INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES APPENDIX

THE INTRAMURAL CORONARY ARTERY (IMCA) with a diameter of 50-500 µm is believed to be a critical segment for blood supply to the inner layers of heart muscle, and heart contraction has considerable mechanical influence on the IMCA (4). However, dynamic observation of configurational changes in the IMCA has been severely limited in conventional angiography.

We recently developed a novel microangiographic system using monochromatic synchrotron radiation (SR) as an X-ray source and a high-definition video camera as a detector to visualize small vessels with a diameter of as low as 50 µm in various organs (6). To date, there is no established means of quantitative measurement of vessel configuration using this microangiographic system. Digital image processing has been applied to conventional angiography over the past few decades, and rapid development of computer networks has made it possible not only to transfer digitized medical images to a remote site but also to utilize a program in the public domain for quantitative analysis of vascular configurations (9).

In this study, we comparatively analyze the characteristics of branching patterns of the IMCA with those of the epicardial coronary artery (EPCA) and also with those of the distal ileal artery (DIA) in the intestinal organ, using digital processing for high-definition microangiography that allows quantification of small vessel diameters with high accuracy and reproducibility with a personal computer and a public domain program. In addition, we describe the details of this quantitative method.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES APPENDIX

Experimental protocol. Seven dogs were anesthetized with subcutaneous morphine hydrochloride (3 mg/kg) and intravenous -chloralose (80 mg/kg), intubated, and artificially ventilated with air mixed with oxygen to maintain arterial blood gases and pH within normal limits (Pa_O2 ~100 Torr, Pa_CO2 25-40 Torr, pH 7.35-7.45). All animal experiments were performed in accordance with the Guidelines of Tokai University School of Medicine on Animal Use, which conforms to the Guide for the Care and Use of Laboratory Animals [National Institutes of Health (NIH), 1996]. For coronary angiography a left thoracotomy was performed in four dogs, and a silicon tube bypass was positioned between the left subclavian artery and the left anterior descending artery (3). The dogs were set nearly supine. The SR beam direction was set so as to pass through the left ventricular free wall from the posterobasal to the anteroapical direction. We also conducted fine adjustment of each dog's posture to obtain an optimal visual field: a target diagonal branch ran along the horizontal axis in the upper one-third of the visual field, and the SR beam was nearly perpendicular to the virtual plane including the diagonal branch and its IMCAs (7). Contrast material with 37% nonionic iodine [Iomeprol (Eisai Pharmaceutical, Tokyo) or Iopamidol (Nihon Schering, Osaka)] was injected into the bypass (3 ml/s for 1-2 s) while SR irradiated the dog. For ileal angiography an abdominal incision was made in the remaining three dogs, and a segment of the lower ileum ~15 cm in length was hung above the abdominal wall with surgical ties. The bypass was set between the femoral artery and the superior mesenteric artery, and the angiographic procedure was performed with the contrast material (3 ml/s for 3-4 s).

Evaluation of accuracy of measurement. The accuracy of the method of quantification was tested by two independent observers for 37 vessel segments of the coronary arteries and the DIAs (52-667 µm in diameter). Interobserver variability was assessed using linear regression analysis with SEE and r. In addition, the method of Bland and Altman (2) was applied to evaluate the mean difference between measurements obtained by the two observers and the SD of differences. For direct estimation of the accuracy, we also placed a copper wire with a known diameter of 130 µm beside the target vessels and measured the diameter of each wire at three to seven different points (total: 31 points).

Digital angiographic methodology. SR is characterized by high brilliance, tunability of X-ray photon energy, and extreme collimation. The high brilliance allows us to increase sensitivity to a small amount of contrast material in a short exposure period, and the tunability of X-ray energy allows us to obtain the maximum difference for the X-ray absorption coefficient between the contrast material and the tissue. The extreme collimation also assists us in image quality in terms of spatial and density resolution because divergence and scatter of X-ray photons are eliminated. Monochromatic SR with an energy level of 33.3 keV, which is just above the K-edge absorption of iodine (33.17 keV) was obtained from Beamline-14 at the Photon Factory in the National Laboratory for High Energy Physics, Tsukuba, Japan, as described schematically in a previous paper (6). The SR beam formed a contrast image of the object on a fluorescent screen (HR-mammo, Fuji Film, Tokyo). A square area with a side length of 20.0 ± 0.01 mm was scanned by a high-definition pick-up tube with 1,125 scanlines, which converted incident photons efficiently into a electric signal using an avalanche phenomenon. Modulation-transfer-function chart study revealed that the present system enabled us to identify adjacent leadlines of 16 line pairs/mm [Kyokko X-ray test chart Type-14 (2-20 line pairs/mm), Kasei Optonix, Tokyo; Ref. 14]. As for contrast resolution using a vascular phantom (type 76-700, Nuclear Associates, New York), the minimum vascular phantom (0.5 mm in diameter) with a minimum concentration was visualized (2.5 mg/ml of iodine) through a 75-mm-thick acrylic block. A scanning mode of the camera was progressive (noninterlaced), and one frame consisted of a single field. Because images were obtained by continuous X-ray exposure, the exposure time was equal to the signal frame time. The lag of the camera and X-ray-to-light converting screen was a few milliseconds and was shorter than the exposure time. Subsequently, a frame memory (192 megawords of 12 bits, Zenisu Keisoku, Tokyo) digitized the output to a resolution of 12 bits/pixel, 1,024 × 1,024 pixels/frame, and 15 frames/s.

