Morphometric applications in anatomic pathology

Morphometric Applications in Anatomic Pathology LAWRENCE D. TRUE, MD The components of the cell and tissue changes in many diseases are variable and can therefore be quantified. Characterization of these quantitative changes provides data that is useful not only for making a definitive, cell- and tissue-based diagnosis of disease, but also for predicting the course of disease. The spectrum of changes found in malignant tumors, ie, cell grade, architecture, cellularity, extent of invasion, nature and extent of inflammatory reaction, exemplify this range of quantifiable features. The diagnosis and prognosis of nonneoplastic diseases, ie, myopathy and metabolic bone disease, can also be determined by quantitating tissue changes. Morphometry is the quantification of changes in the "objects" of tissues, ie, cells and organelles, and their organization, using quantitative evaluation tools. The principles of morphometry have been known for a century. With the increasing availability of affordable, powerful computer systems and increasingly flexible and user-friendly software has come

easier ability to measure these changes. This article discusses the principles of morphometry with illustrations of types of analysis (ie, area fraction, object counting, shape and size analyses, and multiparametric analyses) using examples of these applications with discussions of error sources and limitations of morphometry. HUM PATHOL 27:450--467. Copyright © 1996 by W.B. Saunders Company Key words: morphometry, stereology, prognosis, fractal, volume, area, image analysis, neural net, automated cytology. Abbreviations: Pap, Papanicolaou; SER, smooth endoplasmic reticulum; FISH, fluorescent in situ hybridization; NRF, nuclear roundness factor; MEN H, multiple endocrine neoplasla type H syndrome; NCI, nuclear contour index; NOR, nucleolar organizing region; AgNOR, nucleolar organizing region in a nucleus stained with silver; FDA, Food and Drug Administration.

Since the early 1900s, histological features of normal and diseased cells have been measured to diagnose and predict the course of disease. Nuclear size was shown to be increased in cancer cells and in cells undergoing mitoses in the 1920s. 1"2The observation that the range in sizes of nucleoli in malignant and nonneoplastic cells partially overlap was shown in the 1930s. 3 Within the past 15 years, several reviews4-H and monographs ~2-16 have been published describing uses of morphometry in diagnosis and in the characterization of tissue changes in disease. Other relevant monographs present the principles of morphometry, stereology, video microscopy, and image processing. 17-20 However, morphometry is a technique that has been little used by practicing pathologists in making tissue diagnoses. This article presents the current contexts in which pathologists might consider using morphometry as a diagnostic tool, provides examples of types of morphometric analyses, discusses sources of error, and concludes with predictions concerning the future use of morphometry. For applications that are not cited herein, the reader is referred to either monographs, particularly the books by Baak, 14'15 o r to the current literature.

carcinoma 21 and breast carcinoma 22 exceeds 30%. A commonly used tool to assess observer variability is the kappa statistic, which measures the degree of observer concordance on a scale of 0 to 1 where 0 = no agreement and 1 = perfect agreement. Kappa values of 0.5 and 0.4 have been reported in counting mitoses and in grading nuclear pleomorphism, respectively; these kappa values reflect poor concordance. 23 The sources of variability amongst diagnosticians include the use of different visual templates of grade, which arise from different educational or experiential backgrounds, and the fact that different pathologists emphasize the features on which grade is based, ie, nuclear size and pleomorphism, nucleolar size, and the texture of chromatin, differently.24 Morphometry potentially decreases variability. . To provide a more quantitative scale than is provided by nonnumerical characterizations of degrees of alteration of structures. Grades are ordinal assessments of changes in cells and tissue to which numbers are typically assigned. 25 Morphometric approaches to evaluating changes in tissue are likely to be more reproducible than ordinal grading because they are quantitative. Relative changes in a structural feature of a cell usually have a physiological basis. For example, during the S phase of the cell cycle, both nuclear and cell volume progressively enlarge. This change is attributed, in part, to the increased DNA content of nuclei undergoing a G1 to G2 uansition. . To increase sensitivity in identifying minimal changes in features. For example, cytologically normal intermediate cells from patients with cervical intraepithelial neoplasia have abnormalities in the quantity and distribution of nuclear chromatin compared with cells from patients without cervical intraepithelial neoplasia. 26 Similar marker cells have also been found in patients with squa-

RATIONALE TO USE MORPHOMETRY Reasons to quantify features by morphometry include the following (Table 1): 1. To decrease variability in quantifying features of cells and tissues that can be decreased. Nonmorphometric quantification of tissue changes have high rates of observer variability. For example, interobserver variability in grading bladder From the Department of Pathology, University of Washington Medical Center, Seattle, WA. Address correspondence and reprint requests to Lawrence D. True, MD, Department of Pathology, Box 356100, University of Washington Medical Center, Seattle, WA 98195-6100. Copyright © 1996 by W.B. Saunders Company 0046-8177/96/2705-000455.00/0

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MORPHOMETRY IN PATHOLOGY(Lawrence D. True) stroy tissue are used. For example, in situ hybridization with chromosome-specific probes has shown great heterogeneity in the n u m b e r of chromosomes 1, 7, and 10 within different regions of the same prostate cancer. 33 DNA ploidy analysis by flow cytometry is less sensitive to regional heterogeneity o f ploidy. . Less expensive c o m p u t e r and image analysis hardware and better software and morphometric algorithms have been developed within the past 10 years. These developments have made m o r p h o m e t r y more accessible and useful to pathologists.

TABLE 1. Reasons to Quantify Features by Morphometry 1. To decrease the variability in quantitating features o f cells and tissues 2. To provide a numerical, reproducible scale of quantitative features 3. To increase sensitivity in detecting minimal changes 4. To evaluate the effect of changes in methods o f tissue processing 5. For use as a quality control tool 6. To provide shape and size standards for teaching and diagnosis 7. For use as a research tool 8. Availability o f faster, cheaper computers and better algorithms for data analysis

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mous cell carcinoma of the oral mucosa 27 and with bladder carcinoma. 2s Morphometry also offers the possibility of stratifying a disease process by a greater n u m b e r of categories than can be done by visual estimation of extent of change. If a quantitative scale is more precise and reproducible than one based on visual assessment, the scale can be expanded to include more categories. This would permit a greater number of management and treatment options. To quantify the effect of changes in a m e t h o d of tissue processing. For example, m o r p h o m e t r i c analysis o f the degree o f tissue shrinkage with different methods of tissue fixation provides more precise quantitation than does a visual estimate of shrinkage. 29 To provide a tool for assessing both the variability o f laboratory assays, eg, by measuring degree of tissue shrinkage, and the variability of estimates of quantitative changes, eg, the grade of cervical dysplasia. 24 To provide reference standards for diagnosis and teaching. Quantitative methods can be used to verify that structures exceed in size a categorical diagnostic threshold, eg, prostatic epithelial cell nucleoli that exceed 1.6 # m in diameter are found only in prostate carcinoma and not in benign prostate glands. ~° To use as a research tool. The revelation that abnormalities in cytologically benign cells from the mucosa of patients with dysplasia elsewhere in that mucosa, eg, cervix, 26 bladder, 2s and oral cavity,27 support the hypothesis that all of the cells o f an epithelium that contains a cancer are affected by the neoplastic process. This phen o m e n o n is termed "field effect." Furthermore, certain m o r p h o m e t r i c abnormalities, eg, chromatin texture, correlate with biochemical changes at both karyotype level in thyroid tumors 31 and at the DNA level in colon neoplasms. 32 A coarser chromatin texture, defined in one study as the variance in the optical density of pixels of nuclear images, correlates with greater degrees of loss of cancer-associated g e n e s Y Because tissue m o r p h o m e t r y is based on intact cell and tissue structure, data can be obtained that are lost when techniques that de4~1

PRINCIPLES Morphometric studies are currently based on the analysis of two-dimensional s t r u c t u r e s - - sections of cells and of tissue. Three-dimensional (stereologic) information is derived from these two-dimensional data, either by making assumptions about the three-dimensional structure regarding object size and shape or by directly calculating the third dimensions. Third-dimensional data can be obtained by Directly measuring dimensions in the vertical plane, either by confocal microscopy or by reconstruction of serial sections 34-36 Using computer-based image convolution techniques Using recently developed algorithms for obtaining stereologic information ~7'~8 For one-dimensional information, such as linear distances, and for two-dimensional calculations that do not require assumptions about object size or shape, extrapolations can be made to the third dimension with little error. The principle that point density and area fractions provide data sufficient to determine volume density and volume fractions was established by DeLeese. 1~ The precision o f measurements is reflected in the variances of the data. To minimize variance requires a sampling strategy that identifies the sources of greatest variance and increases the extent of sampling the source of greatest variability until variance is acceptable. The size of a data set depends on the variances associated with the specific features that are being measured.

