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INNOVATIVE METHODOLOGY
1Department of Biomedical Engineering, University of California, Irvine, California; 2Center for Sensory-Motor Interaction, Aalborg University, Aalborg; 3Department of Medicine, Skejby Syghus, Aarhus; and 4Center of Excellence for Visceral Biomechanics and Pain, Aalborg Hospital, Aalborg, Denmark
Submitted 28 May 2004 ; accepted in final form 23 November 2004
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ABSTRACT |
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carotid artery; femoral artery; coronary artery; conductance catheter; cylindrical model
The nonuniformity in electric field is known to be very significant in the aorta under in vivo conditions (13), primarily because of the complex electrical properties of blood cells under dynamic flow conditions (6, 21–28, 31–32). The error due to parallel conductance is also very significant. The common approach to correct for this offset is to change the conductivity of blood by injection of hypertonic NaCl solution (as much as 9% NaCl) into the pulmonary artery (1, 4). The transient change of blood conductivity is extrapolated to zero to determine the parallel conductance. The major shortcoming of this technique is that saline loading with multiple measurements may alter the calculated value (9–10) and hemodynamics (4, 8, 29).
We (19) recently proposed a method that addresses these difficulties and allows accurate measurement of absolute CSA for the coronary artery in vitro. In medium size vessels, unlike the ventricle and aorta, the blood can be completely displaced transiently by an injection of NaCl solution. Hence, the complexities of the blood rheology are eliminated because the electrodes sense the electrical impedance of the NaCl solution during the brief bolus injection. Furthermore, because the NaCl injection displaces the blood and does not mix with it, it is unnecessary to use a highly hyperosmotic solution of NaCl. We have shown that two injections of slightly hyperosmotic and slightly hyposmotic NaCl (1.5% and 0.5%, respectively) solutions can be used in conjunction with a modified cylindrical model to calculate the CSA and parallel conductance of the coronary artery in vitro (19). We obtained excellent agreement with A-mode ultrasound (US) measurements. The goal of the present study was to validate the method under in vivo conditions in several medium-size vessels (e.g., carotid, femoral, and coronary arteries).
Our hypothesis is that correction of the errors introduced by a nonhomogeneous electric field and current leakage due to conductance outside of the vessel lumen can provide an accurate method for in vivo measurement of absolute lumen CSA in medium size vessels (e.g., femoral, carotid, and coronary arteries). Our rationale is to optimize the design of the conductance catheter to yield a nearly homogeneous electric field. Furthermore, a brief (3–5 s) displacement of blood from the lumen of a medium size vessel with injection of two solutions of NaCl (e.g., 0.5% and 1.5% NaCl) with known conductivities will provide an accurate estimate of the parallel conductance and hence the absolute lumen CSA. Accurate assessment of absolute lumen CSA will provide a powerful diagnostic and treatment tool for the invasive cardiologist.
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METHODS |
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 | (1) |
, L, and CSA are the specific conductivity of the fluid, the distance between detection electrodes, and the lumen CSA of the vessel transverse to the detection electrode, respectively. The conductance G is the ratio of the current induced by the outer electrodes and the potential difference measured between the detection electrodes. Typically, a parameter 
is multiplied by the CSA in Eq. 1 to account for the nonhomogeneity of the electric field. In the present analysis, we assume that the field is homogeneous and that is equal to 1. We elaborate on this assumption in DISCUSSION.
Because Eq. 1 has two unknowns (CSA and Gp), we make two injections, one of slightly hyperosmotic NaCl solution (1.5%) and a second of slightly hyposmotic NaCl (0.5%) solution, so that a repeated application of Eq. 1 to each of the two solutions provides two equations with two unknowns. Kassab et al. (19) showed previously that CSA and Gp have the following form:
 | (2) |
 | (3) |
1 and 2 (19). If we assume that the vessel has a circular cross section, we can compute the diameter as D = (4CSA/
)1/2, namely,
 | (4) |
represents the difference in a given quantity for the two injections.
