A Bayesian Approach for Dealing With Uncertainties in Detection of Coronary Artery Stenosis Using a Knowledge-Based System Krzysztof J. Cios, Lucy S. Goodenday, and Donald K. Wedding II University of Toledo (K.J.C.. D.K.W.) Medical College of Ohio (L.S.G.) KNOWLEDGE-BASED SYSTEM will be discussed that A combines subjective Bayesian methods with rules speci- fied by cardiologists to diagnose coronary artery stenosis from postexercise myocardial perfusion scintigrams. This expert system's application was to determine which of the three main coronary arteries had the dominant stenosis: left anterior descending (LAD), right coronary artery (including the posteriod descending) (RCA), or circumflex (CCX). The system also indicated when a patient had a normal myocar- dial perfusion pattern (no stenosis). The system was run on a set of scans from 91 patients and the results were compared with an existing expert system that uses the Dempster- Shafer theory of evidence for dealing with uncertainties. The input data used for this system was derived from the stress thallium-201 (TI-201 radioactive counts in 30 regions of the scintigraphic cardiac image from planar views, as shown in Fig. 1. Original gray level images were digitized and then prepro- cessed to produce a series of numbers representing the percent perfusion defect for each region using methods described in references [ I , 21. Post-exercise TI-201 scintigraphy has been found to add sensitivity and specificity to the diagnosis of ischemic heart disease. In general clinical practice, such scans are inter- preted simply by visual appearance, although computerized methods are now becoming widely available. The interpreting physician does not usually make any statement regarding the expected site(s) of coronary stenosis. Such correlation has been attempted in the past [3, 4, 51, but is generally not strong enough to be clinically useful. To determine whether the presence or absence of coronary WALL Figure 1. The 0739-5175/89/1200-0053$01.00 01989 IEEE ERA stenosis and the site of predominant stenosis could be ascertained automatically, several methods were used prior to this investigation. Using preprocessed scintigraphs from patients with known coronary artery anatomy, classification into normal and abnormal, and by site of major stenosis, was attempted with various classification techniques, inlcuding fuzzy clustering, pattern recognition, and an expert system. The fuzzy clustering method 161 was able to determine the major site of coronary stenosis with 91 percent predictive accuracy when asked for clusters only of left anterior descending, left circumflex, or right coronary artery, but failed to identify a normal group as being characteristically different from those with isolated right coronary artery stenosis. A classification system based on vector analysis I71 was also found to give moderately good results, but only for patients with known coronary artery disease. Expert system methodology was then employed in an attempt to model the thinking of the nuclear cardiologist. This type of system uses rules obtained by interviews with human experts to build a knowledge base from which the system can make inferences about the new data presented to it. Such a system was designed and implemented in Prolog with the Dempster-Shafer theory of evidence to deal with uncertain information. When tested on the initial set of 66 scintigraphs, excellent diagnostic accuracy was obtained t81. In order to obtain this level of accuracy, however, it was necessary to employ 70 rules. Since previously published work was based on a much smaller data set, we show, for later comparison, the results using fuzzy clustering on the larger data set now available is: Sensitivity Specificity LAD 87% 100% RCA 100% 86% ccx 82% 82% Predictive Accuracy 9 1 % LEFT LATERAL ,L ANTERIOR SE PTI WALL ADFY r.. br. INFERIOR LEFT ANTERIOR OBLIQUE WALL I N FE ROAPICAL three views of the left ventricle and the numbering schema of the regions. DECEMBER 1989 IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE 53
Transcript
A Bayesian Approach for Dealing With Uncertainties in Detection of Coronary Artery
Stenosis Using a Knowledge-Based System Krzysztof J. Cios, Lucy S. Goodenday, and Donald K. Wedding II University of Toledo (K.J.C.. D.K.W.) Medical College of Ohio (L.S.G.)
KNOWLEDGE-BASED SYSTEM will be discussed that A combines subjective Bayesian methods with rules speci- fied by cardiologists to diagnose coronary artery stenosis from postexercise myocardial perfusion scintigrams. This expert system's application was to determine which of the three main coronary arteries had the dominant stenosis: left anterior descending (LAD), right coronary artery (including the posteriod descending) (RCA), or circumflex (CCX). The system also indicated when a patient had a normal myocar- dial perfusion pattern (no stenosis). The system was run on a set of scans from 91 patients and the results were compared with an existing expert system that uses the Dempster- Shafer theory of evidence for dealing with uncertainties.