METHODOLOGY C h o i c e of Technique The choice of measurement technique depends on the nature of the ceils or tissue being analyzed, the type o f measurement being undertaken, and the cost, measured both in time and in expense of hardware and software. 39 Techniques can be categorized as follows: manual, partially automated, automated with user interaction, and fully automated (Table 2). Manual approaches should be based on sampling schemes that make the work efficient and systematic, using such tools as overlaid grids and point counting. Although complex

HUMAN PATHOLOGY Volume27, No, 5 (May 1996) TABLE 2. Types of Morphometric Techniques 1. Manual 2. Partially automated 3. Automated with interaction by investigator 4. Fully automated without interaction by investigator

forms can be manually analyzed with appropriate sampling strategies and grids, 13 partially automated approaches using such data accumulation devices as digitizing tablets make the work more efficient. Image analysis systems allow full automation, eg, hands-off, automated analysis of Papanicoloau (Pap) smears. Image processing, which involves enhancement or geometric manipulation of a video image, can produce new data that may be more useful than nonprocessed image data. For example, images of Pap smears that are processed through sequential cycles of image dilation and erosion lead to the removal of objects that lack sufficient contrast for image analysis.4° In some situations, interaction by the pathologist with the image produces more accurate results. For example, by defining the boundaries between partially overlapping cells, the pathologist prevents such a cell pair from being erroneously classified as a single cell. Furthermore, graylevel thresholds, which provide the bases for segmenting the objects of interest, may be more accurately set interactively than automatically. Successful image analysis requires that objects of interest be separated from other image data. Distinction of objects from "background noise" allows segmentation of the image. Segmentation divides an image into two r e g i o n s - - t h e region that contains objects of interest for analysis, eg, cells or nuclei, and background data. In general, scene segmentation is based either on the optical density of stained objects or on the intensity of objects when fluorescent markers are used. Although some objects can be readily distinguished from background and, thus, segmented, eg, silver grains in an autoradiograph, others cannot, such as nuclei whose edges blend in light density with the cytoplasm, and ultrastructural organelles that cannot be specifically labeled with an electron-dense marker. For these latter situations, either a partially interactive m e t h o d or a completely manual approach is recommended. An automated imaging system would not be the best choice with respect to efficiency or even accuracy in such a situation. Other measurements, such as obtaining linear distances, may be done with sufficient accuracy and greater efficiency manually. Although fully automated systems cannot be used for many applications, a prominent exception is automated cervical cytology. Despite the complexity of images of Pap smears, some of these systems have exhibited greater predictive power in recognizing cervical dysplasia than has the average cytologist. In other situations, a completely manual approach is more efficient than a partially automated approach. For example, point counting to determine the area fraction of an object, such as mitochondria, is more efficient than tracing profiles of mitochondria on a digitizing tablet. 41

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The choice of technique should be based on the goal of maximizing efficiency and minimizing variance. For example, proliferation rates of tumors can be measured by 1. Counting mitoses, which can only be done manually because there are no automated image procedures that recognize mitoses. 2. Counting cells that express the Ki67 antigen; Ki67 is expressed in all cycling cells. 42 Immunoperoxidase histochemistry will label Ki67-expressing cells with an optically dense compound. Either cells can be manually counted or the n u m b e r of objects (cells) expressing Ki67 can be determined by image analysis using immunoreactivity as the basis for image segmentation. In choosing the technique, one should remember that the results of different methods are not necessarily comparable. Referring to the example cited, the ratio of cells in metaphase to all cycling cells often differs with cell type and disease state. Likewise, the volume of an object or area can be determined in several ways. If homogeneity of size and shape of nuclei is assumed, the area of cross-sectional profiles provides the basis for determining the nuclear volume. 1. Indirectly, by measuring the areas of individual nuclear profiles using a digitizing tablet to manually trace the profiles 2. By segmenting nuclei stained with a nuclear dye, using an image analysis system. Software can determine the area of individual nuclear profiles. 3. By measuring intercepts using a volumeweighted mean nuclear volume approach. In contrast to the first two approaches, a volumeweighted approach compensates for the fact that large objects will be overrepresented, which yields an erroneously high value for the mean nuclear volumeY Similarly, different methods can be used for measuring regions, such as volume of prostate cancer within sections of a prostate gland. Methods include 1. Point counting using a grid superimposed on microscopic sections of the prostate gland, 44 2. Measuring the area fraction of tumor either traced from sections 45 or projected on to a digitizing tablet 46 3. Visually estimating the area that is cancer 47 All methods show that the volume of prostate cancer has prognostic importance. Regardless of the measurement m e t h o d used, the volume of cancer in a prostate has been found to inversely correlate with prognosis.

APPLICATIONS

Types of Applications Types of applications are listed in Table 3. Linear Distance

Linear distances, eg, linear extent of carcinoma in a prostate biopsy, depth of melanoma invasion, proxim-

MORPHOMETRY IN PATHOLOGY (Lawrence D. True)

IABLE 3. 1. 2. 3. 4. 5.

Types of Applications

Linear distance Object c o u n t i n g Area fraction F o r m f a c t o r s - - s i z e a n d shape Complex measurements

ity of malignant t u m o r to a margin, or maximal twodimensional size of a malignancy, are measurements on which patient m a n a g e m e n t decisions are based. Because these measurements can be made using ocular micrometers or stage verniers, more time-consuming techniques such as planimetry or image analysis would most likely not yield data o f any greater prognostic power. More complex linear measurements, eg, the linear extent of a surgical margin of a radical prostatectomy specimen that is involved with prostate cancer, 4s could be done using a m o r p h o m e t r i c setup, such as a planimeter interfaced with the microscope by a camera lucida, for greater precision. Whether the increased accuracy of planimetry c o m p a r e d with superimposing a ruler along the surface justifies the added time consumed in m o r p h o m e t r y is unknown.

Object Counting Counting objects in tissue, such as mitoses, is done both for establishing diagnoses, eg, distinguishing benign and malignant uterine smooth muscle tumors, 49 and for estimating prognosis of tumors, such as breast carcinoma. 5°'5~ Correcting for volume fraction of the sample that consists of nuclei in mitosis provides a more accuratej~rognostic figure than does mitotic frequency in some, a z but not all, ~3 situations. Another approach to quantifying proliferation uses immunohistochemistry to identify cycling cells. Ki67 is a protein expressed by all cycling cells. It is detectable in fixed tissues using the MIB1 monoclonal antibody. Expression o f Ki67 correlates with the percentage of cells in the G2, S, and M phases of the cell cycle. 42 Because the Ki67 antigen is expressed t h r o u g h o u t the cell cycle, a higher percentage of cells are immunostained than the n u m b e r o f mitotic cells in the rectaphase o f their cell cycles. T h e percentage of cells expressing the Ki67 antigen is sufficiently high in many tumors, such as lymphomas, that automated object counting becomes a m o r e efficient m e t h o d of estimating proliferation than does counting mitoses. In more slowly proliferative tumors, such as prostate carcinomas, the fraction of ceils expressing Ki67 reactivity is so low, eg, less than 5%, that choice of sampling strategy becomes important to minimize variability. If the number, size, and shape of a tissue constitu e n t is irrelevant for a particular assay, an object counting approach may be an efficient m e t h o d of determining tissue constitution. Using such an approach, the n u m b e r o f profiles o f small vessels, also referred to as the angiogenesis, o f both breast and prostate cancers has been shown to have prognostic significance. 54'55 Area Fraction The area fraction o f tissue (or percentage of sample) that consists o f a particular structure or process is 453

of importance in a variety of situations, eg, the proportion of a lung carcinoma that is necrotic and the extent of renal interstitial fibrosis secondary to chronic lupus nephritis. Visual estimates of area fraction can vary widely among observers. For example, estimates of bone marrow cellularity vary up t o 5 6 % . 56 A morphometric approach is likely to result in lower variability. One o f the most efficient ways to determine area fraction is by using a grid superimposed over an image or projected onto a microscopic field of view with a sidearm optical attachment. 4~ The percentage of points of grid line intersects that overlay the object or objects of interest is the area fraction. Intersects n e e d be placed no more closely than the size of the object. However, manual point counting methods are not always very efficient; eg, a semiautomated m e t h o d for determining area fractions in b o n e is more efficient than a point-counting method.. 57 As an example, it is more efficient to express the a m o u n t of smooth endoplasmic reticulum (SER) in a cell as an area fraction than to count the n u m b e r of profiles of SER. 5s

