May 2011, VOLUME 196

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May 2011, Volume 196, Number 5

Medical Physics and Informatics

Original Research

A Bayesian Network for Differentiating Benign From Malignant Thyroid Nodules Using Sonographic and Demographic Features

+ Affiliation:
1All authors: Department of Radiology, Stanford University School of Medicine, Richard M. Lucas Center, 1201 Welch Rd, Office P285, Stanford, CA 94305.

Citation: American Journal of Roentgenology. 2011;196: W598-W605. 10.2214/AJR.09.4037

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OBJECTIVE. The objective of our study was to create a Bayesian network (BN) that incorporates a multitude of imaging features and patient demographic characteristics to guide radiologists in assessing the likelihood of malignancy in suspicious-appearing thyroid nodules.

MATERIALS AND METHODS. We built a BN to combine multiple indicators of the malignant potential of thyroid nodules including both imaging and demographic factors. The imaging features and conditional probabilities relating those features to diagnoses were compiled from an extensive literature review. To evaluate our network, we randomly selected 54 benign and 45 malignant nodules from 93 adult patients who underwent ultrasound-guided biopsy. The final diagnosis in each case was pathologically established. We compared the performance of our network with that of two radiologists who independently evaluated each case on a 5-point scale of suspicion for malignancy. Probability estimates of malignancy from the BN and radiologists were compared using receiver operating characteristic (ROC) analysis.

RESULTS. The network performed comparably to the two expert radiologists. Using each radiologist's assessment of the imaging features as input to the network, the differences between the area under the ROC curve (Az) for the BN and for the radiologists were –0.03 (BN vs radiologist 1, 0.85 vs 0.88) and –0.01 (BN vs radiologist 2, 0.76 vs 0.77).

CONCLUSION. We created a BN that incorporates a range of sonographic and demographic features and provides a probability about whether a thyroid nodule is benign or malignant. The BN distinguished between benign and malignant thyroid nodules as well as the expert radiologists did.

Keywords: artificial intelligence, bayesian network, thyroid nodules

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Thyroid nodules are extremely common—found in 4–8% of adults by palpation, 10–41% by ultrasound, and 50% at autopsy [1, 2]. High-resolution ultrasound is the primary imaging modality for evaluating these nodules. Current management guidelines from the American Thyroid Association recommend diagnostic thyroid ultrasound for all patients with thyroid nodules [3]. Furthermore, potentially malignant nodules should undergo ultrasound-guided fine-needle aspiration (FNA) to achieve tissue diagnosis. Accurately deciding whether a thyroid nodule is potentially malignant is thus crucial; unwarranted suspicion results in excessive biopsies, whereas insufficient suspicion leads to missed thyroid malignancies.

Many sonographic features have been described and studied individually as potential predictors of thyroid malignancy [4]. These features include size, multiplicity, echogenicity, presence of microcalcifications, margin, contour, shape, architecture, and vascularity. For example, microcalcifications are present in 26–59% of all thyroid cancers, and hypoechogenicity is present in 26–87% of all thyroid cancers (see [5] for review). Although these trends exist in the distinction of benign and malignant thyroid nodules, there is also overlap in their appearances and no individual feature can reliably separate benign from malignant nodules [5]. Most of the articles published focus on the sensitivity, specificity, and positive predictive value of individual features of thyroid cancer. Given the high prevalence of thyroid nodules in the adult population, most of which are benign, a rational selection strategy is needed for determining which subset of nodules to biopsy because it would be cost-prohibitive to biopsy all of them. There is thus a clear need for a robust approach to estimating the probability that a given thyroid nodule is malignant (i.e., needing FNA) given all of the sonographic features of the nodule that are mutually informative about the underlying disease.

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Fig. 1 Flowchart shows Bayesian network for diagnosis of thyroid nodules as benign or malignant.

Estimating the probability of an event (e.g., malignancy of a thyroid nodule) given a set of indicators of that event (e.g., sonographic imaging features) is a problem that lends itself well to a Bayesian network (BN) model. These models have been used in many areas of medicine to estimate the probability of disease, such as diagnosing renal cystic lesions, predicting breast cancer risk, and identifying deep venous thrombosis [69].

