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Page 1: Quantitative morphology: methods and materials∗ I. Stereology and morphometry

EUROP. J. OBSTET. GYNEC. REPROD. BIOL., 1977,7/l, 43-52 0 ElsevierlNorth-Holland Biomedical Press

REVIEW ARTICLE

Quantitative morphology: methods and materials* I. Stereology and morphometry

J.P.A. Baak *, J. Oort, G.M. Bouw ’ and L.A.M. Stolte ’

Department of Pathology and ’ Department of Obstetrics and Gynecology, Free University Hospital, De Boelelaan Ill 7, Amsterdam, The Netherlands

_

BAAK, J.P.A., OORT, J., BOUW, GM. and STOLTE, L.A.M. (1977): Quantitative morphology: methods and materials. I. Stere- ology and morphometry. Europ. J; Obstet. Gynec. reprod. Biol,, 711, 43-52.

In quantitative morphology, two lines can be discerned: (1) stereology and morphometry, and (2) densitometry. Using these methods, differences can be demonstrated which are missed with the routine subjective methods. This paper deals with stereology and morphometry. Stereological procedures which aRow the assessment of volume percentages, surfaces, lengths, numbers, and diameters are discussed in the light of dimension reduction. The effect of tissue shrinkage on these parameters is considered. Finally, application of stereological procedures to an endometrial biopsy is shown.

quantitation; dimension reduction; tissue shrinkage; example

Introduction

The diagnosis of a pathologist may be of a qualita- tive and a quantitative nature. For example, ‘basal cell carcinoma’ is a qualitative diagnosis; hyperplasia

of the islets of Langerhans is an example of a quanti-

tative decision.

Generally speaking, quantitative analysis of micro-

scopical pictures has long been subordinated to quali- tative description. This may have been caused by the preference of the human mind for pattern recognition rather than quantitative appraisal. Whereas the human capacity to detect minimal qualitative changes is very outstanding, quantitative estimations are remarkably inaccurate, This is especially obvious if it is remem- bered that a red circle surrounded by a green zone seems to be of a different size than an isodiametrical green circle enveloped by a red zone.

* Fellow of the Royal Dutch Cancer Foundation.

However, in recent years there has been an increas- ing interest in quantitative microscopy, and especially in the quantitative evaluation of microscopical pic- tures by measurements and calculations. There are several reasons to explain this.

Subjective estimations of quantitative features are often very inaccurate, and quantitative differences and changes may be too small to be recognized with the naked eye. Measurements, however, do reveal these minute differences (Weibel and Elias, 1967; Weibel, 1969). This is especially true if large (bio- logical) interindividual differences and changes are present. The more so, if features show considerable time- or age-dependent variations. Another reason for objective measurements is the need to express descriptions in objective terms, in order to ensure adequate comparisons or to allow correlations with other data (e.g. biochemical values, clinical data).

All this is especially true for gynecopathology. Fo’i example, endometrium shows important age- and

43

Page 2: Quantitative morphology: methods and materials∗ I. Stereology and morphometry

44 J.P.A. Baak et al.: Quantitative morphology: I. Stereology and morphometry

time-dependent variations.. In the endometrium there is a close interrelation between structure and function, as hormonal changes are reflected in mor-

phology (Dallenbach-Hellweg, 1975). And indeed,

quantitative methods in microscopy have shown to be

very useful in this field of pathology. A striking

example of this is the study of endometrium after

bleeding due to progesterone loading. For more than

forty years, this bleeding could not be explained by

routine microscopical examination, as these endome-

tria looked perfectly normal. However, the applica- tion of quantitative methods revealed significant dif-

ferences (Boschma, 1974; Boschma, Baak, Oort and

Stolte, 1974). Another example is the detection of

differences in the placenta of small-for-date babies

and normal fetuses (Bouw, 1975). Finally, many arti- cles stress the importance of quantitative microscopy

in cytology (see Wied and Bahr, 1971). For all these reasons, it is to be expected that

quantitative methods in microscopy will become more and more important, especially in gynecopa- thology. Therefore, an overview will be given of methods and materials in quantitative morphology. The term ‘quantitative morphology’ instead of quantitative microscopy is used, if it is the structure

of the three-dimensional organ and not the micro- scopical section itself in which we are interested.

