The effect of image distortion on 3-D reconstruction of coronary bypass grafts from angiographic views.

Three-dimensional (3-D) reconstructions of coronary bypass grafts performed from X-ray angiographic images may become increasingly important for the investigation of damaging mechanical stresses imposed to these vessels by the cyclic movement of the heart. Contrary to what we had experienced with coronary arteries, appreciable reconstruction artifacts frequently occur with grafts. In order to verify the hypothesis that those are caused by distortions present in the angiographic images (acquired with image intensifiers), we have implemented a grid correction technique in our 3-D reconstruction method and studied its efficiency with phantom experiments. In this article, the nature of the encountered artifacts and the way in which the dewarping correction eliminates them are illustrated by a phantom experiment and by the reconstruction of a real coronary bypass vein graft.

In-vivo measurements of wall shear stress in human coronary arteries.

BACKGROUND: Wall shear stress (WSS) is closely associated with arteriosclerosis. WSS values for various vessels and species are available, but fully in-vivo measurements in human coronary arteries have not yet been reported. OBJECTIVE: To measure WSS in undiseased coronary arteries of adult patients at rest. METHODS: We recorded the temporal average value (APV) of the instantaneous maximal blood velocity in the three vessel segments of angiographically normal coronary artery bifurcations in 21 patients undergoing cardiac catheterization to treat various diseases by means of a 0.036 cm Doppler wire (FloWire). In total, 36 bifurcations were examined. The 36 x 3 cross-sectional areas (CSA) were determined by means of a three-dimensional angiographic technique. The three flows, Q1 (inflow), Q2, and Q3 of each bifurcation were calculated according to Q=0.5 x APV x CSA. For each segment, WSS was calculated as WSS=32 eta Q/(pi D3) (where blood viscosity eta=3.5 mPa s and D is vessel diameter). Only the 54 WSS values obtained from the 18 flow triplets which satisfied the equation Q1/(Q2+Q3)=1 better than did the 18 other ones were retained. RESULTS: The 54 WSS values ranged from 0.33 to 1.24 Pa (mean 0.68 Pa, SEM, 0.027 Pa). They did not depend significantly on Q (r=0.07; P=0.60) and the CSA (r=0.24, P=0.08) but the second relationship approached significance. CONCLUSION: The obtained mean WSS value (0.68 Pa) is half the value predicted for coronary arteries from optimality principles. It is also smaller than many values reported for human carotid, renal, and femoral arteries.

Accuracy of coronary flow measurements performed by means of Doppler wires.

To estimate in patients the accuracy of coronary flow measurements performed by means of 0.014" Doppler wires, the time-averaged maximal blood velocity (APV) was recorded in the 3 branches of 36 angiographically normal coronary artery bifurcations selected in 21 patients undergoing cardiac catheterization for various diseases. Contrast medium injections filmed under two incidences allowed identification of the 3 sample volume locations and computing of the 3 corresponding vessel cross-sectional areas (CSA) at subsequent data analysis. Multiplication of the velocities APV/2 (range: 3 to 20.5 cm/s) by the CSA (obtained by averaging the two calibrated vessel diameters; range: 1.6 to 5.4 mm) yielded 108 flow rates (range: 5.4 to 169 mL/min). The average relative flow error was then estimated using the continuity equation (Q(in) = Q(out,1) + Q(out, 2)) and the central limit theorem. The result was that the relative flow error decreased from 30% at Q = 30 mL/min to 13% at Q = 160 mL/min. We conclude that coronary flow measurements are reasonably accurate, except perhaps for very low flows.

A new technique for improved densitometric quantification of coronary artery stenoses in angiographic images.

In vitro studies have demonstrated that densitometric quantification of coronary artery stenoses is superior to geometric methods to assess non-circular lumens. However, in patients, several authors have reported significant discrepancies between area reduction percentages obtained densitometrically from two different imaging projections. Some of the factors causing the discrepancies can be reduced by simple precautions taken during image acquisition. Some others may be compensated for during analysis. Nevertheless, two factors remain problematic. The first is the inadequate spatial orientation of the vessel axes at the stenotic and reference cross sections with respect to the x-rays. The second is the difficulty in identifying the same vessel cross section in both planes at the time of analysis. We have designed a new densitometric technique that eliminates the error contributions of these two factors. The technique requires simultaneously acquired biplane coronary angiograms and biplane images of a translucent cube bearing steel markers acquired in exactly the same biplane geometry. Using the two projection matrices calculated from the images of the cube, the centerlines and the edges of the coronary arteries can be reconstructed in space from the biplane angiograms. The angles between the vessel axes and the x-ray beams can be determined and the densitometric cross sections can be corrected accordingly. Moreover, the 3D reconstruction allows the identification of the same cross section in the two planes for the determination of the area reduction percentages. Validation measurements were performed on a Perspex phantom and in patients, before and after angioplasty. In both types of measurement, the interplane discrepancies could be roughly halved. The densitometric technique presented can be incorporated into routine angiography and could become a strong alternative to the geometric approach that is presently dominating this field.

A new densitometric approach to the assessment of mean coronary flow.

