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Remote densitometric analysis of stenotic lesions
REMOTE DENSITOMETRIC ANALYSIS OF STENOTIC LESIONS*
T.
SANDOR,B.
SRIDHARand S. PAULIN
HarvarJ Medical School, Peter Bent Brigham Hospital and Beth Israel Hospital, Boston, Mass. 02115 (USA)
(Received: 25 June. 1978) SUMMARY
In conventional densitometric evaluation of stenoses the digitized angiogram is displayed on a multi-grey-level scope to.facilitate operator interaction. With a remote terminal, linked to the computer with regular telephone lines, such display is unacceptably slow. To circumvent this dificulty, the projection of the original image is used for interactions through a sonic pen digitizer interfaced to the computer. A coordinate system can be defined on the projected image, in addition to the blood vessel segment to be analyzed by the operator. The computer can retrieve these features on the stored pre-digitized image to carry out the quantitative evaluation of the stenosis. This method reduces the time of analysis and allows several institutions to share the same computing facility.
SOMMAIRE
Duns le mtthode classique devaluation densitometrique des stknoses, l’angiogramme code est place sur un &ran d niveaux multiples d’intensite de gris d fin de faciliter le travail de l’operateur. Duns le cas d’un terminal tloigne, relic d I’ordinateur par ligne ttlkphonique ordinaire, une telle methode est Xune lenteur inadmissible. Pour tourner cette dificulte’ on utilise la projection de l’image initiale en passant par
* Supported by USPHS grants HL20895, HL05832. GM01910, RR05489 ROl HL19003 RAD and ROl CA23246. Send correspondence to: T. Sandor, D.P., Sidney Farber Cancer Institute, Department of Radiology, Rm. 92,44 Binney Street, Boston, Mass. 02115 (U.S.A.)
15 inc. J. Bio-Medical Computing (10) (1979) 15-22
@Elsevier/North-Holland
Scientific Publishers Ltd.
16
T. SANDOR,
B. SRIDHAR,
S. PAULIN
I’intermtdiaire rl’un codeur numtrique relic a l’ordinateur. Un systeme de coordonnkes peut t%re dejini, sur l’image projetee, d I’emplacement de la partie du vaisseau sanguin que roptrateur lloit analyser. LZortEinateur peut retrouver ces eltments sur l’image precodde a ftn de realiser l’evaluation quantitative de la stenose. Cette metholle reduit le temps Xanalyse et permet h plusieurs institutions de partager lies moyens comrnuns de calcul. INTRODUCTION
Diagnostic information contained in high-quality coronary angiograms is currently extracted subjectively by the radiologist. As recent studies have indicated, such subjective judgement of the percent stenosis in coronary arteriograms, for instance, is very inaccurate (Bjork et al., 1975; DeRouen et al., 1977; Zir et al., 1976). Computer processing of the angiograms offers improved precision. Most of the available techniques for quantitative angiographic analysis, such as evaluation of ventricular volume, stenotic blood vessels, etc., are operator-interactive with the operator identifying a desired feature in the image, and the computer performing the necessary analysis. In the case of stenoses, the aim of the analysis is to obtain a measure for the constriction of the blood vessel by comparing the amount of contrast medium at the normal segment of the vessel with that of the abnormal segment. Percent stenosis is defined as: % Stenosis=
1-g
1
x 100
[
N
(1)
where MA and MN refer to the amount of contrast medium at the abnormal and normal segments, respectively. Densitometry can determine these quantities if the measured optical density is proportional to the amount of the absorbing matter (contrast medium). For monochromatic X-rays:
4 = IOev [ -_(cLIp)~l
(2)
where I, and I,, denote attenuated and original X-ray intensities, p/p is the mass attenuation coefficient, and x indicates mass per unit area. Equation (2) is the well known Lambert-Beer law (Lambert, 1760; Beer, 1882). Rewriting eqn. (2) gives: log+;.
