In vitro experiments

We used glass pipes of a length of 20 cm in the in vitro model. They had defined inner diameters of 1.5, 2.5, 3.5, 4.5, and 5.5 mm to simulate coronary vessel. The glass pipes were perfused by a roller pump with heparinized blood from volunteer donors. Careful attention was paid for an exact calibration of the pump flow before each measurement using volumetric calibration. Setting different pump speeds according to physiologic velocities of coronary blood flow, the mean flow velocity was varied between 5 and 180 cm/s. The motor currency of the roller pump was directly supervised by a personal computer via an analog-digital interface. Careful attention was paid to keep the motor currency stable during all flow velocity recordings. Twenty measurements were taken at each flow velocity after repositioning of the Doppler wire in the mid segment of the glass pipes. The wire was twisted and moved until a stable signal was obtained before each measurement. The mean value of the average peak velocity (APV) sampled by continuous recording over a two minute period was taken for further analysis at each perfusion speed.

Measurements of coronary flow velocity in vivo

Calculations and statistical analysis

The Reynolds number (Re) can be calculated from the mean luminal diameter (MLD) multiplied with the flow velocity (APV/2) and the density (Q) divided by the viscosity of blood (n):

MLD = mean luminal diameter, APV/2 = mean of average peak velocity, Q = density of blood (1,060 kg*m^-3), n = viscosity of blood (4*10^-3 Pa*s).

The laminar flow profile of blood changes to a turbulent flow above the CRN. The flow velocity of the CRN was calculated using the MLD which was obtained by QCA in all patients. Blood flow rate (BF) was calculated from the APV divided by 2 and the luminal area (LA) of the vessel (π*(MLD/2)²) [21]:

BF = LA * APV/2 = APV/2* π*(MLD/2)²

BF = blood flow, LA = luminal area (π* vessel radius ²); APV/2 = mean of average peak velocity, MLD = mean luminal diameter.

The correlation coefficient (r) and its square value (r²) were obtained by computerized calculation with Excel 2000 (Microsoft Corp.). All values are expressed as mean ± standard deviation.

In vitro studies

In vivo measurements

It was the aim of our study to transfer the in vitro findings to the clinical routine of intra-coronary flow velocity measurements in diseased coronary arteries of patients in the catheter laboratory. It was unclear whether these critical flow velocities could occur in a relevant number of patients. However, these measurements were performed irrespectively of the inherent deviation caused by the described phenomena.

The flow velocity was measured in 23 patients (31 %) in the right coronary artery (RCA), in 18 patients (35 %) in the circumflex artery, and in 34 patients (65 %) in the left anterior descending artery. A PCI was necessary in 42 patients (56 %). In these patients the CFVR increased from 1.6 ± 0.40 to 2.7 ± 0.35 after PCI. Only 12 patients received a stent due to an angiographically unsatisfying result of the balloon inflation. We measured the maximum hyperemic APV value in 43 patients before, and in 32 patients after an angioplasty. Among those 43 patients were 33 patients (77 %) in whom the angioplasty was deferred due to an initially recorded CFVR above 2.0. Peak APV values were measured in 32 patients (76 %) post angioplasty. In 10 patients (24%) the recording of the APV reached its maximum before the intervention. However, the highest individual APV value of each patient was used for further analysis. Figure 3 summarizes the maximum values of the hyperemic APV of all patients.

Peak values of APV varied between 14 cm/s and 154 cm/s. In 15 patients (20 %) the maximum APV exceeded the velocity of the CRN. In 7 patients (9.3 %) the maximum APV in the RCA, and in 8 patients (10.7 %) the maximum APV in the left coronary artery exceeded the velocity of the CRN. The average maximum values of the APV were 79 ± 17.2 cm/s after PCI (n = 32), and 61 ± 14.7 cm/s before angioplasty (n = 43).

In vitro measurements

We were able to demonstrate an excellent correlation between perfusion volume and the calculated volume derived from Doppler flow velocity measurement under in vitro conditions at low flow velocities as previously described by other research groups [22]. At flow velocities above the CRN of about 500, flow volume calculations based on the shift of the Doppler signal showed a tendency to underestimate the blood flow as illustrated by Figure 4. This phenomena can be explained by our hypothesis that the Doppler wire measured the true peak value of APV under turbulent conditions, since the intra-luminal peak APV is diminished under turbulent flow conditions. It does not reach the same value which would have been recorded with equal perfusion volumes under laminar flow conditions.