RATIONALE AND OBJECTIVES: The authors present an angiographic method to measure absolute coronary blood flow in patients. METHODS: The left or right coronary tree is three-dimensional (3D)-reconstructed from biplane coronary angiograms. This allows the determination of the intravascular volumes needed for flow measurement. The 3D distance traveled by the contrast medium during one cardiac cycle is determined by appropriately thresholding the "concentration-distance", curves computed on two pairs of images taken one cardiac cycle apart. RESULTS: The angiographic flow measurements were compared with nearly simultaneous flow determinations obtained with an intracoronary ultrasonic Doppler flow velocity measuring device. The mean relative difference between the Doppler and the 3D measurements was 11% and the two sets of flow values correlated well (r = 0.81). CONCLUSIONS: A method for the determination of mean coronary flow is presented. The procedure is simple and can be incorporated easily into clinical routine.

Towards a gold standard for quantitative coronary arteriography.

Densitometric quantification of coronary artery stenoses in angiographic images can be problematic for two reasons: (i) the x-rays are inadequately oriented with respect to the vessel segments of interest at image acquisition; (ii) non-linear effects due for instance to beam hardening, scattered radiation and veiling glare may reduce the accuracy. As a consequence, appreciable discrepancies between degrees of stenosis measured in two different projections can occur. To overcome these limitations, we have designed and tested a combined correction that compensates (at subsequent analysis) for the error contributions due to the cited sources. It implies 3D reconstruction of the vessel segments of interest and consequently requires an appropriate biplane coronary angiogram. In experiments performed with a dedicated phantom, application of the correction improved the correlation between measured and true area reduction percentages (without correction: y = 1.04x - 4%, r = 0.97, SEE = 6%, n = 35; with correction: y = 1.02x - 0%, r = 0.99, SEE = 3%, n = 35). Applied to ten area stenoses measured biplane in patients and exhibiting strong interplane discrepancies, the correction had a comparable effect (without correction: y = 0.83x - 11%, r = 0.86, SEE = 9%, n = 10; with correction: y = 0.83x + 2%, r = 0.98, SEE = 4%, n = 10). The new densitometric method could possibly be used as a gold standard in the objective evaluation of geometric methods in patients.

Is the indicator dilution theory really the adequate base of many blood flow measurement techniques?

The indicator dilution theory is the underlying model of many blood flow measurement techniques used daily in hospitals, for instance in cardiac catheterization laboratories. The basic version of this theory applies to a "stationary" flow system with one inlet and one outlet, into which a small amount M of indicator is injected "suddenly" at time t = 0 at the inlet. The quintessence of the theory consists in three equations, which themselves result from some apparently simple assumptions about the considered flow systems. The first equation states that the (constant) flow Q through the system can be calculated by use of the known amount of indicator, M, and of the indicator concentration-time curve c(t) recorded at the outlet. The second one allows the calculation of the "mean transit time" t* of fluid and indicator particles through the system from the curve c(t). The third equation, V = Qt*, yields the system volume V. It is generally believed that these three equations would be absolutely valid if the assumptions of the theory could be perfectly fulfilled. We show, by considering a simple model, that all three equations are actually incorrect for most flow systems when the detector used to record the curve c(t) is of the "trans-illumination" type, as is the case for instance in dye dilution methods and in many angiographic or CT techniques. A further consequence is that t*, which is truly the "center of mass" of the concentration-time curve c(t), does not have the well known property of being the adequate parameter for flow determinations. Many flow measurement techniques thus appear to have no theoretical base.

The impact of vessel orientation in space on densitometric measurements of cross sectional areas of coronary arteries.

Under ideal conditions, densitometric measurement of a coronary arterial cross section in biplane angiographic images should result in nearly equal cross sectional areas for both planes. However, quite appreciable discrepancies have been found by some authors in patients. In this study, the role of inadequate spatial orientation of the vessel axes relatively to the x-rays was assessed by use of a 3D technique applied to 60 stenoses (45 pre PTCA and 15 post PTCA) in simultaneously acquired digital biplane coronary angiograms of 27 CAD patients. The 3D technique yields two radius values per projection directly in mm at any arterial cross section of interest. This was used to determine the areas Ar(in mm2) of the reference cross sections. As with catheter calibration, these cross sections were thus assumed to be more or less circular, but out-of-plane effects and errors due to a catheter diameter determination in pixels were avoided. The areas of the stenotic sections were then determined densitometrically (in mm2) from the two projections (1 and 2) according to As1 = ArDs1/Dr1, resp. As2 = ArDs2/Dr2, where Dr1, Dr2, Ds1 and Ds2 are the conventional densitometric areas of the reference and stenotic cross sections measured in planes 1 and 2. As expected, the areas As1 and As2 correlated only moderately: As2 = 0.92 As1 + 0.7 mm2, r = 0.82, n = 60, SEE = 1.4 mm2. The 3D method also yielded the two spatial angles between the local vessel axis and the X-rays of both planes. These two angles were then used to correct each densitometric area for inadequate orientation. With the corrected densitometric areas As1c and As2c, the correlation improved to: As2c = 1.05 As1c + 0.03 mm2, r = 0.93, n = 60, SEE = 0.8 mm2. Inadequate orientation of the cross sections in space thus appears to be an important factor of inaccuracy in densitometric measurements of stenotic cross sections in patients.