Method of morphometric evaluation of spinal and autonomic ganglia

Journal of the neuroloyical Sciences, 1974, 22 : 65-71

65

i ' Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

Method of Morphometric Evaluation of Spinal and Autonomic Ganglia KENNETH OFFORD, MICHIYA OHTA, ROGER F. OENNING AND PETER JAMES DYCK

Mayo Clinic and Mayo Foundation, Rochester, Minn. (U.S.A.) (Received 25 September, 1973)

INTRODUCTION

Systematic morphometric studies of spinal and autonomic ganglia of man in health and in diseases of the peripheral nervous system have not been reported. This lack exists because these ganglia often are not removed at autopsy and because semiautomatic methods have not been available for determining the volume of ganglia, the number of neurons, and the frequency distribution of the diameters of their cytons (cell bodies). The method described in this report utilizes measurements with an ocular micrometer, a particle-size analyzer, and a digitizer attachment of a programmable calculator (Hewlett-Packard 9810). Computer calculation of the morphometric determinations and their plotting was accomplished with the same programmable calculator and peripheral devices. The method described here is an improvement over previously available methods. It uses the actual diameter of the nucleolus, as judged from consecutive sections, rather than the spurious mean diameter obtained from the distribution of diameters in single sections. It establishes the relationship between nucleolus diameter (Y) and cyton diameter (X). Based on this relationship, it corrects the frequency of a particular diameter of cyton for the split-cell counting error of nucleoli with an associated diameter. The correction used is an application of Abercrombie's formula (1946). HISTOLOGIC METHODS To measure the ganglion volume and the number and sizes of nerve cells, the ganglion has to be removed in its entirety at autopsy. In these studies fixation has been according to the schedule outlined by Ohta, Offord and Dyck (1974). The ganglion is embedded in paraffin and serially sectioned in the transverse plane at a constant section thickness. A staining procedure that produces intensely-stained nucleoli and enough staining of other cellular elements to facilitate measurement of the diameter of nerve cells is required. For This investigation was supported in part by Research Grants NS-5811 and NS-7541 and Research Contract 72-2200 from the National Institutes of Health, Public Health Service, and by grants from the Gallmeyer Fund, Miller Fund, Upton Fund, and Heller Fund.

66

K. OFFORD, M. OHTA, R. F. OENNING, P. J. DYCK

evaluation of the nucleolus-to-cyton diameter relationship and Ior the counting of ~ucic~ik a~ ocular micrometric method was utilized. The evaluation of nerve cell diameters was accomplished o~ photographic enlargements with the use of a particle-size analyzer. Errors in the results of histometric evaluation may be attributed to postmortem autolysis and artifacts of histologic preparation. The first can be avoided at least in part by using only tissues which are removed within a few hours of death. Artifacts of histologic preparation cannot be entirely avoided. Some variation in section thickness is inevitable, and the section thickness should be measured. Although it is recognized that generalized and localized shrinkage may occur with any histologic preparation, the ganglion-toganglion variation is lessened when the same method is used for all ganglia evaluated. Generalized shrinkage has a lesser effect when the results are expressed per ganglion than when expressed per vohime of tissue, METHOI) Of: HISTOMETRIC EVALUATION ,4bhre~iation~ und Symbol.~ ,4 A(.j)

Coefficient in Y = A + B X + ( ' , \ 2 and Y(k)= A + B X (k)+ CX (k) 2. Cross-sectional area (in mine) observed under mag-area corresponding to j t h photograph corresponding to ith section. B Coefficient in Y= A + BX + C?(-1 and Y(k) = ,4 ~ BX (k) ~ C,\ (k):. C Coefficient in Y = A + B A + C X : and Y ( k ) = A ~-BX(k)-~--('X(k):. CF(k) Correction factor to correct for spht-cell counting error of nucleoli associated with cytons in kth interval of cyton diameters. d(k) Uncorrected n u m b e r of cytons with diameters in kth interval ofcyton diameters a m o n g those whose diameter was measured. d(+) Total uncorrected number of cytons of all sizes whose diameters were measured. DNR(k) Estimate of density of cytons that have diameters in kth interval in entire ganglion: units are number/ram 3. i Refers to specific ith section of I sections. I Total number of sections into which ganglion was sectioned. Note that section I is not necessarily the first section identified as being part of the ganglion nor does the l t h seciion represent the last section so identified. .j Refers to specific j t h photograph taken of some ith section of J photographs, J Total number of sections photographed. ij Section n u m b e r i associated with the j t h photograph (ij = i). k Refers to specific kth of K intervals of cyton diameters. K Total n u m b e r of intervals of cyton diameters. mag-area Magnification used to obtain cross-sectional area. mag-diam Magnification used to obtain diameter of cytons. m(k) Diameter associated with middle of kth interval of cyton diameters (in ram) as observed at mag-diam. NI(j) N u m b e r of nucleoli microscopically observed in section associated with j t h photograph. NI(+) Estimate of uncorrected number of nucleoli in entire ganglion. T Section thickness (in microns). TDNR Estimate of density of cytons of all sizes in entire ganglion : units are number;ram ' TNR Estimate of number of cytons of all sizes in entire ganglion. X Cyton diameter (in microns). X(k) Cyton diameter (in microns)associated with middle of kth interval. Y Nucleolus diameter (in microns). Y(k) Nucleolus diameter (in microns) associated with middle of kth interval. Transverse sections of constant width, T ttm, are cut serially through the entire ganglion. The first and last sections of the ganglion are defined as containing parts of at least 10 cytons, I of which contains a recognizable nucleolus. Beginning with the first section identified as being part of the ganglion and systematically at intervals of approximately 100 sections, up to and including the last section, the entire cross section is observed and photographically enlarged to a known magnification (mag-area). We shall adopt the notation that : j = photograph n u m b e r and j = 1, :., ~ ..... I i = section n u m b e r and i = 1, 2 . . . . . 1 i i ~- i (the section number corresponding to the .jth photograph).