Form Factors

Size. Sizes of objects, eg, tumor nuclei, and of regions, eg, volume of tumor, both can contribute to making diagnoses, eg, distinguishing reactive cells from malignant cells, and to providing data of prognostic significance, eg, nuclear area in low-stage carcinomas of the urinary bladder and volume of adenocarcinoma within a prostate. Different methods of measuring nuclear area (or volume) yield different results. Only the volume-weighted mean nuclear area of n o n - s m a l l cell carcinomas of the lung and of ductal carcinomas of the breast correlate with survival. O t h e r calculations of tumor cell v o l u m e - - m e a n nuclear profile area, density of nuclear profiles, and volume fraction of n u c l e i - - d o not provide prognostic information. 5~'59'6° Shape. Nuclear shape has been used both to identify disease, eg, involvement o f a lymph node by mycosis fungoides 61'62or lymphoma, 6~ and to predict the behavior of cancer, eg, low-stage prostate carcinoma. 64 Presence of malignancy and worsened prognosis is directly a function of the degree to which nuclei are out-ofround. Complexity, hence, out-of-roundness, of a surface can be expressed either as a function of the ratio of circumference of a circle containing the object of interest, eg, nucleus, to the actual perimeter of the object, or as a fractal dimension. Fractals are geometric patterns that retain their form at different scales of measurement. The fractal dimension is the numerical relationship between measurements o f a morphometric property made at different scales of magnification. 65 Complex shapes, such as the coastlines o f c o u n t r i e s 66 or surfaces of lymphocytes, 6v can be expressed as fractal dimensions. Isotropic objects, which have dimensions that are unaffected by orientation, such as spheres, can be efficiently evaluated morphometricaUy because one need not be c o n c e r n e d about the orientation of such objects in space. The frequency histograms of the profiles of spheres of different diameters is characteristic, x7 The

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diameters of spheres o f different sizes in a collection of spheres can be calculated from these profiles. 68 T h e dimensions o f objects o f moderately complex shape, such as skeletal muscle fibers, can likewise be determ i n e d from the frequency histogram of dimensions of profiles of these obiects if their profiles are randomly o r i e n t e d ) 7 However, anisotropic objects, which are objects that are preferentially aligned in a tissue, n e e d to be sampled in a m a n n e r such that all orientations are represented. Many biological structures are not randomly oriented in tissue and, hence, exhibit anisotropy. Even with this constraint, m o r p h o m e t r i c evaluations o f cross sections of skeletal muscle have provided a basis for distinguishing different diseases. Primary myopathy can be distinguished from secondary myopathy based o n a function of the ratios of the cross-sectional areas of type II and type I fibers and the variance of the areas of type II fibers. 69

Complex Measurements Combinations of m o r p h o m e t r i c features can be used for diagnosis and classification. Shape features o f nuclei, including skewness of area, length of the major axis, and nuclear roundness, provide the basis for distinguishing hepatoceUular carcinoma from regenerative nodules. Based on these parameters, the positive predictive value of a neural net classifier of nuclear dimensions is 100%, and the negative predictive value is 85%. 7° A neural network is an approach to data analysis that classifies objects based on the relative importance, or weight, of features. T h e net has learned the relative weights of objects from analyzing a training set of objects. 7]'7~ Data analysis with a neural net contrasts with traditional approaches that classify objects by rules that assign objects to classes based on presence or absence of a feature or of a dimension that exceeds a threshold value. T u m o r grading is based on combinations of changes in the architecture and cytology of neoplastic cells. Features that contribute to grading vary with the type of tumor. However, the degree of concordance amongst pathologists in grading tumors, such as carcinomas of the breast, 2~ bladder, 21 and cervix, is low. For example, using modified Bloom-Richardson grading criteria, there is only fair observer agreement in grading breast cancers (kappa = 0.55) and in recognizing features that contribute to grading, such as degree of tubule differentiation (kappa = 0.64), mitotic activity (kappa -- 0.52), and nuclear pleomorphism (kappa 0.40).2~ Nuclei o f breast cancer cells can be " g r a d e d by image analysis, presumably with greater reproducibility.7~Dysplastic squamous cells of the cervix can be accurately classified with multiple different classifiers, including shape features, nuclear size, nuclear: cytoplasmic ratio, and chromatin distribution. 75 The ability to classify cervical epithelial cells using m o r p h o m e t r i c features has provided the basis for the commercial development of automated cytology systems. 70 Different systems handle cervical Pap smears and image data differently. Two systems prepare monolayers of" the sample. T h e advantage of monolayers is

that there is less overlap of cells than in conventional smears. A potential disadvantage is that contextual information of the preparation, such as exudate and cell crowding, is lost. Furthermore, because these preparations use aliquots of the sample, there is a possibility of sampling error. A recent article reports that monolayer samples accurately represent the entire smear, indicating accurate sampling. 77 Some automated cytology system class~sfycells based on hierarchies of m o r p h o m e t r i c features. A different approach uses a neural net to identify microscopic fields with abnormal cells. 71'72 In contrast to imaging systems that d e p e n d on scene segmentation to identify individual cells that are then morphometrically analyzed, this system analyzes all of the contents of microscopic fields and only partially relies on successful segmentation of cells, whose boundaries often overlap or have insufficient contrast with the background for identification. Based on a training set of Pap smears that have already b e e n classified, the neural net weights features of both single cells and of images of views to select the most abnormal cells and images. 79's° In preliminary trials, this system identified rare dysplastic cells in smears that had b e e n classified as normal in initial review; there were virtually no false negatives. 28'4°'81 Use of this system to retrospectively analyze smears that had previously been diagnosed as negative found rates of false negativity that ranged from an insignificant 0 . 2 % 82 to 15%. 83 Although these trials suggest that a neural net may be a more accurate classification tool than hierarchical classification approaches, a comparison of several approaches to classifying cervical cells, including a decision tree, discriminant function analysis, and a neural net, showed that all three methods were equally accurate. 84 Regardless of which particular m e t h o d proves most accurate and efficient, automated cytology, either for rescreening in a quality assurance program or for primary screening, appears i m m i n e n t as a routine diagnostic tool. s5 A similar approach is being used to classify urine cytology samples, d° As described previously, the sensitivity of a morphometric-based classification system is sufficiently high and reliable that changes can be recognized in cells from patients with dysplasia that are classified as normal by t r a d i t i o n a l cytology.26"28 T h e spatial distribution of objects of interest can be informative. For example, the gradient in the density actin filaments in cells correlates with direction of cell migration, s7 T h e distribution of differences in gray-level values of pixels provides a basis for texture analysis of images. T h e distribution of chromosomes in nuclei can be d e t e r m i n e d from images of nuclei in which chromosomes have been localized by fluorescence in situ hybridization (FISH) using chromosome-specific probes. These studies show that the distribution of chromosomes is not random. Chromatids of c h r o m o s o m e 15 are closer to each other and to the center of the nucleus than are chromatids of c h r o m o s o m e 1. 8s Chromatin texture, which can be morphometrically determined, provides a reliable basis for distinguishing small cell from n o n - s m a l l cell lung carcinoma, 6° for subcategorizing dysplastic epithelial cells, eg, transitional cell car-

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MORPHOMETRYIN PATHOLOGY(LawrenceD. True) cinomas of different g r a d e y and for diagnosing soft tissue tumors. °° In a study of bladder tumors, the textural features o f greatest importance were the nuclear size, variance in the optical density of nuclei, and degree of chromatin clumping. 89 T h e r e is a correlation between textural features and molecular changes. Single, quantifiable changes in single c h r o m o s o m e s - - a translocation--results in a change in the nuclear structure that is reflected in the chromatin texture. 3~ Colonic a d e n o m a and carcinoma nuclei can be distinguished by differences in the coefficient of variance of nuclear pixel optical densities. These differences correlate with fractional allelic losses of c h r o m o s o m e regions that are involved in the pathogenesis of colonic carcinoma, s~ T h e variability of immunoreactivity o f cells is a n o t h e r type of image texture that has clinical relevance in some situations. Greater variances in the average density of nuclear immunoreactivity for sex steroid receptors in breast cancers and o f a n d r o g e n receptor immunoreactivity in prostate cancers is associated with a p o o r e r prognosis. 9~'q2 Architectural features o f diseases provide a basis for m o r p h o m e t r i c categorization and diagnosis. Sclerosing adenosis and tubular carcinoma can be morphometrically distinguished based on glandular surface density and luminal form factor. °s

Specific Applications by Organ System Below are examples o f applications, by organ. Although this list is incomplete, because the n u m b e r of m o r p h o m e t r i c analyses exceeds what can be included in this article, the examples are selected to represent timely problems, as well as a diversity of organs, diseases, and types of problems.