A BN can be created by two different methods: It either can be trained from a large set of data or can be built without training using existing knowledge of the sensitivity and specificity of the features for predicting disease. Given that sonographic features predictive of malignancy in thyroid nodules have been extensively studied and that the sensitivity and specificity of these features for predicting malignancy are readily available in the literature, we chose the second method. This method was also beneficial because a large dataset to train the BN would not be required, thus permitting all case material to be used for testing the model.

We created a BN that incorporates the multitude of imaging features from previously published studies. Our hypothesis was that the BN can provide an estimate of the probability of malignancy with an accuracy similar to that of an expert radiologist. The probability of disease produced by the BN could be useful in providing an objective basis for deciding which thyroid nodules should undergo biopsy.

Materials and Methods
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This retrospective study was HIPAA compliant and was approved by the institutional review board (IRB). The requirement for written informed patient consent was waived by the IRB.

Construction of the Bayesian Network

A BN is a graphical model comprising nodes that represent variables in the model, and edges between the nodes represent probabilistic relationships between the variables. Nodes are data structures that contain an enumeration of possible values that the variables can assume, referred to as “states”; they also store probabilities associated with each state (e.g., the probability that a finding will be observed in thyroid cancer). The probabilities for each possible state for a given variable must always add up to a total of 100% or 1.0 by the laws of probability.

We created a BN comprising a node called “thyroid nodules” representing the pathologic diagnosis of thyroid nodules (i.e., benign or malignant). The BN also includes nodes for the sonographic findings (each node named according to the finding), with states in the nodes representing the possible observations for a given finding (e.g., hypoechoic, isoechoic, hyperechoic). Two nodes in the BN were created for patient demographics: age and sex. Thus, the BN includes both radiologic and clinical information. The BN includes edges connecting the nodes that encode the conditional dependence relationships among the variables. Each of the nodes representing sonographic findings is associated with a probability table that quantifies the probability of each state of the node given the values of incoming nodes. The baseline probability, referred to as “prior probability,” of thyroid cancer is also included in the BN. The structure of our BN is shown in Figure 1. To construct our BN and perform inference, we used the Netica development environment (Norsys Software).

We performed an extensive literature review to identify specific sonographic features that have been well studied as predictors of thyroid malignancy [5, 1023]. These features were included in our network (Table 1). Given that age and sex also significantly influence the probability of a nodule being malignant, we included these demographic features in our model. The prior probabilities of thyroid malignancies by age and sex were derived from the Surveillance, Epidemiology, and End Results (SEER) database [24]. We put cases in discrete categories by patient age: < 50 years (75% of the study population) and ≥ 50 (25% of the study population). Females and males each account for half of the population. Table 2 shows the conditional probability table for malignant nodules given patient age and sex.

TABLE 1: Sonographic Features Included in the Bayesian Network

TABLE 2: Probability of Malignant Thyroid Nodule in Patients Given Age and Sex

The conditional probability tables for the sonographic features were constructed from the literature review during which we collected data about the sensitivity and specificity of each sonographic feature. The sensitivity and specificity of each feature from various studies often differed significantly. For example, the sensitivity of microcalcification varies from 26% in some studies to 59% in others [14]. To address this large range of values, we also collected the number of nodules used to derive these performance values. We then calculated the average of the sensitivity and specificity for each feature weighted by the number of nodules in each study. When needed, we scaled the weighted averages of all possible values for the same sonographic feature so that they summed to 1. In a few cases, a weighted average sensitivity and specificity for a feature could not be calculated because of marked variation in how these features are categorized in the literature (i.e., architecture and vascularity); for those features, we sought the opinion of a radiologist specializing in thyroid imaging. The conditional probability tables for the eight sonographic features are shown in Table 3.

