CELL MEASUREMENT 



64 



CELL MEASUREMENT 



cross sections of cell nuclei, the bound- 

 aries of many cells such as sea urchin 

 eggs, nerve cells, the central zone of 

 cells undergoing division, ovarian fol- 

 liculi, glomeruli, blood vessels and 

 ducts, may all be described in terms 

 of their geometrical parimeters. 



A quantitative measurement of the 

 area, eccentricity, and geometric center 

 of these structures may often be made 

 by means of an elliptometer (Hamilton, 

 J. D. and Barr, AL L., Stain Tech., 

 1948, 23, 123). 



Essentially the elliptometer method 

 provides a means of fitting an ellipse of 

 light to a camera lucida drawing of the 

 cell or structure. Alternatively in 

 principle, the camera lucida drawing 

 board may be replaced by a ground 

 glass screen and an ellipse of light of 

 suitably controlled intensity, angle, 

 and size matched to the structure as 

 viewed directly in the ocular of the 

 microscope. In both methods, by 

 direct graphic means, the axes of their 

 equivalent ellipse or ellipse of best fit 

 is then determined. 



In the instrument a variable circular 

 iris such as a camera diaphragm, is 

 used to define a cone of light arising 

 from a point source. Point sources of 

 light provided by a zirconium or con- 

 centrated arc lamp are quite suitable 

 and make possible the construction of 

 the apparatus without the use of a con- 

 densing lens system to define a point 

 source. The cone of light falls upon 

 a screen upon which is mounted a grid 

 of graph paper. An alternative to the 

 above design uses a lens between the 

 illuminated diaphragm and the screen. 

 The lens provides an image of the 

 diaphragm in the perpendicular plane 

 of the screen. 



The screen maj^ be rotated by means 

 of an attached arm which rotates in a 

 sleeve bearing lying parallel to the hori- 

 zontal lines of the grid. By tilting 

 the screen out of the vertical plane it 

 is thus possible to create a family of 

 ellipses. The minor axes will be con- 

 trolled and fixed by the diameter of 

 variable diaphragm. The points at 

 which the ellipse touches the horizontal 

 and vertical grid lines may be deter- 

 mined and the axes calculated by addi- 

 tion. 



In practice the camera lucida draw- 

 ing is placed flat on the screen and the 

 elliptometer aperture and screen angle 

 adjusted to give the best fit. The two 

 ends of the major axes are marked on 

 the drawing for future reference, and 

 the grid values noted. 



Derived Measurements: a) Area: If A, 

 and B, are the major and minor diam- 



eters of the ellipse then the area is 

 K TT A,B,/4 n^ where K is a propor- 

 tionately constant depending on the 

 grid system used and the magnifica- 

 tions entering into the camera lucida 

 tracing. In our experience with motor 

 nerve cells (Barr, M. L. and Hamilton, 

 J. D., J. Comp. Neur., 1948, 89, 93) 

 the areas determined by elliptometer 

 and planimeter measurements agree 

 within five per cent on an absolute basis 

 in comparing individual cells, and the 

 statistical parameters of populations 

 examined by the two methods of meas- 

 urement are of equal value when con- 

 trol and experimental populations are 

 compared. Area measurement using 

 the elliptometer are more rapid and less 

 fatiguing than planimeter measure- 

 ments. 



b) Center and Foci: The center and 

 foci of elliptic sections may be readily 

 determined by using a rule or by graphic 

 methods. If the plane of section is 

 transverse, sagittal, or coronal, a refer- 

 ence line running dorsal-ventral or 

 antero-posterior or medio-lateral may 

 be drawn through the center of the 

 elliptic figure. The orientation of the 

 ellipse or the location of inclusions or 

 other features of the figure, may then 

 be measured with respect to the axes 

 of the body as a whole. By this type 

 of orientation and definition for ex- 

 ample, it has been possible to show that 

 the axone hillock of motor cells of the 

 dorso-lateral group of the ventral horn 

 arise predominantly in the ventral 

 medial quadrant of the cell. 



c) Eccentricity: The eccentricity is 

 the ratio of the minor to the major 

 axis B/A. The eccentricitj^ of indi- 

 vidual sections may possess some value 

 as a descriptive measurement. The 

 average eccentricity of populations may 

 be of value in following the time course 

 of changes of shape, as for example in 

 hypertrophy, cell division, or blastula 

 development. 



d) Cell Shape and Value: Consider 

 an ellipsoid having major, intermediate, 

 and minor diameters, A, >B, -^ C, 

 lying at random in space related to the 

 plane of section. The eccentricities of 

 sections drawn from an ellipsoidal 

 population, homogenous in respect to 

 shape (but not necessarily size) will 

 range from a maximum C/B (which 

 may be unity if the body is an ellipse 

 of "revolution) to a minimum C/A. 

 This distribution of eccentricities is 

 true even if the plane of section does 

 not pass through the center of the el- 

 lipsoid. 



The eccentricity data may be used 

 to secure an estimate of the shape and 