Breast T h e p r o p o r t i o n of breast cancer cells in metaphase forms the basis of a prognostic index, the multivariate prognostic index, which is a complex function of mitotic activity, tumor size, and lymph n o d e status. 5° When tumor cellularity and t u m o r cell size are also taken into account, 94 mitotic counts expressed per square millimeter or per 1,000 cells yield values o f greater predictive power than mitoses per high-power field of magnification. 95 Similarly, the percentage of t u m o r cells that express MIB1 immunoreactivity provides prognostic data. 96 Extent ofvascularity, expressed as spatial density of profiles o f vessels, correlates directly with decreased time to t u m o r recurrence. 55'97 T h e m e a n nuclear size and variance in nuclear size o f breast cancer cells correlates inversely with degree of estrogen receptor expression and with better survival.98'5~ Because both mitotic activity and variance in nuclear size contribute to visual grading o f breast carcinomas, using modified Bloom-Richardson grading criteria, and because there is no better than fair observer agreement in assessing nuclear pleomorphism, mitotic activity, and in grading breast cancers, m o r p h o m e t r y offers the potential of improving reliability in grading these t u m o r s . 23'74 More complex, multifactoral m o r p h o m e t r i c analy-

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ses, using combinations of geometric, textural, and distributional features, can differentiate benign breast epithelial ceils from carcinoma cells in cell smears and can distinguish sclerosing adenosis from tubular carcin o m a Y Greater variances in the average density o f immnnoreactivity for sex steroid receptors in breast cancers is associated with a p o o r prognosis. 92

Respiratory Tract The length: diameter ratio of the longest microvilli has been used to distinguish mesothelioma and adenocarcinoma. 99 However, immunohistochemistry is a more reliable tool because this m o r p h o m e t r i c technique is laborious and subject to sampling errors; tangential sectioning o f long microvilli renders their appearance misleadingly short, and the longest microvilli may not be sampled. T h e percentage o f a lung t u m o r that is necrotic is o f prognostic value. ]°° At higher magnification, the volume fraction of neurosecretory granules in the tum o r cells o f carcinoids and smallcell carcinomas predicts survival of a patient who has one o f these cancers that has metastasized. ]°1 In contrast to cancers of some other organs, the size and shape o f nuclei in u p p e r respiratory tract carcinomas are of debatable prognostic value. 1°2'~°3 However, mean nuclear area provides the basis o f distinguishing cell types, both benign from malignant and histological subtypes of malignancies. Whereas mesothelioma nuclei have an area that exceeds 40 # m 2, the area of benign reactive mesothelial nuclei is less than 30 #m2. I°4 T h e nuclei o f reactive alveolar type II cells (mean nuclear area, < 5 0 # m 2) are smaller than the nuclei from pulmonary adenocarcinoma cells whose mean nuclear area exceeds 54/.tm2.1°5 T h e threshold o f mean nuclear profile area of small cell carcinomas compared with n o n - s m a l l cell lung carcinomas is 44 /.tm2.60 Subtle multiparametric m o r p h o m e t r i c differences from normal enable marker squamous cells to be identified in the oral mucosa in patients with squamous cell carcinoma of the u p p e r respiratory tract. 27

Gastrointestinal System Quantification of liver fibrosis in patients with cirrhosis gives prognostic information. ~°6 Morphometric characterization o f a variety of nuclear features provides the basis for distinguishing carcinoma cells from benign ceils in ductal tumors o f the pancreas, ]°7 tumors o f the rectum, ]08 and liver turn'ors. 7° In the study of liver tumors, classification o f cells using a neural net had positive predictive value o f 100% and a negative predictive value o f 85% 7o Colonic a d e n o m a and carcinoma nuclei can be distinguished by differences in the coefficient of variance of nuclear pixel optical densities. These differences correlate with fractional allelic losses of chromosome regions and genes that have been implicated in the pathogenesis of colonic adenocarcinoma. 32

Urinary System The mean area o f tumor cell nuclei has prognostic power in low-stage carcinomas o f both kidney and blad-

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der. 1°9I~1 T h e most useful size threshold for prognosis is a nuclear area o f 45 /zm2. H° Mean nuclear area of higher-stage tumors, such as transitional cell carcinomas o f the bladder, lacks i n d e p e n d e n t prognostic power.112 Correcting the mean nuclear area for subpopulations of t u m o r cells with very large areas so that they are not oversampled provides greater prognostic power for both t u m o r types. 43'113 Chromatin texture, which can be characterized by a m o r p h o m e t r i c approach, provides a reliable basis for subcategorizing dysplastic transitional epithelial cells, s9 T h e most important textural features are nuclear size, variance in optical density o f nuclei, and degree o f c h r o matin clumping. By analyzing textural features of nuclei, marker cells in bladder mucosa of patients with bladder carcinoma can be detected. 28 M o r p h o m e t r y can help predict the functional effects o f histopathological changes in nonneoplastic renal disease. In chronic renal failure, there is a strong correlation (r = .8) o f creatinine clearance with distal tubular damage/atrophy, and a weaker (r > .65) correlation with interstitial widening and proximal tubular d a m a g e . m T h e extent of interstitial fibrosis and o f intireal sclerosis in a u t o i m m u n e connective tissue diseases can be reproducibly quantified, and may provide a basis for predicting longevity of renal function, n5 Glomerular hypertrophy predicts the development of focal glomerulosclerosis in a subset of patients with minimalchange nephrotic syndrome. H6

Gynecologic System Categories or grades of atypia/dysplasia o f uterine epithelial cells can be distinguished using combinations of m o r p h o m e t r i c and densitometric features. 75 Commercial systems to identify dysplasdc and malignant cervical squamous cells are available for either rescreening or primary diagnosis. 7s'79 T h e sensitivity o f m o r p h o m e t tic classification is sufficiently high and reliable that changes can be recognized in cells from patients with squamous dysplasia of the cervix that were classified as normal by traditional cytology.26

Prostate T h e linear distance o f a prostate needle core biopsy that is involved with cancer predicts, with variable accuracy, the a m o u n t of cancer in the prostate. 117 Similarly, the a m o u n t of cancer in chips o f prostate predicts the volume and stage o f the primary t u m o r and correlates with patient o u t c o m e ns as does the linear extent o f a surgical margin of a radical prostatectomy specimen that is involved with prostate cancer. 48 Analogous with breast carcinoma, degree of angiogenesis in primary prostate carcinomas has prognostic significance. 54'5~ Furthermore, the capillary density in sections of primary prostate carcinomas that metastasized to b o n e was greater than that of tumors that had not metastasized to bone. H9 A nucleolar size greater than 1.6/zm distinguishes prostatic adenocarcinoma from other diseases or conditions that affect the prostate and are associated with p r o m i n e n t prostate epithelial cell nucleoli. 3° T h e mean

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nuclear volume of prostate carcinoma cells correlates with response to endocrine therapy; in fact, response is apparently proportionate to m e a n nuclear volume. 12° The area (hence, volume) of radical prostatectomy specimens that have cancer correlates both with pathological markers of higher-stage tumors and with time to possible r e c u r r e n c e / p r o g r e s s i o n of tumor. 121 T h e behavior of localized, stage B prostatic carcin o m a can be predicted by measuring the nuclearroundness factor (NRF).64 T u m o r cell nuclei that are less spherical, and consequently have a higher NRF, are more likely to be of higher stage. 122 NRF is measured by tracing the contours of nuclei on a digitizing tablet. Similar perturbations in nuclear size and shape distinguish the cells of prostatic intraepithelial neoplasia from nonneoplasdc cells. 123 Nuclear texture features have provided a basis for grading prostate c a r c i n o m a ] 24 However, the applicability of a nuclear grading scheme is problematic because current clinicopathological studies are most frequently based on the Gleason scheme of grading; this grading scheme is based on t u m o r architecture. Another use o f image texture is assessing the variability of immunoreactivity o f cells. Increased variance in the average density of androgen receptor immunoreactivity in prostate cancers is associated with a p o o r prognosis. 91