MORPHOMETRIC EVALUATION OF SPINAL AND AUTONOMIC GANGLIA

67

On each of the jth photographs we calculate the cross-sectional area (mm2). The cross-sectional area is obtained with a Hewlett-Packard 9864A digitizer attached to a 9810A programmable calculator. We refer to this area on the j t h photograph corresponding to the ith section as A(j). A section volume (mm3) ' is calculated by multiplying the cross-sectional area, after correction for mag-area magnification, by the section thickness (ram). To calculate the volume between two distant sections, the average of the two section volumes is multiplied by the number of sections between them. The formula for the volume of the ganglion, !~\ is d

V=_~(, 1000×(mag-area)-}T _.___~]~

[G-i, + I]×[A(2)+

+ j=E3[(ij-ij_,)x(A(j)+ A(.j-I)] }.

The next step is to obtain an estimate of the total uncorrected number of nucleoli in the ganglion. To this end, we observe microscopically the number of nucleoli in the same J sections as were photographed. We let NI(j) represent the number of nucleoli microscopically observed in the ith section corresponding to the j t h photograph. If two nucleoli are observed in the same nucleus, only one is counted. Linear interpolation is again used. The uncorrected (for split-cell counting error) number of nucle01i between two distant sections is calculated by multiplying the average number of nucleoli in the two sections times the number of sections between them. Repeating this procedure over the entire ganglion and s u m m i n g the results, we obtain the uncorrected number of nucleoli, NI(+ ), in the ganglion. This can be expressed in the following form:

N I ( + ) = ½.{[NI(1)+NI(2)][i2-i ,+1] + ~ [(ij-ij ,)×(NI(j)+NI(j-1))] }, j=3

The next step involves establishing the relationship between nucleolus diameter, Y, and cyton diameter, X, both measured microscopically in microns. After a nucleolus is identified, a check is made to see if the nucleolus appears in an adjacent section: then the diameter of the nucleolus is measured in the section where it appears largest. In this same section, the diameter of the associated cyton is also measured. Our assumption is that Y=I(X) where we have chosen

Y=/t +BX +CX 2 . A, B, and C are the coefficients obtained by a least squares fit to the parabola. We routinely enter A, B, and C into our program, which is written for a Hewlett Packard 9810 with an on-line tape cassette and 9864A digitizer. A linear relationship between nucleoli diameter and cyton diameter frequently suffices, in which case we enter A and B and set C =0. The choice of the particular form off(X) is arbitrary. If the choice is between a parabola, Y = A + B X + C X 2, and a straight line, Y = A + B X , a formal statistical test is available for testing the significance of C (Snedecor and Cochran 1967). The same J cross sections are then photographed at a known magnification (mag-diam). The diameters of all cytons with a visible nucleolus are measured with the particle-size analyzer. The frequency with which cytons fall into an interval of diameters is recorded. For generality, k refers to an interval of diameters and d(k) = frequency with which cyton diameters were observed in kth interval of diameters k = 1,2 ..... K K

d(+)=

y~ k

d(k).

1

Because the nucleolus is subject to split-cell counting error, the distribution of cyton diameters must be corrected for this error. However, in general, larger cytons have a larger nucleolus and, therefore larger cytons tend to be overcounted and small ones, undercounted. With the coefficients A, B, and C obtained above and X(k), the actual cyton diameter associated with the middle of the kth interval, we could express the nucleolus diameter, Y(k), associated with the kth interval of cytons diameters as

Y(k) = 14+ B [X (k)] + C [X(k) 2] in which

X(k)

1000re(k) mag-diam

and

m(k) = diameter associated with middle of kth interval of diameters in m m (k - 1, 2 ..... K ) .