It is apparent that the total conductance is the sum of the conductance in the vessel lumen and the conductance through the vessel wall and surrounding tissue (current leakage) as expressed by Eq. 1. To assess the contribution of the current leakage or Gp, we can evaluate the contribution of Gp to the total conductance as follows:
 | (5) |
Impedance catheter. We designed and constructed the impedance catheters used in the present study as described previously (19). Briefly, two electrodes that were spaced 1 mm apart formed the inner (detection) electrodes. The other two electrodes that were spaced 4 mm on either side of the inner electrodes formed the outer (excitation) electrodes. These dimensions were designed in relation to the dimension of the vessels of interest in an attempt to homogenize the electric field as determined in the finite-element analysis (19). A side hole was made in the catheter distal to the electrodes for bolus injection and pressure measurement. The four wires that were exteriorized from the conductance catheter were connected to an electronic conductance module. This module drives a 5-kHz, 20-µA [root mean square (RMS)] constant current between the two outermost electrodes and measures the resultant voltage between the two inner electrodes. The voltage detected, modulated in amplitude by the impedance changing through the bolus injection, has a frequency in the vicinity of 5 kHz. Our data acquisition has a sampling frequency of 75 kHz, with two channels–the current injected and the detected voltage, respectively. The American Safety Standards for leakage current are in the order of 10–20 µA, but these apply at 50–60 Hz. Hence, the currents used are safe for in vivo studies (1).
Calibration of impedance catheter.
The calibration of the impedance CSA measurement system was performed at body temperature (36–38°C) in five glass tubes of known CSA ranging from 7.065 mm2 (3 mm in diameter) to 78.5 mm2 (10 mm in diameter). Each of the five tubes was filled with the NaCl solution, and the catheter was in turn placed into the center of each tube to record a voltage. When the voltage was plotted against the CSA, we obtained a hyperbolic relation as given by Eq. 2, with Gp equal to zero because the wall of the tube is an insulator. A nonlinear regression was used to determine the conductivity because current and L are known quantities. The calibration was carried out for each of the NaCl solutions (0.5% and 1.5%). As expected, the conductivity of the 1.5% NaCl solution was approximately three times that of the 0.5% NaCl solution.
Experimental preparation. All animal procedures conformed to the "Guiding Principles in the Care and Use of Animals" of the American Physiological Society. Eight Danish Landrace-Yorkshire pigs weighing 60–70 kg were used in the present study. The animals were premedicated with azaperone (4.8 mg/kg) and midazolam (0.6 mg/kg). The animals were then given ketamine hydrochloride (10 mg/kg iv) and midazolam (0.6 mg/kg iv) and subsequently transorally intubated. The surgical anesthesia was maintained by isoflurane (1–2%). Four 5-Fr sheaths were inserted into the left and right common carotid arteries and right and left femoral arteries. Four flow probes (Transonic Flow) were also placed around the two carotid and femoral arteries to measure volumetric flow rate. At the conclusion of the carotid and femoral measurements, an additional sheath was introduced through the ascending aorta to access the left anterior descending coronary artery (LAD) after a midline sternotomy. The blood pressure was monitored through the sidearm of the sheath. The impedance catheter (diameter range of 1.0–1.5 mm) was inserted through each of the sheaths, in turn, to access the carotid and femoral arteries and the LAD. The order of measurements was carotid artery, femoral artery, and LAD. Once the measurements on both carotid arteries were completed, the surrounding tissue was dissected away for one of the carotid arteries to assess the effect of dissection on Gp. At the conclusion of this measurement, the vessel was ligated to create flow overload in the other carotid artery. The measurement was repeated in the contralateral vessel to assess the degree of vasodilatation in response to flow overload.
Two-injection method.
Initially, the voltage difference across the detection electrodes was measured in the bloodstream to establish a baseline. Approximately 5–8 ml of 1.5% NaCl was then infused into the lumen of the vessels, typically at a rate of 1–3 ml/s (
blood flow rate in the vessel). The voltage baseline was reestablished by the blood flow for several minutes (2–3 min), followed by an injection of 0.5% NaCl in an identical manner. Because the level of the applied current is constant, the time-varying voltage induced was converted into the sum of the conductances of the blood and the surrounding tissue segment between the inner electrodes. The conductance was computed as the ratio of the root mean square (RMS) of the driving current divided by the RMS of the voltage across the detection electrodes. Equation 4 was used to compute the diameter of the vessel given the difference in specific conductivities of the two solutions and their respective conductances. The change in local blood pressure during the injection was recorded.
