29
Clinica Chimico Acta, 65 (1975) 29-37 0 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
CCA 7321
AN AUTOMATED, DIRECT METHOD FOR MEASURING AD~OCYTE CELL SIZE
MICHAEL P. STERN* and FRED CONRAD Stanford Heart Disease Prevention Program, of Medicine, Stanford, Calif. (U.S.A.)
Stanford
University
School
(Received May 26,1975)
Summary Current methods for direct determination of fat cell size are optical and non-automated. They are thus tedious, but have the advantage of providing estimates of the variance of a cell size distribution, as well as a measure of the mean cell size. An indirect method based on counting the number of osmiumfixed fat cells derived from a known wet weight of adipose tissue is also available. This method is automated and thus rapid, but does not provide information about the variance of the cell size distribution. In the present paper we describe a direct, automated method of fat cell sizing that provides estimates for both mean cell size and the variance of the cell size distribution. The correlation between our method and an indirect method based on counting osmium-fixed cells was 0.96. Transformation of the volume distribution to diameters indicated that cell diameters appeared to be normally dist~bu~d, confining the observations of others.
Introduction In recent years me~urements of the size of adipocytes from both human and animal sources have found a wide variety of applications in bio-medical research. Two basic approaches (one direct, and the other indirect) have been used to make these measurements. Ordinarily, the direct approach is optical in nature and non-automated. Individual fat cells are observed under a microscope and are sized directly using a calibrated eyepiece. Typically, several hundred cells must be sized in this way in order to obtain statistic~ly valid results. The optical approach is thus extremely tedious. Although some efforts have been made to automate a non-optical, direct method [l],such an approach has thus * Address for reprints: Michael P. Stern, Department of Medicine, Stanford, Calif. 94305. U.S.A.
of Medicine,
S.005,
Stanford
University
School
30
far not gained wide acceptance. The direct approach has the advantage of providing a measure of both the mean and the variance of a cell size distribution. An automated, but indirect, method of sizing fat cells has also been described by Hirsch and Gallian [2]. This method is referred to as indirect, since the fat cells in a measured amount of adipose tissue are counted rather than sized directly. A weighed amount of adipose tissue is fixed in osmium tetroxide. This treatment dislodges the fat cells from their tissue matrix. The isolated, osmium-fixed cells can then be collected quantitatively and counted in an automatic particle counter. A duplicate weighed specimen of adipose tissue is extracted using lipid.solvents. In this way, both the number of fat cells per unit wet weight of adipose tissue and the lipid content per unit wet weight of adipose tissue can be determined. By relating these two measurements, the average amount of lipid per fat cell (i.e. fat cell size) can be calculated. This method is automated, and thus rapid. On the other hand, it requires expensive instrumentation and necessitates an independent measurement of adipose tissue lipid content. Unlike the direct method, it provides a measure of mean cell size only, and gives no information about the variance in cell size. In order to combine the advantages of both approaches, we have attempted to develop and validate a method of sizing adipocytes that is both direct and automated. Methods Source of adipose tissue Adipose tissue was obtained either from the epididymal fat pads of male mice or from human subjects. Specimens from adults were obtained from the subcutaneous tissue of the right lower quadrant of the abdomen using an open biopsy technique. Specimens from children were obtained from cut-down sites in the groin at the time of cardiac catherization or from the subcutaneous tissue of the chest wall during cardiac surgery.* Frepara tion of tissue After trimming away connective tissue, the adipose tissue specimens were washed free of blood with saline and sub-divided into smaller fragments. The wet weights of these fragments ranged from 25 to 50 mg. One-half of the fragments were fixed in osmium tetroxide according to the method of Hirsch and Gallian [2]. These fragments were incubated for 72 hours at 37°C in solution of 2% osmium tetroxide and 0.5 M collidine buffer (pH 7.4). This treatment caused the fat cells to become separated from their tissue matrix. The resulting isolated cells were then washed with saline through a 250 pm Nitex screen, after which they were harvested quantitatively on a 25 pm Nitex screen and transferred to a beaker containing a known amount of saline preparatory to being counted by an automatic particle counter (vide infra). Those fragments of adipose tissue which were not fixed in osmium tetroxide were transferred to Folch (chloroform/methanol, 2 : 1, v/v) reagent for * Adipose specimens from the 5 children with congenital heart disease were obtained with the kind assistance of Dr David Baum, Department of Pediatrics, Stanford University School of Medicine.
