EP1002293A1

EP1002293A1 - Breast screening - early detection and aid to diagnosis

Info

Publication number: EP1002293A1
Application number: EP98937356A
Authority: EP
Inventors: Barry Thornton
Original assignee: Breast Screening Decision Support System R & D Syndicate
Current assignee: Breast Screening Decision Support System R & D Syndicate
Priority date: 1997-08-08
Filing date: 1998-08-07
Publication date: 2000-05-24
Also published as: WO1999008225A1; AUPO848197A0; EP1002293A4

Abstract

A method of analysis of a set of mammograms of a current patient to provide an indication of malignancy, including the steps of: a) performing a fractal analysis on the set of mammograms of the current patient to obtain a plurality (n) of fractal dimension values of features in the set of mammograms; b) comparing the fractal dimension values obtained from the mammograms of the current patient, with a database of fractal dimension values for mammograms of patients having a verified diagnosis and predicting the possible presence or absence of malignancies in the current patient by comparing similarities in the sets of fractal values.

Description

Breast screening - early detection and aid to diagnosis Introduction

The present invention relates generally to the field of mammography and in particular the invention provides a system and method which is capable of guiding a radiologist to make diagnostic decisions with a higher degree of reliability. Background of the Invention

Although there is strong evidence that regular breast screening significantly reduces the risk of death from breast cancer, only a relatively small number of Australian women are being screened. Referring to Figure 1, a flow chart is shown illustrating the process of screening and re-screening adopted in Australia while Figure 2 shows the screening pathway and the organisational units involved in the screening program in the Australia. However the process is voluntary and recruitment levels are low. According to a report, Australia's Health, 1992 only 22 per cent of women aged between 40 and 64 have had a mammogram within the previous three years. Women aged between 45 and 49 years had the highest rate of screening (25 per cent), while those between 60 to 64 years had the lowest rate (17 per cent). One reason for this is that many women do not know about mammograms, particularly those who do not speak English at home, those with low family incomes and those who live outside the metropolitan area. The report says that deaths from breast cancer have risen slightly from 25.0 deaths per 100,000 women in 1971 to 26.2 deaths per 100,000 in 1985-90. The report adds that assuming there are no advances made in the treatment of breast cancer, or reduction in risk factors, the breast screening program is not expected to significantly reduce the death rate from breast cancer. Even by 2005, the reduction in the death rate is expected to be only 16 per cent.

Breast cancer is curable particularly when detected at early stages and given proper treatment. Early detection through mammography in almost 50% of cases depends on the presence of characteristic microcalcifications in conjunction with other mammographic readings. (In isolation microcalcifications would account for only about 30% of cancer detection). The typical calcifications seen in breast cancer are clusters of tiny calcium based deposits having thin linear, curvilinear, or branching shapes. However, difficulties exist in interpreting some calcifications when they are tiny and clustered but do not conform to the recognised malignant characteristics s ich as cluster shapes, sizes and spacial distribution.

In some cases it is important to use the complementary tests of mammography and sonography in the investigation of patients with breast symptoms.

Referring to Figure 3 a diagram is provided of a benign cystic lesion with modelled zones (1-5), showing the bulk of the cyst 4,5, a fibrous boundary zone 3, a microcalcification zone 2 and an external zone 1 of normal tissue. Typical dimensions of such lesions are d=~5-10 mm. Malignant type tumours do not characteristically have a fibrous outer zone. Zones 4 and 5 are more likely to be different in malignant cases whereas these zones are more likely to be equal in many benign cases and cysts.

In Figure 4(a) a simple sonogram is illustrated for a patient aged 34, who presented for examination with pain. The sonogram ilhistrates a simple cystic lesion that had been palpated by the clinic surgeons. In Figure 4(b) a mammogram for the patient of Figure 4(a) is illustrated. This part of the mammogram shows two simple cystic lesions seen on ectiography with grouped microcalcifications between the cysts (arrowed). Histological examination proved this impalpable calcified area to be intraductal carcinoma with early encepholoid carcinoma.

Figure 5 diagrammatically illustrates the locations of microcalcifications in the main histological types of ductal carcinoma: a) In comedocarcinoma the calcifications form at the centre of the involved cut; b) In cribriform carcinoma the psammomatous calcifications form in the cavities of the spongy tumour tissue.

The proposed methods aim at resolving uncertainties at those suspected lesions. However, it must be noted that there are other important "signs" for malignancy from mammography as summarised below. Direct Signs

The so-called classical mammographic signs of malignancy are:

1. A mass, usually stellate, but occasionally circumscribed (less than 5%) and often mixed configuration.

2. Clustered fine calcifications that are often irregular with linear and branching patterns. However, these are easier described than recognised. The variations and settings of both of these signs, separately and in combination, are numerous. Careful side-by-side comparison of the mammograms of both breasts of a patient is essential. Furthermore, these signs can be very subtle and require meticulous inspection of the mammograms, including the routine use of a magnifying glass, for their recognition. Careful comparison with film from a previous visit can reveal subtle changes and findings that would otherwise be missed. Indirect Signs As well as these so called "direct signs", there are, in addition, a number of other indicators which we will call "indirect signs". These are often best recognised by comparison with previous films, and include: 1. Focal density (especially when not present previously: developing density) and/or distortion (stellate area). 2. Focal duct prominence (especially solitary).