Endocrine System Adrenal medullary hyperplasia in relatives o f patients with multiple endocrine neoplasia type II (MEN II) syndrome can be reliably identified by serial reconstruction of morphometrically analyzed sections of adrenal gland. Kz5 Based on structural features of nuclei, adenomatous nodules, adenomas, and well-differentiated thyroid carcinomas can be distinguished from each other.~1.126,127

Hematopoietic System Nuclear shape has been used to diagnose disease, ie, involvement of a lymph n o d e by mycosis fungoides61.62 and lymphoma,63 T h e complexity of nuclear profiles in lymphoid cells being evaluated for T-cell lymphoma is t e r m e d the nuclear c o n t o u r index (NCI). T h e NCI is a function of perimeter and area. A circle has an NCI of 3.54. Cells with an NCI greater than 11.5 are mycosis fungoides cellsY2 Lymphomas can be morphometrically classified by cell type based on nuclear area, nuclear ellipticity, nuclear irregularity, chromatin texture, and nucleolar size into four histological categories: small cleaved, small noncleaved, large cleaved, and large noncleaved lymphoma} 2s T h e same parameters can help distinguish centrocytic lymphoma from other cleaved follicular center cell lymphomas) 29 Lymphocytes of different functional types and of different diseases, ie, lymphomas or leukemias of selected types, can be distinguished by the fractal dimensions o f their cell surfaces} 3°

Bone and Soft Tissue Primary and secondary myopathies can be distinguished based on the ratios of the cross-sectional areas

MORPHOMETRY IN PATHOLOGY(Lawrence D. True) TABLE 4. 1. 2. 3. 4. 5. 6.

Sources of Error

Object identification Tissue processing Scale at which m e a s u r e m e n t is m a d e Precision H o l m e s effect Densitometry

of type II and type I fibers and the variance of the areas of type II fibers. 69 Changes of bone in metabolic diseases are most reliably assessed morphometrically. "~7'~3~M o r p h o m e t r y can also contribute to the diagnosis and prognosis o f soft tissue tumors. Chromatin texture j~rovides a basis for diagnosing this category o f tumor. ~ Cytometric features contribute to predicting the behavior of malignant fibrous histiocytoma of the extremities.133

Nervous System T h e size o f the brain, which is an anisotropic structure that lacks symmetry in most dimensions, can be morphometrically calculated from sections, where three-dimensional information is derived using such newly developed mathematical m o r p h o m e t r i c approaches as "Cavalieri's estimator. ''37'~4 The n u m b e r o f neurons in specific regions o f the brain can be calculated using estimators of three-dimensional distribution. 1°'1s5]~7 Neuronal count should correct for shrinkage o f the brain with age and for n o n u n i f o r m distribution of neurons within a specific region.

Skin (Melanoma) Size and shape parameters have f o r m e d the basis for predicting the survival of patients with m e l a n o m a of skin. The maximum depth of invasion by primary melanoma, ~3s the shape o f the tumor, ~39 and the tumor volume ~4° all correlate with survival. ERRORS

T h e r e are multiple potential sources of error in m o r p h o m e t r y (Table 4). Identification of the O b j e c t of Interest T h e r e is m a r k e d variability in the consistency with which observers identify objects such as mitoses or immunostained cells. One explanation for this variability is that these objects are not precisely defined. Identification o f these objects, or tissue elements, can also be problematic. For example, the extent of invasion of the desmoplastic variant of m e l a n o m a can be very difficult to visualize with certainty because the spindle cells o f this variant resemble fibroblasts. Another source o f error is the use o f inadequately precise criteria for defining the object or objects of interest. For example, identification o f a mitosis has been problematic. TM T h e definition of a mitosis includes absent nuclear m e m b r a n e and condensation of 457

chromosomes. When mitoses are counted using precise criteria, and if tumor cellularity and tumor cell size are also taken into account, mitotic counts per square millimeter or per 1,000 cells yield figures o f greater predictive power than simple counts of mitoses per high-power field of magnification. 142 The n u m b e r of nucleolar organizing regions, (NORs) in nuclei correlates with the proliferative rate of those cells. However, the n u m b e r of NORs in nuclei that are stained with silver (AgNORs) differs depending on the counting criteria, because there is no standard definition for an AgNOR. What is also problematic is uncertainty about guidelines for counting AgNORs. It is unknown whether the n u m b e r of AgNORs or the area fraction of nuclei that consists of AgNORs best predicts proliferative rate. 143 An image analysis system, which identifies objects by segmenting images based o n differences in gray level values of pixels, is also subject to variability. Variability can result from either the procedure, when stains are too low in contrast or lack sufficient specificity to form a reliable basis for gray level-based separation o f object and background, or from the observer, who sets the threshold. Software routines, eg, image convolution filters or look-up tables that spread the gray level range o f pixels at boundaries, can sharpen indistinct gray-level boundaries. T h e r e are situations, however, in which image processing of boundaries provides inaccurate information. For example, applying smoothing or boundaryenhancing routines to cell surfaces produces inaccurate measurements of cell surface complexity, or inaccurately low fractal dimensions. 14~ Conversely, the fractal dimension of an object digitized at too low a magnification for the pixel density of the camera results in a fractal dimension that is too low. 145 Thus, fractal test objects should be digitized at a magnification where a single pixel is smaller than the finest detail of the object but larger than the finest detail of the substrate on which the object is located. For example, if the object is printed, the pixel should be larger than detectable irregularities in the print, such as fibers. Information from the third dimension based on confocal microscopy data can improve the accuracy o f segmentation. 146Thresholds chosen by different observers to distinguish stained and unstained structures, such as nuclei, differ. An alternative is to automate segmentation by using the same gray-level threshold for all samples in a study. Although the n u m b e r of objects selected by a fixed threshold correlates well with the n u m b e r selected by a threshold set by an observer for each specimen, there is a tendency for the fixed threshold to select objects in a m a n n e r so that the total object area fraction is greater. ~47 Another error source in using fixed thresholds arises from differences in intensity of staining of the object of interest because samples and staining runs may result in markedly different intensities of reaction product. Finally, objects of interest may have overlapping borders. A consequence o f applying an automated object recognition routine to such an image without editing overlapping structures is that object counts and object areas will be lower than their actual values.

HUMAN PATHOLOGY Volume27, No. 5 (May 1996)

Manually setting a gray-level threshold to segment' an image into immunostained cells and nonstained ceils presents a different source of error in object identification. Staining may be either so faint or so focal that interobserver variance in counting Ki67-positive cells is large• In addition, n o n t u m o r cells, such as lymphoid infiltrates of carcinomas or lymphomas, contain proliferating cells. An awareness of this proliferating, nonneoplastic c o m p o n e n t will help avoid counting these benign cells. Another important point regarding object identification is that the class of objects may differ with the assay. Specifically, because proliferation assays measure different funcuonal properues o f ceils, the results of assays are not directly comparable. For example, the n u m b e r of cells in S-phase of the cell cycle is a smaller percentage than all cycling cells, which the KI67 antibody detects. Imprecision in identifying the object of interest can lead to error. For example, using Ki67 immunoreactivity as a marker for assessing the proliferation rate of a lymphoma may p r o d u c e e r r o n e o u s results if the relative content of benign, Ki67-immunoreactive cells is not taken into account. Double labeling by irnmunohistochemistry may provide a basis of distinguishing lymphoid cells by i m m u n o p h e n o t y p e , if their phenc~ types differ. Another source of error is defining the boundary of those objects that lack a histologically definable border. Determining n e u r o n a l content of different regions of the brain can be problematic, particularly for regions that lack a histological border• One solution is to use fiduciary reference points; these are features or locations c o m m o n to each serial section or image• Alignm e n t o f these points provides a reasonable alignment of the image planes in the third dimension• Another solution is to apply region-specific pattern recognition routines to consistently identify a region and thus provide a basis for comparing different samples. ~48 Tissue Processing