(3)
t
From the definition of the optical density : D=log,,
$ t
(4)
REMOTE ANALYSIS
OF STENOSES
17
where 16 and Z;refer to radiant flux incident on and transmitted by a photographic emulsion. Since I is proportional to I’, it follows from eqns. (3) and (4) that: D=kx
(5)
where k is the proportionality constant. Equation (5) is the basic assumption for densitometry. However, when the X-rays generate the photographic transparency, the absorption coefficient is no longer constant but a function of the photon energy, E, that is p = p(E). For high-energy X-rays, when the beam passes through matter, the low energy photons are rapidly depleted and the beam becomes quasi-monochromatic. Such quasi-monochromaticity can be achieved in clinical diagnostic equipment by appropriate filtration of the X-ray beam. To determine the quantities in eqn. (l), optical density distributions representing the normal and abnormal segments of the blood vessel image have to be extracted. The present paper describes an approach to the analysis of stenotic lesions based on the above principle by 2 hospitals sharing one mini-computer. The site of the analysis was located 0.5 mile from the computer, which was linked to it by a regular dedicated telephone
Tests for the linearity of densitometry
To test the validity of eqn. (5), the following experiment was performed. Radiolucent tubings of known diameter were filled with contrast medium and placed in 20 cm of water. Cine-angiograms of these blood-vessel phantoms were taken on 35-mm film with an X-ray image intensifier used in clinical procedures. The images were digitized and from them one-dimensional optical density distributions were extracted perpendicular to the axis of the blood vessel phantom. The area enclosed by the distributions of the respective phantom images was computed and plotted against the known geometric cross-sectional area of the tubings. The results indicate good linearity in a range of about l-4 mm ‘blood vessel diameter’ (Fig. 1). From this one can conclude that the exposing X-ray beam is hard enough and the estimations based on monochromaticity are valid. Equipment
In this study, 35-mm tine-coronary angiograms were used. The tine-frames were scanned with an Optronics Photoscan at a scanning resolution of 25 pm. The density was digitized into 8 bits and the data were stored on 9-track magnetic tapes. These tapes were used as an input to a PDP 11/70 computer, which had among its peripherals a Tektronix 4010 terminal with binary display capability, a sonic pen contour digitizer, and an RPO4 disk of 44 million word storage capacity. The computer had an RSX 11/D operating system. The binary terminal and the contour digitizer were located at another institution within a half-mile from the
18
T. SANDOR, B. SRIDHAR, S. PAULIN
a IO-
0
500
1000
1500
COMPUTED PROFILE AREA (arbitmry unitq
Fig. 1 Evaluation of linearity in densitometry by using blood vessel phantoms.
computer and linked to it via a dedicated telephone line. The system configuration is shown in Fig. 2. Analysis of stenosis The procedures, designed to be operator-interactive, used the projected image of the 35mm film. The sonic contour digitizer was mounted on the projection screen. Using the projected image for interactive procedures requires establishing coordinate systems for the film and the scanned image, as well as scale factors. To do this, a reference feature of the image must be chosen by the following criteria: (1). The feature must be present in all coronary angiograms. (2) It must serve as reference for translation as well as rotation. (3) It must be retrievable by the computer program.
TELEPHONE
to
LINE COMPUTER
MICROPHONE -VANGUARD PROJECTOR
arrows
indicate
data
FILM
flow
Fig. 2 Schematic diagram of remote analysis of stenotic lesions.
REMOTE ANALYSIS
19
OF STENOSES
(4) The operator must be able to identify the above feature on the film without ambiguity by using a coordinate digitizer. The feature shown in Fig. 3, which is the boundary of the tine-frame, satisfies the above criteria and was chosen as the reference. The long edge AB provides a reliable reference for the orientation. The point B, where the curve BC meets the curve AB, provides reference for translation. A simple one-time calibration can determine the relative scale factor between the projected image and the scanned image. This remains valid, provided the adjustments in the projector are not altered. There are other alternatives for selecting reference points on the image. For instance, the images of 2 steel balls, 3-4 mm in diameter, can be used very conveniently as reference points. When the balls are mounted on the surface of the image intensifier, their images are superimposed on the film as a result of the X-ray exposure. Since these images are circular their center of mass can be easily found by an appropriate computer algorithm. This method cannot be used, however, for the analysis of films exposed in the past and stored in departmental libraries. As was mentioned earlier, the analysis of stenosis requires the extraction of optical density profiles from the digitized blood vessel image. The direction of the profiles should be perpendicular to the axis of the blood vessel..In the present method the operator supplies this direction to the computer as described below.
