Graefe's Arch Clin Exp Ophthalmol (1994) 232:432-437 © Springer-Verlag 1994
Johan Sj6strand Nils Conradi Laila Klar6n
How many ganglion cells are there to a foveal cone? A stereologic analysis of the quantitative relationship between cone and ganglion cells in one normal human fovea
Received: 27 August 1993 Revised version received: 21 January 1994 Accepted: 12 February 1994 J. Sj6strand ([~l) • L. Klar6n Department of Ophthalmology, University of G6teborg, Sahlgren's Hospital, S-413 45 G6teborg, Sweden N. Conradi Department of Pathology, University of G6teborg, Sahlgren's Hospital, S-413 45 G6teb0rg, Sweden
Abstract Published studies on humans and monkeys show discrepancies in the reported quantitative relationship between cones (C) and ganglion cells (G). Data on human foveal retina suggest that it cannot accommodate the midget on-off system in addition to other functional channels. Foveal cell densities along the vertical meridian (0-1.8 mm eccentricity) were estimated in one normal human retina using the disector method. Cell ratios were calculated from cumu-
Introduction For a deeper understanding of the human fovea, detailed knowledge of the density and the topography of the sampling units, i.e. photoreceptors and neurons, is needed. The mosaic formed by the cone and rod receptors of the human retina has been extensively studied, and parameters such as density and spacing of the photoreceptors and geometry of the sampling arrays have been defined with good agreement between different human and primate studies [6, 12, 25]. Due to the lateral displacement between the foveal cones and the ganglion cells it is difficult to analyze the wiring of the synaptic connections of the foveal cones. Using the Golgi technique, Boycott and coworkers [2, 3] have extended our knowledge about qualitative details of the neural circuitry in the primate fovea. Based on morphological observations the anatomical pathways of the human central retina have been described [13-15]. These studies indicate that a single cone in the fovea is synaptically connected to a dual system of midget bipolar and midget ganglion cells. In agreement, electro-
lative total numbers. G density peaked at 0.65 mm eccentricity and C density at the foveola. Cumulative cell numbers showed a more rapid increase in G than in C with increasing eccentricity. G/C ratios of 2.7--3.4 were found using lateral displacement data modified from macaque. Using one estimate of displacement from the sections, the G/C ratio was 3.0. This study shows that there are on average three ganglion ceils per foveal cone in humans, as in monkeys.
physiological studies of cats and monkeys have revealed that two parallell systems of neurons, i.e. on and off channels, relay spatial information to the visual cortex [review: 2D]. Since there are other ganglion cells relaying information from several cones, this would mean that the ratio of ganglion cells to cones must be higher than 2.0 in the fovea. Since the postreceptoral neurons are displaced from the fovea, a comparison of cone and ganglion cell numbers is a complex task and requires knowledge of lateral displacement between the cone inner segments and the synaptically connected ganglion cells at different eccentricities. The difference in the data presented for quantitative cone and ganglion cell relationships between humans and monkeys may be due to such measurement problems and the difficulty of counting ganglion cells at the border of the fovea [4, 5, 18, 24]. Many studies on human retina, especially those using whole mounts, report foveal ganglion cell densities that, when cumulative numbers of ganglion cells (G) and cones (C) are considered, result in a G/C ratio well below 2.0. To solve this problem and related aspects such as the basis for visual
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resolution a n d cortical magnification, as recently d o n e for m o n k e y s [23, 24], the G densities of central h u m a n fovea m u s t be carefully evaluated. In a p r e v i o u s w o r k we have d e m o n s t r a t e d t h a t unbiased estimates of G density of the h u m a n fovea m a y be o b t a i n e d by the disector m e t h o d [4, 21]. T h e aim of the present s t u d y was to further explore the d i s c r e p a n c y between structural a n d physiological findings a n d q u a n t i t a t i v e d a t a t h r o u g h a stereological analysis of the G a n d C relationships. T h e densities were recalculated to n u m b e r s . U s i n g lateral d i s p l a c e m e n t d a t a modified f r o m m a c a q u e , the c u m u l a t i v e n u m b e r s were used for G / C ratio calculations. F r o m one estimate of lateral disp l a c e m e n t in the sections, a m e a n central G / C ratio c o u l d be calculated. A s s u m i n g t h a t this ratio was constant over the eccentricities examined, c o r r e s p o n d i n g lateral displacements c o u l d be calculated.