31
Fig. 1. Cell sizing system, including cell counting oscilkmope. Insert. Typical frequency distribution
apparatus. multichannel analyzer, teletypewriter, of fat cell volumes displayed on oscilloscope.
and
determination of adipose tissue lipid content. These specimens were later homogenized, extracted with hot Folch solution, and their lipid content determined gravimetrically.
Adipocy te sizing Indirect method. The osmium fixed fat cells obtained
from a known wet weight of adipose tissue were counted using a Celloscope automatic particle counter (Particle Data, Elmhurst, Ill.). By dividing the number of fat cells per unit wet weight of adipose tissue into the lipid content per unit wet weight obtained from a duplicate specimen, the average lipid content per fat cell (fat cell size) was de~rmined. Fat cell lipid content was typically detained in triplicate for each specimen. Coefficients of variation for replicate (5 or more) determinations ranged from 6.1 to 9.0% (average, 7.6%). Direct method *. As each fat cell is counted in the automatic particle counter, an electronic pulse is generated, the size of which is proportional to the volume of the fat cell [3]. These pulses were fed into a multichannel analyzer (Nuclear Data 555, Chicago, Ill.) where they were assigned to one of 128 channels on the basis of their size. The resulting histogram can be viewed on an oscilloscope, and the data can also be printed out digitally using a teletypwriter. A punched paper tape can also be produced to facilitate data entry into a computer. The entire system is pictured in Fig. 1. A typical histogram is shown in the insert. + Current
versions of the ~s~m~ntation used are commercially available from Particle Data Inc., Box 265, Elmhurst, Ill. 60126. The necessary equipment is sold as a package and aI3 necessary interfacing between components of the system is provided by the COmPanY.
32
The instrument was calibrated using corn pollen particles (vide infra) so that for any given amplifier setting, a specific volume in nanoliters could be assigned to each channel. The mean fat cell volume in nanoliters was then calculated from the histogram as follows: 128
Cell volume = C n,u,/N
(I)
i= 1
Where ni = the number of particles in the ith channel, ui = the volume in nanoliters represented by the ith channel and N = the total number of particles counted. The standard deviation of the cell size was calculated as:
SD
=
. .
~niu?p(~niui)2]“’ _
__ -..___
N(N-1)
The channel numbers were calibrated using corn pollen particles. These particles had previously been sized optically, and had been found to have a mean diameter of 93.05 pm. Assuming them to be spherical, the volumes of several hundred were computed using the formula, volume = (1/6)(nd3 ), and the average volume in nanoliters was determined. The mean channel for corn pollen particles was then determined at several different amplifier settings using Equation 1 and substituting channel number for Vi. The mean channel number for corn pollen determined at the amplifier setting corresponding to the setting used for measuring the fat cells, was considered to represent a volume equal to the computed average volume of corn pollen particles. Since mean channel determined at amplifier settings which are either fractions or multiples of this setting may be considered to represent volumes equivalent to the corresponding fractions or multiples of the computed mean corn pollen particle volume, a calibration line can be produced. In general, it was necessary to use higher amplifier settings to obtain satisfactory histograms from specimens containing predominantly smaller cells as compared with specimens containing predominantly larger cells. In such cases, we used the corn pollen calibration line appropriate to the particular amplifier setting at which the fat cell size measurements were carried out. The data presented in this paper were collected using two different amplifier settings. With the higher setting, used for smaller cells, the 1st channel corresponded to a cell diameter of 19.6 pm and the 128th channel corresponded to a cell diameter of 99.0 pm. With the lower setting, used for large cells, the 1st channel corresponded to a cell diameter of 35.0 pm and the 128th channel corresponded to 176.5 pm. Results The relationship between cell volume by the direct method and cell lipid content by the indirect method is shown in Fig. 2. The results of the indirect
33
IDENTITY
LINE
"I
I
i 0
I 0.3
I 0.2
0.1
I 0.4
I 0.5 yg/CELL
CELL LiPID CONTENT
1 0.6
BY INDIRECT
I 0.7
I cl.8
I 0.9
I
METHOD
Fig. 2. Comparison of fat cell sizes measured by the direct and indirect method.
