidics applications (including electrophoresis, dielectrophoresis, electrorotation, polymerase chain reaction (PCR), surface microfluidics etc.), and other applications like measurement of defects, fatigue, and impurities.