These signs assume even greater significance when there are physical findings in the same region. Other Imaging Modalities

Other methods of detecting breast cancers early have been available and can provide a supplement to mammography. Each has some advantages and disadvantages medically and economically. Included in these methods are ultrasound, thermography (static or dynamic), computed tomography for a 3D representation constructed from a large number of 2D X-rays taken anatomically at progressive angles covering a 360° range and magnetic resonance imaging (MRI). The latter is considered very diagnostic but costly. It is used to measure nuclear magnetic moments, the characteristic magnetic behaviour of specific nuclei. Because these values are significantly modified by the immediate chemical environment, however, magnetic resonance imaging measurements provide information about the molecular structure of various solids and liquids. MRI images show great sensitivity in differentiating between normal tissues and diseased tissue, but is not efficient in detecting early disease in the breast (Australian Institute of Health Report (1990), "Screening Mammography Technology" Better Printing Services, N.S.W.). By the early 1980s magnetic resonance imaging techniques had begun to be used in medicine. MRI presents a hazard-free non-invasive way to generate visual images of thin "slices" of the body by measuring the iclear magnetic moments of ordinary hydrogen nuclei in the water lipids (fats) of the body. By the late 1980s MRI had proved superior to most other imaging techniques in providing images of the brain, heart, liver, kidneys, spleen, pancreas, breast and other organs but, as previously mentioned, is not efficient in detecting early disease in the breast (Australian Institute of Health Report 1990, Screening Mammography Technology). MRI provides relatively high-contrast, variable-toned images that can show tumours already existing, blood-starved tissues and neural plaques resulting from multiple sclerosis. Because it is a very expensive modality and requires long examination times, it is unsuitable as a screening tool. Also, it is not as good in 2D spatial resolution as mammography.

Ultrasound has been shown to often augment mammography in situations such as dense breasts and cyst/solid differentiation. Light scanning infra-red transillumination has also yielded iseful diagnostic information when examining some patients with dense glandular breasts b it can also be a controversial modality.

The comprehensive use of a suitably selected multi-modality approach to the detection of breast cancer seems a logical step. Historically, all breast imaging modalities have been compared to mammography, the "gold standard". Other imaging methods: ultrasound, static thermography, trans-illumination, CT and MRI have not demonstrated sLifficient abilities to substitute for mammography in diagnosis or screening. Studies of multi- modality protocols should be conducted to determine which modalities work best together as adjuncts to mammography in the comprehensive diagnosis of breast cancer at the earliest possible stage.

The aim of embodiments of the present invention is to provide: (i) observer independent parameter(s) based on fractal analysis of these microcalcification features of calcium hydroxyapatite and weddelite deposits which become even more important when visual fatigue of clinicians occurs in extended reading of mammograms (80 or more mammograms /hour is common), and

(ii) a visual presentation of particular fractal dimensions of a region of interest in order to highlight visual inspection of that region for particular classes of clusters in a mammographic image. However it is important not to override the experienced clinician whose judgement appears to be a complex mental process based on visual information processing, difficult to quantify, but which in the case of most experienced radiologists gives good results. Summary of the Invention

The present invention provides a method of analysis of a set of mammograms of a current patient to provide an indication of malignancy, including the steps of: a) performing a fractal analysis on the set of mammograms of the current patient to obtain a plurality (n) of fractal dimension values of features in the set of mammograms; b) comparing the fractal dimension values obtained from the mammograms of the current patient, with a database of fractal dimension values for mammograms of patients having a verified diagnosis and predicting the possible presence or absence of malignancies in the current patient by comparing similarities in the sets of fractal values.

Preferably the different fractal dimensions are measured from a plurality of different views.

In the preferred embodiment the different fractal dimensions are calculated from the mammograms taken from two different x-ray views and preferably the different fractal dimensions are measured from mammograms taken from the cranio-caudal (cc) view and the oblique (ob) view.

In the preferred embodiment, an (n) dimensional plot of (n) fractal values for each previously verified patient diagnosis is created and a critical pair of surfaces is apparent such that almost all coordinates on one side of the pair of surfaces represents a benign condition and almost all coordinates on the other side of the pair of surfaces represent malignant conditions. Cases with coordinates in between the surfaces are indeterminate. There can still be an occasional malignant case in the benign space and vice versa, which would obviously need further separate investigation quite apart from the indeterminate locations.

Some fractal dimensions are of more diagnostic value than others. In the examples of Figures 10 and 11, both use a 3D plot of three particular fractal dimensions which provide an initial visual indication of separation of the groLips of pathology-proven malignant and benign cases except for a small imber of cases which have not been resolved correctly just by three fractal dimensions. They would represent false positive and false negatives if additional quantitative (sealed) ratings of the radiological clinical data were not made using the methods described in this application hereinafter (on page 9 onwards) in conjunction with the fractal dimension data. c) The data extracted from the mammograms is obtained by digitising the mammograms using both a greyscale representation and a black and white representation with a selected threshold for the transition from black to white. The greyscale data and the threshold data are then used as input to a computer program to generate different fractal dimension data. It is also found that improved results can be obtained by selecting the size of the area analysed (ie. how much of the area surrounding the Region of Interest (ROI) is included in the analysis). It has been found that analysis of areas of the mammogram 1 to 1.5 cm square and 4 to 4.5 cm square provide effective results. In the preferred embodiment different sets of fractal dimensions are prepared by analysing two areas corresponding to 1.2 cm and up to 4.2 cm square respectively covering the region of interest on the actual mammogram.