Different approaches to quantitative microscopy

In quantitative microscopy different approaches

can be discerned. The most simple and widespread

method is that of estimating the feature subjectively:

the number of glands is increased, there are many mitoses, etc. As argued above, subjective assessments

of quantitative features are very inaccurate. So, this

technique only can be regarded as reliable if large dif-

ferences or changes are present. No doubt, it is the

simplest and fastest method available for quantitative

evaluations. A second approach is the method to assign the fea-

ture class-wise, for example as absent, moderate and

severe (perhaps indicated as +, ++ and ++t). This method has been used frequently, e.g. to assess the

degree of inflammation or tissue damage. A third approach is the application of measure-

ments as a part of routine examination of sections.

This, for example, has been applied to the above-

mentioned diagnosis of hyperplasia of the islets of Langerhans in the pancreas.

The fourth type is the mere use of quantitative methods, without using qualitative descriptions. This method has been applied by many authors to various specimens, both cytological and histological. Exam- ples of quantitative cytological investigations are computer recognition of cell nuclei from the uterine

cervix (Bibbo, Bartels, Bahr, Taylor and Wied, 1973), the study of the effect of intrauterine copper on the DNA content in isolated human endometrial cells

(Hagenfeldt and Johannisson, 1972), and evaluation

of Papanicolaou stain for quantitative microscopy (Bahr, Bartels, Bibbo, De Nicolas and Wied, 1973).

Quantitative microscopical investigations of histo,og-

ical specimens are very numerous, as are those dealing

with mammary carcinoma (Underwood, 1972), coro- nary and aortic atherosclerosis (Rissanen and Pyoralill,

1972) and immunohematological diseases (Tsuna-

kawa, 1968; Schenk, 1971). Naeye (1965) in a very

detailed study, described organs from infants of dia-

betic mothers. Furthermore, quantitative microscopy

has proven to be useful in the study of the ‘sudden

infant death syndrome’ (Baak and Huber, 1974a,b,

Emery and Carpenter, 1974; Naeye, 1974). In the foilowing we will restrict the terms ‘quan-

titative morphology’ and ‘quantitative microscopy’

to those investigations which are exclusively quantita-

tive in nature (approach four in the above mentioned

distinction). In quantitative microscopy, two lines can be dis-

cerned: 1. stereology and morphometry, and 2. densitometry. Stereology includes methods that allow direct deri-

vation of quantitative features of structures from

two-dimensional sections, on the basis of geometrico-

statistical reasoning (Weibel, 1969).

Mqphometry is the quantitative description of a

structure (and thus it can be the result of stereology). Densitometry is measurement of the absorption

(=extinction = optical density = the amount of light

absorbed by a certain object) (Atkins, 1970). Whereas stereology and morphometry are exten-

sions of simple measurements performed in sections, densitometry (or photometry) has come from another point, namely attempts to automatize micro-

Page 3: Quantitative morphology: methods and materials∗ I. Stereology and morphometry

J.P.A. Baak et al.: Quantitative morphology: I. Stereology and morphometry 4.5

scopy. So far, in gynecology quantitative microscopy has largely been restricted to cytology and to

attempts to automate cytology, and densitometry has formed the major part of this quantification. How- ever, the development of rapid methods for electron-

microscopical sample processing of cytological speci-

mens makes it probable, that stereology and morpho- metry will become more important even in cytology.

The more so, since in the histological preparation of

gynecological specimens, stereology and morpho-

metry have proven to be very useful (see above), and

also because stereology is essential in those situations,

in which sections of cells or tissues are made, as will

be explained in the following.

solutions should be developed. For example, in the guinea pig thymus we have found a tendency for cor- tical layers to be arranged in the direction of the long

axis of the thymus lobe. The solution was simple: all sections were mounted with their long axis perpen-

dicular to the longest side of the glass slide (Baak and

Huber, 1974b).