Ultrasonic measurements. The computed value of diameter was then compared with B-mode ultrasonic measurement at the same locations. Real-time measurements in B mode were performed with 7.5-MHz linear and curved array transducers and a Toshiba US machine (Power Vision 6000). The carotid, femoral, and coronary artery diameters were measured in a consistent fashion by the same experienced ultrasonographist (A. Hørlyck). The measurements were made with the pig in the supine position. The US measurements were made at the same position of the artery as the detection electrodes because the detection electrodes were visualized in the lumen of the vessel. Hence, a direct comparison was made between the conductance and US diameters.
Statistical analysis.
The relation between the ultrasonic (U) and impedance (I) diameter measurements were expressed by DI = DU + 
, where and are empirical constants that were determined with a linear least squares fit and a corresponding correlation coefficient R2. In a Bland-Altman scatter diagram, we plotted the percent differences between the two measurements of diameter [(DU – DI)/DU x 100] against their means [(DU + DI)/2 x 100] (3). In the scatter diagram the precision and bias of the method can be quantified. We also determined the RMS error to further assess the reliability of the technique. Finally, we assessed the repeatability of the technique by making measurements in duplicates. We calculated the means and SD of the differences. We used the SD of the differences as the repeatability coefficient (4).
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RESULTS |
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Figure 4A shows the relation between the computed diameter with the impedance catheter (Eq. 4) and that measured with B-mode US. Thirteen of the data points correspond to the carotid arteries, three to the femoral arteries, and four to the LAD. The results were expressed by a linear least squares fit as DI = 1.02DU – 0.102 (R2 = 0.948). To determine the agreement between the two methods, we made a Bland-Altman plot (3) of the percent difference in diameters between the two methods against their mean value. Figure 4B shows the Bland-Altman plot, where the mean and SD were found to be 0.78% and 5.0%, respectively [top and bottom dotted lines represent mean + 2SD (10.8%) and mean – 2SD (–9.2%), respectively]. The RMS error for the impedance measurements was 4.8% of the mean US diameter.
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We computed the %Gp in the lumped two-compartment model. We found that 60.8 ± 12.2%, 78.4 ± 6.4%, and 72.0 ± 10.3% of the conductance lies outside of vessel lumen in the carotid artery, femoral artery, and LAD, respectively. The difference in the %Gp values for the femoral and coronary arteries is not statistically significant, but they are significantly larger than that of the carotid artery. Furthermore, the %Gp is significantly reduced when the carotid vessel is dissected away from the surrounding tissue (40.6 ± 4.0%).
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DISCUSSION |
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The effect of blood rheology on electrical conductivity is more significant for blood vessels, and in particular smaller vessels, than for the heart. In the heart, the blood motion is turbulent and hence the blood orientation is fairly random, unlike the streamlined flow in vessels, where the cells align along the long axis of the vessel. The alignment and consequently the electrical properties change throughout the cardiac cycle with each pulsatile blood pressure wave and shear stress. Despite these complexities, Kornet et al. (20) proposed that the CSA can be accurately measured throughout the cardiac cycle in the aorta of a piglet. The stipulation for the accuracy of their measurements lies in the calibration of the dependence of blood conductivity on temperature, hematocrit, and shear stress. The proposed two-injection method is far simpler because it completely eliminates the effect of blood during the transient injection. It also eliminates the need for multiple injections of hypertonic saline solutions (17.5% NaCl) (20) into the right atrium, which may not be tolerated in patients with renal insufficiency.
The diameter predictions made with our proposed method were compared with B-mode ultrasonographic measurements, which are considered to be the gold standard. We found excellent agreement between the two methods, as shown in Fig. 4. All measurements were bound within the mean ± 2SD, which contains 
95% of the measurements if the differences are normally distributed. Because the differences within ±2SD are not experimentally or clinically significant, the two methods can be used interchangeably (3). The RMS for the impedance diameter measurements was 4.8% of the mean US diameter. The proposed method not only was found to be accurate but was also very reproducible, as shown in Fig. 5. The repeatability coefficient was found to be within 2.4% of the mean of the two measurements.