The fractal dimensions are calculated for each combination of viewpoint/threshold/area by one of several known methods of fractal analysis.

Methods by Caldwell (1990) and Clarke (1986) are considered useful as they are surface area related. Both are suitable for 2-3D calcvilations of fractal dimensions.

Preferably only one of these methods of calculation of the fractal dimensions is used on the digitised images of the ROI without thresholding being affected. In the preferred embodiment it is the Clarke method modified as described later in this specification, using the Caldwell of surface calculation, under the sub-heading "Estimation of 2-3D Type of Fractal Dimension". It should be noted that for calculation of fractal dimensions in 1-2D, the Box-Count Method (Voss, R.F. (1986) "Characterization and Measurement of Random Fractals", Physica Scripta, Vol. T13, 27-32) is used. This is required for calculation of fractal dimension of the image of ROI when thresholding is applied to it (ie, binary image, "black and white"). In the preferred embodiment eight fractal dimension values are determined for each set of mammograms of each patient as set out in the following table. However, as previously mentioned, it has been determined that certain ones of these dimensions appear to be more effective as diagnostic indicators and in some embodiments only these more indicative dimensions are used.

An initial subset of 3 such fractal dimensions is shown in the last column of Table 1, but the method applies to the use of all 8 fractal dimensions (eg, see results labelled Bl and B2 in Table 4) These 8 dimensions might be reduced to a smaller number as more test cases become available.

Illustrated in Figures 10, 11 cc = cranio - caudal view ob = oblique view

Table 1 Eight Fractal Dimensions found useful in Mammography.

The interface region between most of the malignant and benign cases indicated by fractal dimensions is observed by initial inspection on-screen with reference to the database of previously verified cases in which the actual condition of the patient has been verified by pathology. A database of such historical data can be used to indicate a surface in n dimensional space up to 8 dimensions depending upon the particular dimensions selected. For visual indication 3 dimension are used which are the most diagnostic.

In a further preferred embodiment the data from fractal analysis is combined with other more objective data to enhance the accuracy of the foregoing output indication. This objective data is provided by a radiologist examining each mammogram and grading of features conventionally Lised in respect of several categories. In a preferred embodiment the radiologist uses the particular categories and scales specified in Table 2 below, to grade the microcalcifications in each mammogram or set of mammograms and have the radiologist's initial diagnosis expressed as "overall impression" using the conventional used grading shown in the bottom row of Table 2:-

Table 2: Description and rating scales of some qualitative features obsei ed by radiologists.

By combining some or all of these gradings such that each grading scale provides an additional dimension in the multi-dimensional space of diagnostic indicators the method of the invention is able to provide an indication having greater accviracy. Preferably the individvial characteristic gradings b it excluding the "overall impression" grading given by the radiologist are used in conjunction with the fractal data. The radiologist's "overall impression", being subjective, is excluded from the present method so as to be independent of the radiologist's diagnosis. The vahies of shape and uniformity parameters are subjective on the scale of 1-5, but are not the radiologist's "overall impression" diagnosis. Brief Description of the Drawings

Embodiments of the invention will now be described, by way of example with reference to the accompanying drawings in which:-

Figure 1 is a flow chart of the pathway for mammographic screening in Australia and assessment and subsequent routine re-screening.

Figure 2 is a diagram of the mammographic screening pathway in Australia and organisational units responsible for each screening component;

Figure 3 is a diagram of a benign cystic lesion with modelled zones (1-5) where zone 1 is the external zone of normal tissue, zone 2 is the microcalcification zone, zone 3 is the fibrous bovindary zone and zones 4 and 5 are the bulk of the cyst;

Figure 4(a) is a simple transverse sonogram for a patient aged 34 illustrating a simple cystic lesion; and (b) is a mammogram for the same patient showing two simple cystic lesions and a group (indicated) of microcalcifications between the cysts (Croll, ]., "Ultrasonic Differential Diagnosis of Tumors" (Ed. Kossoff, G., and Fukuda, M., 1984) P.105).

Figures 5 (a) and (b)schematically illustrate two types of ductal carcinomas;

(a) In comedocarcinoma the calcifications form at the center of the involved duct (Lanyi 1988);

(b) In cribriform carcinoma the psammomatous calcifications form in the cavities of the spongy tumour tissue (Lanyi 1988);

Figure 6 is a diagram illustrating the two planes of view for the cranio-caudal and oblique mammography views of a suspect location labelled as planes '5' and '4' in the Figure with two other planes X_α and X₂ intersecting nipple location (Lanyi 1988);

Figure 7 shows 2 examples of suspicious microcalcification clusters (Lanyi 1988);

Figure 8 is a diagram illustrating a method of surface area measurement used in Caldwell's method of fractal dimension measurement; Figure 9 is a diagram illustrating a method of surface area measurement Lised in Clarke's method of fractal dimension measurement.