(1) The images to be analyzed are digitized and the date are fed into the disk of the computer. (2) To define analyzing windows enclosing the normal and stenotic segments of the blood vessel, the operator, with a sonic pen, marks 3 points per window on the image in the frame of reference of the projected image. The analyzing windows are parallelograms with respective sides parallel and perpendicular to the blood vessel axis. By defining them, the operator provides the direction for the optical density profiles to be extracted. (31 The coordinates of the analyzing windows in the projected images are
Fig. 3 Feature
selected on a tine frame boundary
for the reference
system
20
T. SANDOR, B. SRIDHAR, S. PAULIN
transformed to coordinates in the scanned image, and the computer automatically extracts and displays a prescribed number of profiles which can be displayed on a binary scope (Fig. 4). (4) The operator, using thumb-wheel controlled electronic cursors, marks the borders of the profiles, and the computer determines the area they enclose. The-values obtained are displayed in bar diagrams (Fig. 5). (5) In a question-and-answer mode, the operator identifies the normal and abnormal segments of the vessel from the bar diagram and the percent stenosis value is computed in accordance with eqn. (1). Accuracy cord&rations There are 2 major possible sources of error.
(1)
Error made by the operator in identifying reference marks. Introducing some redundancy minimizes this. The operator marks several points instead of the minimum required. This is considered superior to tracing the edge, when more mistakes are likely to be made.
Fig. 4 Image profiles from the normal and stenotic regions of the blood vessel. Each profile has a label consisting of the profile number (left) and the area value (right, given in arbitrary units). The x-marks indicate the shoulders of the profiles as marked by the operator.
REMOTE ANALYSIS OF STENOSES
21
Fig. 5 Bar diagrams representing area values of the profiles for the normal (AREA ONE) and stenotic (AREA TWO) regions. The left side of the figure shows the details of the analysis.
(2) Errors in coordinate determination:
the program does not cause gross errors since the search is confined to the edge of the tine-frame which is approximately known. Decision is improved by choosing a large number of edge elements (100) and fitting a straight line by means of a least squares fit. Since the dimensions of the curved portion of the frame-boundary and the resolution of scan are known, another check is made to compare the dimensions and verify the reference system. To check the accuracy of the system, a grid consisting of lines having a thickness of 3-picture elements was superimposed on a coronary angiogram. Some of the points of the grid were marked with the sonic pen and were transferred to the display of the scanned imagery on the storage scope. From the positions of the transferred points with respect to the grid, the error involved was estimated to be of the order of 3-picture elements. The grid was also used to determine the distortion of the projection system. For our applications we found that the distortion is small enough to be neglected.
22
T. SANDOR, B. SRIDHAR, S. PAULIN DISCUSSION
Displaying digitized pictures for operator-interactive analysis is a common problem in image processing. The method described in this paper circumvents the difficulties and makes possible use of the high-quality projected image for interactive procedures. This approach has several other benefits:
(1) Remote terminals do not have to be linked by high frequency telephone lines to the computer, because feed-back information and other results can be transmitted at sufficient speed via regular telephone lines. In our environment, the data can be transmitted at a rate of 4800 bauds. (2) More than one institution can share the same computing facilities by using regular lines. Grey-tone display devices can be replaced with binary storage scopes. (3) Analysis time decreases. An operator performing the analysis without the (4) aid of the sonic pen must first display the scanned image of the angiogram on a grey level display device (Paulin and Sandor, 1975). To locate the stenotic region, he has to threshold and magnify the picture several times to obtain sufficiently high image quality. The analysis then proceeds as described earlier. CONCLUSION
Introduction of a sonic pen as an interactive device for a computerized densitometric analysis of tine-coronary angiograms facilitated remote analysis of the image. This would have been practically impossible without using an expensive high-frequency cable link-up with the computers. It was found that such analysis can be performed with greater ease, in shorter time, and with high accuracy.
RFiFERBNCE?S
BEER,A., Bestimmung der Absorption des roten Lichts in farbig& Flussigkeiten, Ann. Phys. (Leipzig) 86 (1882). BJORK,L. SPINDOLA-FRAN@H., COHN,P. F., VANHOUTEN,F. X. and ADAMS,D. F., A comparison of the diagnostic value of 70 mm camera and 16 mm tine camera recordings in coronary arteriography, Am. .I. Car&o/., 36 (1975) pp. 474-478. DEROUEN, T. A., MURRAY,J. A. and OWEN,W., Variability in the analysis of coronary arteriograms, Circulntion 55 (1977) p. 324. LAMBERT, J. H., Photometria siue de mensura et grarlibus luminis c&rum et umbrae, Augsburg, Germany; (1760). PAULIN, S. and SANDOR,T., Densitometric assessment of stenoses in coronary arteries, Proc. Sot. Photo-Opt. Instrum. Eng., 70 (1975) p. 337. ZIR, L., MILLER,S. W., DINSMORE, R. E., GILBERT,J. P., HARTHORENE, J. W., Interobserver variability in coronary angiography, Circulation 53 (1976) p. 627.