TABLE 3: Conditional Probability Tables for Sonographic Features in the Bayesian Network


We selected 99 thyroid nodules, 54 benign and 45 malignant, from 93 patients (75 females, 18 males; age range, 16–97 years; mean age, 52 years) who underwent ultrasound-guided FNA from 2003 to 2008 at our institution. The 45 malignant nodules comprised all the malignant nodules diagnosed during that time period by radiologists not involved in this study. The 54 benign nodules selected were the most recent consecutive benign nodules diagnosed during this time period by radiologists not involved in this study. All final diagnoses were determined by cytology. Thirty patients eventually underwent thyroidectomy at our institution. All surgical pathology results confirmed cytologic pathology results from FNA. The cases were selected consecutively to reduce bias related to case selection or case difficulty.

The 45 malignant nodules included 40 papillary thyroid carcinomas, one follicular carcinoma, one lymphoma, and one poorly differentiated carcinoma. In addition, one follicular adenoma and one Hürthle cell adenoma were grouped with the malignant nodules because surgical excision and pathologic examination are required for definitive determination of malignant potential.

Evaluation of Sonographic Images

Two radiologists, one with 8 years of experience (radiologist 1) and the other with 20 years of experience (radiologist 2), independently reviewed the sonographic images of the 99 thyroid nodules without any knowledge of the prevalence of malignancy in this set of nodules. The radiologists reported whether each sonographic feature was present in the images. These observations were used by the radiologists to make their decision about the diagnosis for the case, and the same observations were evaluated in the BN to obtain the BN's diagnosis for the same case. To indicate their diagnosis for each case, the radiologists rated each nodule in terms of suspicion of malignancy on a scale of 1–5: 1, benign; 2, probably benign; 3, not sure; 4, probably malignant; or 5, malignant. These ratings represented the radiologists' estimates of the probability of malignancy as an ordinal variable.

We used the BN to evaluate the probability of malignancy for each of the 99 thyroid nodules that had been evaluated by the radiologists. For each patient, age and sex as well as the sonographic features reported by each radiologist separately were input into the BN to calculate the probability of malignancy. Separate evaluations of the probability of malignancy were performed using the readings from each radiologist separately because the radiologists may differ in the sonographic features they observe. In this way, the probability of malignancy produced by the BN could be directly compared with the suspicion of malignancy assessed by the individual radiologist.

Statistical Analyses

To compare the diagnostic accuracy of the radiologists' assessments based on visual observations with that of the BN in evaluating thyroid nodules, we used receiver operating characteristic (ROC) analysis. Standard binomial ROC curves were generated for the radiologists and for the BN based on each radiologist's rating of the suspicion of malignancy and the probability assessment from the BN by using the maximum likelihood estimation [25]. The analyses were implemented using software (ROCKIT 1.1B, Kurt Rossmann Laboratories for Radiologic Image Research). The overall diagnostic accuracy for the radiologists and the BN were estimated by calculating the area under the respective ROC curves (Az) using the ROCKIT software. The differences between the Az value of the BN and that of each radiologist were also calculated. To test the equivalence in performance between each radiologist and the BN, we performed Westlake equivalence tests on the Az with an equivalence limit of 0.1 at a confidence level of 95% [26].

Several individual ultrasound features have been associated with malignant thyroid nodules [5] that could be as useful as the BN. To evaluate the utility of single features for diagnosing thyroid nodules, we compared the sensitivity and specificity of six such individual features—the presence of microcalcification, presence of capsular invasion, solid architecture, echogenicity, taller-than-wide shape, and irregular margins—with the performance of the BN.

The Cohen kappa coefficient for interreader (radiologist) agreement was calculated using the statistical computing language R (R Project for Statistical Computing) to measure the degree of agreement between the two radiologists regarding the presence or absence of each sonographic feature. A kappa value of up to 0.40 indicated positive but poor agreement, a kappa value of 0.41–0.75 indicated good agreement, and a kappa value of greater than 0.75 indicated excellent agreement.

Some sonographic features are more informative about the diagnosis of thyroid nodules than others. To measure how much knowing any particular sonographic feature reduces the uncertainty about the diagnosis of a thyroid nodule, mutual information between various nodes representing sonographic features and the node representing the diagnosis of thyroid nodules (“thyroid nodules”) was calculated using the Netica software.

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We evaluated our network using 99 thyroid nodules from 93 patients. ROC curves of the predictions by the BN and the two radiologists are shown in Figure 2A, 2B. The Az for the BN was similar to those of the radiologists.

