TomaschJ-1968

Notes about [TomaschJ-1968] 1.

This paper has lots of data about number of efferent and afferent fibers cell counts in human cerebellum.

Summary of data in this paper:

TomaschJ-1968 cell and fiber counts in human

Cell or fiber	Description	Quantity
purkinje	Total number both hemispheres	15 million
cortico-pontine	# fibers from cerebral cortex to pons	19.14 million (for one side)
ponto-cerebellar	# cells in pons, same as number from pons to cerebellum	23.085 million
inferior olive	# fibers entering cerebellum from inferior olive (one side)	0.5 million
Inferior cerebeller peduncle	number of axons	0.52 million (one side)
cerebellar nuclei	total number neurons (one side)	311,404
dentate nucleus	total number neurons (one side)	284,000
nucleus globosus	total number neurons (one side)	16,153
emboliforme nucleus	total number neurons (one side)	10,381
fastigii nucleus	total number neurons (one side)	5210
superior cerebellar peduncle	number of axons (one side)	0.782 million
superior cerebellar peduncle afferents (one side)	number axons into cerebellum through superior cerebellar peduncle	less than 1/2 number of fibers (0.782 / 2)
superior cerebellar peduncle efferents (one side)	number axons leaving cerebellum through superior cerebellar peduncle	about 311,000 (total number nuclei, 311,404; maybe less number fastigii nuclei, 5201)

Excerpts from the paper:

cortico-pontine (From cerebral cortex to pons).

19.14 million axons (for one side).

ponto-cerebellar (from pons to cerebellum).

Total of 23.085 million nerve cells within the pontine grey. May range from 17 to 25 million neurons.

Ratio of ponto-cerebellar to cortico-pontine

From 1:1.37 to 1:2.25. “This overall convergence ratio may not be uniform for every individual circuit, it indicates a definite reduction, however, in the number of unit-elements involved from the peduncular to the pontine level.”

Number of purkinje cells.

“A range of from 14-25 million Purkinje-cells [in the whole cerebellum] seems, therefore, well established. Estimates for the number of granular cells in the cerebellar cortex range front 10 to 100 billion cells (Braitenberg and Atwood). According to Fox and Barnard (1957), there are in the macaque 960 granular cells for 1 Purkinje cell.”

Ratio of mossy fibers to purkinje cells

“From the granular cells a re-convergence of the same overall ratio is taking place, the number of Purkinje-cells, according to the figures of Lojda being of the same order of magnitude as the estimate for the number of pontine nerve cells. In other words, there is a 1:1 relationship between the numbers of pontine nerve cells and of Purkinje-cells.”

Number of fibers from inferior olive

“The inferior olivary nuclear complex provides the second largest source of cerebellar afferents. Among four male subjects, including the 56 year old male refered to above, Moatamed (1966) counted and estimated a figure of 0.5 million cells for the nuclei of one side. This range of cell frequencies was confirmed by Escobar et al. who found in one human subject, age and sex not stated, 0.45 million cells in the dentate olivary nucleus alone. Thus with 1 million neurites entering the cerebellum from this source, this inflow is only 1/23 that of pontine origin. After decussating, these neurites enter the cerebellum via the inferior cerebellar peduncle.”

Number fibers in inferior cerebeller peduncle

“The estimate comes to 0.52 million axons and 0.45 million of these are myelinated. [One side]. The difference accounting for un-myelinated axons is 7.4%.”

Number of pinal and vestibular afferents into the cerebellum

“An estimate of both spino-cerebellar tracts at the level above the pyramidal decussation, renders a figure of 0.204 million axons: of these 0.147 million are myelinated.”

Number of vestibular nucleus cells

“The number of vestibular nuclear cells is 0.245 million according to Blinkov and Ponomarev (1965). No information is available at present about the proportion from this source for cerebellum and for spinal cord.”

Number of cerebellar deep nuclei cells.

“The number of cells in the cerebellar nuclei of man was counted and estimated in 3 male subjects (Heidary and Tomasch, 1969). Cell-frequencies in all nuclei of one hemisphere are 311,404+ 3,835 neurons. Of this total, 284,000 cells belong to the dentate nucleus, 16,153 to the nucleus globosus, 10,381 to the emboliforme nucleus and only 5210 to the nucleus fastigii.”