T.
SANDOR,B.
SRIDHARand S. PAULIN
HarvarJ Medical School, Peter Bent Brigham Hospital and Beth Israel Hospital, Boston, Mass. 02115 (USA)
(Received: 25 June. 1978) SUMMARY
In conventional densitometric evaluation of stenoses the digitized angiogram is displayed on a multi-grey-level scope to.facilitate operator interaction. With a remote terminal, linked to the computer with regular telephone lines, such display is unacceptably slow. To circumvent this dificulty, the projection of the original image is used for interactions through a sonic pen digitizer interfaced to the computer. A coordinate system can be defined on the projected image, in addition to the blood vessel segment to be analyzed by the operator. The computer can retrieve these features on the stored pre-digitized image to carry out the quantitative evaluation of the stenosis. This method reduces the time of analysis and allows several institutions to share the same computing facility.
SOMMAIRE
Duns le mtthode classique devaluation densitometrique des stknoses, l’angiogramme code est place sur un &ran d niveaux multiples d’intensite de gris d fin de faciliter le travail de l’operateur. Duns le cas d’un terminal tloigne, relic d I’ordinateur par ligne ttlkphonique ordinaire, une telle methode est Xune lenteur inadmissible. Pour tourner cette dificulte’ on utilise la projection de l’image initiale en passant par
* Supported by USPHS grants HL20895, HL05832. GM01910, RR05489 ROl HL19003 RAD and ROl CA23246. Send correspondence to: T. Sandor, D.P., Sidney Farber Cancer Institute, Department of Radiology, Rm. 92,44 Binney Street, Boston, Mass. 02115 (U.S.A.)
15 inc. J. Bio-Medical Computing (10) (1979) 15-22
@Elsevier/North-Holland
Scientific Publishers Ltd.
16
T. SANDOR,
B. SRIDHAR,
S. PAULIN
I’intermtdiaire rl’un codeur numtrique relic a l’ordinateur. Un systeme de coordonnkes peut t%re dejini, sur l’image projetee, d I’emplacement de la partie du vaisseau sanguin que roptrateur lloit analyser. LZortEinateur peut retrouver ces eltments sur l’image precodde a ftn de realiser l’evaluation quantitative de la stenose. Cette metholle reduit le temps Xanalyse et permet h plusieurs institutions de partager lies moyens comrnuns de calcul. INTRODUCTION
Diagnostic information contained in high-quality coronary angiograms is currently extracted subjectively by the radiologist. As recent studies have indicated, such subjective judgement of the percent stenosis in coronary arteriograms, for instance, is very inaccurate (Bjork et al., 1975; DeRouen et al., 1977; Zir et al., 1976). Computer processing of the angiograms offers improved precision. Most of the available techniques for quantitative angiographic analysis, such as evaluation of ventricular volume, stenotic blood vessels, etc., are operator-interactive with the operator identifying a desired feature in the image, and the computer performing the necessary analysis. In the case of stenoses, the aim of the analysis is to obtain a measure for the constriction of the blood vessel by comparing the amount of contrast medium at the normal segment of the vessel with that of the abnormal segment. Percent stenosis is defined as: % Stenosis=
1-g
1
x 100
[
N
(1)
where MA and MN refer to the amount of contrast medium at the abnormal and normal segments, respectively. Densitometry can determine these quantities if the measured optical density is proportional to the amount of the absorbing matter (contrast medium). For monochromatic X-rays:
4 = IOev [ -_(cLIp)~l
(2)
where I, and I,, denote attenuated and original X-ray intensities, p/p is the mass attenuation coefficient, and x indicates mass per unit area. Equation (2) is the well known Lambert-Beer law (Lambert, 1760; Beer, 1882). Rewriting eqn. (2) gives: log+;.
