EXPERIMENTAL
NEUROLOGY
Quantitative
Analysis
Granular ROBERT
Departments
52, 295-310 (1976)
Cells D.
of Dendritic
Branching
from
Dentate
LINDSAY
Human AND
ARNOLD
of Anatomy and Psychiatry and of California, Center for
University
B.
Pattern Gyrus
SCHEIBEL
the Brain the Health
of
Research Sciences,
l
Institute,
Los Angeles, California 90624 Received
February
9, 1976
The three-dimensional structure of Golgi-impregnated neurons was studied using modern data-collecting techniques. Branch length and branch angle distributions were examined and found to have a wide range of observed values. These types of distributions imply a stochastic design for the bifurcating structure. No apparent pattern was found in the branching configuration. Branch lengths were studied using both centrifugal and centripetal ordering. Results of this analysis indicate that branching probability is not uniform over the entire dendritic tree and may be dependent on the dendritic surface area.
INTRODUCTION The young neuron in the central nervous system of higher evolved animals has relatively short and thick dendritic processes which develop into a complex system of branches. The description of size, shape, and density of the dendritic arborization seemsto be characteristic for groups of neurons. The subjective characteristics derived from observational techniques have been used to classify neurons into types. However, closer examination of dendritic branching patterns reveals continuous structural variation within each neuron type. The classification of neurons in a precise and logical manner will require an understanding of the design principles for dendritic structure. These complex dendritic structures are studied objectively by using statistical analysis of quantitative data. Early attempts at using statistical 1 This study was supported by USPHS Grant NS 10567, National Institute of Neurological and Communicative Disorders and Stroke. We thank Barbara Lindsay for her assistance in the preparation of this paper. 235 Copyright All rights
0 1976 by Academic Press, Inc. of reproduction in any form reserved.
296
LINDSAY
AND
SCHEIBEL
analysis to study dendritic structures were made by Sholl (9). Recent quantitative studies on the branch length and branch angle analysis of dendritic structures have been reported by Smit et al. (lo), Uylings and Smit (ll), Hollingworth and Berry (4), and Lindsay and Scheibel (6). Our study combines classical histological methods and modern datacollecting techniques to determine the three-dimensional structure of neurons, The branch lengths and branch angles are calculated from the threedimensional structural data. Frequently distributions and statistical parameters are determined for various categories of branch lengths and branch angles. Expe&ental
Methods
The histological preparations used in this study were rapid Golgiimpregnated thick serial sections of adult human dentate gyrus. Small blocks of tissue were fixed in Lillie’s neutral buffered formalin for 2 days (8). The blocks were placed in the rapid Golgi chromating solution for 3 days, #then in a silvering solution for 24 hr. They were dehydrated and embedded in Parlodion (3). The blocks were serially sliced on a sliding microtome at a thickness of 120 pm in a transverse orientation. The tissue slices were mounted on slides using Permount and cover glasses. Serial sections carefully prepared by the above method can be used to trace individual fibers from one slice to the next. This technique makes possible the complete reconstruction of the dendritic domain and as much of the axonal domain as is desired (5). For this quantitative study, a group of 20 granular cells was selected from the dentate gyrus of a 51-year-old female. All of these neurons were located in a block of tissue 1 mm thick that was cut transversely to the hippocampal formation one-third of the way distal from the anterior pole. The structures of the selected neurons were reconstructed using the Video Computer Microscope and the Anatomical Reconstruction Graphics Operating System developed by one of the authors (7). The data model used to represent the bifurcating structure of neurons is a stick or wire model. The three-dimensional coordinates in space were given for each inflection, branch, and end point. A code associated with the coordinate point and the sequential order of the points determine the connectivity of the points and hence the stick-like structure (Fig. 1). The neuron was viewed with a microscope coupled to a television camera. An x-y recording device attached to the television monitor and a potentiometer connected to the fine focus control of the microscope provided the computer with spatial coordinates of a point brought into best focus. The computer was programmed with an operating system that guided the operator through the measuring procedure and presented him
DENDRITIC
BRANCHING
IN
DENTATE
CYRUS
297
FIG. 1. A simplified sticklike figure representing the measured data. Each dot indicates a three-dimensional coordinate point. A code associated with each point is used to signify inflection, branch, or endpoint.