In this paper we will pay special attention to ste-

reology and morphometry. Another paper will deal with densitometry, as part of techniques and appara-

tus to quantitate and automatize microscopy.

The total standard deviation Stat is the result of the biological variation Sr,, the measurement error

S,, and observation inaccuracy S,. The latter defines the minimal error of the measurement, and so, the

sample size. Estimation of the latter is important not

only because of accuracy, but also because of eff- ciency. It should therefore be remembered that the size of a probability interval is diminished only with the square root of the sample size increase (u-

m). If a representative sample is obtained, a stereolog-

ical formula can be applied.

Stereology and morphometry Stereological formulae

For light and electron-microscopical study of tis- sues and electron-microscopical study of cells, micro-

scopical sections are needed. These sections are thin enough to be regarded as two-dimensional samples of a three-dimensional specimen. Therefore, during tis-

sue processing dimension reduction takes place. This reduction has important consequences for the quanti- tative features of structures in the specimen (Weibel

and Elias, 1967; Weibel, 1969), since measurements in microscopical sections are not directly representa- tive for the quantitative features in the organ. To

overcome this difficulty, stereology is needed.

Stereological formulae have been intensively

reviewed by several authors (Weibel and Elias, 1967;

Underwood, 1970; Fischmeister, 1975). Therefore, in

this paper, we will restrict ourselves to summarizing

the most important of them in Table I, and simply

give some comments to this table.

Using point-counting, a three-dimensional feature

has been reduced to zero dimension. Hilliard and

Cahn (196 1) have shown, that the overall error in the

assessment of volume percentages with point-

counting is smaller than with the other methods.

Moreover, point-counting has great practical advan-

tages. Tissue sampling

Tissue sampling precedes measurements and ste-

reological reasoning, and is essential for morphometry

(Chalkley, 1943). As to this, two factors are of im- portance, being the presence or absence of a certain orientation of the structure in the organ ((an)iso- tropy) and the total standard error of the result.

Typical examples of anisotropic organs are skeletal muscles and lymph nodes, whereas thymus and thy- roid are isotropic. Therefore, a qualitative evaluation precedes stereological analysis. Depending on the

result, the sample is taken. In doubtful cases, special

Estimation of the accuracy of the measurement is

related to the number of points applied and the vol-

ume density of the structures. Weibel (1963) has given a graphical representation of the relation between these factors together with the relative error of the result, E,. Theoretically, the larger the number of points applied, the smaller E,. However, in no case

should the error exceed the observation error S,, which can be assessed by recounting the same picture several times.

The dimension of the outer surface of three- dimensional structures in organs is reduced in the same way as their volumes during tissue sectioning.

Page 4: Quantitative morphology: methods and materials∗ I. Stereology and morphometry

TA

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Page 5: Quantitative morphology: methods and materials∗ I. Stereology and morphometry

J.P.A. Baak et al.: Quantitative morphology: I. Stereology and morphometry 47

b Linear integration

c Pobnt counting d. Curvlmetry

Fig. 1. Illustration of stereological principles for the estimation of volume percentages (a-c), surface densities (d, e) and length

density (f).

Therefore, the profile of a surface (two-dimensional)

is a line (one-dimensional). This is a well-known fact in pathology. For exam-

ple, if the surface of the alveoli in emphysema is

diminished, the length per unit area in the micro-

scopical section is diminished in the same way. Look- ing through the microscope much less alveolar tissue is seen.