The amount of the mean underestimation of the flow velocity measured by Doppler wire was 13.1 % under relatively high perfusion speeds above the CRN. The inaccuracy of the Doppler wire was 4.2% under laminar flow. These results qualify the Doppler wire as a valid, and highly exact tool for quantitative coronary blood flow measurements under low flow velocities associated with a laminar flow profile. The CRN is reciprocally dependent on the vessel diameter given by the MLD. The velocity at the value of the CRN exceeds the normal physiological range in vessels with an MLD below 2 mm. Thus, we would suggest to place the Doppler wire in a distal non-branching segment of the coronary artery to achieve the highest accuracy of the flow velocity measurement. On the other side, the accuracy of measuring the MLD by QCA is limited in smaller and more calcified vessels [23].

In vivo measurements

According to an inaccuracy of only ± 4.2 % under laminar flow conditions we regard intra-coronary Doppler wires as a valid tool for quantification of coronary blood flow at rest. However, several studies investigated hyperemic blood flow after pharmacological stimulation by papaverine or adenosine. Under resting conditions, we did not observe flow velocities which were above the velocity at values of the CRN. But under hyperemic conditions, about 20 % of patients reached flow velocities above the velocity of the CRN after injection of adenosine. Based on our in vitro observations, we assume that the Doppler shift derived flow velocity underestimates the coronary peak blood flow in one fifth of patients by about 13 %.

Measurements of CFVR can be relevantly influenced by a maximum APV above the CRN. For example, the measured CFVR would be 2.3 instead of 2.6 due to the occurrence of turbulent flow during hyperemia after an angiographically successful PCI. According to the results of the DEBATE II Study, the responsible cardiologist would expect a higher restenosis rate in this patient, considering the implantation of a stent [24]. The APV values at rest were below the velocity of the CRN in all patients. Thus, an overestimation of the CFVR related to an underestimated baseline APV does not appear very likely to happen under regular flow conditions.

Novel technologies like the so-called fractional flow reserve (FFR), or intra-coronary thermo-dilution can quantify high coronary blood flow with predominantly turbulent character independently of the present flow profile [25, 26]. One may speculate, that changes of coronary flow profile from laminar to turbulent might have been one reason for previously reported discordance between CFVR and FFR [27]. Since turbulent flow occurs when reaching relatively high flow velocities, and healthy subjects without coronary artery disease show higher flow velocities in pharmacological tests compared to patients suffering from coronary artery disease, we assume that turbulent flow may be observed more often in healthy vessels [28]. However, measuring CFVR in diseased vessels results in relatively low peak flow velocities, therefore the chance of turbulent flow interfering with the Doppler measurements may be of less importance.

The in vitro evaluation of the CRN was performed using smooth glass pipes. In contrast to the ideal situation inside glass pipes we assume an even lower CRN in vivo when measuring APV in calcified coronary vessels. Therefore, an underestimation of flow velocity recordings might happen more often in patients than suggested by our in vitro experiments. However, we do not expect a CRN much below 500 which could also influence the accuracy of intra-coronary Doppler flow measurements at rest [29].

The velocity of the CRN depends on the vessel diameter. Saphenous vein bypass grafts show higher diameters compared to native coronary arteries which can reach MLD values of up to 8 mm. Relevant variations of the velocity distribution in vein bypass graft were uncovered by laser Doppler anemometry [30]. Thus, the flow velocity of the CRN may be reached more often in vein grafts than in native coronary vessels. Flow velocity measurements in a bifurcation of a coronary artery may also influence the quality of the flow profile [31].

Recently, coronary flow reserve was also analyzed in transthoracic Doppler studies [32]. Further studies should evaluate the influence of turbulent flow on flow velocity measurements with transthoracic Doppler.

Limitations of the study

We were able to demonstrate an effect of high flow velocities on the validity of blood flow measurements with Doppler wires in smooth glass pipes. In contrast to coronary arteries these pipes did not have any elastic component, nor bending, calcification of the wall, local dissections, previously implanted stents, intramural thrombus, side branches, or changes in vessel diameter which all have an influence on the flow profile possibly causing turbulent flow [33, 34].

Especially the elastic component, changes in diameter, and the hematocrit influencing the viscosity of the blood might have a major influence on the CRN in human coronary arteries [35, 36]. The derived blood flow was underestimated only at high flow velocities under in vitro conditions. In a study population of 75 patients, 20 % achieved such high flow velocities above the CRN during maximal hyperemia. Today, higher doses of adenosine are given i. c. for induction of hyperemia [37]. Therefore, the proportion of patients achieving coronary peak flow velocities above the value at the CRN may be even higher due to this more intensive pharmacological stimulation. As mentioned above, in comparison to smooth and straight glass pipes, turbulent flow might occur more often in coronary arteries which show an increasing proportion of previously implanted stents. On the other hand, the elastic vessel wall can reduce the amount of turbulent flow. However, we see limitation of transferring the results of the in vitro measurements directly to the in vivo Doppler studies.