A schematic eye for the opossum

A SCHEMATIC

EYE FOR THE OPOSSUM

E. OSWALDO-CRUZ, J. N. HOK~

and A. P. B. SOUSA

Department of Neurobiology. lnstituto de Biofisica da UFRJ. Centro de Ciencias da Saitde. Bloc0 G. 20.000. Rio de Janeiro. RJ. Brasil (Received

7 February

1978: in recked

jorrn

28 Juue

1978)

Abstract-Schematic values were determined for the elements of the dioptric system of the eye of a marsupial. D. marsupialis aurifa. Based on measurements on excised eyes a schematic eye was developed for this species. The following aspects of the opossum’s eye are discussed: real. entrance and exit pupils. retinal illumination and uniocular optical field. The extent of the retinal visual field was determined and the resulting cyclopic field established. The position of the blind and optic axes in space were indirectly determined by correlating the posture of the head under experimental and normal conditions. and the horizontal meridian was found to lie 4” below the blind axis. a determine les valeurs schematiques du systtme dioptrique de I’oeil du marsupial. D. On a etablit un oeil schematique pour I’opossum a partir de mesures faites sur des yeux Cnuclees. On discute les aspects suivants de I’oeil de I’opossum: pupilles reelle. d’entree et de sortie, illumination retinienne. et champ optique unioculaire. L’extension du champ visuel retinien a et& determine et le champ cyclopique resultant a ite ttablie. Les positions des axes optique et aveugle dans I’espace ont ite determines d’une facon indirecte a travers de la correlation entre la position de la fete de I’animal sur les conditions normal et experimental. Le mtridien horizontal se localise 4’ dessous de I’axe aveugle. R&m&On

marsupialis

aurira.

1STRODL’ffIO.U

At the introduction of their intensive study of the optics of the cat’s eye. Vakkur. Bishop and Kozak (1963) commented on the scarcity of optical informations relating to the eye of experimental animals. Since then there has been a considerable development in this field and schematic eyes have been calculated for various animals regularly used in vision research. Schematic eyes have been proposed for mammals: cat (Vakkur and Bishop. 1963); rabbit (Hughes. 1972); rat (Block. 1969; Massof and Chang, 1972); and bat (Suthers and Wallis. 1970); birds: pigeon (Marshall, Mellerio and Palmer. 1973;): fish: goldfish (Charman and Tucker. 1973); frog (DuPont and DeGroot, 1976). Few papers on schematic eyes discuss the consequences of modifying those variables which are under control of the autonomic nervous system in the intact eye. In the extensive investigation of the cat’s eye by Vakkur and Bishop (1963) there is a detailed analysis of the size and position of the real. entrance and exit pupils. Block (1969). studying the rat’s eye. comments on the changes of retinal illumination and of depth of focus resulting from variations in pupillary diameter. In the course of studies of the physiological properties of the visual system of the opossum (Rocha-Miranda, Linden, Volchan. Lent and Bombardieri, 1976; Sousa. Gattass and OswaldoCruz. 1978) it became clear that an essential preliminary step was the determination of the optical properties of this animal’s eye and the establishment of a schematic eye for this species. This paper presents the results of measurements of the characteristics of the various components of the refractive system of the adult opossum’s eye. Calculations of the schematic eye are based on a simplifica-

tion of Gullstrand’s procedure included as an Appendix to the English translation of Helmholtz’s, Handbuch der Physiologischen Optik. The position and size of real. entrance and exit pupils are calculated and the influence of pupillary diameter on retinal illumination is analysed. In addition, the optical and retinal visual fields, their spatial relationships in normal posture and the resulting cyclopic field are also determined. MATERIAL

ASD

METHODS

Our data were obtained from excised eyes of adult opossums. Linear measurements were made with a Zeiss dissecting microscope equipped with a calibrated eyepiece and also on photographs. Photographs were obtained by means of a camera attached to a Zeiss dissecting microscope equipped with a 200mm focal length lens. The objects were photographed under saline. and in each series a photograph of a steel calibrated rule. which was used to adjust the final magnification of the prints, was included. Radii of curvature of cornea1 and lens surfaces were calculated from measurements obtained from the enlarged photographic prints. An Abbe refractometer was used to determine the refractive indices of aqueous and vitreous humours. An indirect procedure similar to that used by Vakkur and Bishop (1963) in the cat and by Hughes (1972) in the rabbit was employed to determine the refractive index of the lens. Conrentions