Quantitative analytic methodology of vessel diameters. Image processing, including a median filter, was performed on a personal computer (Power Macintosh 8100/100AV, Apple Computer) without frame averaging or irreversible data compression (11, 13). Linear interpolation between adjacent pixels was also applied to perform quantitative analysis at a better effective pixel side length of 9.75 ± 0.05 µm (i.e., side length of visual field/2,048 pixels) (10). Temporal subtraction was performed on the ileal angiograms between two still frames just before and during injection of the contrast material.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES APPENDIX

Self-similarity in branching patterns of IMCA. The degree of diameter reduction at a branching point was nearly constant in any of the distal IMCAs labeled 1'-8' in Fig. 1. As shown in Fig. 2A, the plots correlated linearly between the daughter diameter and the mother diameter in distal IMCAs. This indicated that the diameter reduction with branching was self-similar in the IMCA. The degree of diameter reduction of the IMCA was almost identical with those of the EPCA and DIA (Fig. 2B): the regression line of the IMCA (L1: y = 0.737x  2.18, SEE = 32.3 µm, r = 0.817) demonstrated no significant difference (P < 0.05) from those of the EPCA (L2: y = 0.838x  16.7, SEE = 80.0 µm, r = 0.925) and DIA (L3: y = 0.755x + 8.63, SEE = 24.5 µm, r = 0.893). However, the connecting segment where the proximal IMCA branched off from the EPCA was characterized by an abrupt decrease in diameter, which was quantified by a regression line (L4: y = 0.182x + 90.2, SEE = 52.9 µm, r = 0.646) significantly different from the other three lines (Fig. 2B). This represented that the pattern of diameter reduction from the proximal EPCA to the distal IMCA was discrete at the connecting segment between them. As precisely described in the APPENDIX, the abrupt diameter reduction at the connecting segment between the EPCA and IMCA possibly induces a power cost ~1.7-1.8 times greater than the symmetric branching within the EPCA and IMCA.

View larger version (135K): [in this window] [in a new window]   Fig. 1.   Example of coronary angiogram. Intramural coronary arteries (IMCAs) branch off from epicardial branches of epicardial coronary arteries (EPCAs) and show intramyocardial self-similar branching (numbered with a prime). Numbers at IMCA-EPCA junctions are coincident to x-axis of Fig. 3.

View larger version (33K): [in this window] [in a new window]   Fig. 2.   Correlation between pre- and postbranching diameter. A: line of regression (L1) represents a self-similar pattern of diameter reduction with branching in IMCA. B: this pattern was almost identical to that in EPCA (L2) and distal ileal artery (DIA) (L3), whereas a different pattern was present at a junction between IMCA and EPCA (L4).

View larger version (27K): [in this window] [in a new window]   Fig. 3.   Relative decrease in diameter along a sequence of branching off of IMCA from EPCA. Relative diameters of EPCA and proximal IMCA (A and B, respectively), normalized to diameters at most proximal branching node in visual field, are plotted against order n of branching off as numbered in Fig. 1. D0 and Dn, EPCA diameters of most proximal and nth descendant branches, respectively; d0 and dn, IMCA diameters in same manner.

Evaluation of accuracy of measurement. The dual measurements of the 37 vessel segments by two observers were highly correlated (r = 0.999) and were almost identical, as shown by the regression equation (y = 1.02x  1.07, SEE = 6.36 µm; Fig. 4A). The analysis of Bland and Altman (2) revealed a mean difference of 2.38 µm and an SD of differences of 6.71 µm (Fig. 4B). In addition, the mean diameter (±SD) of the reference wire measured at a total of 31 points was 131.17 ± 13.34 µm, which demonstrated quite a small difference from the known diameter of 130 µm.