Tissue processing involves multiple steps in which tissue c o m p o n e n t s are chemically modified• Physiological factors, such as delayed fixation, high temperature, and circadial effects, can change the tissue concentration of a constituent, eg, mitoses. ~4° T h e nature of the fixative and the conditions of fixation, eg, pH, temperature, and duration of fixation, alter dimensions of tissue components. Error in counting objects, such as mitoses, can result from shrinkage of the tissue containing the objects. W h e t h e r such steps influence the relative area fractions o f objects should be evaluated for each tissue constituent that is to be analyzed• For example, the nuclear volume o f ethanol/acetic a c i d - f i x e d diploid nuclei in the brain is 50% less than that of rapidly frozen nuclei; in contrast, there is no difference in tetraploid nuclei processed by these two different methods. 15° The mitotic frequency in breast cancers is not very sensitive to m i n o r changes in processing conditions• TM The degree of shrinkage with formalin differs with different tissues. T h e shrinkage factor of lung is 0.6,

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which contrasts with a value of 0.8 for the spleen, s In another example, the n u m b e r of neurons in the brain reportedly decreases with age. Virtually all of the difference in n e u r o n c o u n t at different ages is explained by greater shrinkage of brain with age. Consequently, young brains, which shrink more, appear to have more neurons than older brains. 136'152 Standardizing measurements of size, shape, and distribution may not remove all sources of bias, which can contribute to a variance of 40% in the estimate of n u m b e r of neurons, a53 T h e volume of a structure of irregular shape, such as a region of the brain, can be more accurately estimated Wl h Cavahen s esumator than by attempting to trace an outline of the region of interest. 1a5 Fixation can influence the detectability of cell-specific molecules• With respect to proteins, prolonged fixation in formalin decreases reactivity for various reagents, including keratin immunoreactivity 154 and number of histochemically identifiable AgNORs per nucleus. AgNOR numbers are lower in formalin-fixed tissue, which causes coalescence of particles, than in paraformaldehyde-fixed tissue. 1~5 •t

•

•'

"

•

Scale

The spatial resolution at which a structure is analyzed can affect dimensions. For such objects, the greater the degree o f spatial resolution, the higher the linear dimension• This p h e n o m e n o n is termed the Coast o f England effect. 6~ Consequently, the finer that measurements o f the coastline are made, the greater will be the measured distance of the coast. Objects characterized by this feature have n o n i n t e g e r values for their fractal dimension. As a n o t h e r example, the alveolar septal surface area and the surface area of Golgi membranes differ markedly at different light microscopic and ultrastructural magnifications, respectively.58 Fractal dimensions are d e t e r m i n e d by taking measurements at different magnifications. In situations where the sample is so small that different magnifications cannot be used, a fractal dimension can be determined by using different scales o f measurement at a constant magnification. 156']~7 Precision

Current instruments allow the user to make highly precise measurements. Digitizing tablets have a spatial resolution in the micrometer range. Image analysis instruments can achieve equally high resolution using optical magnification and cameras with high (1,280 × 1,024) pixel density. However, because greater resolution is costly in time and c o m p u t e r memory, the challenge facing the investigator is to conduct the analysis at a level o f spatial resolution high e n o u g h to answer the question that is posed without being so high that time is wasted• T h e ergonomics of tracing outlines on a digitizing tablet is subject to error; when h a n d motion in tracing the objects is either too fast or too slow, precision decreases. • Errors in digitizing tablets are exemplified by studies of the nuclear roundness factor of prostate cancer nuclei• T h e sources of interobserver variability in this semiautomated m o r p h o m e t r i c proce158

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dure include ergonomic features, such as the location of nuclei on the tablet and the speed of tracing. 146 At tracing speeds both above and below the optimum, variability increases. When the desired level of precision approaches the spatial resolution of the measuring system, there is the possibility that values may be inaccurately high. This p h e n o m e n o n is termed "staircasing. ''6 For example, inappropriately high values for a curved boundary are obtained if each boundary pixel is connected, because the pixelated boundary will "wander" back and forth across the true, curved boundary. " S m o o t h i n g " the pixelated boundary by connecting alternating pixels results in a more accurate value. Automated image analysis systems are also subject to observer-based imprecision. At boundaries between object and background that have similar optical densities, the imaging instrument might not be able to set an accurate threshold. Unless the operator intervenes to select the boundary, the threshold for selecting objects of interest may be inaccurate.

TABLE 5. Sampling Considerations l. 2, 3. 4. 5. 6.

Sample size How representative is sampling? Distribution of objects Scale dependency of feature measurements Uniformity of size and shape Efficiency of analysis

The immunologic reagents should be titered to saturate binding sites of antigens. The conditions of the enzyme-substrate reaction should be optimized so that the concentration of the electron donor, eg, hydrogen peroxide, of the enzyme substrate, eg, diaminobenzidine, and of reaction conditions (pH, temperature) are optimized. These considerations are critical in quantitative immnnohistochemistry. 162 Sampling

The following questions should be addressed to avoid errors in sampling (Table 5).

Holmes Effect

Morphometry assumes that objects are infinitesimally thin. At a level of spatial resolution where dimensions of objects of interest approach section thickness (for example, the diameter of small neurosecretory granules--100 n m - - i s equal to that of high-quality, ultrathin electron microscopy sections), the portion of objects of interest within the section may bias measurements of the dimensions of objects of interest. The thicker a section, the greater will be the area fraction of the most dense structure or structures within the section. Thus, specimen thickness should be less than the m i n i m u m dimension of the object of analysis. The dependence of area fraction of objects on section thickness has been shown with nuclei using histological sections from 2 to 8 # m in thickness. 29 This mathematical approach corrects for overprojection of the object when section thickness is not negligible but the volume of the object is large. 135 For example, the relative number of chromosomes per cell nucleus is the same using FISH when touch preparations of cell are analyzed as when sections of nuclei are used. 16° Densitometry

In situations where histochemical stains are used to segment images, maximum contrast should be achieved between all portions of the object of interest and the background. When antigen immunoreactivity serves as the basis of segmentation, the immunostaining conditions should be established to maximize the signal:noise (immunostained object:background) ratio. To optimize signal:noise ratio, these guidelines should be followed161: Antibodies specific to the object of interest should be used. Polyclonal antibody preparations that contain antibodies reactive with other molecules in other objects will increase the background. 459

Adequacy of Sample Size Is the sample size sufficiently large to obtain meaningful results? A morphometric analysis should sample the specimen to an extent sufficient to minimize variability. The investigator can monitor how close sample size approaches an acceptable variance by calculating a running mean. When the running mean stays within a predetermined range of variability, eg, 5%, as subsequent measurements are made, the sample size is deemed adequate. I63 Failure of the running mean to stabilize to an acceptable value, eg, <5%, indicates a failure in the sampling strategy. Explanations of a suboptimal strategy include scale problems and a nonrandora sampling.

Randomness Is random sampling being conducted in a truly random manner to represent the objects being analyzed with respect to position, size, shape, and orientation? In a well-conducted morphometric study, objects to be analyzed are selected by a rule that is uniformly applied to all specimens. Variability is minimized if sampling is systematically random, la4 All objects must have an opportunity of being represented. 165 The sampling rule may direct truly random sampling by using a random number table to locate the coordinates of objects to analyze on a glass slide. Practically, systematic sampling also satisfies the requirement of random sampling, eg, analyzing all cells intersected by a superimposed lattice of points. Sampling that is biased toward the sought result should be avoided. For example, by analyzing the length of the nuclear membranes of the most atypical nuclei in a sample regarded as malignant and the least atypical nuclei in the benign sample, the finding that malignant nuclei have nuclear profiles of irregular shape is selected. Variability can be signifi-