Figure 10 graphically illustrates the results of fractal analysis of mammographic data from a first gimip of patients; Figure 11 graphically illustrates the results of fractal analysis of mammographic data from a second group of patients; and Figure 12 graphically illustrates sensitivity and specificity of the model "dist" (distribution of microcalcification). Detailed Description of the Preferred Embodiments

In order to evaluate the effectiveness of methods of classifying benign and malignant cases in breast screening mammography, in accordance with embodiments of the present invention, a set of 112 cases generated from 103 subjects was used on a 'blinded' basis for our evaluation. These mammograms were provided by the Western Sydney Breast Screening Unit. After classification, the results were compared with the known pathology results for the same cases to determine the classification performance plus the sensitivity and specificity performance of the methods used. Both quantitative data such as fractal dimensions obtained from our programs and qualitative data provided by the radiologists were used to classify the cases. The data provided by radiologists was provided using a rating scale (Table 2) based on fractal considerations. Three methods ( a Bayesian approach,

Multiple Logistic Regression and an Artificial Neural Network) were tested as classifiers of the data from the mammograms and the results compared.

Models established from data from a first source (the Wesley Breast Clinic) or combined sources (Wesley and a small group of similar quality Netherlands cases) have been used to predict the outcome of each individual case in the subseq iently acquired (Western Sydney) set of data. We use the following three conventional measures which indicate the performance of a particular classification method. In the usual way, sensitivity is defined as the proportion of positives that are correctly identified as positive. Specificity is the proportion of negatives that are correctly identified as negative. The overall correct classification rate (or correct class) gives the proportion of correctly classified cases among all cases studied. Basic Source Material- Mammograms

In total, a set of 112 cases from Western Sydney, taken from 103 subjects have been studied for the use in the analyses (several subjects had more than one Region Of Interest (ROI)). Referring to Figure 6, there are two mammograms from each subject: a cranio-caudal (cc) view and an obliq ie (ob) view. It should be noted that the ROI with microcalcifications was not magnified in the Western Sydney cases SLipplied and in some cases, only one view was supplied whereas the preferred method requires both the cc and ob views and preferably with the ROI magnified as was the case in the earlier Wesley Breast Clinic cases. A scanner was used to digitise each mammogram and the digitised image was then saved in GIF format. The resolution was set to 100 pixels per cm. Methods for the Data Requisites Quantitative Data

As explained previously, two procedures have been implemented to calculate the fractal dimension of the ROI of the calcifications Lising the Caldwell et al method (1990). The first procedure, the modified Clarke/Caldwell method, is for calculating the fractal dimension of a selected region on the mammogram without applying any thresholding method to the image. The second is the Box Count Method for calculating the fractal dimension of a binary image of calcifications obtained after using a thresholding method on the image.

Two areas covering the ROI are selected for the analysis (420 x 420 pixels and 120 xl20 pixels) on each mammogram taken from two views. That is to say four regions are selected. It should be noted that the smaller region of the ROI is inside the larger region. The larger region includes tissue surrounding the actual microcalcifications while the smaller region mainly covers the area where the microcalcifications are located. These four regions are then processed with and without thresholding so that, in total, we acquire 8 image data sets for each individual case and we compute the corresponding 8 fractal dimensions. The eight are labelled as follows: rccc, rice, weec, wicc, rcob, riob, wcob and wiob. In these labels, the first character "r" denotes the region of 120 x 120 pixels while "w" means the whole larger area of 420 x 420 pixels. The second character "i" or "c" corresponds to the image without or with thresholding to extract the microcalcifications respectively. The last two characters represent the cc or ob views. Qualitative Data and Rating Scale Used

Qualitative data of the type shown in Table 2 was also provided by the radiologists examining the mammograms (one at the Wesley Breast

Clinic, Brisbane and the other at the Western Breast Screening Unit, Sydney) in a form specified for the project. These parameters were chosen from a range of possible observables used by clinicians and were rated on a scaling system suggested from fractal based considerations. They are summarised in Table 2 set out previously in this specification. 1. Fractal Dimension

(a) Estimation of 1-2D (ie., in range "1 to 2 dimensions"! Type of Fractal

Dimension

Some thresholding techniques are needed to apply to the digitised mammograms before we can estimate the fractal dimension of the extracted calcifications. A threshold technique is described in Section 2. The fractal dimension of the extracted calcifications are between 1 to 2. The box-count method is employed to estimate the fractal dimension. It is described by Voss (1986) that

where N(u_k ) is the count of boxes that cover the extracted calcification at the scale of u_k . By taking the natural logarithm of both sides of the above equation, it becomes

The slope obtained by a linear regression of ln[N(w_t )] on ln(l / υ_k ) will give the estimated value for D . (b) Estimation of 2-3D fie,, in range "2 to 3 dimensions") Type of Fractal

Dimension

There are many methods for the estimation of fractal dimension. Caldwell et al. (1990) and Byng et al. (1996) employed a method developed by Lundahl to estimate the fractal dimension of a selected region on a mammogram. Similar investigations have been made by MarroqLiin et al.

(1996) using the Reticular Cell Counting Method (Chan et al. 1995). Only the surface area related algorithms (Caldwell, C.B., Stapleton, S.J., Holdsworth, D.W., Jong, R.A., Weiser, W.J., Cooke, G. and Yaffe, M.J. (1990) "Characterisation of Mammographic Parenchymal Pattern by Fractal Dimension", Physics in Medicine and Biology, Vol. 35, No 2, 235-247 and Clarke, K.C. (1986) "Computation of the Fractal Dimension of Topographic Surfaces Using the Triangular Prism Surface Area", Computers & Geosciences, Vol. 12, No 5, 713-722) are reviewed here. Their differences will be pointed out. A modified method derived from these two algorithms has been adopted in the preferred embodiment.