(3)
t
From the definition of the optical density : D=log,,
$ t
(4)
REMOTE ANALYSIS
OF STENOSES
17
where 16 and Z;refer to radiant flux incident on and transmitted by a photographic emulsion. Since I is proportional to I’, it follows from eqns. (3) and (4) that: D=kx
(5)
where k is the proportionality constant. Equation (5) is the basic assumption for densitometry. However, when the X-rays generate the photographic transparency, the absorption coefficient is no longer constant but a function of the photon energy, E, that is p = p(E). For high-energy X-rays, when the beam passes through matter, the low energy photons are rapidly depleted and the beam becomes quasi-monochromatic. Such quasi-monochromaticity can be achieved in clinical diagnostic equipment by appropriate filtration of the X-ray beam. To determine the quantities in eqn. (l), optical density distributions representing the normal and abnormal segments of the blood vessel image have to be extracted. The present paper describes an approach to the analysis of stenotic lesions based on the above principle by 2 hospitals sharing one mini-computer. The site of the analysis was located 0.5 mile from the computer, which was linked to it by a regular dedicated telephone
Tests for the linearity of densitometry
To test the validity of eqn. (5), the following experiment was performed. Radiolucent tubings of known diameter were filled with contrast medium and placed in 20 cm of water. Cine-angiograms of these blood-vessel phantoms were taken on 35-mm film with an X-ray image intensifier used in clinical procedures. The images were digitized and from them one-dimensional optical density distributions were extracted perpendicular to the axis of the blood vessel phantom. The area enclosed by the distributions of the respective phantom images was computed and plotted against the known geometric cross-sectional area of the tubings. The results indicate good linearity in a range of about l-4 mm ‘blood vessel diameter’ (Fig. 1). From this one can conclude that the exposing X-ray beam is hard enough and the estimations based on monochromaticity are valid. Equipment
In this study, 35-mm tine-coronary angiograms were used. The tine-frames were scanned with an Optronics Photoscan at a scanning resolution of 25 pm. The density was digitized into 8 bits and the data were stored on 9-track magnetic tapes. These tapes were used as an input to a PDP 11/70 computer, which had among its peripherals a Tektronix 4010 terminal with binary display capability, a sonic pen contour digitizer, and an RPO4 disk of 44 million word storage capacity. The computer had an RSX 11/D operating system. The binary terminal and the contour digitizer were located at another institution within a half-mile from the
18
T. SANDOR, B. SRIDHAR, S. PAULIN
a IO-
0
500
1000
1500
COMPUTED PROFILE AREA (arbitmry unitq
Fig. 1 Evaluation of linearity in densitometry by using blood vessel phantoms.
computer and linked to it via a dedicated telephone line. The system configuration is shown in Fig. 2. Analysis of stenosis The procedures, designed to be operator-interactive, used the projected image of the 35mm film. The sonic contour digitizer was mounted on the projection screen. Using the projected image for interactive procedures requires establishing coordinate systems for the film and the scanned image, as well as scale factors. To do this, a reference feature of the image must be chosen by the following criteria: (1). The feature must be present in all coronary angiograms. (2) It must serve as reference for translation as well as rotation. (3) It must be retrievable by the computer program.
TELEPHONE
to
LINE COMPUTER
MICROPHONE -VANGUARD PROJECTOR
arrows
indicate
data
FILM
flow
Fig. 2 Schematic diagram of remote analysis of stenotic lesions.
REMOTE ANALYSIS
19
OF STENOSES
(4) The operator must be able to identify the above feature on the film without ambiguity by using a coordinate digitizer. The feature shown in Fig. 3, which is the boundary of the tine-frame, satisfies the above criteria and was chosen as the reference. The long edge AB provides a reliable reference for the orientation. The point B, where the curve BC meets the curve AB, provides reference for translation. A simple one-time calibration can determine the relative scale factor between the projected image and the scanned image. This remains valid, provided the adjustments in the projector are not altered. There are other alternatives for selecting reference points on the image. For instance, the images of 2 steel balls, 3-4 mm in diameter, can be used very conveniently as reference points. When the balls are mounted on the surface of the image intensifier, their images are superimposed on the film as a result of the X-ray exposure. Since these images are circular their center of mass can be easily found by an appropriate computer algorithm. This method cannot be used, however, for the analysis of films exposed in the past and stored in departmental libraries. As was mentioned earlier, the analysis of stenosis requires the extraction of optical density profiles from the digitized blood vessel image. The direction of the profiles should be perpendicular to the axis of the blood vessel..In the present method the operator supplies this direction to the computer as described below.