Using radiologist 1's assessment as input, the BN achieved an Az value of 0.85 (95% CI, 0.76–0.91), whereas radiologist 1 had an Az of 0.88 (95% CI, 0.78–0.94). Using radiologist 2's assessment as input, the BN achieved an Az of 0.76 (95% CI, 0.66–0.84), which is comparable to that radiologist's Az of 0.77 (95% CI, 0.66–0.84). The differences in Az values were small: –0.027 (95% CI, –0.0978 to 0.0434) and –0.005 (95% CI, –0.0813 to 0.0715) for radiologists 1 and 2, respectively; in both cases, equivalence between the BN and each radiologist in terms of the Az was shown to be within 0.1 (p < 0.05).

The results of our evaluation of the sensitivity and specificity of individual sonographic features in the prediction of malignancy compared with the performance of the BN are shown in Figure 2A, 2B. None of the single features performed as well as the BN.

Figure 3 shows the mutual information between various sonographic and demographic features and the diagnosis of thyroid nodules in our BN. Results from analyzing mutual information in the BN suggest that capsular invasion and microcalcification are the two features that are most predictive of malignancy in thyroid nodules.

The kappa values of interreader agreement between the radiologists are shown in Figure 4. Good agreement was seen for all sonographic features. The best agreement was for microcalcification and ring-down artifact.

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Methods from artificial intelligence such as BNs have been introduced to help clinicians determine diagnoses, make therapeutic decisions, and predict outcomes [27]. A goal of introducing such methods in assessing thyroid nodules is to provide an objective basis for making a decision to biopsy and to reduce variations in practice in making that decision.

Radiologists perform two tasks when reviewing ultrasound images of thyroid nodules: First, they observe the imaging features and, second, make an interpretation about the combination of those features to determine the likelihood of malignancy. Variations in interpretations and decision making by radiologists evaluating thyroid imaging may thus result from variations among readers in misperception of imaging findings and inconsistent decisions in evaluating the perceived findings. A BN can assist with the second, but not the first, task by integrating the various features to determine the probability that a nodule is malignant. This probability value provides an objective basis for making a decision for managing the patient, such as biopsy, follow-up, or routine care; specifically, the decision to biopsy could be based on whether the probability of malignancy of the nodule exceeds a prespecified threshold.

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Fig. 2A Receiver operating characteristic curves constructed from discrete ratings of suspicion of malignancy by two expert radiologists and probability estimates of Bayesian network. Radiologist 1 (A) and radiologist 2 (B). Performance of each feature individually (i.e., presence of microcalcification, solid architecture, irregular margins, taller-than-wide shape, presence of capsular invasion, and hypoechogenicity) is also shown.

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Fig. 2B Receiver operating characteristic curves constructed from discrete ratings of suspicion of malignancy by two expert radiologists and probability estimates of Bayesian network. Radiologist 1 (A) and radiologist 2 (B). Performance of each feature individually (i.e., presence of microcalcification, solid architecture, irregular margins, taller-than-wide shape, presence of capsular invasion, and hypoechogenicity) is also shown.

Because the output of the BN depends on the input imaging features, accurate observation of the correct sonographic features is clearly important; this task is not addressed by the BN. Specialized computer-assisted detection applications are being developed to improve perception of radiology findings that, in synergy with BN models, could help radiologists more comprehensively with radiologic interpretation. In addition, atlases of imaging findings, such as BI-RADS for breast imaging findings, could improve the consistency and quality of radiology observation and reporting. The BN may also be helpful in evaluating the imaging findings by providing a checklist of important imaging features for radiologists.

In this study, we showed that a BN using sonographic and demographic features can accurately distinguish between benign and malignant thyroid nodules, performing comparably to subspecialty-trained radiologists in diagnosing thyroid malignancy (p < 0.05) (Fig. 2A, 2B). As a result, a BN could potentially improve the performance of nonexpert radiologists who may be able to observe sonographic findings but may not necessarily have the experience to determine the malignant potential on the basis of the imaging findings.