Calculations Lateral displacement is the term used for the finding that C of a certain eccentricity will be linked to G of a larger eccentricity. As an effect of this, the area including G will also be larger than that for the corresponding C. Therefore, it is necessary to compare numbers (N) in corresponding areas and not direct density values at different eccentricities. To achieve this, the nasal hemiretina was divided into elliptic hemiannuli with a vertical width of 0.1 ram. The relation between the vertical and the horizontal radius was set at 1:1.2 [6]. The number of ceils in each hemiannulus was calculatd as the heminannulus area multiplied with the density of cells, approximated from extra- and interpolation of our estimated density values. Densities at each eccentricity were expressed as the mean value of the density along the superior and inferior vertical hemimeridian. To calculate the cumulative numbers of cells with increasing eccentricity, the number of cells in each hemiannulus was gradually summed to give the cumulative count.
Results Densities a n d n u m b e r s
Material and methods Stereology The study was performed on the left eye of a 39-year-old white male [4]. In short, the preoperative examination showed normal morphology of the fovea, and visual acuity was _>1.0; the eye was removed during surgery for maxillary carcinoma, fixated in a buffered mixture of 3% glutaraldehyde and 3% paraformaldehyde after it had been opened in the pars plana and sent for histopathological analysis. The extended stereological analysis was made on specimens taken along the vertical superior and inferior hemimeridian (perpendicular to the axis from the foveola to the center of the optic disc) through the foveola and embedded in epoxy resin. Cell densities (N/mm 2) were estimated in plastic sections, 1 gm thick, using the disector method [4, 22]. In short, estimates were made by counting cell nuclei present in one but not the next section in vertical strips of the retina, 0.1 mm wide, w, at eccentricities measured in the sections. Hence, the volume (1/) of the disector was V= w x h x d, where h is the height of the cell layer and d is the section thickness. The corresponding retinal surface (A) is A = w x d. G and C densities were estimated using the same sections. The cell densities of the G layer was corrected for a 5% contribution of displaced amacrine cells [26] in order to give G densities.
Table 1 Densities, hemiellipse area and cumulative numbers of ganglion cells with increasing eccentricity
a Corrected for displaced amacrine cells (see Material and methods)
Eccentricity (ram)
0.0-0.1 0.2~0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.9-1.0 1.3-1.4 1.7-l.8
T h e density of G increased g r a d u a l l y f r o m an eccentricity of ~ 0.20 m m to a p e a k of 5 4 9 0 0 / m m 2 at an eccentricity of 0.65 m m (Table 1, Fig. 1). T h e n u m b e r of G within a h e m i a n n u l u s increased c o n t i n u o u s l y with increasing eccentricity (Fig. 2). In contrast, C density p e a k e d at the center of the fovea a n d fell rapidly with increasing eccentricity (one o r d e r o f m a g n i t u d e within i ram, Table 1). D u e to this, a n d despite the increasing surface of the h e m i a n n u l i with increasing eccentricity, the n u m b e r of C per h e m i a n n u l u s r e m a i n e d c o n s t a n t after a small p e a k at 0.3-0.4 m m eccentricity. C u m u l a tive cell n u m b e r s within a hemiellipse s h o w e d a m o r e rapid increase in G t h a n in C with increasing eccentricity (Table t, Fig. 3). T h e increase a p p e a r e d to follow an exponential function for G but was linear for C. T h e estimates presented were used for calculations in two different w a y s : (1) calculations of G / C ratio based on lateral d i s p l a c e m e n t figures a l o n g the vertical meridian for m a c a q u e m o n k e y s in the literature; (2) calcula-
Density
Area of hemiellipse (ram 2)
Cones (N/mm 2)
Ganglion cells a (N/ram 2)
115000 60000 47500 35000 20000 18500 12500 12500 7500
23800 35000 47700 54900 48875 38000 38 000
0.019 0.17 0.30 0.47 0.68 0.92 1.88 3.68 6.09
Cumulative numbers in hemiellipse Cones (N)
Ganglion cells (N)
2167 12742 19010 24948 29 095 33 628 47416 70035 92710
4230 10168 20 059 33 512 83012 157900 249 585
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tions of lateral displacement based on a mean G/C cell ratio estimated from one lateral displacement value measured in the sections.