In the same way, the length density L, (length of structures in an organ, e.g. the length of blood ves-

sels) is related to the number of intersection points per unit area. If normal distribution can be assumed the usual 95% confidence limits of the above men- tioned measurements can be found with the formula

X, + 1.96a

where X, is the result obtained. Another useful one-dimensional characteristic of

structures in the organ can be calculated with the vol-

ume to surface ratio. From this, mean diameter and

radius of cells and nuclei in the organ can be calcu- lated:

D n,c = v/s X 6

r,,, v/s X 3

The v/s ratio has been used for the estimation of the mean diameter of endometrial glands, and for the assessment of the mean thickness of stromal layers in hyperplastic and malignant endometria. It was found, that both parameters had a high discriminating power

Page 6: Quantitative morphology: methods and materials∗ I. Stereology and morphometry

48 J.P.A. Baak et al.: Quantitative morpholmy: I. Stereology and morphometry

between both groups (Baak, Oort, Stolte, Janssens, Braaksma and De Graaff, 1975).

So far, rather direct relationships existed between the features and their profiles. This is not so for two other features, which are important in routine diag-

nosis, namely diameter distributions and numerical densities.

Diameter distributions are of importance, e.g. in

the diagnosis of aniso-nucleosis. The exact assess-

ment, however, is difficult, and the problems involved

have been thoroughly discussed by Haug (1967) and

Weibel (1969). We will therefore restrict ourselves to

a short description rather than a profound explana- tion.

Let us assume a collection of randomly distributed

isodiametrical nuclei in an organ. The thickness of a

random section, which is taken from the organ is

smaller or of about the same size as the diameter of

the nuclei. From some of the nuclei the greatest dia- meter will be included in the sections, but from

others segments will be sectioned with a smaller

diameter. Therefore, the circular profile distribution in the section will contain smaller circles than the ori- ginal distribution of isodiametrical nuclei in the

organ, as a consequence of which the mean diameter of the circular profiles is also smaller than the mean nuclear diameter. This result can be improved upon by increasing the section thickness. However, optical limitations restrict the possible resolution to the use of routine sections, in which the above-mentioned

presupposition is rule rather than exception (section

thickness in the same order or smaller than the mean

diameter of the spheres). Different methods have been described to calcu-

late the ‘real’ diameter distribution from the circular

profile distribution. The most simple relation is

D2d lr

(Giger and Riedwyl, 1969)

where D= mean diameter of the spheres, and a=

mean diameter of their circular profiles. Elias and Hennig (1967) have developed a graph-

ical method, which can be easily computerized, and in our experience yields good results.

There is no direct relationship between the num- ber of profiles per area and the number of structures per volume (numerical densiry). From a theoretical

point of view, this is understandable. Numbers are of

zero dimension, and in the process of dimension reduction during tissue processing numerical densities

would theoretically disappear. The relative falsity of

this theory is due to the relation between the thick-

ness of the section (which is nearly, but not exactly, two-dimensional) and the diameter of the particles,

which are not really zero dimensioned. Here, also, the

mean diameter of the structures is of importance. In

fact, counting the number of profiles will result in

an overestimation of the numerical density unless sec- tion thickness and mean diameter are also taken into

account, as has been shown by Haug (1967). If sec- tion thickness is small in relation to spherical diam-

eter, other relations are valid. These have recently

been dealt with by Weibel (1969). In recent years, more attention has been paid to

shape factors. According to Underwood (1970) no less than twelve shape factors have been mentioned in the literature, but Fischmeister (1974) has shown,

that only one of those is purely shape dependent, and

unaffected by the absolute values of volume fraction, surface and particle size in a system.

The influence of tissue shrinkege on morphometric

results

Considerable changes in tissue volume occur

during the process of fixation and dehydration in

alcohol. Aherne and Dunnill (1966) measured the

length of tissue blocks before and after tissue process-

ing in order to estimate the linear shrinkage p. From

here areal shrinkage p2 and volume shrinkage p3 were

calculated. The results of stereological data were mul- tiplied with the reciprocal value of the shrinkage fac-

tors (I/p; l/p’; l/p3), and the values obtained were regarded to be representative for the original morpho-

metric features in the organ before tissue processing.