The input data used for this system was derived from the stress thallium-201 (TI-201 radioactive counts in 30 regions of the scintigraphic cardiac image from planar views, as shown in Fig. 1.
Original gray level images were digitized and then prepro- cessed to produce a series of numbers representing the percent perfusion defect for each region using methods described in references [ I , 21.
Post-exercise TI-201 scintigraphy has been found to add sensitivity and specificity to the diagnosis of ischemic heart disease. In general clinical practice, such scans are inter- preted simply by visual appearance, although computerized methods are now becoming widely available. The interpreting physician does not usually make any statement regarding the expected site(s) of coronary stenosis. Such correlation has been attempted in the past [3, 4, 51, but is generally not strong enough to be clinically useful.
To determine whether the presence or absence of coronary
WALL
Figure 1. The
0739-5175/89/1200-0053$01.00 01989 IEEE
ERA
stenosis and the site of predominant stenosis could be ascertained automatically, several methods were used prior to this investigation. Using preprocessed scintigraphs from patients with known coronary artery anatomy, classification into normal and abnormal, and by site of major stenosis, was attempted with various classification techniques, inlcuding fuzzy clustering, pattern recognition, and an expert system. The fuzzy clustering method 161 was able t o determine the major site of coronary stenosis with 91 percent predictive accuracy when asked for clusters only of left anterior descending, left circumflex, or right coronary artery, but failed to identify a normal group as being characteristically different from those with isolated right coronary artery stenosis. A classification system based on vector analysis I71 was also found to give moderately good results, but only for patients with known coronary artery disease.
Expert system methodology was then employed in an attempt to model the thinking of the nuclear cardiologist. This type of system uses rules obtained by interviews with human experts to build a knowledge base from which the system can make inferences about the new data presented to it. Such a system was designed and implemented in Prolog with the Dempster-Shafer theory of evidence to deal with uncertain information. When tested on the initial set of 66 scintigraphs, excellent diagnostic accuracy was obtained t81. In order to obtain this level of accuracy, however, it was necessary to employ 70 rules.
Since previously published work was based on a much smaller data set, we show, for later comparison, the results using fuzzy clustering on the larger data set now available is:
The basic problem with the above methods is that they are not able to distinguish those patients having coronary artery diseases from those with normal coronary arteries. They perform well, however, when abnormal patients are defined a priori.
METHOD An expert system consists of a knowledge base and an
inference engine. The knowledge base is a combination of facts and rules and is used by the inference engine to determine a solution or response. The technique of dealing with uncertainties inherent in the scintigraphic data used in this expert system is the Bayesian method [91. In this method of modeling an expert system, facts are modeled as nodes of a decision tree. Each node is associated with a number that represents the prior probability that the fact is true. This is the probability of truth when no other supporting or detracting evidence is available. Subjective certainty is a more accurate term in this case than probability, because the prior probabil- ity is supplied by an expert who draws more upon experience than statistical data. For the sake of simplicity, the term "probability" will be used instead of "subjective certainty."
The relationships between the nodes (facts) are depicted as arcs that join the nodes together. The node located on the lower level of the tree represents evidence, and the node that is higher up represents hypothesis. The evidence either supports or detracts from the hypothesis by its truth or falsehood. The t w o numbers associated with the arc de- scribe how necessary and sufficient the evidence is for the hypothesis. They are used to recalculate the probability of the hypothesis once knowledge of the evidence is known. In order to calculate the new certainty of the hypothesis, the prior probability must be converted into odds form. Conver- sion between odds and probability is done using the formula:
O ( h 1 = P ( h )/(1 - P ( h 1)
where O ( h ) and P ( h ) represent the odds and probability of the hypothesis with no evidence available.
Once the odds have been determined, the new odds of the hypothesis can be calculated by multiplying the old odds by a lambda value [IO]. The lambda value is equal to the smaller value (the necessity factor) if the evidence proves false, and the greater value (the sufficiency factor) if the evidence is true. This relationship can be described as follows: if the evidence is true, the odds of the hypothesis are increased by the sufficiency factor; if the evidence is not true, then the odds of the fact being true are lessened by the necessity factor. If the probability of the evidence being true falls between 1 and 0 (true and false), then the lambda can be determined by interpolating along the line between the necessity and sufficiency values [l 11. With the lambda known, the new odds and probability of the hypothesis are calculated in the following manner:
I f several nodes can be used as evidence to support one hypothesis, then the new odds is simply the product of the
lambdas from each evidence node multiplied by O ( h ) . If information is known from only some of the evidence nodes, the lambdas for those nodes are calculated as above. The lambdas of the evidence nodes for which there is no information known have a value of one, thus having no effect on the final odds of the hypothesis.