Traditional optical conventions are followed in the present study. Light rays enter the system from left to right. Refractive surfaces are designated by A and numbered consecutively in the order encountered, beginning with A,. the anterior surface of the cornea. This surface is considered as the reference point for distance measurements; distances to the right of A, are positive. Surfaces convex to the entering light rays are defined as having positive radii of curvature (r). The refractive indices of the various

263

264

E.

OSVGLDO-CRUZ.

J. N.

HOKOC and A.

traversed by the light rays are also numbered from left to right. starting with )I,. the refractive index of air. The first principal point of a systsm is identified by the capital letter H suffixed by the numbers of the related surfaces. and the second principal point being similarly represented but bearing a prime. Two methods were used to e*aluare the reflectance of the tapeturn: in the first. a 2-3mm wide vertical strip of the posterior segment of a freshly excised opossum eye was laid flat on a black matte surface. This strip. obtained at the level of the optic disc. included both tapetal and non-tapetal areas of the retinal epithelium. The preparation was illuminated by diffuse white light and the light reflected from different regions measured by means of a Zeiss photometer coupled to a Zeiss microscope. In the second method the whole eye was mounted in a chamber and the fundus visualized by means of an indirect ophthalmoscope (American Optical. model 305). The relative luminance of tapetal and non-tapetal regions of the fundus was measured optically by coupling an SE1 spot photometer to the eyepiece of the ophthalmoscope.

P. B. SOCSA

media

REX! L-I’S

The eye of the opossum is nearly sphericaf. The axial diameter of the eye adopted for the determination of the schematic eye is 9.98 mm. In a sample of 26 eyes the equatorial diameter was found to be 10.08 + 0.34 mm. The dome shaped cornea occupies approximately two fifths of the bulbus oculi. The limbus is at 3.96 + 0.56 mm from the anterior cornea1 vertex and at that level cornea1 diameter is of the order of 9.55 mm. Since the anterior and posterior surfaces of the cornea have different radii of curvature the cornea is thinner at its vertex than at its basal region. The heavily pigmented iris extends from the ciliary body to the anterior surface of the lens, In conditions of high luminosity the pupil is punctiform: in darkness it becomes fulIy dilated exposing almost the whole anterior surface of the lens. The Iens. as in other nocturnal animals. is neariy spherical, and it is held in place by a well-developed suspensory Iigament attached to the ciliary body. The sclera. formed by coarse fibrous connective tissue. varies in thickness. being more developed at the insertions of the extraocular muscles and at the entrance of the optic nerve. The inner surface of the sclera is lined by a layer of tightly packed pigment cells that extends to the level of the ciliary body. In the upper half of the eye a reptilian-like retinal tapeturn is observed. as already described by Walls (1942) and Braekevelt (1976) and illustrated by Lindsay Johnson (see plate XIII of Duke-Elder, 1958). Retinal vascularization shows a pattern of IO-12 radially oriented vessels. There is no macroscopic evidence for a region of specialization for central vision. The opossum has well-developed extra-ocular muscles which exhibit the general mainmalian organization such as the provision of a trochlea for the tendon of the superior obliquous. The principal departure is the presence of a well developed retractor bulbi. The optic nerve makes an S-shaped curve near its exit point. which is slightly displaced to the nasal side with respect to the geometrical axis of the eyeball.

The dimensions, radii of curvature and the relative positions of the various structures used in the calculations of the schematic eye are illustrated in Fig. I.

The Corneu

The cornea1 curvature was measured on photographic prints in a sample of I_! excised eyes. In addition the radius of curvature of the anterior surface was measured by means of a modified Java!-Shiotz keratometer in a sample of 92 eyes. Radius

of curcam-r.