According to Baur (1969) percentage volumes are not influenced by tissue shrinkage. However, due to shrinkage the number of boundaries of profiles as well as the number of their tissue sections (visible in the projection screen of the microscope) increases. Therefore, surface and linear densities increase. So, for the latter two measurements, correction factors should be applied to obtain the original data. In a subsequent paper Baur (1973) discerns homogeneous

Page 7: Quantitative morphology: methods and materials∗ I. Stereology and morphometry

J.P.A. Baak et al.: Quantitative morphology: I. Stereology and morphometry 49

and heterogeneous (equable and unequable) tissue shrinkage. The first deals with tissues in which all component parts shrink to the same extent, in con- trast to tissues showing heterogeneous shrinking. For

both, correction formulae are given (Baur, 1973):

Heterogeneous shrinkage

v,q;.’ P3

s, = s,* -L . P2

Homogeneous shrmkage

v,=v,* S,=S$.p

where V,* and S$refer to data after fixation.

Sometimes it may be advisable to control tissue

shrinkage in paraffin by other mounting media, such as celloidin. Much less shrinkage is induced by the latter. This method has been used in placental mor-

phometry (Bouw, 1975). The routine method of fna-

tion and dehydration with formalin (or formalin-con- taining fixations) and alcohol result in shrinkage to

about 75% of the original volume. Since this is a con-

stant finding with very little variation, for most cases a roughly estimated shrinkage factor may give satis-

factory results. It can even be postulated that no

correction is needed at all, if tissue processing and shrinkage remains the same. In that case the same

error is constantly considered. For the correlation of

physiological and morphological data, however, a

more exact calculation may prove to be necessary.

An example of a stereological analysis of endometrial

biopsies

It is our intention to give an impression of how a

stereological analysis works rather than to apply all possible combinations of all possible stereological for- mulae .

Random sections, cut at 6 pm thickness and stained with haematoxylin and eosin are used. Sec- tions are examined with the aid of a projection micro- scope (e.g. Visopan, Reichert; Glarex, Zeiss) *. A 16-

* We have used the Glarex, and the measurements of the lat- tice are suited for the projection screen of this apparatus. The type of microscope, however, is not essential.

points coherent test system according to Weibel, Kistler and Scherle (1966) was used. In this system, the end points of the short lines are arranged triangu- larly. These points can be used for volume density estimations, while the total length LT of the short

lines is used to count the intersections with bound-

aries of profiles to assess surface densities. The total

test area AT defined by the total number of test

points Pr and the unit area A of one test point is used to assess linear densities and, if desired, numerical

densities. If Pr is the total number of test points, the

total test line length LT is

(= 29.93 mm in this case, since Pr = 266) .

where z is the length of one test line divided by the

magnification factor. The test area A, is

A, = fix Z' = 0.088 mm2

where A,, is the area of one test point.

In our case, the total test area AT is

Ar = f Pr X flX Z' = 23.40 mm2

The measurements of the lattice are 9 X 8 cm.

Stereological analysis (schematically shown in Fig.

2) was as follows. At Xl00 magnification (objective

X 10) glandular and stromal tissue is differentiated

using a leukocyte counter. Starting at the left upper corner of the specimen, the tissue is counted in chan-

nels 1 (stroma, symbol: PJ, 2 (glandular epithelium, symbol: Pge) and 3 (glandular lumina, symbol: Pa). If these counts are performed in one field, surface densi-

ties of inner and outer surface of the glands are regis- trated in channel 4 (outer surface of the glands =

contact surface of glands and stroma (symbol: Ior)

and channel 5 (inner surface of the gland, symbol:

Its). Hereafter, the number of glandular transsections in the field are counted in channel 6 (length density of glands, symbol: Q). Glandular profiles which are

partly outside the test area are counted if they con-

tact the upper and left side, and ignored if in contact with the lower and right side of the test area. In all

measurements, distorted tissue or empty places are ignored. All measurements in channels l-6 having

been performed, the next field in the X-direction is measured, and so forth. The results of the countings

Page 8: Quantitative morphology: methods and materials∗ I. Stereology and morphometry