Evidence for a hypothesis can be combined in logical relationships AND, OR and NOT 1111. The AND and OR relationships simply take the minimum and maximum proba- bilities, respectively, of the supporting evidence. For exam- ple, Fact l , Fact2, and Fact3 are all evidence for Hypothesis1 and they are all combined with the AND relationship:
Factl AND Fact2 AND Fact3-+HypothesisI
If Fact l , Fact2, and Fact3 have probabilities of being true of 0.25, 1.0, and 0.80, respectively, then the probability used in computing the lambda is 0.25, since it is the minimum value. If the combining relationship were changed to OR, then the probability for computing the lambda for the hypothesis would be 1 .O (the maximum).
This rule for using logical combinations, of course, is making the assumption that all the facts are statistically independent of each other, even though this may not be true. Note that this way of combining facts is different from the method described above. In the present method, one lambda value is calculated from the three facts and then multiplied by O ( h ) . In the first method, three separate lambdas would be found, and all three multiplied by O ( h ) t o find the odds of the hypothesis with evidence known:
O(h le1, e2, e3)=Lamdal Lamda2 Lamda3 O ( h )
In the case of the NOT relation, the sufficiency and necessity factors are reversed. In other words, if the evidence is true with a probability of 1, then the lambda is the lower value (the necessity factor), which would tend to disprove the hypothesis. I f the probability of the evidence were 0, then the lambda would be the higher value (the sufficiency factor), which would tend to support the hypothesis. Again, if the probability of the evidence being true is between 1 and 0, the lambda is found by interpolating along the curve, as depicted in Fig. 2.
IMPLEMENTATION A Prolog-based system was constructed to combine the
subjective Bayesian method described above with rules for diagnosing coronary arterial stenosis. The rules used for this system were adapted from rules specified by a cardiologist for a previous expert system that used the Dempster-Shafer approach to dealing with uncertainties [8].
The input data were derived from pre-processed scinti- graphic myocardial perfusion images of the left ventricle taken in three views: anterior (ANT), left lateral (LAT), and left lateral anterior oblique (LAO). The stress thallium-201 radioactive counts for 30 regions of the heart (10 for each of the three planar views) were measured for each patient. These gray level images were then preprocessed, resulting in a series of numbers. Each of the 30 numbers that described the perfusion defects in each region of each view was in a range of 0 to 100. These 30 numbers were used as the input values for the leaf nodes of the Bayesian decision tree. The probability (subjective certainty) of each subsequent node was calculated using the above described methods for coronary artery stenoses in LAD, RCA and CCX. The stenosis with the highest certainty of causing the perfusion defect was considered to be the expert system's diagnosis. Since this system was designed t o diagnose the most significant stenosis, the other stenoses certainties were disregarded. I f
54 IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE DECEMBER 1989
t
0 P,(E) 1
P(E) Figure 2. The interpolation rule.
all of the stenosis certainties on a particular scintigram were below a certain cutoff value, then that scan was diagnosed as having a normal perfusion pattern, i.e., no stenosis was present.
As described above, a previous expert system [81 was designed to diagnose which coronary artery had the predomi- nant stenosis. It gave good results in diagnosing stenoses, but was not designed t o diagnose patients with normal myocardial perfusion. However, the system using the Bay- esian subjective method was designed t o separate normal from abnormal. Another advantage of the Bayesian approach as compared to the Dempster-Shafer approach is that the
Dempster-Shafer method does not take into account the severity of a particular perfusion defect. If a region of the cardiac image has a perfusion defect value above some cutoff point, it is considered as having a defect present in that region. The expert system only asks true and false questions about the defects present; it does not take into account the size or severity of the defect. The implementation of the Bayesian approach allows gradual change in the form of more weight to be given t o a defect value of 0.75 than to one of 0.5, for example. This is due to the fact that the lambda value that affects the hypothesis (the higher level node) is a function of the defect size. The greater the defect, the greater the certainty that the hypothesis is true. Below are shown diagrams of the Bayesian decision trees for the diagnosing stenosis in LAD (Fig. 31, RCA (Fig. 4). and CCX (Fig. 5) arteries. The values for prior probabilities and sufficiency and necessity factors were gathered by interviewing cardiolo- gists.