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Starting with Schein's data on lateral displacement (C inner segment to retinal G) and adjusting them for size differences between humans and macaque monkeys [19], approximative values for lateral displacement were calculated (cf legends to Fig. 5). Using these, G/C cell ratios were calculated using the cumulative numbers of G and C (Fig. 3). The calculated ratios (range 2.8-3.4) are shown in Table 2.
Fig. 1 Densities of ganglion cells (o) and cones (e) along the vertical meridian from 0 to 1.8 mm eccentricity
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Fig. 2 Numbers of ganglion cells (©) and cones (e) within elliptic hemiannuli of the nasal hemiretina with a vertical width of 0.1 mm
At an eccentricity of 1.6 mm the total lateral displacement was estimated to 0.20 mm by examining the angle of Henle's fibers in sections. Using this lateral displacement the corresponding cumulative numbers for G and C cells (Fig. 3) resulted in a mean ratio between G and C of 3.0. With the cumulative numbers presented, a + 25% error in the estimated lateral displacement gives a ratio ranging from 2.7 to 3.3. By dividing the cumulative number of G by 3.0, a new graph could be drawn which shows the distributional characteristics between numbers of C and theoretical units of three G (Gtu). In Fig. 4, similar cumulative values for numbers of Gtu and C (y values) are reached at different eccentricities (x values). The difference between the x values gives the average total lateral displacement. The results of this calculation are shown in Fig. 5, together with the original data in macaque from Schein [19] and the recalculated values.
250000 Table 2 Ratio between ganglion cells and cones (cumulative numbers) along vertical meridian after aligning corresponding eccentricities using lateral displacement valus from macaque monkeys adjusted to human retinal size
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Eccentricity Cumulative (ram) number a
Eccentricity b Cumulative (ram) number
0.4 0.8 1.2 1.5
0.811 1.232 1.570 1.795
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Fig. 3 Cumulative numbers of cones (dotted line) and ganglion cells (continuous line) in a hemiellipse of the nasal hemiretina with increasing eccentricity
19010 38306 57460 74 597
51412 126008 193548 247 984
2.7 3.3 3.4 3.3
a Calculations based on cumulative cell counts within nasal hemiretina central of the given eccentricity u Lateral displacement values from macaque monkeys (Schein 1988) adjusted for size difference to human were used
435
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Fig. 4 Cumulativenumber of cones, C (dotted line) and the cumulative number of theoretical ganglion cell units, Gtu (continuous line), estimated from the cumulativenumber of ganglion cells divided by estimated mean G/C ratio, 3.0 (see text). An arrow has been used to mark one example of eccentricitieswhere cumulative Gtu and C numbers are the same. Assuminga constant G/C ratio, the length of the arrow is an estimate of the lateral displacement. The calculated lateral displacement for different eccentricities is shown in Fig. 5
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Fig. 5 Lateral displacement according to Schein's data [19] on Macaca fascicularis (dotted line) and adjusted to humans (interrupted line) (size adjustment factor of 1.33). For adjusting lateral displacement values and eccentricity values an angular conversion of 206 ~tm/deg was used for the macaque monkeys [see 19 for discussion] and 275 gm/deg for the human [7]. The third (continu-
ous) line is the calculated displacementfrom our data assuming a constant G/C ratio of 3.0 (see Fig. 4)
Discussion Our present and previously reported data on G density in central human retina [4] show higher numbers of G than found in most studies using retinal whole mounts. The whole mount technique has the possible disadvantage that resolution may be influenced in layers several
cells thick. Discrepancies between retinal whole mounts and vertical sections have also been described in monkeys examined by the same researchers [8]. On the other hand, retinal whole mounts are very good for estimating the densities and mosaics of receptors, since these can be oriented parallel to the light in the microscope. The estimated C densities found in the present study using the disector are very close to those reported in retinal whole mounts [6]. This gives strong support to our G data, since the densities were estimatd by the same method in the same sections as used for C counts. Estimating ratios between cells within the same set of sections means that the thickness of the section or volume shifts during preparation no longer influence the results, thus excluding errors that could have influenced the density values. The G/C ratio, as used here, will prove most valuable for estimating G and C loss in relation to reductions in visual acuity, although it should be remembered that the G value probably includes cells not directly involved in forwarding information necessary for spatial resolution [10, 15]. Previous quantitative data on the magnitude of lateral displacement of G in the human fovea are scarce. The calculations of