Lundahl et al. (1985) developed a method for determining the fractal dimension of digital coronary angiograms. Caldwell et al. (1990) and Byng et al. (1996) used that method (a similar version) to determine the fractal dimension of digitised mammograms (region or sub-region of the image of the breast alone). Bartlett (1991) has investigated the method with a minor modification of vising weighted least squares regression and has commented aboLit the method that it may be used with confidence only if the range of dimensions of interest is small.

In the Caldwell's method, the digitised image is vis ialised as a three dimensional image, having columns of different heights. Fig. 8 shows the top area and two "exposed" sides of a particLilar rectangvilar column. The functional relationship of A(ε_k ) and ε_k is

where A(ε_k ) is the exposed surface area of the columns measured with a square of side ε_k , λ is a scaling constant and D is the fractal dimension of the image. After taking the nature log of both sides of the above equation, the equation becomes

lnμ( ] = lnμ) + (2 - D) ln(s_t )

A linear regression of ) will then perform to estimate the slope, say b, and hence D = 2 - b can be evaluated. It should be noted that D ~ 2 implies a smooth planar surface, while D —2.99 implies a very rough 3 dimension surface. Moreover, the fractal model is considered a good one if the regression correlation is high (Lυ.ndahl et al. 1985). The differences between the method of Lundahl et al. and that of

Caldwell et al. (1990) are that the former has taken the unit length u as 1 and has not stated precisely how they calcLilate the height of the rectangular column at different ε_k . Also, the matrix has the size of (n + 1) x{n + l) and the indexes i and ; in the equation of A(ε_k ) for the side area start from 1 to n_k. With an upper limit of n for calculating the side area, it means that side areas of the two outer boundaries are included. It seems not too appropriate as it introduces some edging effect.

The other method proposed by Clarke (1986) to estimate the fractal dimension of topographic surface is to use a triangular prism to calculate the surface area. Fig. 9 illustrates how the four triangular prisms connected. Also, he has used a different scheme to choose different scale, ie., 2 ^" where k = 1, ..., m and the matrix has the size ofn x n where n = 2"^1'1 + 1. Presumably, the model that has been taken by Clarke is

Therefore, the fractal dimension then is calc ilated as 2 - fa, where b is the slope of the line from the log-log regression of surface area A ε_k ) vs the area ε of the square. The surface area calculations are definitely different between

Caldwell et al. and Clarke. More importantly, their underlying models are different. The one from Caldwell et al. is related to Richardson's Law (Mandelbrot, 1977), ie.,

M(ε) = Kε^e"-

where M(ε) is the measured property of a fractal and the respective e_d and f_d are the Euclidean dimension and the fractal dimension. In the case of surface area, e_d = 2. It seems to us that Richardson's Law applies to exact self-similarity.

The model of Clarke is chosen but instead of calculating the surface area using the triangular prism, the rectangular column approach suggested by Caldwell et al. (1990) is adopted because of the computational efficiency. The Box Count method as vised for the 1-2D calculations can detect differences in cluster shape and distribution because it involves a number of grid "boxes" at different scales used to cover the region of calcification and counts are made of calcifications in these different sized grid boxes. The modified Caldwell/Clarke method used for 2-3D calculations relies only on the total svirface area at different scales in a 3D representation which is provided by the imaged viewed without any thresholding, the representative "height" of columns on the pixels above the 2D plane depending on the opacity and intensity of the pixels in the digitised image of the various calcifications. Because the method relies on total surface area of a cluster, it is sensitive to changes in shape and size of a cluster and to differences in uniformity between different clusters. 2. Threshold Method

Thresholding is a well-known technique for image segmentation. It tries to extract objects from their background. The method of Otsu (1979) has been employed. It is a global, point-dependent techniqvie. It is global thresholding because it thresholds the entire image with a single threshold value. If the threshold value is determined solely from the gray level of each pixel (without considering the local property in the neighbourhood of each pixel), the threshold method is called point dependent (instead of region- dependent).

The Otsu method is based on discriminant analysis. It maximises the class separability. The recommended discriminant criterion fvmction (or measures of class separability) is where are are the between-class variance and the total variance of levels, respectively. Since is independent of f (a gray level value belong to a set of gray level for a given image), maximisation of η with respect to t is equivalent to maximise . Once the optimal threshold value t* is determined, a binary image can be obtained.

Another method using wavelet transform has been developing to extract the microcalcification. It is expected that this method will provide a better segmented image of the microcalcification.

Methods Used for Classification into Benign and Malignant Cases

In development work visual 3-D plotting of 3 particular fractal dimensions out of the 8 available has been found to indicate a possible separation of benign and malignant cases. Figure 10 shows the plot of 211 cases examined to date prior to processing the Western Sydney data. The new test results (Western Sydney) are then plotted separately in Figvire 11.

Again, the same indication of possible separation seems present.