68

K. OFFORD, M. OHTA, R. F. OENNING, P. J. I)Y('K

We correct the observed cyton frequency m each of tile K intervals by Abercrombics lorw,',lla (1946) ioi the nucleolus diameter associated with each intcrx al. Let CG (k) = correction factor to multiply observed frequency ofcytons with dtametcrs a,;ocmted with kth interval, to obtain corrected frequency associated with that inlerval: m eeneral. J

= ~::: rik)' When parabola is appropriate form of Y(k), T

CF(k) --

ii

4-:/~

T~

2[~0;;;-i~)q . . . . . .

i.l-~m00;;,(k)q~

+ C

i _ _ _

kmag_diam]

v

~mag_diamJ t

We can then compute an estimate of lhe percentage of cytons with diameters associated with the kth interval according to

PNR(k)

100 [CF(k)] [d(k)]

(k = t "~

K}

V liCE(k)] [,t(k)] in which PNR(k) represents an estimate of the corrected percentage of total cytons having diameters in the kth interval of diameters within the entire ganglion. We can also project to estimate the corrected member ofcytons having diameters in the kth interval of diameters within the entire ganglion We represent this for the klh interval by NR(k) in the following formula:

NR(k) =

NI(~-):,< CF(k) × d(k)

d(+)

(k = 1,2 . . . . . K}.

An estimate of the n u m b e r of cytons of all sizes in the entire ganglion, denoted by TNR, hence is

TNR = ~ NR(k). With this information, we can estimate the corrected number of cytons with diameters in the kth interval per m m 3 of ganglion volume. We represent this by DNR(k) in the following formula:

DNR(k) :

NR(k) i:

(k =-!

"1

K)

In addition we can express an estimate of the density of cytons of all sizes, denoted by 1 DNR, by the following formula :

TDNR =

TNR V

VA LI DATIt)N The usefulness of the procedure depends on there being a significant relationship between cyton diameter and nucleolus diameter. To demonstrate that this relationship exists, we made the described measurements on the first sacral spinal ganglion of a 17-year-old boy without known disease of the peripheral nervous system. A straight line adequately represented the observed data: Y - 1.3672 + 0.0674X m ~ hich / is nucleolus diameter (in microns) and X is cyton diameter (in microns). sample size (N) - 100 correlation coefficient (r) = 0.8662. The test for the observed slope being different from zero was highly significant (P < 0.0005). As reported in the following paper (Ohta, Offord and Dyck 1974) we have found a similar significant relationship in all of the 19 first sacral spinal ganglia of m a n studied. Table 1 presents the appropriate correction factors based on the same ganglion, to demonstrate how the correction factor, CF(k), changes with cyton and hence nucleolus diameter. The interval corresponding to k = 4 contained the smallest cyton observed, the interval corresponding to k = 10 contained the mean cyton diameter of the 100 cytons observed, and the interval corresponding to k = 20 contained the largest

MORPHOMETRIC EVALUATION OF SPINAL AND AUTONOMIC GANGLIA

69

TABLE 1 CORRECTIONFACTORS k

m (k)

4 5 10 20

CF (k)

CF' (k)

3.144 20.960 2 . 7 8 0 3.696 24.640 3.028

0.742 0.725

0.755 0.737

6.456 43.040 4.268

0.652

0.658

0.542

0.545

I1.976

X (k)

Y(k)

79.840 6.748

cyton observed. The pertinent data were T=8 microns: mag-diam=150: m(k)=O.936+O.552k and Y(k) = 1.3672 + 0.0674X (k). Hence, CF(k)

=

8 + I 1.3672+0.0674I(0.936+0.552k ) x {\ i 51000~] 0 / J }"

DISCUSSION

The formula used in the determination of ganglion volume yields results similar to the formula of Konigsmark, Kalyanaraman, Corey and Murphy (1969). Although we appreciate the theoretical appropriateness of the formula of Floderus (Konigsmark 1970), which takes into account "unseen or uncounted fragments", we have chosen not to use it for two reasons. First, the change that it introduces into the correction factor, CF(k), is small compared to the role that changing nucleolus diameter plays. To demonstrate this we have included in Table 1 a column labeled CF'(k), a correction factor that includes a correction for "unseen fragments" which we have estimated to have a maximal diameter of 1.0/~m; this can be written as

cr'(k) =

T

in which T and Y(k) are as defined previously and Z = maximal diameter of the unseen fragments (in microns). The formula for the correction factor, CF'(k), obtained by applying the Floderus formula to the previous sample data is CF'(k) =

8

8+

2 .~[1"3672 + 0.0674 (0.936 + 0.552k) ( 1000~l 2 _ IL_012 ' 2 \~/J

The relative importance of the correction for unseen fragments varies, of course, with the section thickness, T, the maximal diameter of the unseen fragments. Z, and the diameter of the nucleolus, Y(k). We think that, with T > 8 pm, Z__< 1 pro, and Y(k)> 2.5 #m, the correction for unseen fragments is insignificant. In addition, it is our speculation that the maximal diameter of the unseen fragment is a function

70

K. OFFORD, M. OHTA, R. F. OENNING, P. J. DYCK

I ./

®i~

Microtome

.