Because the BN generates a probability estimate that a thyroid nodule is malignant, a potential benefit of the BN is that it may be useful to patients and radiologists in a shared decision to biopsy ultrasound-detected nodules. Because the prior probability of malignant thyroid nodules is low, many thyroid nodules currently undergoing biopsy are benign. If a tool such as our BN is used to objectively calculate the probability of malignancy in a given nodule, patients and radiologists could make decisions about whether to biopsy a suspicious thyroid nodule more objectively. This objectivity would potentially reduce the number of unnecessary thyroid biopsies and improve their positive predictive value. In fact, such an improvement has been shown in applying BNs in mammography [28]. Because thyroid carcinomas are generally slow growing and are associated with a good prognosis, it may be acceptable to have a sensitivity lower than 100% to achieve a relatively high specificity to reduce unnecessary biopsies.

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Fig. 3 Mutual information between various sonographic and demographic features and diagnosis of thyroid nodules in Bayesian network.

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Fig. 4 Bar graph shows agreement (Cohen's kappa) between two radiologists for each sonographic feature. Feature taller-than-wide shape is not included because it is objective measure of whether anteroposterior dimension of thyroid nodule is greater than transverse dimension and thus does not vary among readers.

There are two general approaches to creating BN models: first, inputting data for the BN to “learn” and, second, building them based on data in the literature, expert knowledge, or both. In the first approach, the parameters of the BN are learned by mining a large dataset of cases in which the diagnoses of the cases are established [9]. This approach requires a large dataset for training and could be impractical because it requires thousands of annotated cases. We chose to create a BN using parameters from previously published studies. The ultrasound characteristics of thyroid nodules have been extensively studied (Table 1), and a BN provides a means of integrating that knowledge into a single model.

In reviewing the literature, we found that different studies on the predictive power of the same imaging feature for malignancy showed different, either slight or marked, sensitivities and specificities. Many factors, such as patient population and ultrasound equipment, may account for these differences. We accounted for these differences by weighing the sensitivity and specificity from each study by the size of the patient population. In this way, we could take into account the results from multiple articles studying the same feature, while providing reasonable approximations of what the “true” sensitivity and specificity are for each imaging feature. Our results show comparable performance between the radiologists and the BN. Training the BN using data may potentially produce a better model in the future.

We obtained most of the conditional probabilities for our BN from the weighted average of sensitivity and specificity reported in the literature. However, the data for architecture and vascularity were not available because the terms used in the literature to describe those features vary markedly. For example, vascularity is classified into many different stages and types in the literature. This variability in terminology strongly suggests the need for a controlled terminology for reporting the ultrasound imaging features of thyroid nodules. Controlled terminology is well established in other radiology domains such as breast imaging, where BI-RADS, a controlled terminology, is used to describe mammographic features [29]. In our project, we made the first step toward creating a set of mutually exclusive but collectively exhaustive descriptors (Table 1) for common ultrasound features of thyroid nodules that could ultimately become the basis for a controlled terminology for thyroid nodule evaluation.

The results of our study suggest that our BN performs similar to subspecialty-trained radiologists who assessed the nodules for malignancy potential after performing a feature assessment. It is possible that feature assessment may have helped the radiologists in their evaluations of the nodules by enumerating all the important features. We attempted to compare the performance of our BN with that of the radiologists who performed the original ultrasound evaluation. Unfortunately, because biopsies were performed immediately after the original ultrasound for all the nodules, the radiologists were not compelled to provide a diagnosis. Instead, they simply deferred to the pending pathology report. Only 33.3% of the nodules (33/99) had a suggested diagnosis on the original ultrasound reports: 26 were labeled suspicious and seven were labeled as potentially benign, only with benign sonographic features. All these diagnoses were concordant with the final pathology reports.