with a dynamic visual presentation of the data. When the structural data had been recorded in a permanent file on magnetic tape, the data could be analyzed using a standard higher-order computer language such as Fortran. Analyticul Methods Branch lengths and branch angles were easily calculated from the structural data using a Fortran program. Each dendrite was processed individually. The sequenceof points was scanned for branch and end codes. Fiber lengths between these points were calculated and stored in a two-dimensional array in such a manner as to preserve the topological structure of the dendrite. For each branch point there was an incoming branch and two outgoing branches. An angle was formed by each outgoing branch and the extended direction of the incoming branch. Thus a branch angle was associated with each outgoing branch of the structure. The angles were also stored in a two-dimensional array. The branch length and branch angle arrays were stored on magnetic tape for statistical analysis. A statistical analysis program was developed to read the branch length and branch angle arrays from magnetic tape and to select measuresto form a data set. The data set was considered as a distribution of some measure of the structure and the mean, variance, standard deviation, and standard deviation of the mean were calculated. The frequency distribution was also determined. An arbitrary theoretical function could be fitted to the experimental distribution, and the “goodness of fit,” the chi-square statistic, was calculated.
298
LINDSAY
AND
SCHEIBEL
Fro. 2. Photographs of Golgi-impregnated granular cells of human dentate gyrus. (a) Classical three-layer construction (X 25). (b) Somata of the granular cells in the granular layer and their dendrites projecting into the molecular layer (X 100). (c) Initial segments of dendrites protruding randomly from the surfaces of the somata (X 400). (d) Dendritic protrusions arching rapidly and projecting toward the molecular layer (X 400). (e) Development of one dendrite into a major structure compared to the other dendrites of a single cell (X 400). (f) Dendrites of granular celk densely covered with spines (X 400). (g) Dendritic terminal branches
DENDRITIC
BRANCHING
IN
TABLE Statistical
DENTATE
299
GYRUS
1
Parameters
for Major Ascending Dentate Cyrus Granular
Dendrites Cells”
of Human
n
F
UP
(r
x2
v
P
a
0
S-N N-N N-T TL S-T S-LN BA
20 107 147 20 147 147 2.54
22.6 61.3 144.7 1413.8 284.4 139.7 40.6
3.3 3.9 5.6 138.6 4.9 5.5 1.4
14.6 40.8 67.8 619.9 59.5 66.5 23.0
0.55 0.47 0.98 0.95 1.22 1.72
3 1.5 27 23 27 10
0.64 0.96 0.68 0.46 0.20 0.07
0.107 0.037 0.031 0.004 0.080 0.032 0.077
2.5 2.5 4.5 5.0 23.0 4.5 3.0
D See text
for symbol
definitions.
Two theoretical functions were used in this study. The first was the gamma density function (2). A continuous random variable x with range O
NEUROLOGY
Quantitative
Analysis
Granular ROBERT
Departments
52, 295-310 (1976)
Cells D.
of Dendritic
Branching
from
Dentate
LINDSAY
Human AND
ARNOLD
of Anatomy and Psychiatry and of California, Center for
University
B.
Pattern Gyrus
SCHEIBEL
the Brain the Health
of
Research Sciences,
l
Institute,
Los Angeles, California 90624 Received
February
9, 1976
The three-dimensional structure of Golgi-impregnated neurons was studied using modern data-collecting techniques. Branch length and branch angle distributions were examined and found to have a wide range of observed values. These types of distributions imply a stochastic design for the bifurcating structure. No apparent pattern was found in the branching configuration. Branch lengths were studied using both centrifugal and centripetal ordering. Results of this analysis indicate that branching probability is not uniform over the entire dendritic tree and may be dependent on the dendritic surface area.
INTRODUCTION The young neuron in the central nervous system of higher evolved animals has relatively short and thick dendritic processes which develop into a complex system of branches. The description of size, shape, and density of the dendritic arborization seemsto be characteristic for groups of neurons. The subjective characteristics derived from observational techniques have been used to classify neurons into types. However, closer examination of dendritic branching patterns reveals continuous structural variation within each neuron type. The classification of neurons in a precise and logical manner will require an understanding of the design principles for dendritic structure. These complex dendritic structures are studied objectively by using statistical analysis of quantitative data. Early attempts at using statistical 1 This study was supported by USPHS Grant NS 10567, National Institute of Neurological and Communicative Disorders and Stroke. We thank Barbara Lindsay for her assistance in the preparation of this paper. 235 Copyright All rights
0 1976 by Academic Press, Inc. of reproduction in any form reserved.