method are expressed both in micrograms of lipid per cell and in nanoliters, for ease of comparison with the direct method. Cell lipid content was transformed into nanoliters by assuming that fat cells are essentially spherical and have a density equal to that of triolein (0.915 g/cm3) [Z] . The correlation between the two methods is 0.96, indicating that approx~ately 92% of the variance in cell volumes measured by the direct method can be attributed to its relationship with fat cell lipid content as measured by the indirect method. The least
I
MEAN = 56.7~ SD= 14.2~ _
MEAN
24
32
40
48
56
DIAMETER
Fig. 3. Frequency
64 bi
72
80
= 101.2
u
88 DIAMETER
(~tb
distribution of fat cell diameters from adipose specimen obtained from a mouse,
Fig. 4. Frequency distribution of fat cell diameters from adipose specimen obtained from an adult human subject.
I
I
I
MEAN = 56.7 SD - 14.2
100
92
84
76
66
60
DIAMETER
52
44
36
28
l&i)
Fig. 5. Cumulative frequency distribution of fat cell diameters
on
probit PaPer (same data as
Fig. 3).
I
MEAN = 101.2 SD = 26.2
DIAMETER Fig.
6.
Fig. 4).
CumuIative
011
frequency distribution of fat cell diameters plotted on probit
PaPer
(same
data
as
35 TABLE
I
MEAN AND STANDARD MENS
DEVIATION
Indirect method, mean volume (Ill)
Direct method, mean volume ? S.D. (nl)
0.055 0.089 0.123 0.271 0.393 0.498 0.702 1.010
0.068 0.076 0.127 0.295 0.378 0.423 0.653 0.986
? f + + ? f. f +
OF FAT CELL VOLUMES
FROM
SELECTED
ADIPOSE
SPECI-
0.018 0.075 0.108 0.261 0.265 0.321 0.480 0.569
squares regressi.on line through the data has a slope which is not significantly different from 1 and an intercept which is not significantly different from 0 by the Student’s t test. Figs 3 and 4 show histograms of fat cell diameters computed from fat cell volumes, using the formula: d = (6uln)’ 13. The same data plotted as cumulative frequency distributions are shown in Figs. 5 and 6. Also shown in Figs 5 and 6 are the theoretical cumulative frequency distributions, calculated under the assumption that fat cell diameters are normally distributed, and that the sample means and standard deviations give satisfactory estimates of the true population means and standard deviations for the cells contained in these specimens. It is seen that over most of the range, the actual and the theoretical distributions coincide reasonably well. The departure from the theoretical distribution at the low end of the size range, observed in Fig. 5, can probably be explained by the fact that the cells are harvested on a 25 pm Nitex screen. Thus, cells having diameters less than 25 pm are lost. It seems doubtful that these losses would seriously bias the estimates of mean fat cell size. In any case, the results shown in Fig. 2 indicate that the error introduced by such losses affects both the direct and the indirect method to a similar degree. Table I shows the mean and standard deviation of fat cell volumes determined by the direct method for selected adipose tissue specimens. Discussion The results presented in this paper indicated that the automated direct method of sizing adipocytes which we have developed gives estimates of fat cell size which are substantially similar over a wide range to those obtained with the original method described by Hirsch and Gallian [2]. The direct method, however, has the advantage of not requiring an independent measure of the wet weight or of the lipid content of the adipose tissue specimen. Thus, any errors inherent in these measurements are avoided. Moreover, eliminating these measurements may provide an additional advantage when only limited amounts of adipose tissue are available for study. In addition, the direct method permits an estimate of the variance in the
36
