IJBEM, Vol. 5, No. 1, 2003

Accuracy of Conductance Catheter Measurements in a Realistic Numerical Heart Model: Validation of Reciprocal Equivalent Distance Extrapolation

Rodney W Salo

Basic Research Group, Guidant Corporation, St. Paul, Minnesota, United States of America

Correspondence: Rodney Salo, Guidant Corporation, 4100 North Hamline Avenue, St. Paul, MN 55112, United States of America.
E-mail: rodney.salo@guidant.com, phone 651-582-4034.

Abstract. The simple computational model used clinically to convert conductance or impedance to volume in conductance catheter measurements is only applicable for uniform current densities. A more sophisticated model, incorporating distances to the current sources into a single term, the equivalent reciprocal distance, uses extrapolation to the condition of infinitely distant current sources to satisfy the requirement for uniform current density. When volumes calculated with the new computational model are compared to traditional calculations in a realistic three-dimensional finite difference model of a four-chamber heart, the RMS error over a range of volumes from 20 — 80 ml decreases from 11.2 ml to 0.4 ml for nonconductive tissue and from 13.4 to 6.8 for a physiologic tissue conductivity of 0.2 S/m.

Keywords: Conductance Catheter; Intracardiac Impedance; Reciprocal Equivalent Distance; Volume Conductor; Finite-Difference Model

1. Introduction

The electrical potentials generated by current sources in a volume conductor are related to the spatial distribution of conductive material within the volume conductor. The potential difference between two electrodes of a conductance catheter is used to compute the volume of blood in the left ventricle between planes defined by the electrodes. Assuming uniform current density, the volume, V, can be computed by Eq. 1.

(1)

ρ is the resistivity of blood

L is the distance between measuring electrodes

R is the resistance measured between electrodes.

Despite the inapplicability of the basic assumption of uniform current density, conductance catheter derived volumes have been used clinically for more than twenty years, particularly to generate pressure-volume loops characterizing cardiac function.

Field extrapolation, or more descriptively: Reciprocal Equivalent Distance Extrapolation (REDE) provides a more accurate foundation for volume computation by rejecting the assumption of uniformity and providing an algorithm that implicitly corrects for differences in current source position. REDE is based on the fact that the electrical potential about a current source in free space is given by Eq. 2

(2)

q is the charge at the source

ε is the permittivity of the volume conductor (in this case blood)

r is the distance from the source

Applying this concept to a tetrapolar electrode arrangement, with current sources d1, d2 and sense electrodes s1, s2, the potential difference between two electrodes, ΔΦ is given by Eq. 3 [Salo, 1989].

(3)

ε, q defined as in equation 2, the charge at the other source is - q

r_d1-s1is the distance from source 1 to sense electrode 1

r_d2-s2is the distance from source 2 to sense electrode 2

r_d2-s1is the distance from source 1 to sense electrode 2

r_d1-s2is the distance from source 2 to sense electrode 1

1/r_equ is defined as the reciprocal equivalent distance to put Eq. 3 into the form of Eq. 2

A regression between resistances measured by a given pair of electrodes for several different positions of current sources and the reciprocal equivalent distances for each electrode arrangement yields a linear equation from which it is possible to extrapolate the resistance that would be measured at 1/r_equ = 0. The ventricular volume can be more accurately computed from the extrapolated resistance, using Eq. 1, since, for infinitely distant sources, the current density in the volume conductor is uniform [Salo, 1989].

2. Methods

The REDE approach was applied to potentials generated in a three-dimensional, finite-difference numerical heart model, including an ellipsoidal left ventricle and a pouch-like right ventricle, previously described [Salo, 1986]. The model was run for seven different sizes of the left ventricle with left and right ventricular volumes remaining equal. As ventricular volume decreased, wall thickness increased to maintain a fixed total wall mass (volume). The model was run for four different tissue conductivities ranging from 0.0 S/m to 0.3 S/m for several different positions of the pairs of current sources along the major axis of the left ventricle.

Potential differences between node pairs along the major axis were converted to resistance measurements by dividing by the source current. Extrapolated resistances were determined by REDE and volumes were computed from these extrapolated resistances using Eq. 1. The individual segment volumes were summed to generate the total ventricular volume. Volumes were also computed from raw resistances using Eq. 1 for comparison.

3. Results

Left ventricular volumes computed from raw resistance measurements and extrapolated resistances for seven sizes of the model heart are shown in Fig. 1.

Figure 1 . Total left ventricular volume computed from modeled raw resistance measurements using Eq. 1 (left panel) and from resistances extrapolated by REDE (right panel) plotted against the actual left ventricular volumes for modeled hearts with four different tissue conductivities.

4. Discussion

Volumes computed from raw resistances are nonlinearly related to the true volume with a slope < 1.0 as is evident in Fig. 1. This relationship is much more linear for extrapolated volumes with a slope of 0.98 (r = 0.9998) for the heart with insulating walls. This slope increases with increasing conductivity. If a correction factor of 0.75 is applied and, assuming a physiological tissue conductivity of 0.1 to 0.2 S/m and accurate correction for offset (nonzero y intercept), the RMS error over all seven volumes is 0.4 ml - 6.8 ml. This compares to RMS errors of 11.2 ml Δ 13.4 ml for volumes computed from raw resistances using the best correction factor. Thus, measurement error is reduced by more than 50% by using the REDE approach. The improvement is even larger at greater volumes (> 100 ml).

References

Salo RW. The theoretical basis of a computational model for the determination of volume by impedance. Automedica 11: 299-310, 1989.

Salo RW, Wallner TG and Pederson BD. Measurement of ventricular volume by intracardiac impedance: theoretical and empirical approaches. IEEE Trans Biomed Eng 33:189-95, 1986.