Quantitative methods have then been used for assessing the visual indications in numerical terms to obtain the percentage of correct classifications followed by an evaluation of the sensitivity and specificity for the individual methods used. As previously stated three classification methods have been employed to date in our analysis. They are (a) the Bayesian Method, (b) a multiple logistic regression procedure from the EPISTAT statistical package and (c) an Artificial Neural Network method. A brief outline of the methods (a), (b) and (c) is given below prior to presenting the results. (a) Software System for Bayesian Methodology

Statistical aids to medical diagnosis can use several classical and highly efficient techniques: such as discriminant analysis, probit and logistic regressions. However, the validity and efficiency of these methods rely upon assumptions sometimes difficult to verify, in the early stages of a study. Our interest in a Bayesian approach to the statistical analysis is the total absence of such assumptions. Bayesian analysis models the entire decision process, including the experimental data analysis, prior knowledge and possible consequences of decisions. Therefore, one would expect it to be particularly useful in the medical field, since medical decisions involve the interpretation of experimental data as well as notions of prior probabilities and of the cost of diagnostic errors. Several software systems can be adapted for Bayesian applications in medicine.

The decision we are required to make is to choose, for a given patient, one of K possible diagnoses; in other words, the patient is svipposed to be in one of instates, called states of nahire Θ_k. Assigning a state θ_k to a patient is called action a_k.

Factors which intervene in the decision making process are: • Sample information, provided by statistical investigation of experimental data.

Suppose we have selected a set of N experimental arguments (i = 1, . . . N) as a basis for the diagnosis, and established their density distributions, d_j,_k ("marginal distribution"), given each state θ_k [k = 1,...K). The joint probability density relative to each state k must then be evaluated from marginal distributions, so that joint probabilities of every state k for a patient/, fP_k{J), can be calculated. In the simplest case of independent argviments this function is given by a formula

• The Prior Information

The prior information, coming from our past experience, expressed in terms of prior probabilities π{t ) of each state t .

Bayes formula for posterior probability PP_k (/) of each state of nature for a patient/, is as follows:

PP_k (J) = (π(θ_k )JP_k (J)) / (∑ π(θ,)JP_t (J)).

7=1

• Decision Making

The possible consequences of the decision, ie., losses corresponding to every possible decision in every possible case (for example, what is the danger for a patient suffering from disease A of being recognised as having disease B). They are expressed as the elements of a loss matrix L{θ[, a_k). According to Bayesian Statistical Decision Theory, the best decision for the patient j is the one minimising the posterior expected loss (π, a_k), that is the say the mean value of losses relative to the different states of nature weighted by their respective posterior probability

WJ[π, _k)) = ∑ L i^ a^ PPi iJ)

7=1

In other words, the optimal decision corresponds to the diagnosis of lowest expected loss. (b) Multiple Logistic Regression Multiple logistic regression is used to predict a dichotomous outcome variable from one or more predictor variables which may be measured on any scale (categorical, ordinal or interval). The procedure has the option of stepwise selection of predictors to build a model Linder a user-specified significance level to include a variable and a different significance level to remove a variable from the equation. The user also needs to select a Cutoff Probability Value for the Classification Table between O and 1 (the recommended value for overall optimum classification is 0.5). See Table 3 for the details of the description of the values a, b, c, d vised in the conventional table shown there. The formula used in the logistic model is

Pr {xι ...x_k)

1 + exp[-(α _j + Bx_x + ...+B_kx_k)]

where α is a stratum-specific constant and βj . . . β_k are the respective coefficients of the predictors x_t . . . x_k. (The predictors in our case were the parameters described previously as Methods for the Data Reqviisites) Table 3 below is used to represent how many true positives, true negatives, false positives and false negatives occurred after we had acquired the pathology results for the cases studied. The corresponding sensitivity, specificity and overall correct classifica tion rates are calculated as follows: Predicted

+

True + a b c d

a

Sensitivity = x 100% a+ b d

Specificity = x 100%o c + d a+ d Correct Classification = — ^'Z1^- — x 100% a+ b+c+d

Table 3 Definition of ^'" Sensitivity" , "Specificity and "Correct Classification" Using the Classification Table shown. fc) Artificial Neural Networks

Artificial Neural Networks are empirical models that approximate the way it is thought neurons act in the hviman brain. It is used to mimic some of the brain's capabilities.

The ANN classifier can be thought of as a black box: patient data is input and a classification is provided as outpvit. In between there is a network process which converts the input data to the output class. This is meant to be rovighly analogous to what happens in the brain whereby an inpvit pattern is converted into a perceptron via neural networks.

It is known that the properties of any artificial neural network depend heavily on factors such as structure, learning time and the extent of training data. This means that a small change in network topology, learning cycles and other parameters can produce a great change in its behaviour. The goal is to find a set of network parameters which give statistically stable results and maintain stability across different sets of training and test data. While it is thought that Neural Networks provide an attractive methodology, to date the results have not been as good as the Bayesian method. However, further work using the actual spatial patterns in the mammogram as input is being investigated.. Results (a) Bayesian Method