296
LINDSAY
AND
SCHEIBEL
analysis to study dendritic structures were made by Sholl (9). Recent quantitative studies on the branch length and branch angle analysis of dendritic structures have been reported by Smit et al. (lo), Uylings and Smit (ll), Hollingworth and Berry (4), and Lindsay and Scheibel (6). Our study combines classical histological methods and modern datacollecting techniques to determine the three-dimensional structure of neurons, The branch lengths and branch angles are calculated from the threedimensional structural data. Frequently distributions and statistical parameters are determined for various categories of branch lengths and branch angles. Expe&ental
Methods
The histological preparations used in this study were rapid Golgiimpregnated thick serial sections of adult human dentate gyrus. Small blocks of tissue were fixed in Lillie’s neutral buffered formalin for 2 days (8). The blocks were placed in the rapid Golgi chromating solution for 3 days, #then in a silvering solution for 24 hr. They were dehydrated and embedded in Parlodion (3). The blocks were serially sliced on a sliding microtome at a thickness of 120 pm in a transverse orientation. The tissue slices were mounted on slides using Permount and cover glasses. Serial sections carefully prepared by the above method can be used to trace individual fibers from one slice to the next. This technique makes possible the complete reconstruction of the dendritic domain and as much of the axonal domain as is desired (5). For this quantitative study, a group of 20 granular cells was selected from the dentate gyrus of a 51-year-old female. All of these neurons were located in a block of tissue 1 mm thick that was cut transversely to the hippocampal formation one-third of the way distal from the anterior pole. The structures of the selected neurons were reconstructed using the Video Computer Microscope and the Anatomical Reconstruction Graphics Operating System developed by one of the authors (7). The data model used to represent the bifurcating structure of neurons is a stick or wire model. The three-dimensional coordinates in space were given for each inflection, branch, and end point. A code associated with the coordinate point and the sequential order of the points determine the connectivity of the points and hence the stick-like structure (Fig. 1). The neuron was viewed with a microscope coupled to a television camera. An x-y recording device attached to the television monitor and a potentiometer connected to the fine focus control of the microscope provided the computer with spatial coordinates of a point brought into best focus. The computer was programmed with an operating system that guided the operator through the measuring procedure and presented him
DENDRITIC
BRANCHING
IN
DENTATE
CYRUS
297
FIG. 1. A simplified sticklike figure representing the measured data. Each dot indicates a three-dimensional coordinate point. A code associated with each point is used to signify inflection, branch, or endpoint.
with a dynamic visual presentation of the data. When the structural data had been recorded in a permanent file on magnetic tape, the data could be analyzed using a standard higher-order computer language such as Fortran. Analyticul Methods Branch lengths and branch angles were easily calculated from the structural data using a Fortran program. Each dendrite was processed individually. The sequenceof points was scanned for branch and end codes. Fiber lengths between these points were calculated and stored in a two-dimensional array in such a manner as to preserve the topological structure of the dendrite. For each branch point there was an incoming branch and two outgoing branches. An angle was formed by each outgoing branch and the extended direction of the incoming branch. Thus a branch angle was associated with each outgoing branch of the structure. The angles were also stored in a two-dimensional array. The branch length and branch angle arrays were stored on magnetic tape for statistical analysis. A statistical analysis program was developed to read the branch length and branch angle arrays from magnetic tape and to select measuresto form a data set. The data set was considered as a distribution of some measure of the structure and the mean, variance, standard deviation, and standard deviation of the mean were calculated. The frequency distribution was also determined. An arbitrary theoretical function could be fitted to the experimental distribution, and the “goodness of fit,” the chi-square statistic, was calculated.
298
LINDSAY
AND
SCHEIBEL
Fro. 2. Photographs of Golgi-impregnated granular cells of human dentate gyrus. (a) Classical three-layer construction (X 25). (b) Somata of the granular cells in the granular layer and their dendrites projecting into the molecular layer (X 100). (c) Initial segments of dendrites protruding randomly from the surfaces of the somata (X 400). (d) Dendritic protrusions arching rapidly and projecting toward the molecular layer (X 400). (e) Development of one dendrite into a major structure compared to the other dendrites of a single cell (X 400). (f) Dendrites of granular celk densely covered with spines (X 400). (g) Dendritic terminal branches
DENDRITIC
BRANCHING
IN
TABLE Statistical
DENTATE
299
GYRUS
1
Parameters
for Major Ascending Dentate Cyrus Granular
Dendrites Cells”
of Human
n
F
UP
(r
x2
v
P
a
0
S-N N-N N-T TL S-T S-LN BA
20 107 147 20 147 147 2.54
22.6 61.3 144.7 1413.8 284.4 139.7 40.6
3.3 3.9 5.6 138.6 4.9 5.5 1.4
14.6 40.8 67.8 619.9 59.5 66.5 23.0
0.55 0.47 0.98 0.95 1.22 1.72
3 1.5 27 23 27 10
0.64 0.96 0.68 0.46 0.20 0.07
0.107 0.037 0.031 0.004 0.080 0.032 0.077
2.5 2.5 4.5 5.0 23.0 4.5 3.0
D See text
for symbol
definitions.
Two theoretical functions were used in this study. The first was the gamma density function (2). A continuous random variable x with range O