lateral displacement from a Gtu (three G to one C), established by measuring lateral displacement at one eccentricity, gives astonishingly good agreement with the shape and magnitude of the modified data from Schein's work [19] as well as with other results on macaque [17]. We estimated a displacement of approximately 0.35-0.45 mm for eccentricities of up to 1 mm. It should be noted that our lateral displacement values represent an average and that the length of individual Henle fibers may vary. Other studies on macaque along the horizontal [17] and the vertical (H. W/issle, personal communication) meridian suggest a more constant displacement close to the foveola, in contrast to the decrease in displacement towards the foveal center shown in Fig. 5. However, in relation to the radius of the foveola, i.e. the G-free zone, an effective lateral displacement of around 0.3 mm is not implausible for G connected to the foveolar cones. Yodelis and Hendrickson [27] describe synaptic pedicles 300-350 gm from the center of the human fovea at 45 months postnatally. Interestingly enough, the radius of the rod-free zone or foveola decreases during development from 22 weeks of gestation to 45 months post partum with approximately 450 gin, with a stable number of C within this zone [27]. If this displacement of the centermost rod nuclei is taken as a marker of the postnatal cental displacement of foveolar C relative to their G, the degree of postnatal foveolar changes are in accord with our estimates of lateral displacement in humans. Using figures for lateral displacement at various eccentricities along the vertical hemimeridian as modified from the macaque monkey [19], a G/C ratio between 2.7 and 3.4 was found. Since a mean G/C ratio of 3 was
436
obtained using our one displacement value, this strongly supports the data on displacement along the vertical meridian reported by Schein [19] and W/issle and coworkers (H. W/issle, personal communication) and implies that the factor used for size adjustment is justified. The findings indicate that a G/C ratio below 2.7 or above 3.4 is implausible in the normal fovea. According to ratio determinations at four distinct eccentricities using adjusted lateral displacement values, there was no indication in the present study for any decline of the G/C ratio out to a vertical eccentricity of 1.6 mm or 5.8 deg. A G/C ratio of around 3 for central human retina therefore appears to represent a reasonable estimate for future calculations. W/issle et al. [24] found in the macaque retina a G/C ratio falling from 3 at 0.5 deg eccentricity to 2 at 4.5 deg eccentricity, using density values along the nasal hemimeridian and a circle for calculations of displacement effects. Ultrastructural and Golgi analysis of the human central fovea have given strong evidence that every foveal and parafoveal C has a connection to two midget bipolars [13] and two midget G [14]. The presence of such C channels mediated by the midget cell system for medium and long wavelength C will efficiently transmit the spatial information from the foveal C array. In addition to midget G there are other types of G, for example parasol G [10], in the primate central retina. The present finding of a mean number of three G per foveal C therefore allows for C synaptic connections to bipolars and G other than those of the midget system. G/C ratios in accord with our finding of three G per central C in the human fovea have been found in primate central retina [24]. Therefore there seems to be no indication that
postreceptoral G densities will limit the central resolution imposed by the C mosaic of the normal human fovea. However, under pathological conditions a decreased G density seems to correspond to a decrease in visual resolution [4]. The cumulative numbers of G within the elliptic area central to 1.8 mm or 6.5 deg eccentricity along the vertical meridian can, in our subject (39 years of age) be estimated at 0.5 million. There are a mean of 1.25 million [1] or 1.4 million [11] axons, according to quantitative estimates of retinal G axons, in the optic nerve in this age. Thus, approximately 35-40% of all retinal G subserve the central 6.5 deg (vertical radius) of the visual field. In conclusion, the present findings show that there are in average three ganglion cells per central cone. This means that the human central retina has a quantitative capacity to accommodate not only an on-off midget cell system but also other functional channels (see W/issle and Boycott [23] for discussion). Further studies are needed to elucidate the postreceptoral wiring in the human retina. Recent studies of macaque retina indicate that convergence of the cone signals to the ganglion cells occurs with increasing eccentricity first at the level of cone bipolars [16, 17], and that more peripherally two or more cones may connect into the midget system [3, 15]. With the present methodology this question may be addressed in future studies and the findings compared with psychophysical data [9, 26]. Acknowledgements This study was supported by the Swedish Medical Research Council (grants 02226, 07121), the Handlanden H Svensson Foundation and "De Blindas V/inner".
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