Each selection of different parameters is called a "Model" for the analysis. With reference to Table 4, the resvilts for a model (Model A) for the "Wesley & Netherlands" data using only wccc, wiob, wcob as used in Fig 10, the sensitivity, specificity and the correct classification were 68%, 82% and 76% respectively. The same model with the Western Sydney data (as in Fig. 11) has the corresponding performance measures as 67%, 48% and 54%. A much better model (Model B) is to use all 8 of the fractal dimensions and all of the qualitative predictors (except the "Overall impression" predictor by the radiologist which is excluded so as to enable a comparison to be made between the model and the human expert performance) . When the "Wesley & Netherlands" data is used to establish this model, the sensitivity, specificity and the correct classification were 80%, 88% and 85%. The corresponding measures when the "Western Sydney" data is used were 67%, 88% and 81%. In another model (Model C) the single predictor "Overall impression" was used with the choice of the grading limits between 1 and 3 to define the "benign" category. We initially chose "Overall impression" = 3 as an upper limit of negative (benign) classification. The "Wesley" data gave the values of sensitivity, specificity and correct classification as 73%, 82% and 79%. Since two "Overall Impression" values (the retrospective and prospective interpretation by the two radiologists) were provided for the "Western Sydney" data, their respective individvial performances are reported under the label of Model C2 and C3. The corresponding performance measures of the first observer were 73%, 80% and 77% while that of the second observer are 78%, 62% and 67%. All of the above resvilts are svimmarised in Table 4. In addition we tested a separate (unlabelled) model with a single predictor called "Distribution" ( "dist" ) characterising the type of distribution of the microcalcifications (for cases with spreading along ducts/radiating towards the nipple) When this last type of model established from the "Wesley" data was used to predict the outcome from the "Western Sydney" data, the sensitivity, specificity and the correct classification of the blinded pathology results were 33.3%, 94.7% and 75.0% respectively. A graphical presentation of these results is shown in Figure 12 where TP, FN, TN and FP denote True Positive, False Negative, True Negative and False Positive respectively. The dark region of the top bar indicates the proportion of subjects that is positive. The lower bar consists of segments representing the proportions of individuals with TP, FN, TN and FP test outcome.

The "double-bar diagram" is a visvial representation of the analysis of test performance. It has the practical advantage of being easily drawn by most standard graphics software packages (Brenner, H. (1994). "Visual Presentation of Analysis of Test Performance", Journal of Clinical Epidemiology, 46, 1151-1158.)

Whereas the strength of mammography is its detection ability and therefore its sensitivity, its weakness is in its specificity. This is important in regard to advising women of negative (benign) screening results. The fractal based methods described appear to provide assistance in forming judgements based on specificity.

Table 4: The performance of models A and B established for Diagnostica's Bayesian Method. Model C is obtained by comparison of radiologist's "Overall Impression" with the true outcome.

Separately from the model with a single predictor called "Distribution", all other models developed from the Bayesian methodology (See Table 3) indicate that the models work well within each individual data source. However, this is not the case when models established from the one data set (Wesley) are vised to predict the other data set (Western Sydney). The reasons for this are probably due to the original data selection method for Wesley cases compared with the sampling from Western Sydney and the different distribution of malignancy in the two set of data. (b) Multiple Logistic Regression

Multiple Logistic Regression gave similar results using the model with the predictor "Distribution". Some other models can achieve the correct classification as high as 81% but did not perform as well when used to predict new cases from other source. They encovinter similar difficulties as those mentioned above in the comments on the Bayesian method results.

(c) Artificial Neural Network

An Artificial Neural Network using all 8 fractal dimensions based on the "Wesley & Netherlands" data gave a correct classification of 88% . With the qualitative data alone, the correct classification rate for the "Wesley" data alone was 80% . Up to the present time with the data which is available for the ANN, no model except the one using the "dist" predictors has an acceptable performance on predicting the outcome of new cases coming from a different source. Therefore, it is suspected that cases from a particular source must be provided for training a neural network before it is used to predict new cases in that source. Current Equipment Times for the Process

When a new case is investigated, two mammograms (one taken from cc view and the other from ob view) are required and the suspicious region(s) marked by a radiologist. Assuming a final model has been established from the above three classification methods, Table 5 shows the time required for each component of the entire analysis for a single case in isolation.

Table 5: The estimated time components required to process a new individual suspicious (needing careful observation) case in isolation. (In practice, scanning would be off-line and image manipulation time could be shortened.)

It should be noted that about 16 minutes out of the total 18 minutes is used for the scanning and image manipulating. The actually time for analysing the outcome is only about 2 minutes. In the studies of computer- aided diagnosis at the University of Chicago Department of Radiology scanning of all dovibtful mammograms is done off-line by staff on a "production" basis each day. In the development work described above, we have collected mammogram images from several sources [Wesley Breast Clinic, Netherlands data base, Lawrence Livermore National Laboratory (LLNL) / University of California San Francisco, Wolfson Image Analysis Unit (UK) and SENO (FRANCE)]. Therefore, we have a collection of images in digitised form (scanned by ourselves or provided in digitised form) of different resolution and quality covering different subject populations from different regions or countries. The images from the Wolfson Image Analysis Unit are cases of stellate distortion and do not have immediate use in our microcalcification project. The occurrence of microcalcifications is in only about 30-40% of mammograms and of these only a small percentage turn out to be malignant so it was necessary for vis to be provided with additional malignant examples in order to test the ability of our methods to distingviish malignant from benign. Therefore, the statistical distribution from each source is different in these tests. Also we point out that qualitative parameters from different centres were obtained by different observers. Therefore for our method, the observers were required to follow the same set of guide lines, ie., vise the same set of parameters and same grading levels as in Table 1 when they assessed the mammograms. Perhaps, in current practice different observers may use exactly the same set of parameters or may give different weights to the parameters in their assessment.