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cantly decreased if a systematic sampling strategy is followed. By using a standardized sampling approach, variance in counting mitoses can be minimized and an interobserver correlation coefficient of greater than .90 can be achievedJ 66'~67 In some situations, r a n d o m sampling may decrease efficiency and sensitivity. For example, if the feature being quantified occurs in only a subset of cells, or in a defined region of a sample, eg, the focus of greatest mitotic activity,55 sampling should be restricted to that region. Conceivably, the proliferative portion of a tum o r that most predicts the prognosis may be that region of the tumor that is at the periphery, and not the whole set o f tumor cells. Distribution T h e distribution of objects of interest is a consideration in sampling. Tissue-based studies have shown greater heterogeneity in feature distribution than is demonstrable by biochemical techniques. For example, the chromosomal ploidy of tumor cells within a given t u m o r differ in prostate carcinoma 33 and bladder cancer. 16s Using chromosome-specific probes, the cells within a given prostate cancer vary significantly with respect to numbers o f chromosomes 7 and 10 in each tumor cell. 33'j69 Vascularity is not uniformly distributed t h r o u g h o u t a given t u m o r section; only the regions at the periphery of an invasive breast carcinoma that had the greatest concentration of vessels had prognostic significance. 55 Another example of uneven distribution of objects is the finding that the n u m b e r o f AgNORs in normal and neoplastic squamous is unevenly distributed. AgN O R n u m b e r is greatest in the parabasal layer of normal squamous epithelium, and at the periphery of nests of invasive squamous cell carcinomas of the esophagus. Variation in AgNOR content of esophageal squamous carcinomas is sufficiently great that determination of representative AgNOR content is problematic if the location o f the region o f the cancer that is being sampled is not known. Scale Another assumption is that measurements are not sensitive to scale. However, the values of dimensions of some objects are scale d e p e n d e n t . 17° For example, the surface of adenomatous polyps of the colon have a greater value when measured at high magnification than at low magnification. 171 These surfaces have a fractal dimension greater than 1. At the ultrastructural level, the surface area of endoplasmic reficulum increases with the magnification at which it is measured. 5s Size and Shape T h e assumption that objects of a certain type have a uniform size and shape is not necessarily true. Some objects, such as neurosecretory granules, appear to have a uniform shape and size. W h e t h e r there are subpopulations of objects, such as granules of different diameters, can be assessed by comparing a frequency distribution

histogram of the granules with distribution histograms of objects, such as spheres, of uniform or multiple diameters. 17 Tangential sectioning of skin can give an artifactually high n u m b e r for depth of invasion of melanoma. T h e measured region may not be the most deeply invasire region. Similarly, basing distinction between adenocarcinoma and mesothelioma o n finding the longest microvilli to measure subjects this type of analysis to sampling error. Tangential sectioning of long microvilli renders their appearance misleadingly short; conversely the longest microvilli may not be sampled. Characterizing the proximity of tumors to surgical margins is usually based on a single 6-#m section taken from a 3-ram-thick block of tissue. Based on the assumption that the tumor has a uniform distance to the margins, a single section would be considered representative. However, analysis of the 2,000 or more serial sections of a radical prostatectomy specimen showed that this assumption is not necessarily valid because cancer abutted the margin in multiple additional foci in the serial sections. 172 Assumptions about uniformity of size and shape are essential for efficient object counting. In two-dimensional sections, mitochondria appear to have relatively uniform sizes and shapes. However, in at least one type of cell, thick sections demonstrate that what appears to be multiple mitochondria in a single cell are actually sections from a single, complex, branched mitochondrion. 173 In an object o f such irregular size and shape as the region of cancer in a prostate, the error in reproducibly measuring the region is potentially large. T h e large size of error in this morphometric application may explain why the technique of determining volume by visual estimation of area 47yields correlations that are similar in prognostic ~ower to more precise m o r p h o m e t r i c m e a s u r e m e n t s ) 2 Bladder cancer provides a n o t h e r example in which chromosomal n u m b e r estimated by FISH in sections underestimates the n u m b e r of chromosomes determinated by FISH on dissociated, three-dimensionally intact cells. 16s Because not all chromosomes are sampled in sections, the rate o f undersampling FISH signals has been rep o r t e d to be 60% that of whole nuclei. 174 Recently developed m o r p h o m e t r i c approaches deal with some of the issues of complexity of size and shape of objects and the limitation o f two-dimensional representations o f objects in deducing stereological infor-mation. J75 As discussed above, uncertainty about the uniformity o f the size and shape in the vertical dimension o f the object o f interest, eg, the region that is cancer or a specific region in the brain, can be a large source of error. In such situations, volume can be determined using the Cavalieri method. 39 If object n u m b e r is not important, the degree to which a class of objects contributes to total volume can be determined by calculating the area fraction of the object. T h e r e are other situations where the assumption that objects have a uniform shape is not valid. Cancer nuclei in biopsy specimens are smaller and r o u n d e r than in prostatectomy specimens of the same tumor. 176 Furthermore, the shape of nuclei in prostate cancers that invade periprostatic tissue is more out o f r o u n d

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than portions of the same nuclei within the prostate. A consequence of a n o n u n i f o r m distribution of nuclear roundness is that the m o r e " o u t - o f - r o u n d " nuclei may not be sampled in a biopsy of the prostate gland. Because nuclear roundness is a prognostic m a r k e r of prostate cancers, the origin of a sample affects the prognostic accuracy o f the m e a s u r e m e n t . A n o t h e r type of assumption m a d e a b o u t h o m o g e neity of objects that are within a field of viewing or illumination is that the illumination a n d virtual image of the objects are n o t distorted by the light source or the optical path. Although software p r o g r a m s have shading correction routines that are designed to correct for a b a c k g r o u n d that is n o t uniformly illuminated, it is preferable to have a light source a n d optical path that are as n e a r uniform as possible. 18'161

Efficiency of Analysis Because quantification o f tissue p h e n o m e n a can be laborious, efficiency in data collection should be maximized. W h e n the object of interest represents a small fraction of the population, the most efficient way to decrease variability is to increase sampling at the level where variability is greatest. A rule o f t h u m b is to ~, do m o r e less well. ~ , 1 7 7 ' 1 7 8 In assessing the effect of magnification on the area fraction o f hepatocytes that is SER, investigators f o u n d that the most efficient way to decrease variability was to measure SER in a large n u m b e r of animals, in contrast to measuring m o r e profiles of SER in a larger n u m b e r of hepatocytes f r o m the same n u m b e r o f animals. 17s Very accurate measurements can be m a d e with current c o m p u t e r systems. However, one should resist the temptation to obtain very accurate m e a s u r e m e n t s of a small n u m b e r of objects, at least until the contributions of intersubject and interorgan variability to total variability have b e e n assessed. In measuring the m e a n nuclear area of transitional cell carcinomas, interobserver variation acc o u n t e d for 50% o f total variability; this e x c e e d e d other assessed sources o f v a r i a t i o n - - i n t e r p a t i e n t , interlaboratory, intraobserver, interfield, a n d internuclear. 2° O n e goal is to achieve an o p t i m u m balance between sampling an image at a high rate, or high sampling density, or sampling m o r e quickly at a lower sampling density. A rule of t h u m b is to sample at a density of 0.5 × the smallest resolvable feature, or linear dimension, of the object o f interest. T e r m e d the Nyquist criterion, this is equivalent to sampling at twice the highest spatial frequency. A c o n s e q u e n c e of this sampling app r o a c h is that objects that are smaller than the object or objects o f interest will not be representatively sampled.

PROSPECTS AND FUTURE DEVELOPMENTS Future Prospects

M o r p h o m e t r y is not currently considered to be a standard tool to be used by anatomic pathologists in the evaluation of cells or tissues or in the tissue-based diagnosis or prognosis of disease. T h e r e are various

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TABLE 6. 1. 2. 3. 4. 5. 6. 7.

Future Prospects

Training in morphometry Acceptance as a standard of practice Reimbursement Proof of value Expense (money and time) Standardization Competition with other types of tests

explanations as to why m o r p h o m e t r y is not widely used as a diagnostic tool (Table 6): 1. Training in m o r p h o m e t r i c and image analysis techniques a n d in the interpretation and analysis of quantitative structural data is not a comp o n e n t of conventional pathology training. However, m a n y practicing pathologists are interested in learning quantitative techniques for assessing cells a n d tissues. Several pathology societies in N o r t h America, including the American Society of Clinical Pathologists, College of American Pathologists, and the United StatesCanadian Academy of Pathologists, sponsor continuing education courses in m o r p h o m e t r y a n d image analysis. 2. M o r p h o m e t r i c analysis has not b e e n accepted as a standard of practice by any national organization for any disease. Although quantitative data is expected to be r e p o r t e d as a pathological p a r a m e t e r for a variety of tumors, eg, d e p t h of invasion of m e l a n o m a , size of primary tumor, volume of prostatic a d e n o c a r c i n o m a in radical prostatectomy specimens, there is no expectation that these values are based on a m o r p h o metric technique that is any m o r e complex or precise than a linear m e a s u r e m e n t or a visual estimate. 3. Third-party payers have not, in general, recognized m o r p h o m e t r y as a diagnostic tool that is reimbursable. F u r t h e r m o r e , m o r p h o m e t r y is not a Food and Drug Administration (FDA)approved diagnostic procedure. Obstacles to FDA approval have historically included the lack of p r o o f of efficacy a n d the lack of a standardized a p p r o a c h that can be applied, with reproducible results, by different laboratories. T h e lack of standardized ways of p r e p a r i n g tissue and p e r f o r m i n g m o r p h o m e t r y produces different results. T h e first m o r p h o m e t r y - b a s e d applications that will probably receive FDA approval are a u t o m a t e d cytology systems. 4. W h e t h e r quantitative values would be o f greater prognostic value were m o r p h o m e t r i c approaches to be used is unknown. Comparison of visual estimates with morphometrically determ i n e d values with respect to accuracy and reproducibility have, in general, n o t b e e n undertaken for any disease. In the few situations in which such comparison studies have b e e n conducted, m o r p h o m e t r y has not proved to be of greater clinical value. For example, the survival