cell size distribution, whereas the original method of Hirsch and Gallian does not. Among the various reasons why it is important to have information about the distribution of cell sizes is the fact that without such information it is not possible to obtain an unbiased estimate of either mean cell diameter or mean cell surface area from a measurement of mean cell volume. Because of the skewed nature of the volume distribution, one cannot simply carry out a transformation to the other dimensions by a direct application of the relevant geometric formulas. It is necessary to transform the volumes in each size interval separately and then to average the separate diameters and/or surface areas. In the. case of the diameter to volume transformation (although not in the case of the volume to diameter transformation), the formula quoted by Goldrick [4] can be used. This formula makes use of the diameter variance directly : u = (77/6) (3s2d + d3)
Where u = cell volume, s2 = variance in cell diameter, 2 = average cell diameter. To the best of our knowledge, analytical solutions for the other 5 transformations between dimensions have not been derived at the present time. In any case, such equations would require knowledge of the variance of the parameter to be transformed. Both Hirsch and Gallian [2] and Sjostrom et al. [l] have reported, in passing, automated methods for direct sizing of fat cells. However, neither group has advocated this method as their main method for adipocyte sizing. In both cases, the methods had significant disadvantages as compared with the direct sizing method described in this report. Neither group used a multichannel analyzer as we have done. Hirsch and Gallian used a Coulter counter (model B) and a Coulter automatic particle size distribution analyzer (model J) (Coulter Electronics, Hialeab, Florida). The latter instrument operates on a different principle from the multi-channel analyzer which we used. By using an upper and lower threshold, it is possible to arrange to count only those cells falling within a particular size “window”. By making successive counts using different size “windows”, one can construct a histogram similar to the one produced by the multi-channel analyzer. The process of making successive counts is automated. However, this technique is capable only of resolving the size distribution into a relatively small number of size categories as compared with 128 for the multi-channel analyzer. Furthermore, the necessity of making successive cell counts may pose a problem when only small amounts of adipose tissue are available. Thus, the amount of sample available for the repetitive counts for each different size “window” may become a limiting factor. The multi-channel analyzer, in contrast, produces an entire histogram from a single count. Sjostrom et al. have also reported a method for direct cell sizing using a Celloscope [ 11. However, they also did not use a multi-channel analyzer. Their method also requires that successive counts be carried out on a sample of osmium fixed cells. The sensitivity of the Celloscope is increased with each successive count so that smaller and smaller cells are included. In this way a cumulative frequency distribution of cell sizes can be produced. This method permitted these workers to resolve the cell size distribution into 13 size cate-
37
gories. The method also suffers from the necessity of making repetitive cell counts, thus requiring larger initial adipose tissue specimens. Hirsch and Gallian suggested that osmium treatment caused fat cells to swell [ 21. These findings, however, were not confirmed by Sjostrom et al. [l] . Our results (Fig. 2) also fail to support the idea that osmium treatment causes significant swelling of fat cells. Acknowledgments This work was supported by Public Health Service Contract No. NIH-712161-L under the Lipid Research Clinics Program National Weart and Lung Institute, NIH Dept. of H&W., and by the Veterans Administration, Palo Alto V.A. Hospital. References 1 SjiistrBm, L., Bjijrntorp, P. and Vrana, J. (1971) J. Lipid Res. 12, 521-530 2 Hirsch, J. and Gallian, E. (1968) J. Lipid Res. 9,110-119 3 Berg, R.H. (1958) Symposium on Particle Size Measurements, Special Technical Publication No. 234, The American Society for Testing Materials 4 Goldrick, R.B. (196’7) Am. J. Physiol. 212. 777-782
Clinica Chimico Acta, 65 (1975) 29-37 0 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
CCA 7321
AN AUTOMATED, DIRECT METHOD FOR MEASURING AD~OCYTE CELL SIZE
MICHAEL P. STERN* and FRED CONRAD Stanford Heart Disease Prevention Program, of Medicine, Stanford, Calif. (U.S.A.)