(1) The images to be analyzed are digitized and the date are fed into the disk of the computer. (2) To define analyzing windows enclosing the normal and stenotic segments of the blood vessel, the operator, with a sonic pen, marks 3 points per window on the image in the frame of reference of the projected image. The analyzing windows are parallelograms with respective sides parallel and perpendicular to the blood vessel axis. By defining them, the operator provides the direction for the optical density profiles to be extracted. (31 The coordinates of the analyzing windows in the projected images are
Fig. 3 Feature
selected on a tine frame boundary
for the reference
system
20
T. SANDOR, B. SRIDHAR, S. PAULIN
transformed to coordinates in the scanned image, and the computer automatically extracts and displays a prescribed number of profiles which can be displayed on a binary scope (Fig. 4). (4) The operator, using thumb-wheel controlled electronic cursors, marks the borders of the profiles, and the computer determines the area they enclose. The-values obtained are displayed in bar diagrams (Fig. 5). (5) In a question-and-answer mode, the operator identifies the normal and abnormal segments of the vessel from the bar diagram and the percent stenosis value is computed in accordance with eqn. (1). Accuracy cord&rations There are 2 major possible sources of error.
(1)
Error made by the operator in identifying reference marks. Introducing some redundancy minimizes this. The operator marks several points instead of the minimum required. This is considered superior to tracing the edge, when more mistakes are likely to be made.
Fig. 4 Image profiles from the normal and stenotic regions of the blood vessel. Each profile has a label consisting of the profile number (left) and the area value (right, given in arbitrary units). The x-marks indicate the shoulders of the profiles as marked by the operator.
REMOTE ANALYSIS OF STENOSES
21
Fig. 5 Bar diagrams representing area values of the profiles for the normal (AREA ONE) and stenotic (AREA TWO) regions. The left side of the figure shows the details of the analysis.
(2) Errors in coordinate determination:
the program does not cause gross errors since the search is confined to the edge of the tine-frame which is approximately known. Decision is improved by choosing a large number of edge elements (100) and fitting a straight line by means of a least squares fit. Since the dimensions of the curved portion of the frame-boundary and the resolution of scan are known, another check is made to compare the dimensions and verify the reference system. To check the accuracy of the system, a grid consisting of lines having a thickness of 3-picture elements was superimposed on a coronary angiogram. Some of the points of the grid were marked with the sonic pen and were transferred to the display of the scanned imagery on the storage scope. From the positions of the transferred points with respect to the grid, the error involved was estimated to be of the order of 3-picture elements. The grid was also used to determine the distortion of the projection system. For our applications we found that the distortion is small enough to be neglected.
22
T. SANDOR, B. SRIDHAR, S. PAULIN DISCUSSION
Displaying digitized pictures for operator-interactive analysis is a common problem in image processing. The method described in this paper circumvents the difficulties and makes possible use of the high-quality projected image for interactive procedures. This approach has several other benefits:
(1) Remote terminals do not have to be linked by high frequency telephone lines to the computer, because feed-back information and other results can be transmitted at sufficient speed via regular telephone lines. In our environment, the data can be transmitted at a rate of 4800 bauds. (2) More than one institution can share the same computing facilities by using regular lines. Grey-tone display devices can be replaced with binary storage scopes. (3) Analysis time decreases. An operator performing the analysis without the (4) aid of the sonic pen must first display the scanned image of the angiogram on a grey level display device (Paulin and Sandor, 1975). To locate the stenotic region, he has to threshold and magnify the picture several times to obtain sufficiently high image quality. The analysis then proceeds as described earlier. CONCLUSION
Introduction of a sonic pen as an interactive device for a computerized densitometric analysis of tine-coronary angiograms facilitated remote analysis of the image. This would have been practically impossible without using an expensive high-frequency cable link-up with the computers. It was found that such analysis can be performed with greater ease, in shorter time, and with high accuracy.
RFiFERBNCE?S
BEER,A., Bestimmung der Absorption des roten Lichts in farbig& Flussigkeiten, Ann. Phys. (Leipzig) 86 (1882). BJORK,L. SPINDOLA-FRAN@H., COHN,P. F., VANHOUTEN,F. X. and ADAMS,D. F., A comparison of the diagnostic value of 70 mm camera and 16 mm tine camera recordings in coronary arteriography, Am. .I. Car&o/., 36 (1975) pp. 474-478. DEROUEN, T. A., MURRAY,J. A. and OWEN,W., Variability in the analysis of coronary arteriograms, Circulntion 55 (1977) p. 324. LAMBERT, J. H., Photometria siue de mensura et grarlibus luminis c&rum et umbrae, Augsburg, Germany; (1760). PAULIN, S. and SANDOR,T., Densitometric assessment of stenoses in coronary arteries, Proc. Sot. Photo-Opt. Instrum. Eng., 70 (1975) p. 337. ZIR, L., MILLER,S. W., DINSMORE, R. E., GILBERT,J. P., HARTHORENE, J. W., Interobserver variability in coronary angiography, Circulation 53 (1976) p. 627.