The values obtained for the radii based on chord and sagitta measurements were confronted with the outlines of the cornea1 surfaces using a pair of dividers. and the discrepancies observed adjusted by curve fitting. The results obtained indicate that the radius of curvature of the anterior surface (r, = 4.43 + 0.14mm) is larger than that of its posterior surface (rl = 4.15 i O.tSmm). Using the dividers it became clear that a good fit is obtained to an average chord length of 8.50 mm. Beyond this range the cornea gradually flattens out. The sp-erical portion of the cornea covers an angle of approximately 130”. The radius of the anterior surface obtained from the image doubling system of the keratometer was found to be 4.63 + 0.25 mm. As this method better reflects the curvature of axial portions of the cornea. this value was adopted for the schematic eye. The radius of curvature of the posterior surface obtained by the curve fitting method was adjusted pro~rtionally and the value obtained (rL = 4.33) adopted. Thickness. The thickness of the cornea was measured through the dissecting microscope with calibrated eyepieces. Measurements of 28 cornea yielded an average thickness of 0.22 rf: 0.08 mm at the vertex (A,-A,) and from a sample of 19 corneas. 0.24 zt: 0.04mm at the base. Cornea and aqueous humour refracrice indices. Due to the reduced thickness of the cornea it was not possible to obtain refiable measurements of its refractive index using the Abbt refractometer; therefore we have adopted the value of n, = 1.376, identical to that adopted for schematic eyes of man (Gullstrand in Helmholtz, 1924). cat (Vakkur and Bishop, 1963) and rabbit (Hughes, 1972).

I

0

10.08 ’

I

’

1

I”“1 5

10 mm

Fig. 1. The schematic eye: physical dimensions. A scale drawing of the eye showing the values used in the calculations of the schematic eye.

265

A schematic eye for the opossum

The refractive index of the aqueous humour measured at room temperature was found to be equal to n3 = 1.336 (iv = 13). a value that is not significantly altered when corrected for body temperature, assuming alterations identical to those presented by water. The Crysralline Lens position. The position of the vertex of the anterior

surface of the lens was measured on photographs taken with the eye immersed in saline. The value obtained (1.28 k 0.32 mm, N = 23) was corrected for the residual refraction of the saline-cornea interface. Thus, the real distance separating A, from AS was found to be 1.35mm. Radius of curvature. Due to the difficuIties in measuring the radii of curvature of the lens in situ all determinations were carried out on photographs of excised lenses using the same procedure as that employed for the cornea. In a sample of 16 lenses the average radius of curvature for the anterior surface was found to be 3.63 _+0.12 mm (r-s), and for the posterior surface 3.71 + 0.22 mm (r.& The anterior surface of the lens is circufar up to a chord value of 6.44mm, which corresponds to an angular vaiue of 125’. Thickness and equatorial diameter. Measurements made on photographs of a sample of 25 excised lenses standing vertically indicate that the equatorial diameter is equal to 6.78 f 0.26 mm and that its thickness equals 5.51 & 0.29mm (A,A,). The equator of the lens, defined by the intersection of the anterior and posterior radii of curvature, is piaced 2.87 mm behind the anterior vertex of the lens. Lens and vitreous humour refractive indices. The refractive index of the vitreous humour measured in 13 samples was found to be identical to that of the aqueous humour, i.e. n, = 1.336 was the value used in the calculation for the schematic eye. Due to the impossibility of using conventional methods of refractometry to determine the refractive index of the lens, an indirect procedure was adopted. The back focus distance of the lens was measured and, assuming the lens to be homogeneous, the effective refractive index was calcuIated using thick lens theory. Excised lenses were suspended in a cuvette constructed with microscope cover slips and filled with fluorescein in saline solution. The collimated beam of a high intensity light source (Zeiss equipped with HBG2OOW/4) placed 6 m away was deflected to the lower surface of the cuvene by means of a front surface mirror. An iris diaphragm enabled the adjustment of the apperture of the jlluminating beam. A low spatial frequency grating was placed near the inferior surface of the cuvette to facilitate the visualization of the posterior focal point of the lens. The fluorescent image of the emergent light beam was photographed with a 35 mm camera equipped with a macro lens and set normal to the anterior surface of the cuvette (Fig. 2A). Measurements of the distance separating the posterior vertex of the fens from the posterior focal point were made on enlarged photographs (Fig. 2B). The effective refractive index was individualIy determined, using thick lens theory, in a sample of 7 lenses. Data pertaining to rhe radii of curvature (rs and ri) and thickness (A,A,) were entered in a program that calculates the posterior vertex power and the back focus distance (&). Different values for the refractive index (n,) were tried