To illustrate how t o follow the diagram, assume that a TI- 201 scintigram shows that perfusion defects in the ANT6 region measured 0.35 and those in the LAT8 region measured 0.45. This information can then be applied to find out whether the belief that Rule 2 of the LAD tree is correct. The beliefs that defects in ANT6 and LAT8 are present with no prior information are 0.01 4 and 0.029, respectively. Interpo- lating along the curve of Fig. 2 using N = 0.01 and S = 100 for ANT6 at the point P = 0.35 yields a lambda value of 34.688. Likewise, interpolating along the curve of Fig. 2 using N = 100 and S = 0.01 for LAT8 (note that the S and N are switched because it is a NOT node) gives a lambda value of 0.567 when P = 0.45. Converting the prior probability or belief of Rule2 for LAD, which is 0.01, into odds gives the value 0.01 01. The new belief that the odds of Rule2 of LAD is correct, given the information on ANT6 and LAT8, is calcu- lated by multiplying the old value by the t w o lambda values previously found.
Odds(new1 = Odds(old) Lambda(ANT6) Lambda(LAT8)
=0.0101 34.6886 0.5673=0.1986
U T 5AAT 6 r U T 7
Figure 3. Bayesian decision tree for diagnosis of left anterior descending (LAD) coronary artery stenosis.
DECEMBER 1989 IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE 55
RCA I .O1 . 425, .4
RULE 1 r! 11. .1 20, .1
25. .07
525, .4
kc*;l 7, .3 I 17. .3 I 12. . 3 I
57, .01 57, .01 1
RULE 5 I .R: 1
Figure 4. Bayesian decision tree for diagnosis of right coronary artery (RCA) stenosis.
This is transformed into the new probability that the rule is true using the odds to probability formula described above. The new probability is given as 0.1657. This new probability can now be used to calculate the new belief that there is a stenosis in the LAD artery. Following the same procedure described above and using from the diagram N = 1 and S = 7 0 and a prior probability of 0.01, the lambda at the value P = 0.198 gives a lambda of 14.145. The odds that there is a stenosis in LAD is obtained by converting the prior probability of LAD which is 0.015 to the prior odds for LAD which is
0.0152. This value is multiplied by the lambda of Rule2 of LAD just found (1 4.145). The new odds of LAD is calculated to be 0.21 5 and the new probability that there is a stenosis in LAD is then obtained and found to be 0.177. Of course, these calculations can be carried out on every branch and every leaf node of the tree for greater detail.
RESULTS The expert system was tested on TI-201 scintigrams from
patients with known single vessel coronary arterial stenoses
b 0025 I .01 I
RULE 5 i ?
Figure 5. Bayesian decision tree for diagnosis of circumflex (CCX) coronary artery stenosis.
56 IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE DECEMBER 1989
and from patients who were known to have no coronary artery stenosis. The presence of stenosis of at least 7 0 percent in one major epicardial coronary artery was proven by coronary arteriography. Results shown below give sensitivity (how likely it is that the expert system will find, for example, LAD stenosis if it exists), specificity (how certain the user of the expert system can be that a particular expert system diagnosis of, for example, LAD stenosis is correct) and system accuracy (the number of correct diagnoses divided by the total number of scintigraphs examined).
The expert system was first run on 66 patients for which there was prior knowledge that each patient had a single coronary arterial stenosis. These results are shown below along with the results of the Dempster-Shafer method [81 for comparison. Both expert systems were run on the same 66 patients.
Using Dempster-Shafer Method Sensitivity Specificity
LAD 97% 100% RCA 96% 100% ccx 100% 85%
Total System Accuracy: 97%
Using Bayesian Method Sensitivity Specificity
LAD 100% 100% RCA 92% 96% ccx 91 % 83%
Total System Accuracy: 95%
The results of the subjective Bayesian approach t o dealing with uncertainties compare favorably to the Dempster-Shafer approach. We were able to compare the t w o approaches only for abnormal patients, since it is required for the Dempster- Shafer approach that there be prior knowledge that a patient does, in fact, have a single stenosis. The Bayesian method allows for patients without coronary stenosis to be added t o the test data. The system, using the Bayesian approach, determines if a patient has a stenosis or normal myocardial perfusion and it then determines which stenosis is present. There is no prior knowledge required about the patients for use of the Bayesian approach.