50 J.P.A. Baak et al.: Quantitative morphology: I. Stereology and morphometry

Test screen: 16 points, objective X 10 y

I

Count in one field

Stroma - Channel 1 Glandular epithelium - Channel 2 Glandular lumen - Channel 3 Outer surface - Channel 4 Inner surface - Channel 5 Transsections glands - Channel 6

Ignore distorted tissue, empty places /

No -~GO to next field

[+I Regrstrate counts and calculate

Fig. 2. Schematic diagram of the stereological analysis.

in a part of a curettage are shown in Table II. In

Table III, the names of the measurements together with the calculations from these measurements and

the results of the latter are shown. From Table II the

total area results, being Cp, t P,, t Pd) X A,, or

266 X 0.088 mm2 = 23.41 mm2. It also gives the ratio

of stromal and glandular volume densities, i.e. 244 : 42 = 5.8. With the original results, some more

calculations can be made, using the volume to surface ratio. The glands can be regarded as cylinders, and therefore, the mean diameter Ti follows from the for- mula D= 2r = 4 v/s. The mean thickness of the glan- dular epithelium can be calculated as follows: calcu- late the mean diameter of the lumina (1); calculate the mean diameter of the glands (2); subtract (1) from (2); divide the result by 2.

A probably less accurate result is obtained if the mean distance between the outer surfaces of glands is

calculated. This can be done by regarding the inter-

mediate stroma as layers, or broad sheets. This un-

doubtedly is an approximation, at best, and the result should be interpreted with care. The formula used is:

D = 2 v/s, and the result: k250 pm.

TABLE II Results of the countings in a curettage

Channel Counted Symbol * Result

1 Stroma 2 Glandular epithelium 3 Glandular lumen 4 Outer surface glands 5 Inner surface glands 6 Transsections glands

* see text.

ps 224 Rge 23 Rat 19 I a 101

62 176

Page 9: Quantitative morphology: methods and materials∗ I. Stereology and morphometry

J.P.A. Baak et al.: Quantitative morphology: I. Stereology and morphometry

TABLE III Measurements, calculations and results of the stereological analysis of a curettage

No. Name Formula *

1 Percentage volume stroma p$pT 2 Percentage volume glandular epithelium Pge/PT 3 Percentage volume glandular lumen Pgl/PT 4 Percentage volume glandular tissue Pg/PT 5 Total area stroma Ps X Ap 6 Total area glandular epithelium Pge X Ap I Total area glandular lumen Pgl X Ap 8 Total area glandular tissue PgX AP 9 Total area endometrial tissue pT x Ap

10 Surface density outer surface glands 2 x k&T 11 Surface density inner surface glands 2 X Iig/LT 12 Length density glands 2 X Q/VT X ApI _ 13 Mean diameter glands D = 4 v/s = 4 X (‘4’1‘10’) 14 Mean thickness glandular epithelium T = @glands-Dlumina)/Z = (‘13’ - t4 X (‘3’/‘11’)])/2 0.013 mm 15 Mean thickness stromal layers Ts = 2 v/s = 2 x ‘l’i‘l’ 0.249 mm

84.2% 8.1% 1.1%

15.8% 19.7 mm2

2.02 mm2 1.67 mm2 3.69 mm2

23.40 mm2 6.75 mm2/mm3 4.14 mm2/mm3

15.04 mm/mm3 0.094 mm *

* The figures in inverted commas denote to the result of that number in this table; for the numbers 1 to 4, the result is the percent- age of lmm”.

51

Result

Conclusions

Stereology and morphometry seem promising

because of their possibility both to objectivate, and

to detect differences, which cannot be assessed with subjective methods. There are several studies indi-

cating their clinical relevance. Yet we are still at the

beginning. Therefore it is to be expected that quanti-

tative methods in microscopy will become more and

more important, especially in gyneco-pathology.

References

Aherne, W. and Dunnill, MS. (1966): Quantitative aspects of placental structure. J. Path. Bact., 91, 133.

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