Stanford
University
School
(Received May 26,1975)
Summary Current methods for direct determination of fat cell size are optical and non-automated. They are thus tedious, but have the advantage of providing estimates of the variance of a cell size distribution, as well as a measure of the mean cell size. An indirect method based on counting the number of osmiumfixed fat cells derived from a known wet weight of adipose tissue is also available. This method is automated and thus rapid, but does not provide information about the variance of the cell size distribution. In the present paper we describe a direct, automated method of fat cell sizing that provides estimates for both mean cell size and the variance of the cell size distribution. The correlation between our method and an indirect method based on counting osmium-fixed cells was 0.96. Transformation of the volume distribution to diameters indicated that cell diameters appeared to be normally dist~bu~d, confining the observations of others.
Introduction In recent years me~urements of the size of adipocytes from both human and animal sources have found a wide variety of applications in bio-medical research. Two basic approaches (one direct, and the other indirect) have been used to make these measurements. Ordinarily, the direct approach is optical in nature and non-automated. Individual fat cells are observed under a microscope and are sized directly using a calibrated eyepiece. Typically, several hundred cells must be sized in this way in order to obtain statistic~ly valid results. The optical approach is thus extremely tedious. Although some efforts have been made to automate a non-optical, direct method [l],such an approach has thus * Address for reprints: Michael P. Stern, Department of Medicine, Stanford, Calif. 94305. U.S.A.
of Medicine,
S.005,
Stanford
University
School
30
far not gained wide acceptance. The direct approach has the advantage of providing a measure of both the mean and the variance of a cell size distribution. An automated, but indirect, method of sizing fat cells has also been described by Hirsch and Gallian [2]. This method is referred to as indirect, since the fat cells in a measured amount of adipose tissue are counted rather than sized directly. A weighed amount of adipose tissue is fixed in osmium tetroxide. This treatment dislodges the fat cells from their tissue matrix. The isolated, osmium-fixed cells can then be collected quantitatively and counted in an automatic particle counter. A duplicate weighed specimen of adipose tissue is extracted using lipid.solvents. In this way, both the number of fat cells per unit wet weight of adipose tissue and the lipid content per unit wet weight of adipose tissue can be determined. By relating these two measurements, the average amount of lipid per fat cell (i.e. fat cell size) can be calculated. This method is automated, and thus rapid. On the other hand, it requires expensive instrumentation and necessitates an independent measurement of adipose tissue lipid content. Unlike the direct method, it provides a measure of mean cell size only, and gives no information about the variance in cell size. In order to combine the advantages of both approaches, we have attempted to develop and validate a method of sizing adipocytes that is both direct and automated. Methods Source of adipose tissue Adipose tissue was obtained either from the epididymal fat pads of male mice or from human subjects. Specimens from adults were obtained from the subcutaneous tissue of the right lower quadrant of the abdomen using an open biopsy technique. Specimens from children were obtained from cut-down sites in the groin at the time of cardiac catherization or from the subcutaneous tissue of the chest wall during cardiac surgery.* Frepara tion of tissue After trimming away connective tissue, the adipose tissue specimens were washed free of blood with saline and sub-divided into smaller fragments. The wet weights of these fragments ranged from 25 to 50 mg. One-half of the fragments were fixed in osmium tetroxide according to the method of Hirsch and Gallian [2]. These fragments were incubated for 72 hours at 37°C in solution of 2% osmium tetroxide and 0.5 M collidine buffer (pH 7.4). This treatment caused the fat cells to become separated from their tissue matrix. The resulting isolated cells were then washed with saline through a 250 pm Nitex screen, after which they were harvested quantitatively on a 25 pm Nitex screen and transferred to a beaker containing a known amount of saline preparatory to being counted by an automatic particle counter (vide infra). Those fragments of adipose tissue which were not fixed in osmium tetroxide were transferred to Folch (chloroform/methanol, 2 : 1, v/v) reagent for * Adipose specimens from the 5 children with congenital heart disease were obtained with the kind assistance of Dr David Baum, Department of Pediatrics, Stanford University School of Medicine.