View larger version (27K): [in this window] [in a new window]   Fig. 4.   A: interobserver differences. Dashed line and continuous line correspond to line of identity and line of regression, respectively. B: differences between the 2 individual observers. Dashed lines indicate mean difference and SD of differences, respectively, and continuous line corresponds to line of identity.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES APPENDIX

We applied digital high-definition microangiography to the distal EPCA and IMCA in the heart and the DIA in the intestine and quantitatively analyzed these small vessel diameters with high accuracy and reproducibility. These three arterial segments demonstrated elicit self-similar branching patterns for diameter reduction (1, 5). The quantified degree of diameter reduction with branching of the IMCA was as nearly same as that of the EPCA in the heart and almost identical to that of the intestine. However, self-similarity in branching patterns was discrete at the connecting segment between the IMCA and EPCA.

In this study, regression analysis of the relationship between the diameters of a mother branch and a daughter branch showed that an artery continued to divide into two branches of almost equal diameter at a constant rate of change: 0.737, 0.838, and 0.755 in the IMCA, EPCA, and DIA, respectively (L1-L3 in Fig. 2, A and B). However, the slope of the regression line was 0.182 in the connecting segment where an IMCA branched off from an EPCA (L4 in Fig. 2B), and it was significantly smaller than the segments within the IMCA, EPCA, and DIA (P < 0.01). These observations indicated abrupt narrowing of the vessel diameter at the connecting segment of the IMCA to EPCA. Furthermore, the diameter of the EPCA decreased at a constant rate along the sequence of branching off of IMCAs from an EPCA (Fig. 3A), whereas the proximal IMCA segments showed a random change of diameters along the sequence of branching off from the EPCA (Fig. 3B). These results indicated discrepancy of the self-similarity of branching geometry presented at the connecting segment of the IMCA to EPCA.

This lack of self-similarity possibly yields a considerable loss of power cost in the connecting IMCA segment to the EPCA as follows. The frictional power cost involved in the blood stream in an arterial segment, which is derived from Poiseuille's law of flow (8), is minimized when the two daughter branches are equal in diameter (see APPENDIX). As described in the regression analysis in this study (Fig. 2), the daughter diameter relative to the mother diameter was 0.84 in the EPCA and 0.74 in the IMCA, whereas it was 0.18 at the connecting segment between the proximal IMCA and the EPCA. Substituting these results, it was estimated that the abrupt diameter reduction at the connection between the EPCA and IMCA caused a power cost ~1.7-1.8 times greater than the equally divided segments seen within the EPCA and IMCA. A branching angle is the other important factor in the power cost. It was, however, not included in the results of this study, because the X-ray projection was almost perpendicular to the EPCA-IMCA branching, although not for bifurcations within the EPCA and IMCA trees. Murray (8) and Zamir (15) shed light on the mathematical correlation between an arterial branching angle and a diameter change. Murray speculated that the smaller the daughter diameter relative to the mother diameter, the closer to 90° is the branching angle made with the line of direction of the mother branch under conditions where the power cost is minimum. Substituting our results of relative diameters, i.e., 0.838 in the EPCA and 0.182 in the connecting segment from the EPCA to IMCA, Murray's optimal angle of bifurcation was calculated as 82.1°. In our preliminary measurements, the mean branching angle (±SD) at the connecting segment in the projection images was 79.7 ± 21.6° (n = 36), and their difference was very small even if this measurement was not precise enough for direct comparison.

Although several authors have presented the geometry in coronary vascular branching by means of mathematical analysis (8, 15) and experimental measurements using acrylic casts (12), there has been to date no comprehensive presentation of this different branching pattern of the proximal IMCA from the EPCA. The discrepancy of the self-similar pattern of branching in diameter reduction at the junctional segment from the EPCA to IMCA suggests that a developmental process of vessels on the epicardial surface and that in the intramyocardial tissue are independent before completion of the formation of their junctions.

We estimated the theoretical accuracy of our quantitative analysis in the present digital microangiographic system and performed empirical analysis with the results of dual measurement. The minimal lumen diameter measurable in this system, which was defined by twice the diagonal length of a pixel, was estimated as 9.75 (±0.05) ×  = 27.6 ± 0.1 µm. This value was comparable to the result of assessment using the resolution bar chart of 30 µm (16 line pairs/mm) (14). In practical measurements, the study of interobserver variability demonstrated good reproducibility by regression analysis (Fig. 4A), and the method of Bland and Altman (2) only showed small interobserver differences (±SD) of 2.38 ± 6.71 µm (Fig. 4B). In addition, the measured diameter of the reference wire of 130 µm was 131.17 ± 13.34 µm. These results confirmed that the quantitative analysis conformed with theoretical accuracy.

In conclusion, the coronary artery demonstrated a self-similar branching pattern for diameter reduction continuous from the epicardial-to-intramyocardial branching, and the self-similarity was almost identical to that of the intestine. However, a discrepancy of self-similarity was shown at the connecting segment between the IMCA and EPCA. This discrepancy increases the power cost of flow and might contribute to the susceptibility of the inner layers of heart muscle to myocardial ischemia.