The expert system was run again on a data set of 91 patients. Of the 91, 66 had a single coronary artery stenosis and 25 patients had normal coronary arteries. Two new categories were added to the results: NORMAL and ABNOR- MAL. The NORMAL category tells the system's probability of correctly diagnosing a patient with normal coronary arteries; and if a patient is diagnosed as normal, the probability that the diagnosis is correct. The ABNORMAL category tells if a patient is correctly diagnosed as having stenosis regardless of whether or not the correct stenosis was found.
When the prior knowledge of the patients is removed and the expert system must first determine if a patient has normal
DECEMBER
myocardial perfusion or not, then the accuracy of diagnosis is slightly lower. These results can be improved with refine- ments to existing rules or by addition of new rules to the existing knowledge base. The above results can be used to screen out normal patients from the data set. The remaining patients' location of obstructions could then be detected using either the Dempster-Shafer or Bayesian method utilizing prior knowledge that the patients have stenoses present.
CONCLUSIONS The work reported here shows good initial results. The
system is able to determine the coronary artery with the dominant stenosis over 90% of the time when the system is supplied prior knowledge that all the patients have single- vessel stenosis. The system is also able to determine with good accuracy if a patient has a stenosed coronary artery or normal myocardial perfusion when no prior information is available. The program can be used initially to screen out patients with normal scintigrams. Once the patients with normal scintigrams have been removed, the expert system can then be run on the remaining patients, and utilize already existing, prior knowledge that they have stenosed coronary arteries. This improves the reliability of correct diagnosis.
The results obtained are encouraging. It is possible to model the reasoning process of a nuclear cardiologist with good accuracy. The system can be improved by enabling it to diagnose patients with multiple-vessel stenoses. This would be accomplished by altering the lambda values and prior probabilities of the existing rules; also, the rule base would need to be expanded. Other scintigraphic data such as abnormally high right ventricular or lung counts can also be incorporated into the knowledge base. Lastly, data other than scintigrams, i.e., age, sex, cholesterol, blood presssure, etc., may eventually be used by the system in diagnosis of coronary problems.
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Goodenday LS, Nelson AD, Leighton RF, Muswick G, Hire NE, et al.: Prediction of the site of coronary artery obstruction from thallium-201 scintigrams by a quantitative computer technique. Proc IEEE Conference on Computers in Cardiology, 1981, pp. 277-279.
Dunn RF, Freedman B, Bailey IK, Uren RF. Kelly DT: Localization of coronary artery disease with exercise electrocardiography: correlation with thallium-201 myocardial perfusion scanning. Am J Cardiol, 48:837-843. 1981.
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Krzysztof J. Cios received the M.Sc. degree in electrical engineering in 1973. and the Ph.D. degree in computer science in 1984 from the Technical University, Krakow, Poland. He is Assistant Professor of Electrical Engineering at the University of Toledo, Toledo, Ohio. Professor Cios’ research interests include ma- chine learning, pattern recognition, neural net- works, and knowledge based systems. He is a member of the IEEE Computer Society.
Dr. Cios can be reached at the Department of Electrical Engineering, the University of Toledo, Toledo, OH 43606.
Donald K. Wedding, II received the B.Sc. degree in 1987 in electrical engineering, and the M.Sc. degree in 1988 in engineering science from the University of Toledo, Toledo, Ohio. He is presently Software Engineer at the North Island Naval Base, San Diego, Califor- nia. Mr. Wedding is working towards the M.B.A. degree at San Diego State University. He is interested in applying expert systems for use in business applications.
Lucy S. Goodenday received the A.B. degree in chemistry in 1959 from Bryn Mawr College, Pennsylvania, and her M.D. in 1963. Dr. Goodenday is presently Associate Professor of Medicine in the Cardiology Division, and Director of Nuclear Cardiology at the Medical College of Ohio, Toledo, Ohio. She has prac- ticed and carried out research in the field of nuclear cardiology for twelve years. Her spe- cial interests include the application of com- puter techniques to medical diagnosis.
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