31
Fig. 1. Cell sizing system, including cell counting oscilkmope. Insert. Typical frequency distribution
apparatus. multichannel analyzer, teletypewriter, of fat cell volumes displayed on oscilloscope.
and
determination of adipose tissue lipid content. These specimens were later homogenized, extracted with hot Folch solution, and their lipid content determined gravimetrically.
Adipocy te sizing Indirect method. The osmium fixed fat cells obtained
from a known wet weight of adipose tissue were counted using a Celloscope automatic particle counter (Particle Data, Elmhurst, Ill.). By dividing the number of fat cells per unit wet weight of adipose tissue into the lipid content per unit wet weight obtained from a duplicate specimen, the average lipid content per fat cell (fat cell size) was de~rmined. Fat cell lipid content was typically detained in triplicate for each specimen. Coefficients of variation for replicate (5 or more) determinations ranged from 6.1 to 9.0% (average, 7.6%). Direct method *. As each fat cell is counted in the automatic particle counter, an electronic pulse is generated, the size of which is proportional to the volume of the fat cell [3]. These pulses were fed into a multichannel analyzer (Nuclear Data 555, Chicago, Ill.) where they were assigned to one of 128 channels on the basis of their size. The resulting histogram can be viewed on an oscilloscope, and the data can also be printed out digitally using a teletypwriter. A punched paper tape can also be produced to facilitate data entry into a computer. The entire system is pictured in Fig. 1. A typical histogram is shown in the insert. + Current
versions of the ~s~m~ntation used are commercially available from Particle Data Inc., Box 265, Elmhurst, Ill. 60126. The necessary equipment is sold as a package and aI3 necessary interfacing between components of the system is provided by the COmPanY.
32
The instrument was calibrated using corn pollen particles (vide infra) so that for any given amplifier setting, a specific volume in nanoliters could be assigned to each channel. The mean fat cell volume in nanoliters was then calculated from the histogram as follows: 128
Cell volume = C n,u,/N
(I)
i= 1
Where ni = the number of particles in the ith channel, ui = the volume in nanoliters represented by the ith channel and N = the total number of particles counted. The standard deviation of the cell size was calculated as:
SD
=
. .
~niu?p(~niui)2]“’ _
__ -..___
N(N-1)
The channel numbers were calibrated using corn pollen particles. These particles had previously been sized optically, and had been found to have a mean diameter of 93.05 pm. Assuming them to be spherical, the volumes of several hundred were computed using the formula, volume = (1/6)(nd3 ), and the average volume in nanoliters was determined. The mean channel for corn pollen particles was then determined at several different amplifier settings using Equation 1 and substituting channel number for Vi. The mean channel number for corn pollen determined at the amplifier setting corresponding to the setting used for measuring the fat cells, was considered to represent a volume equal to the computed average volume of corn pollen particles. Since mean channel determined at amplifier settings which are either fractions or multiples of this setting may be considered to represent volumes equivalent to the corresponding fractions or multiples of the computed mean corn pollen particle volume, a calibration line can be produced. In general, it was necessary to use higher amplifier settings to obtain satisfactory histograms from specimens containing predominantly smaller cells as compared with specimens containing predominantly larger cells. In such cases, we used the corn pollen calibration line appropriate to the particular amplifier setting at which the fat cell size measurements were carried out. The data presented in this paper were collected using two different amplifier settings. With the higher setting, used for smaller cells, the 1st channel corresponded to a cell diameter of 19.6 pm and the 128th channel corresponded to a cell diameter of 99.0 pm. With the lower setting, used for large cells, the 1st channel corresponded to a cell diameter of 35.0 pm and the 128th channel corresponded to 176.5 pm. Results The relationship between cell volume by the direct method and cell lipid content by the indirect method is shown in Fig. 2. The results of the indirect
33
IDENTITY
LINE
"I
I
i 0
I 0.3
I 0.2
0.1
I 0.4
I 0.5 yg/CELL
CELL LiPID CONTENT
1 0.6
BY INDIRECT
I 0.7
I cl.8
I 0.9
I
METHOD
Fig. 2. Comparison of fat cell sizes measured by the direct and indirect method.