.

.

.

Fig. 1. Diagram showing angle of attack of microtome knite with large and small nucleoli.

of the particle diameter in the sense that, for a given maximal diameter of an unseen particle, Z, it would be easier to obtain such a particle from a smaller diameter nucleolus than from a larger one. The reason is that the unseen fragment from a largediameter nucleolus will be a thinner slice with a smaller angle of attack, 0, to the surface of the nucleolus and hence more susceptible to "sliding over" by the microtome knife (Fig. 1). The second reason for not using the Floderus correction for unseen fragments is the difficulty involved in estimating the maximal diameter of the unseen fragment. The importance of correcting the frequency distribution of cyton diameters for each size of cyton and its associated nucleolus depends on the structure of the original distribution. If the range of sizes is narrow and the nucleolus size is fairly constant, it is of minor importance. If the converse is true, the correction can make a radical difference. With the data in Table 1, suppose we observed 100 cytons in each of the 17 intervals representing the observed diameters in the entire ganglion. In the 4th interval the corrected cytons count would be 74.2; in the 5th interval, 72.5 : in the 10th interval, 65.2 ; and in the 20th interval, 54.2. The mean diameter of nucleoli in the ganglion of the 17-year-old boy, in fact, was 4.189 #m. If one was to use only the mean nucleolus diameter to correct all intervals, the corresponding correction factor, from Abercrombie's formula, would be 8 ...... 8+4.189

0.656

and the corrected count based only on the mean nucleolus diameter would be 65.6 cytons in each interval instead of the appropriate estimates given above. Note that the greatest disparity occurs in the tails of the distribution. By using only the mean nucleolus diameter to correct for split-cell counting error, the number of cytons would be underestimated by 11.6 o,, (0.742-0.656 0.742

x

100 ~;

) ,,

in the 4th interval and overestimated by 21.0~o 0.656 - 0.542

o~42 in the 20th interval.

× lOO OJo

MORPHOMETRIC EVALUATION OF SPINAL AND AUTONOMIC GANGLIA

71

The establishment of the relationship between nucleolus diameter and cyton diameter has been done microscopically on serial sections. If the nucleolus appeared in more than one section, it and the corresponding cyton diameter were measured in the section in which the nucleolus appeared largest. The advantage of this procedure is that one does not measure the spurious diameters of minor segments. The error introduced by such spurious observations is clearly shown in the work of Marrable (1962). SUMMARY

We have demonstrated that, in determining the number of cytons (cell bodies) in a ganglion, it is important to consider the range of sizes of cytons and their associated nucleoli in correcting for the split-cell counting error. We have established the mathematical relationship between nucleolus diameter and cytons diameter microscopically in serial sections. An improved method, utilizing semi-automatic techniques and programmed calculation and plotting, is presented for estimating the volume of the ganglion, the number of cytons of neurons per ganglion, and the corrected frequency distribution of diameters of cytons of neurons.

REFERENCES

ABERCROMBIE, M. (1946) Estimation of nuclear population from microtome sections, Anat. Rec., 94: 239-247. KONIGSMARK,B. W. (1970) Methods for the counting of neurons. In: W. J. H. NAUTAAND S. O. E. EBBESSON (Eds.) Contemporary Research Methods in Neuroanatomy, Springer, Berlin, pp. 315 340. KONIGSMARK,B. W., U. P. KALYANARAMAN,P. COREYAND E. A. MURPHY (1969) An evaluation of techniques in neuronal population estimates: the sixth nerve nucleus, Johns Hopk. reed. J., 125: 146-158. MARRABLE,A. W. (1962) The counting of cells and nuclei in microtome sections, Quart. J. micr. Sci., N.S. 103: 331-347. OHTA, M., K. OFFORD AND P. J. DYCK (1974). Morphometric evaluation of first sacral ganglia of man, J. neurol. Sci., 1974, 22:73 82. SNEDECOR,G. W. AND W. G. COCHRAN (1967) Statistical Methods, 6th edition, Iowa State University Press, Ames, pp. 453-456.