by successive approximations until the back focus distance obtained by calculations coincided with the experimental value. The average value found for this sample was n, = 1.676, and to test the validity of this approach this value was used to determine the posterior vertex power and the back focus distance in saline using the values of r3, r., and ASA adopted for the schematic eye. The results obtained by theoretical calculations using the data adopted for the schematic eye are in close agreement with the experimental value averaged from 7 lenses. The calculated posterior vertex power is 229.57D and that obtained experimentally is 229.08D. while the back focus distances are 5.81 and 5.65 mm, respectively. Therefore the close agreement observed between the experimental and calculated values fully justify the adoption of n,+ = 1.676 for the schematic eye. The Schemutic Eye

Combining the effects of the cornea and crystalline lens systems it was possible to obtain the parameters of the schematic eye. The calculated schematic values for the cornea1 and lens systems as well as those for the schematic eye are summarized in Table 1. Nodal points. In the eye the refractive indices of the first and last media are different; therefore we have an unequifocal system. In such systems object and image rays subtend equal angles at the nodal points. Paraxial rays incident at the anterior nodal point of the eye. N. will emerge from the system as if originating from the posterior nodal point, N’, and parallel to the incidence. The positions of rhe nodal points are derived from PN=F’

= 6.82 mm

and P’N’ =f=

-5.11 mm.

Their position wirh respect to the cornea1 vertex are A,N=PN-PA,=6.82-2.75=4.07mm and A, N’ = A, P’ - N’ P’ = 9.61 - 5.11 = 4SOmm. The results of the calculations described in this section

are summarized in Fig. 3. Posterior nodal distance. The distance separating the posterior nodal point, N’, from the posterior focal point, P’, is the posterior nodal distance, PND. As the posterior nodal point of the eye is almost at the center of curvature of the retina, the PND approximately coincides with the radius of curvature of this surface. Retinal curvature coincides with that determined by the posterior nodal distance for an angular extension of approximately 120’. With the calculated PND of 5.11 mm 1’ in the visual field in the schematic eye is represented by

2n x 5.11 x lo3 360

= 89pm

on the retina. Refractive stare of the eye.

The refractive state of the opossum schematic eye is determined by the position of the photoreceptor

266

E. OS~ALDO-CKLZ. Table

J. N. Ho~cs

and .A. P. B. SOLSA

I. The schemaw opossum

eye of the

~a) ReiractiLe

Index

COf IleLl

0:

1.376

Aqueous

0;

1.336

Lens (total)

Ill

I.676

Vitreous

F,;

1.336

(b, Dimensions Surface

Position

Anterior cornea1 Posterior cornea1 Anterior

(mm)

lenticular

Radius

A,

0.00

r:

4.63

A1

0.22

r.

4.33

Posterior

lenticular

.A> &

I.35 6.56

r, rA

3.63 -3.71

Receptor Posterior

scleral

A> .k

9.68 9.9s

ri v_

- 5.5

(cl Powers ID) Cornea -\nlcrior Posterior Total

surface surface

F, F2 F 12

Lens 81.21 - 9.24 72.09

(dl Distances

F3 F4 F 3-t

from

93.66 91.64 157.07

focal length focal length

Anterior Posterior

principal principal

Anterior

focal point

Posterior .Anterior Posterior

focal

point

nodal point nodal point

H 1 H.:Z P? P:; 5,: N, 2

Out of focus distance Posterior nodal distance Refractits state

layer in relation to the posterior focal point of the system. The anteroposterior dimension of the eye (A,A,I adopted for the schematic eye is A,A, = 9.98 mm. The axial length of the eye was found to be correlated with body weight. The value adopted corresponds to the axial dimension for an animal with 1025 g. the werage body weight of our sample. Thickness of sclera. choroid and pigment layers at the posterior vertex of the eyeball were measured in paratfin sections and corrected for shrinkage. The distal extremity of the receptors was found to lie 300 Aim in front of the posterior vertex of the eye. If the image is considered to be formed at the base of the receptors an additional displacement of 30 pm correspondins to the dimension of the outer segments of the receptors should be taken into consideration. Scher11~7ric ry rrfi-octirr w-or. The distance from