method are expressed both in micrograms of lipid per cell and in nanoliters, for ease of comparison with the direct method. Cell lipid content was transformed into nanoliters by assuming that fat cells are essentially spherical and have a density equal to that of triolein (0.915 g/cm3) [Z] . The correlation between the two methods is 0.96, indicating that approx~ately 92% of the variance in cell volumes measured by the direct method can be attributed to its relationship with fat cell lipid content as measured by the indirect method. The least
I
MEAN = 56.7~ SD= 14.2~ _
MEAN
24
32
40
48
56
DIAMETER
Fig. 3. Frequency
64 bi
72
80
= 101.2
u
88 DIAMETER
(~tb
distribution of fat cell diameters from adipose specimen obtained from a mouse,
Fig. 4. Frequency distribution of fat cell diameters from adipose specimen obtained from an adult human subject.
I
I
I
MEAN = 56.7 SD - 14.2
100
92
84
76
66
60
DIAMETER
52
44
36
28
l&i)
Fig. 5. Cumulative frequency distribution of fat cell diameters
on
probit PaPer (same data as
Fig. 3).
I
MEAN = 101.2 SD = 26.2
DIAMETER Fig.
6.
Fig. 4).
CumuIative
011
frequency distribution of fat cell diameters plotted on probit
PaPer
(same
data
as
35 TABLE
I
MEAN AND STANDARD MENS
DEVIATION
Indirect method, mean volume (Ill)
Direct method, mean volume ? S.D. (nl)
0.055 0.089 0.123 0.271 0.393 0.498 0.702 1.010
0.068 0.076 0.127 0.295 0.378 0.423 0.653 0.986
? f + + ? f. f +
OF FAT CELL VOLUMES
FROM
SELECTED
ADIPOSE
SPECI-
0.018 0.075 0.108 0.261 0.265 0.321 0.480 0.569
squares regressi.on line through the data has a slope which is not significantly different from 1 and an intercept which is not significantly different from 0 by the Student’s t test. Figs 3 and 4 show histograms of fat cell diameters computed from fat cell volumes, using the formula: d = (6uln)’ 13. The same data plotted as cumulative frequency distributions are shown in Figs. 5 and 6. Also shown in Figs 5 and 6 are the theoretical cumulative frequency distributions, calculated under the assumption that fat cell diameters are normally distributed, and that the sample means and standard deviations give satisfactory estimates of the true population means and standard deviations for the cells contained in these specimens. It is seen that over most of the range, the actual and the theoretical distributions coincide reasonably well. The departure from the theoretical distribution at the low end of the size range, observed in Fig. 5, can probably be explained by the fact that the cells are harvested on a 25 pm Nitex screen. Thus, cells having diameters less than 25 pm are lost. It seems doubtful that these losses would seriously bias the estimates of mean fat cell size. In any case, the results shown in Fig. 2 indicate that the error introduced by such losses affects both the direct and the indirect method to a similar degree. Table I shows the mean and standard deviation of fat cell volumes determined by the direct method for selected adipose tissue specimens. Discussion The results presented in this paper indicated that the automated direct method of sizing adipocytes which we have developed gives estimates of fat cell size which are substantially similar over a wide range to those obtained with the original method described by Hirsch and Gallian [2]. The direct method, however, has the advantage of not requiring an independent measure of the wet weight or of the lipid content of the adipose tissue specimen. Thus, any errors inherent in these measurements are avoided. Moreover, eliminating these measurements may provide an additional advantage when only limited amounts of adipose tissue are available for study. In addition, the direct method permits an estimate of the variance in the
36