Our mutual information analysis in the BN was important in showing that not all features are equally informative for the diagnosis of thyroid nodules. Mutual information measures how much knowing one variable (the presence of particular sonographic features) reduces our uncertainty about another variable (whether a thyroid nodule is benign or malignant). The mutual information between various sonographic features and the diagnosis of the thyroid nodule in our BN indicates which features are particularly important in differentiating benign from malignant thyroid nodules. This analysis showed that capsular invasion and the presence of microcalcification are highly informative features (Fig. 3). By comparing the mutual information and kappa agreement for each feature, one can also identify those features that are important for determining the diagnosis but that are difficult for radiologists to determine reproducibly. In our BN, capsular invasion is one such feature: It has the highest mutual information value and a relatively lower interrater agreement (Fig. 3). This lower agreement may be because capsular invasion might be visible on only a few images. Our results for this feature suggest that more attention should be paid to educating radiologists about the importance of detecting capsular invasion to reduce the variation in observing this highly informative feature and to improve diagnostic accuracy in evaluating thyroid nodules.

The presence of certain individual features, such as completely cystic nodules, provides a very good indicator that a thyroid nodule is benign and no biopsy is necessary; in such cases the BN would not be needed to guide care. However, frequently there are cases in which the individual features observed are not highly diagnostic; in these cases, the BN could be helpful by integrating the probability related to those features. In fact, our results showed that the BN performs better than the single-feature classifiers commonly used to predict malignancy (Fig. 1).

There are several limitations to our study. First, our evaluation was performed for 99 biopsy-proven thyroid nodules. Although 99 is a relatively small number of nodules, the performance of our BN compared favorably with the performance of two expert radiologists in these cases. A second limitation is that our particular case mix had a high prevalence of malignancy and thus may not be representative of the case mix seen in broader clinical practice. The radiologists were not aware of the case mix, and the output of the BN does not depend on the case mix in the test setting. A prospective study to confirm our results would be desirable. In addition, our BN included the background prevalence of disease (the “prior probability”). A third limitation is that our BN is built with data collected from an adult population. Although thyroid nodules are uncommon before puberty, those that occur in children are more likely to be malignant [30]. This association between patient age and diagnosis can be modeled in the BN by modifying the conditional probabilities by patient age. In the future we can build a BN specific for the pediatric population and validate it using nodules detected in pediatric patients. A fourth limitation is that our BN assumes that all the sonographic features are conditionally independent, which may not be a valid assumption. However, the performance of our BN also compared favorably with that of the expert radiologists. In addition, other models that make the independence assumption, such as naïve Bayes classifiers, have been shown to perform well in classification tasks similar to that we have undertaken. Zhang [31] offers some theoretic reasons behind the surprisingly good performance of naïve Bayes classifiers.

In the future, we will study the impact of the independence assumption in the BN and refine the BN accordingly. We also plan to build a Website so that our BN can be easily accessed by other radiologists and used in prospective studies of its utility and accuracy. A final limitation is that the radiologists' ratings are subjective; they are not probability ratings per se, whereas those of the BN were quantifiable probabilities. It would be difficult for radiologists to make finergrained judgments reliably, and our ROC results show that the performance of the BN was comparable to the radiologists even given this limitation.

The ultimate goal of the BN is to provide decision support; however, incorporating the BN into the clinical workflow could be challenging. The imaging observations would need to be entered into the system, and it could be disruptive to clinical workflow to expect radiologists to enter their observations into the BN separately from generating the radiology report. If a structured reporting system were used to record the sonographic features observed by the radiologist, the output from that system could be linked to the BN to deliver real-time feedback about the likelihood of malignancy. Alternatively, natural language–processing or voice-recognition systems could be developed to recognize and extract the sonographic features. Linking the reporting process to decision support will enable real-time feedback about likely diagnoses and preferred treatment options.

In conclusion, we have shown that a BN using sonographic and demographic features can accurately distinguish between benign and malignant thyroid nodules in an adult population and that the BN performs comparably to subspecialty-trained radiologists. Our BN may be useful in helping nonexpert radiologists evaluate the malignant potential of thyroid nodules. Ultimately, quantitative estimates of the probability of malignancy in a given thyroid nodule could potentially be used to establish probabilistic thresholds for the decision about whether to perform FNA and could improve the positive predictive value of radiologists in making the decision to biopsy thyroid nodules.


This is a Web exclusive article.

Address correspondence to D. L. Rubin ().

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American Journal of Roentgenology. 1985;145:249-254. 10.2214/ajr.145.2.249
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