F

195.57

Lens

- 13.87 IS.53

pomt point

ehe

.A, (mm)

Cornea Anterior Posterior

Whole

/;, f’34

- 0.02

Whole -8.51 8.51

/‘ /’

- 0.02

H Hj:

3.91 1.21

H H’

- 13.57 IY.53

P vi:

-1.60 12.75

P P’

3.91 1.2-l

N N’

4.61 4.12

?,A ?4;,

‘AS P’ PND K

eye -5.11 6.82 2.36 2.79 -2.75 9.6

I

1.07 1.50

- 0.07 mm 5.11 mm - 1.97 D

the anterior cornea1 vertex to the outer limit of the receptor layer A,Aj is 9.98 - 0.3 = 9.68 mm. The distance from A, to the posterior focal point of the eye P’ was found to be 9.61 mm. indicating that the eye is nearly emmetropic. The refractive error. K. of the schematic eye can be calculated b> h’= (A,A!

II’A,H')

-F

1.336 K = (9.68 - 2.79) x 10-j

- 195.87 = - 1.970.

If we consider the plane of the image to correspond to the base of the receptors (A,Aj = 9.65) the refracti\e error is reduced to K = - I.1 ID.

A

.’ G

~

co

j-----+-----

-I

___-___..&_______

f------

-

~

c ts

Fie 2. Vertex distance photograph. X-Schematic drawing of the photographic arrangement for vertex dijt ante measurements: LS. light source, C. condenser: D. diaphragm; M. front surface mirror: G. graiting: L. lens: 7’. trough: Ca. camera. B-Posterior vertex distance with it parallel incident beam \thi ch fills the lens. interposed by a grid. The lens was photographed immersed in Huorescein-saiinc solution.

768

A schematic eye for the opossum

A,

rt’f’t”“t

0

6.86 -3.71

269

91.64

IO mm

5

Fig. 3. The schematic eye: optical elements. Positions are given in millimeters from the cornea1 vertex. The refractive indices of the various media are indicated by a sufixed letter a.

The Pupil The iris of the opossum is a thin membrane

with its free margin closely applied to the anterior surface of the lens. Thus, the position of the real pupil is determined by its diameter and by the curvature of the anterior surface of the lens. When the iris is fully constricted the real pupil is punctiform, measuring 0.1-0.2 mm, being kated at the anterior vertex of the lens, i.e. t.3S mm behind the cornea1 vertex. As the real pupil dilates it recedes following the curvature of the anterior surface of the lens. Up to a diameter of 6.44 mm its position can be easily calculated since it fies on the spherical segment of the anterior surface of the lens. For larger diameters the teal pupil recedes to the non-spherical peripheral portion of the lens and its position was estimated based on diagrams of the outline of a typical lens. Position and size of rhe entrance and exit pupils. The entrance pupil is the image of the real pupil formed by the cornea1 system, Therefore its size and position can be determined by the relationship between the cornea and the real pupil. The position and size of the exit pupil were deter-

mined by the relationship between the fens and the entrance pupil. These determinations were carried out using Gaussian simplifications and thus the results obtained

are only reliable

for paraxiat

rays.

