Admittance and conductance in cardiac performance

There is an established practice of using the electrical conductance of blood (PV loops) in heart ventricles to determine the instantaneous volume of the ventricle. This technique involves inserting a tetra-polar catheter into the ventricle and measuring conductance. This measured conductance is a combination of blood and muscle and various techniques are used to identify the blood conductance from the total measured conductance. Blood conductance can then be converted to volume using a linear (Baan) or a non-linear (Wei) relationship that relates conductance to volume.

Traditional conductance technology

This approach is based in the idea that the total conductance, G, of a fluid between two electrodes is a function of the fluid's conductivity (reciprocal of resistivity) and volume.

In cardiology, a tetra-polar catheter is inserted into the ventricle and a constant current is applied across the two outer electrodes. This generates an electrical field within the ventricle and the two inner electrodes measure a voltage generated due to the electric field. This measured voltage is proportional to conductance, which is related to blood volume (Baan assumes a linear relation whereas Wei uses a non-linear relation). When used in cardiology, the electric field generated is not limited to the blood (the fluid of interest) but also penetrates the heart wall, giving rise to additional conductance often called "parallel conductance" or "muscle conductance", G_m which must be removed.

Various techniques have been attempted to remove the G_m contribution with varying degrees of success. The most common method is the hypertonic saline technique which involves injecting a bolus of hypertonic saline into the ventricle to alter blood conductivity without affecting the surrounding muscle. Another less commonly used technique involves evacuating the ventricle of blood and measuring muscle conductance alone with a conductance catheter. Clearly both techniques are unreliable, somewhat invasive and fail to account for the continuous variation in G_m over the cardiac cycle.

Improved admittance technology

The Admittance technique is an improvement over the Conductance technique for the real-time removal of muscle conductance G_m. Blood and muscle respond very differently to alternating (AC) electrical currents. The fixed charges in muscle cells create a significant reactance that causes a phase shift (time delay) in the measured signal, relative to the excitation signal. Admittance technology uses this phase shift to determine the instantaneous muscle conductance and remove it from the total measured conductance.

Removal of G_m

The total Admittance (Y), of the blood filled ventricle is given by Y = G_b + G_m + iωC_m where

• G_b is the measured conductance of the blood (the desired signal)
• G_m is the measured conductance of the cardiac muscle (unwanted signal)
• C_m is the measured capacitance of the cardiac muscle
• ω is the angular frequency of the excitation signal

The signals G_m and C_m are both properties of cardiac muscle and vary in a fixed ratio. Thus the ratio of G_m to C_m is equal to the ratio of muscle conductivity (σ) to muscle permittivity (ε). The ratio σ/ε is the constant of proportionality. Although both σ and ε are functions of the health of the heart tissue, they are relatively constant for short periods of time.

Using this proportionality, one can rewrite the equation for G_m as G_m = (σ/ε)C_m

Note that the imaginary component of Y depends only on the amount of muscle in the field of the catheter. This makes it easy to isolate by measuring the phase shift, φ, of the measured signal:
cos(φ) = (G_b + G_m)/Y
sin(φ) = ωC_m/Y
Hence, C_m = Y.sin(φ)/ω
also, G_m = (σ/ε)C_m

Thus, blood conductance is determined as G_b = Y.cos(φ) - G_m

The desired conductance to volume conversion equation can be applied to this calculated blood conductance G_b to obtain blood volume.

Experimental results

Admittance technique involves the measurement of both phase angle and total conductance in the ventricle. Thus, it is possible to observe how the parallel conductance (muscle conductance) varies throughout the cardiac cycle. A plot showing both the blood and muscle contribution are shown in the figure. This plot of blood and muscle conductance shows how the parallel conductance due to muscle varies over the cardiac cycle.

References

1. Chia-Ling Wei; Valvano JW; Feldman MD; Pearce JA (2005). "Nonlinear conductance-volume relationship for murine conductance catheter measurement system". IEEE Transactions on Biomedical Engineering. 52 (10): 1654–61. doi:10.1109/TBME.2005.856029. CS1 maint: Multiple names: authors list (link)
2. Chia-Ling Wei; Valvano JW; Feldman MD; Pearce JA (2007). "Volume Catheter Parallel Conductance Varies Between End-Systole and End-Diastole". IEEE Transactions on Biomedical Engineering. 54 (8): 1480–9. doi:10.1109/TBME.2007.890732. CS1 maint: Multiple names: authors list (link)
3. Krenz M (2009). "Conductance, admittance, and hypertonic saline: should we take ventricular volume measurements with a grain of salt?" (PDF). Journal of Applied Physiology. doi:10.1152/japplphysiol.01089.2009. 
4. Porterfield JE, Kottam ATG, Raghavan K, Escobedo D, Jenkins JT, Larson ER, Treviño RJ, Valvano JW, Pearce JA, Feldman MD (August 20, 2009). "Dynamic correction for parallel conductance Gp and gain factor α in invasive murine left ventricular volume measurements". Journal of Applied Physiology. 107 (6): 1693–1703. doi:10.1152/japplphysiol.91322.2008. CS1 maint: Multiple names: authors list (link)
5. Clarka JE, Kottamb A, Motterlinic R, Marber MS (March–April 2009). "Measuring left ventricular function in the normal, infarcted and CORM-3-preconditioned mouse heart using complex admittance-derived pressure volume loops". Journal of Pharmacological and Toxicological Methods. 59 (2): 94–9. doi:10.1016/j.vascn.2008.10.007. CS1 maint: Multiple names: authors list (link)
6. [1], Marc D. Feldman; Jonathan W. Valvano; John A. Pearce; Chia-Ling Wei, "Method and Apparatus for Determining Cardiac Performance in a Patient with a Conductance Catheter"  (patent application)