The success of the proposed method is predicated on several assumptions. Equations 2 and 3 are based on the assumption that the vessel is under identical conditions during the two injections. Because the vessel diameter is affected by flow rate and blood pressure, those conditions should be reproduced during both injections. The infusion rate was delivered manually by hand with a syringe systematically for both injections by the same operator (G. S. Kassab). In future studies, a pump can be used to make identical injections. The infusion of the bolus increased the local pressure of the blood vessel. We confirmed that the increase in pressure was <10 mmHg during all infusions. The change in diameter of the vessel was insignificant during the injection. as verified by the US measurements. An additional assumption for Eqs. 2 and 3 is that the parallel conductance is identical during the two injections. The critical factor for this criterion was the presence of blood flow, which ensures good washout and reestablishment of baseline in between injections. Unfortunately, the sheath introduced into the vessel lumen for insertion of the impedance catheter completely obstructed the lumen (zero flow) in some vessels. In those vessels, the measurements were not accurate or reproducible. Hence, only those vessels that had significant flow as measured by the flow probe and consequently good washout were considered in the analysis. This is a minor problem, however, because the techniques of vascular catheterization can be used to overcome this problem and the flow through any vessel is rarely zero.
Finally, we assumed that there is no nonhomogeneity of the electric field between the measuring electrodes, i.e., the parameter is unity. It is agreed that the nonhomogeneity of the electric field is much less of a problem when applying the conductance technique in the aorta than in the left ventricle because the vessel more closely adheres to the cylindrical model (11). In blood vessels, Hettrick et al. (12) showed that the value of is near unity for small cylinders (<10 mm in diameter) in a finite-element simulation and in in vitro measurements. Finally, the value of deviates from unity primarily under in vivo conditions because of the presence of blood cells (13). Again, our proposed methodology eliminates the effect of blood cells in vivo during the transient injections.
Our results show that the current leakage or parallel conductance is very significant (>60% of the total conductance). To accurately determine the absolute lumen CSA, we must correct for the Gp as illustrated in the present study. It is interesting that Gp is significantly higher for the femoral artery and the LAD, which implies higher conductivities in these regions. Furthermore, the parallel conductance was predictably decreased when the surrounding tissue was dissected away. The value of parallel conductance did not vanish when the surrounding tissue was dissected away because the posterior aspect of the vessel was still in contact with the surrounding tissue. When the vessel is truly insulated, the parallel conductance through the vessel thickness is negligible.
We used the proposed method to measure the increase in diameter in response to flow overload. We found the mean increase in diameter to be 20%. It is well known that the vessel diameter increases acutely and chronically in flow overload in an attempt to normalize the wall shear stress (WSS). A 26% increase would be required to normalize the WSS because the WSS is proportional to the cube of the diameter (17). Hence, the observed acute response did not normalize the WSS, and it is expected that the vessel would remodel chronically to increase the diameter further to restore WSS (18).
There is no doubt that the transformation of a cardiac catheter into a conductance catheter that allows reliable and accurate assessment of coronary lumen CSA will provide a powerful diagnostic and treatment tool for the invasive cardiologist. This will improve clinical outcomes by avoiding under- or overdeployment and sizing of stents, which can cause acute closure or in-stent restenosis. In addition to the enormous potential for clinical application, a method that allows accurate in vivo measurement of lumen CSA of medium size vessels will have significant potential as a research tool. For example, the method can be used to study the mechanical properties of elastic vessels and the vasoactive properties of muscular vessels in vivo. Furthermore, the combination of this technique with sensors for measurement of pressure and flow will allow a more complete characterization of the hemodynamic conditions of blood vessels and hence enhance our knowledge of the function of the vessel in health and disease. This technique will undoubtedly become an important tool for the cardiovascular physiologist and cardiologist.
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GRANTS |
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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REFERENCES |
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This article has been cited by other articles:
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  Y. Liu, C. Dang, M. Garcia, H. Gregersen, and G. S. Kassab Surrounding tissues affect the passive mechanics of the vessel wall: theory and experiment Am J Physiol Heart Circ Physiol, December 1, 2007; 293(6): H3290 - H3300. [Abstract] [Full Text] [PDF]
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C. Wang, M. Garcia, X. Lu, Y. Lanir, and G. S. Kassab Three-dimensional mechanical properties of porcine coronary arteries: a validated two-layer model Am J Physiol Heart Circ Physiol, September 1, 2006; 291(3): H1200 - H1209. [Abstract] [Full Text] [PDF]
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