Last week, we introduced you to Admittance, a new and more dynamic heart function measurement technique that evolved from its predecessor, Conductance. Today we are going to dive a bit deeper into the theories of operation, including the math behind these techniques, so you will have a better understanding how Admittance evolved and why it is a step up from Conductance-based pressure-volume technology. Let’s start with how it all began, conductance-based pressure-volume loop measurements:

Conductance Theory of Operation

Deriving ventricular volume from a Conductance Catheter is based on a very simple electrical principle: Ohm’s Law:

Voltage (V) = Current (I) X Resistance (R)   V = IR

Conductance (G) rather than resistance is the parameter of interest. Since conductance is the inverse of resistance, Ohm’s Law can be rewritten as:

Voltage = Current/Conductance   V = I/G

Conductance Catheters are comprised of both excitation electrodes and recording electrodes. The excitation electrodes (most distal and proximal electrodes on the Catheter) generate an electrical field inside the heart. This field is generated by an alternating current that is applied (at a constant magnitude) between these 2 outermost electrodes. The inner recording electrodes measure voltage change which is proportional to a change in resistance.
Since the electrical field passes through both blood in the ventricle as well as myocardium tissue, the change in the electrical field, the measured conductance value (Gx), is actually a combination of blood conductance (Gb) and muscle contribution or parallel conductance (Gp).
In 1981, Dr. Baan proposed a relationship between time-varying measurements of total conductance (Gx) to time-varying changes in ventricular volume (Vol). This volume formula takes into account the distance between the recording electrodes (L), blood resistivity (ρ), and the parallel conductance (Gp). It also takes into account the non-uniform nature of the electrical field with the field correction factor, alpha (α).

Baan assumed α to be a constant with a value of one for a uniform current field distribution. Alpha can be calculated after injecting a hypertonic saline injection, also known as dilution technique, to transiently alter blood conductance (G_b) ideally without affecting the surrounding muscle conductance (G_m). A second method to try to quantify volume is cuvette calibration. This method uses actual blood samples to make a more accurate assessment of the ventricular volume by assuming the homogenous electrical field i.e. gain correction α=1, no parallel conductance (Gp = 0) and rho (ρ) values that are taken as a constant. Both of these methods give a single constant value for α, while in reality this value changes from moment to moment in each heart cycle.

Let’s look at this a last statement in more depth, to truly understand the limitation of conductance based pressure-volume loop technology. At systole, when the heart is completely contracted, there is relatively little blood left in the ventricle. This automatically means that the myocardial walls come closer to the catheter and the muscle contribution to the total measured conductance is larger compared to any other moment in the heart cycle. Once the heart is starting to relax, the ventricle is filling with blood, and the ventricle wall is moving away from the catheter. Subsequently, G_b increases and the muscle contribution decrease again. With the conductance approach to pressure-volume loops, this means that you are continuously subtracting an incorrect value from your total measured conductance (Gx) and introducing an error in your measurement

Now let’s look at the second part of Baan’s assumption; α to be a constant with a value of one for a uniform current field distribution. We know that the field distribution is not uniform. So this part of the statement is incorrect, as the electrical field strength decreases non-linearly with distance (E.R. Larson et al. IEEE Transactions on Biomedical Engineering, vol 60, No 8, August 2013). This means measurements of blood conductance farther from the catheter do not have the same strength as those nearer to the catheter. Without correction, this leads to an underestimation of total volume. The larger the volume that is being measured, the greater the underestimation; volume measurements at diastole are thus more prone to underestimation compared to measurements at systole.

Science is just like everyday life, you make decisions to the best of your knowledge at that moment. Choosing a technology to answer your research questions, is very similar. For a long time, conductance was the best technology available. Many scientists worked with it and science has made great progress using it.

Admittance Theory of Operation

Now that we have a clear picture of the limitations of conductance based pressure-volume technology, let’s discuss how Admittance tackles these. Admittance takes advantage of the fact that blood is purely resistive (G_b), while the myocardium has both capacitive (C_m) and resistive properties (G_m). This allows for separation of the muscle contribution to the total measured conductance (G_x), using the field theory.

The capacitive property of muscle causes a time (phase) delay in measured signal. By tracking this delay in real time and mathematically relating it to the resistance of the myocardium, Admittance allows for continuous measurement of muscle contribution/ parallel conductions (G_m) throughout the heart cycle.

So how does this look mathematically? Admittance uses an equation developed by Dr. Chia-Ling Wei to convert conductance to volume. Wei’s equation, in contrast to Baan’s equation, corrects for the non-homogeneous nature of the electrical field distribution by assuming a non-linear relationship between conductance and volume, named gamma (γ), thus improving the accuracy over a wider volume range.

To measure blood volume in real time, values are needed for myocardial conductivity and permittivity (for σ/ε ratio = heart type), blood resistivity (ρ), and reference stroke volume (SV). Default values for ‘heart type’ are provided in the ADV500 by Transonic Scisense. Which setting to choose depends on whether you work with a ‘healthy heart’ or, for instance, an infarct heart, as scar tissue formed after an infarct, handles the electrical field differently compared to healthy myocardium, resulting in a different σ/ε ratio. Researchers also have the option to study the σ/ε ratio using a tetrapolar surface probe provided with the system. Our research application specialists are always available to help you decide on your settings.

In daily lab life, the benefits of Admittance technology, translate into a quick and smooth set-up before your experiments since complicated (cuvette) calibrations are no longer needed. In the 30 minutes it takes to soak your catheter in warm saline, you can surgically prepare your animal, assure that your data collection software is properly set and you are ready to go. Measurement repeatability is improved as you learn what values to expect for phase when the catheter is in the correct position since the live measurement of the phase signal helps you to place the catheter in the middle of the ventricle. The real time correction of the muscle contribution to your total conductance, will deliver more realistic volume data compared to conductance based technology (J.E. Porterfield et al. J. Appl Phys 107: 1693-1703, 2009). The improvements of Admittance should therefore result in more accurate, repeatable, higher quality pressure-volume loop data.

If you are interested to learn how your research will benefit from Admittance technology, please have a look at our Pressure Volume workbook and be in touch. We also offer, in these times of limited travel, state of the art remote live support in your laboratory.