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of patients with superficial bladder carcinomas is no more accurately predicted by mean nuclear area than by visually estimated grade, when controlled for tumor stage. Justifying use o f morphometry, a technique that is more expensive and time consuming than visual estimates of tissue changes, would entail demonstration of greater accuracy and efficacy despite greater cost o f time and materials than is involved in routine microscopy. A statistical tool that could be used to make such comparisons is receiver operator curves analysis, ly9 Receiver operator curves compare the sensitivity and specificity of different assays. T h e area in which m o r p h o m e t r i c techniques might be of greatest value is in providing prognostic information for chronic diseases such as cancer. In general, multiparametric analyses have shown that structural features of tumors that are based on qualitative gross and histological features are of greater predictive power than is quantitative data based on single parameters. ~8° However, quantitative data has been shown to contribute to determining prognosis. For example, the n u m b e r o f mitoses and t u m o r size TM are quantitative values that increase the prognostic power of predicting the course of breast cancer in individual patients. However, the contribution appears not to be so great that the precision of m o r p h o m e t r y is required to increase the prognostic accuracy. 5. T h e r e is a perception that the expense o f morp h o m e t r y - - i n both c o m p u t e r hardware and in t i m e - - i s not justified by the value of the results. However, less expensive techniques can be used. For example, the size and shape features of cancer cells can be d e t e r m i n e d by counting intercepts of overlaid grids. 175Although the value of time required for m o r p h o m e t r i c analyses relative to other techniques has only rarely been evaluated, the time required to do some analyses has b e e n reported. Counting breast cancer cell mitoses averaged 10 minutes per case16Y; 15 minutes per case was required to measure nuclear volume and tabulate mitotic frequency. 59W h e t h e r the data resulting from a specific m o r p h o m e t r i c analysis is worth the time and effort is unknown for virtually all potential applications. Currently, there is no d e m a n d for any more precision or reproducibility than is obtained using current n o n m o r p h o m e t r i c approaches. Furthermore, there is no p r o o f that outcome or response to a particular therapy is sensitive to a specific threshold; multiple parameters are used in stratifying patients by therapy and outcome. 6. T h e lack of standardization in m o r p h o m e t r y has probably delayed its m o r e widespread use. Many potential sources of error cited previously can be minimized by standardization of tissue handling, acceptance o f uniform criteria for identifying objects, standardization of analytical ap-

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proach, eg, n u m b e r of fields, n u m b e r of cells, magnification, criteria for scene segmentation, criteria for identifying the object of interest. Without standardized criteria, data from different studies may not be comparable, and multiinstitutional assessments of the value of m o r p h o m e t r y cannot be undertaken. It is also important to know which values are near thresholds and thus warrant particular attention. Examples include melanomas invasive to 0.76 to 1.5 cm l~s and prostate carcinomas with volumes of 0.5 mL, 3 mL, and 10 mL. 121 7. Some potential m o r p h o m e t r i c applications have been supplanted by biochemical and molecular tests. For example, m o r p h o m e t r y was required to show that some relatives of patients with MEN II syndrome have an enlarged adrenal medulla. ~25 Now that the gene for MEN II has been cloned, molecular techniques can be applied to peripheral blood samples to identify a patient with MEN II. 182 Several developments may lead to more widespread use of morphometry: D a t a Analysis

Morphometric data has b e e n handled in various algorithmic manners, usin~ decision trees for classification, ~s~ statistical analysis, ls4 and backpropagation neural nets. 72'~s5 The relative contribution of the value of a parameter to determining a classification c o m p a r e d with the contribution of other parameters can be assessed by multivariate statistical analysis. One consequence of analyzing the relative importance of a large n u m b e r of variables in classifying a small sample size is that an increase in the n u m b e r of variables is associated with an increased probability that some values will correlate by chance. 71 T h e use of discrete thresholds for subcategorizing tumors may have deterred pathologists from using morphometry, out of an impression that the accuracy of measurement was too low to confidently categorize tumors that were near a quantitative threshold. Different methods of data analysis have been useful in showing the relative lack of importance of discrete thresholds. Neural network analysis has shown that the prognosis of breast cancers is not sensitive to threshold values. For example, it is not important to measure tumor size, which is the basis for the T category of TNM staging, with precision. Using conventional patient and tumor staging data, a neural network might be more accurate at predicting the course of disease in a patient with a breast cancer than current TNM staging. ~s6 However, the degree of precision with which such measurements n e e d to be made is unknown. ~s~ A neural network has shown that m o r p h o m e t r i c parameters are more useful in distinguishing low-grade hepatocellular carcinoma from benign liver conditions, y° Tubular carcinoma of the breast can be distinguished from sclerosing adenosis based on glandular surface density and the coefficient of variation of the luminal form with 96% success using a neural net. For comparison of low-grade thyroid

MORPFIOMETRY IN PATHOLOGY (Lawrence D. True)

neoplasms, analysis of m o r p h o m e t r i c differences by a neural net provides more accurate classification than a discriminant analysis of the same data. ]87 Because the net had not been taught to recognize such other small gland proliferative processes of the breast as microglandular adenosis and ductal carcinoma, which infiltrate as small glands, these diseases could not be identified. 9a

For example, the surface of trabecular bone cannot be described in fractal terms. 194

Acknowledgment. Discussions with Drs David Weinberg and Chester Herman were very helpful in developing some of the ideas expressed in this report. REFERENCES

Types of D a t a

Developments in both hardware and in mathematical approaches have increased the n u m b e r of potential applications and the potential value o f morphometry. Digital devices are more reliable and yield more accurate, reproducible data than analog devices. For example, the linearity of response to light and the stability of charged couple device cameras are better than analog cameras. Stereological values have been extrapolated from two-dimensional information. Assumptions about uniformity of object size and shape must be made. Confocal microscopy enables the investigator to directly determine object thickness. ]46 Confocal microscopy has also been used to improve image resolution. Furthermore, math techniques have been developed to determine object thickness ~4'~ and three-dimensional shape, b~ using an algorithm t e r m e d the "optical dissector. ''1'5 T h e volume-weighted m e a n volume used in r a n d o m o r i e n t a t i o n p i n d e p e n d e n t of nuclear shape--gives information about nuclear size with variability of nuclear size.4~ T h e volume-weighted mean nuclear volume is of greater prognostic power than t u m o r grade in superficial transitional cell carcinomas, but not in T2 bladder tumors. ~1 The development of procedures and algorithms that provide accurate three-dimensional data raises the prospect that complex shapes can be accurately evaluated. Attempts to grade carcinomas, using grading schemes that are based on characterizing gland size and shape, are being developed. 1~4"]8s A relatively novel type o f histopathological datum is the fractal dimension.]89 As described previously, the fractal dimension is an expression of the complexity of a scale-independent shape. T h e type of fractal dimension used to measure object complexity depends on the context of the object. C o m m o n fractal dimensions applied to biological structures are the divider dimension and the box-counting dimension. In the divider method, the length o f a boundary, eg, the coastlines of countries and the surface of cells, is measured with a range of different scales. The log o f the line length is plotted against the log o f the scale length. 66 In the box-counting method, the log of the n u m b e r of squares or boxes contained in the object outline is plotted against the log o f the reciprocal of the box size. ag° Normal structures, including the bronchial tree and the renal arterial system, branch in a fractal manner. ~9L192 Diseased structures, including the interface between an invasive tum o r and the stroma, I9~ the surfaces o f leukemia cells and of different types of colonic polyps, can be distinguished by their different fractal dimensions. ]3°'171 Not all complex histological forms have fractal dimensions.

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