cell size distribution, whereas the original method of Hirsch and Gallian does not. Among the various reasons why it is important to have information about the distribution of cell sizes is the fact that without such information it is not possible to obtain an unbiased estimate of either mean cell diameter or mean cell surface area from a measurement of mean cell volume. Because of the skewed nature of the volume distribution, one cannot simply carry out a transformation to the other dimensions by a direct application of the relevant geometric formulas. It is necessary to transform the volumes in each size interval separately and then to average the separate diameters and/or surface areas. In the. case of the diameter to volume transformation (although not in the case of the volume to diameter transformation), the formula quoted by Goldrick [4] can be used. This formula makes use of the diameter variance directly : u = (77/6) (3s2d + d3)
Where u = cell volume, s2 = variance in cell diameter, 2 = average cell diameter. To the best of our knowledge, analytical solutions for the other 5 transformations between dimensions have not been derived at the present time. In any case, such equations would require knowledge of the variance of the parameter to be transformed. Both Hirsch and Gallian [2] and Sjostrom et al. [l] have reported, in passing, automated methods for direct sizing of fat cells. However, neither group has advocated this method as their main method for adipocyte sizing. In both cases, the methods had significant disadvantages as compared with the direct sizing method described in this report. Neither group used a multichannel analyzer as we have done. Hirsch and Gallian used a Coulter counter (model B) and a Coulter automatic particle size distribution analyzer (model J) (Coulter Electronics, Hialeab, Florida). The latter instrument operates on a different principle from the multi-channel analyzer which we used. By using an upper and lower threshold, it is possible to arrange to count only those cells falling within a particular size “window”. By making successive counts using different size “windows”, one can construct a histogram similar to the one produced by the multi-channel analyzer. The process of making successive counts is automated. However, this technique is capable only of resolving the size distribution into a relatively small number of size categories as compared with 128 for the multi-channel analyzer. Furthermore, the necessity of making successive cell counts may pose a problem when only small amounts of adipose tissue are available. Thus, the amount of sample available for the repetitive counts for each different size “window” may become a limiting factor. The multi-channel analyzer, in contrast, produces an entire histogram from a single count. Sjostrom et al. have also reported a method for direct cell sizing using a Celloscope [ 11. However, they also did not use a multi-channel analyzer. Their method also requires that successive counts be carried out on a sample of osmium fixed cells. The sensitivity of the Celloscope is increased with each successive count so that smaller and smaller cells are included. In this way a cumulative frequency distribution of cell sizes can be produced. This method permitted these workers to resolve the cell size distribution into 13 size cate-
37
gories. The method also suffers from the necessity of making repetitive cell counts, thus requiring larger initial adipose tissue specimens. Hirsch and Gallian suggested that osmium treatment caused fat cells to swell [ 21. These findings, however, were not confirmed by Sjostrom et al. [l] . Our results (Fig. 2) also fail to support the idea that osmium treatment causes significant swelling of fat cells. Acknowledgments This work was supported by Public Health Service Contract No. NIH-712161-L under the Lipid Research Clinics Program National Weart and Lung Institute, NIH Dept. of H&W., and by the Veterans Administration, Palo Alto V.A. Hospital. References 1 SjiistrBm, L., Bjijrntorp, P. and Vrana, J. (1971) J. Lipid Res. 12, 521-530 2 Hirsch, J. and Gallian, E. (1968) J. Lipid Res. 9,110-119 3 Berg, R.H. (1958) Symposium on Particle Size Measurements, Special Technical Publication No. 234, The American Society for Testing Materials 4 Goldrick, R.B. (196’7) Am. J. Physiol. 212. 777-782