Variability in counts for inferior olive and nuclei

“…yet detailed counts and estimates carried out in our laboratory and covering in several instances an age range from the new-born to the pre-senescent age resulted in the case of the olivary nucleus in a coefficient of variation of only 1.5 %. For the three subjects in whom the cerebellar nuclear cells were counted, the coefficient of variation is 1.9%”

Number fibers in superior cerebellar peduncle

“There is general agreement that the large majority of axons arising form the cells of the cerebellar nuclei, leave the cerebellum via the superior cerebellar peduncle, the exception being the fastigio-bulbar tract that leaves via the juxta-restiforme body. In the 56 year old subject, the cross-sectional area of the superior peduncle is 19.51 0.41 mm2. The estimate for the number of fibers found over this area rendered a figure of 0.782 million axons; of this total 0.761 million are myelinated. The percentage of un-myelinated axons is the lowest found for any of the fiber tracts associated with the cerebellum.”

Number fibers leaving and entering via superior cerebellar peduncle

“Although 311,000 cerebellar nuclear cells were found in one hemisphere, the number of axons in one superior cerebellar peduncle was found to be more than twice this figure. This discrepancy may be caused either by the branching of the outgoing axons, as was actually demonstrated in the brachium conjunctivum of sub-primates by Cajal, or it may be due to fibers entering the cerebellum via this tract. The latter occurrence was demonstrated by Brodal and Gogstad (1954) who found extensive rubro-cerebellar connections entering the cerebellum. Thus indirectly a measure is also obtained for this additional source of cerebellar afferents. It would seem that their number should not be higher than about half of the number of axons estimated in the superior cerebellar peduncle. Some cerebellar nuclear cells are said to project to vestibular and reticular nuclei of the brain stem via the juxta-restiforme body, in the form of the fastigio-bulbar tract. As the number of cells in one fastigial nucleus is only 5210, their proportion can not be very high.”

Convergence of cerebellar input to output

“There is a convergence ratio of about 1:25 to 1:38 from the Purkinje-cells to the cells of the cerebellar nuclei. If the overall capacity of cerebellar outflow is gauged by the number of cells found in the cerebellar nuclei, there is a proportion of about 1:40 between cerebellar afferent and of efferent circuits.”

Range in fiber diameters

“Since different speeds of conduction are related to differences in fiber diameters, it would seem significant that the cerebellar afferent and efferent fiber systems show a considerable range in fiber diameters. While fibers in the cortico-pontine system are so fine as to permit 21.85 to be accommodated in a 100 micrometer^2 area, in the inferior cerebellar peduncle only 2.71 are found over the same area. The differential composition of these pathways as to their fiberspectrum would seem to offer some as yet untapped avenues for research with structural as well as functional aims.”

Cerebellar convergence compared to other areas

“Considering that all motor functions are under the constant regulatory influence of the cerebellum, one might have expected the ratio between the number of incoming and out-going fibers to be much lower than 40:1. The overall ratio between afferent and efferent fibers in all spinal roots of one side is only 4.83:1 (Arnell, 1933).”

Possible reason for crebocerebellum connections

“The vast capacity of the cortico-ponto-cerebellar system, 40 times over that of all other afferent sources combined, might find an explanation, if it is assumed, that it is largely to function to retrieve stored information from many different areas of the cerebral cortex, while the other afferent systems seem to be concerned with current stimuli. Thus a correlation between the numerical size of a fiber system and its mode of functioning is implied. Whether and to what extent the numerical size of a fiber-system might vary among individuals, being correlated to development of special skills for instance, remains to be studied.”

Summary of paper

“A survey is presented of quantitative data dealing with the numeri­ cal sizes of the major extrinsic and intrinsic cerebellar cell and fiber systems. Except for the granular cells, which may by a factor of ten (Braitenberg et al., 1958) exceed the routinely quoted figure of 1010, said to comprise the total neuron capacity of the human nervous system at all levels, other cerebellar systems range within more finite limits. Purkinje cells 14-25 million (Kreuzfuchs, 1902, Lojda, 1955), pontine nuclear cells 17-25 million, inferior olivary nuclear complex, bilaterally 0.9 to 1 million neurons (Moatamed, 1966, Escobar et al., 1968), cerebellar nuclei, bilaterally 0.6 million cells (Heidary et al., 1968). Fiber systems range, hemilaterally, the cortico­pontine system from 20 million axons, down to 0.7 million neurites in the brachium conjuuctivum. There is an overall ratio of 40:1 of afferent to efferent neurites.”

1

J. Tomasch. The overall information carrying capacity of the major afferent and efferent cerebellar cell and fiber systems. Stereotactic and Functional Neurosurgery, 30(5-6):359–367, 1968. URL: https://www.karger.com/Article/FullText/103549, doi:10.1159/000103549, Notes: TomaschJ-1968.html (this file).