The position and size of the entrance and exit pupils were calculated for various real apperture values and the results obtained are presented in Figs 4 and 5. Brighrness ofretinal image. The retinal illumination i of the image of a distant object is given by

where i is a constant depending on the transmission losses in the various media traversed by the light rays and on the intrinsic brightness of the source, p is the diameter of the entrance pupil, and D the total refractive power of the eye. Considering the entrance pupil with an apperture of 6.0 mm and the dioptric value that of the schematic eye (195.87D), p2D2 is found to be 1.38. If the

transmission losses are considered to be of the same order of magnitude in different species, the retinal illumination of the image of a distant object when the pupil is Fully dilated can be directly compared. The value found for the opossum is higher than that found for the rabbit (l.lO-calculated based on data from Hughes, 1972), cat (1.19-Vakkur and Bishop, 1963) and man (0.23, see Vakkur and Bishop, 1963). but lower than that reported for the rat (2.13~Block. 1969). The apperture of the system controls the intensity of the retinal image; therefore the pupil plays an important role in the adaptation of the eye to variations in the level of luminosity of the visual environment. In the opossum. with pupil diameters ranging from 0.2 to 6.0mm. sensitivity of the eye can be varied by a factor of approximately 900. This factor is considerably larger than that reported in the cat by Wilcox and Barlow (1975) and in man by

Woodhouse and Campbell (1975). In common with other nocturnal animals the opossum presents a tapetum lucidum over the upper half of the retina. In this animal the tapetum is white with a yellowish tinge and does not display,the iridescence observed in other species. The reflecttvtty of the opossum’s tapetum measured in isolated segments and in intact eyes was found to be I-1.4 log units higher than that of non-tapetal areas.

E. OSW*LDC&RUZ. 1. N. HOKW and A. P. 3. SOLS~

170

-

REAL

EXIT

ENTRANCE

0.4

I

t I

I

5

I

I

2

I 3

I

I

,

4

,

5

,

,

6

,

,

7

REAL PUPIL SIZE mm

Fig. 4. Upper graph: variation in position of the teal (ii. entrance (2). and exit (3) pupils as a function of real pupil diameter. The distances separating the pupillary pianes from the anterior cornea1 vertex are expressed in millimeters. Lower graph: relative position of the exit (4) entrance (5) and real (6) pupils as a function of real pupil size. For small pupillary diameters the exit and entrance pupils lie in front of the real one. As the real pupil dilates the exit pupil recedes. coming to lie behind the real pupil for diameters larger than 5.16 mm.

The Vistrrrl Field

Ohsermior~s in rhe excised eye. The extent of the uniocuiar visual field free from the obstruction caused by extraocular structures corresponds to the optical field ofan exe as defined by Hughes (1976). The relevant portions of the schematic eye used to calculate the limits of the theoretical uniocular field are shown in Fig. 6. Considering the anterior cornea1 surface as the only interface between air and aqueous humour. a ray A upon entering the eye at the cornea-scleral junction and being refracted towards the equator at the opposite side of the lens will make an angle of 5.73’. which corresponds to an angle of incidence of 7.67’. As the normal to the cornea1 surface at the point of entry of ray A makes an angle of 82.33 with the optic axis (OA). this ray makes an angle of 90’ (7.67’ + 52.33’) with this axis. Assuming the eye 10 be symmetrical with respect to OA this leads to a theor-

etical uniocular optical field of 180’. If. in addition. the interface aqueous humour,‘lens cortex is taken into consideration ray A will suffer further refraction. making an angle of 12.5 with the normal to the anterior surface of the lens at its point of entry. As shown in Fig. 6, ray A’ will be refracted towards the posterior surface of the lens. thus it will certainly pass into the vitreous humour. A second. more direct approach of determining the uniocular field consisted in the visualization of the fundus by means of an ophthalmoscope. Freshly excised eyes were mounted on a plastic support adjusted to bring the anterior nodal point of the eye to the center of rotation of a goniometer stage. The stage was rotated and readings taken when the ophthalmoscope target coincided with the retinal borders and with the center of the optic nerve head. Measurements were made along the naso-temporal and dorsoventral axes, In two excised eyes the mean angular extent of the retinal uniocular field was of the order

271

A schematic eye for the opossum

1.3 1.2 I.1 :

ENTRANCE

L

0 I

2

I 3

L

I

I,,,,,

4

5

6

r

REAL PUPIL SIZE mm

Fig. 5. Upper graph: relationship of the diameters of the exit (7). entrance (8) and real pupils (9). Lower graph: magnification of the exit (10) and entrance (11) pupils in respect to the real one as a function of real pupil size.