The results of some methods such as the Bayesian approach depend very strongly on the statistical density distribution of the parameters (not to be confused with physical density of microcalcifications). It is recommended that models and parameters be selected separately from each demographic data source. In the event that any model could perform well across all different sources it would finally be selected. That means that predictors which have been included in such a particular "global" successful model would be the same for all sources but the probability density distribution of those parameters would be estimated from data from the particular source, (eg. Wesley or Western Sydney or elsewhere) It will be appreciated by persons skilled in the art that numerous variations and/or modifications may be made to the invention as shown in the specific embodiments without departing from the spirit or scope of the invention as broadly described. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive.

References

Croll, J., Ed. Kossoff, G., and Fukuda, M. (1984) "Ultrasonic Differential

Diagnosis of Tumors". Voss, R.F. (1986). "Characterization and Measurement of Random Fractals", Physica Scripta, Vol. T13, 27-32

Clarke, K.C. (1986). "Computation of the Fractal Dimension of Topographic

Surfaces Using the Triangular Prism Surface Area", Computers &

Geosciences, Vol. 12, No. 5, 713-722.

Lanyi 1988

Caldwell, C.B., Stapleton, S.J., Holdsworth, D.W., Jong, R.A., Weiser, W.J.,

Cooke, G. and Yaffe, M.J. (1990). "Characterisation of Mammographic

Parenchymal Pattern by Fractal Dimension", Physics in Medicine and

Biology, Vol. 35, No 2, 235-247.

Australian Institute of Health (1990) "Screening Mammography Technology",

Better Printing Service, N.S.W.

Claims

CLAIMS:

1. A method of analysis of a set of mammograms of a current patient to provide an indication of malignancy, including the steps of: a) performing a fractal analysis on the set of mammograms of the current patient to obtain a plurality (n) of fractal dimension values of features in the set of mammograms; b) comparing the fractal dimension values obtained from the mammograms of the current patient, with a database of fractal dimension values for mammograms of patients having a verified diagnosis and predicting the presence or absence of malignancies in the current patient by comparing similarities in the sets of fractal values.

2. The method of claim 1, wherein the different fractal dimensions are measured from a plurality of different views.

3. The method of claim 1 or 2, wherein the different fractal dimensions are calculated from the mammograms taken from two different x-ray views.

4. The method of claim 3, wherein each of the different fractal dimensions are measured from mammograms taken from either the cranio- caudal (cc) view and the oblique (ob) view.

5. The method of any one of claims 1 to 4, wherein a multidimensional plot of a plurality of fractal values for each previously verified patient diagnosis is displayed and a critical pair of surfaces is indicated svich that substantially all coordinates on one side of the pair of surfaces represent a benign condition and substantially all coordinates on the other side of the pair of surfaces represent malignant conditions.

6. The method of claim 5, wherein cases with coordinates in an interface region between the surfaces are indicated as indeterminate.

7. The method as claimed in claim 6, wherein the interface region between the surfaces substantially separating the malignant and benign cases recorded in the database of historical data of previously identified cases in which an actual condition of a patient has been verified by pathology is displayed on a monitor screen and the respective coordinates for the current patient are displayed relative to the displayed interface region for inspection by an operator.

8. The method of claim 7, wherein the database of historical data is vised to indicate a surface in a multidimensional space having from 3 to 8 dimensions.

9. The method of claim 7 or 8, wherein a 3 dimensional space is used for visual indication.

10. The method as claimed in any one of the preceding claims, wherein the data from fractal analysis is combined with objective data to enhance the accuracy of the output indication.

11. The method as claimed in any one of the preceding claims wherein, the data extracted from the mammograms for at least one fractal dimension is obtained by digitising the mammograms vising a greyscale representation.

12. The method of claim 11, wherein the greyscale data are used as inpvit to a compviter program to generate fractal dimension data.

13. The method as claimed in any one of the preceding claims wherein, the data extracted from the mammograms for at least one fractal dimension is obtained by digitising the mammograms and subsequently vising a black and white representation with a selected threshold value for the conversion to a black and white image.

14. The method of claim 13, wherein the threshold data are used as input to a computer program to generate fractal dimension data.

15. The method as claimed in any one of the preceding claims wherein, for each mammogram, one or more areas of interest are identified for analysis.

16. The method of claim 15, wherein areas of interest are in the range of 1.0 to 1.5 cm square.

17. The method of claim 15, wherein areas of interest are in the range of 4.0 to 4.5 cm square.

18. The method of claim 15, 16 or 17, wherein two areas of interest are analysed, the second encompassing the first and having dimensions 3.5 times larger than the first svich that the respective area ration is 12.25.

19. The method of claim 18, wherein the first area is 1.2 cm square.

20. The method of claim 18 or 19, wherein the second area is 4.2 cm square.

21. The method of any one of the previous claims, wherein the fractal dimensions are calculated for each combination of viewpoint threshold/area by one of several methods of fractal analysis.

22. The method of any one of the preceding claims, wherein at least one of the methods of fractal analysis used is surface area related.

23. The method as claimed in any one of the preceding claims wherein, at least one of the methods of calculation of the fractal dimensions is used on the digitised images of a region of interest without thresholding being affected.