of 173.8” f 4.5’ (average from 8 measurements). The same value was found when measurements were made along the dorsoventral axis. However, the optical uniocular field extends beyond the retinal boundaries, for a considerable portion of the ciliary process could be visualized before internal reflections suppressed the ophthalmoscopic image. In this same sample the extent of the optical uniocular field was found to be 188.3’ f 1.2”. In situ esrimates. In order to correlate the retinal surface with the visual space the optic nerve head was chosen as a reference since in the opossum there is no macroscopically observed landmark to indicate the presence of a region of retinal specialization, corresponding to the projection of the center of gaze. The image of the optic nerve head was visualized by means of a reversible ophthalmoscope and its target was made to coincide with the optic nerve head. The

ophthalmoscope was then rotated 180’ and the image of the target projected on the arm of a campimeter. The position of the blind spot was then defined by two angles (JI and w) in a polar coordinate system (Fig. ZE, in Bishop, Kozak and Vakkur, 1962). In a sample of 18 eyes the mean positionof the blind spot was found to be JI = 51.6’ + 6.7’ and o = 45.2” f 4.2’. Position ofrhe optic axis. The optic axis was determined by means of the Purkinje-Sanson images. In 14 animals of the same sample used to define the position of the blind axis, the position of the optic axis was found to be 1(1= 51’ + 11.5” and w = 40.9’ &-7.2”. Thus, on the average the optic axis is located 0.6’ ventral and 4.3’ medial with respect to the center of the projection of the optic nerve head. Position of the eyes. In a previous publication (Sousa er al., 1978) evidence was put forward to

272

E.

OSWALVO-CRLZ.

J. N. HOW< and A. P. B. SOUSA

C.S.

junction

Fig. 6. The limits of the uniocutar theoretical optical field. For details see text.

indicate that in this species the position of paralysis of the eyes does not depart significantly from the prinzory posirion. The values presented above defining the positions of the blind and of the optic axes are those obtained during a series of experiments aiming at the determination of the projection of the visual field in the cortex (Sousa er al.. 1978) in which the head of the animal was held in a campimetric system with an orientation which was determined by experimental conveniences and not that which corresponds to the normal posture of the animal. Xorr~al posture ofrhr had. Observing the opossum in its normal posture. at rest or during locomotion. it became clear that the animal holds its head in a nose-down position. Figure 7 is one of a series of photographs obtained from animals running on a horizontal surface in a diqly lit room. The inclination of the head was evaluated measuring the angle formed by a line joining the center of the eye to the lower border of the nostril with the horizontal plane. In a sample of 54 photographs. taken from 4 different animals. this angle was found to be 51.9’ ri: 2.7’. These measurements showed that the angle made

by the head and the horizontal plane during the experiments in which the position of the blind and optic axes were determined differed along a dorsoventral axis in 33.9’ from that during normal posture and locomotion. ~eter~~zinufiu~? of tlle~.~utio~~plme. It is now passible to define the positions of the blind and optic

axes in space for an animal in its normal posture. A representation of the reference planes and of the angles involved in the determination of the position of the blind axis in respect to the head is illustrated in Fig. 8. The projection of the optic nerve head (ONHI of the eye(E) is indicated in a frontal plane (FPII and its position is defined. as previously presented. by two angular values ($. PJ). The projections. indicated by dashed lines. of ONH upon the basal reference plane (Opt) arid upon a sagirat vertical plane (VP11 passing through the center of the eye. determine two additional angles: w’ and 8. Therefore. o’ is the angle formed by the ONH with the midsagital plane of the eye and 0 is that formed by the ONH with the basal reference plane. when the anima1.s head is held in our experimental conditions. As our reference basal plane makes an angle of 34’ with the horizontal plane (Hz) when the animal is at its normal posture. we have calculated the angles formed by the projections of the ONH with a plane (Hz) making an angle I;) of 34’ with OPl. These projections determine two new angles. o” and 0’. which define the position of the ONH in respect to the animal’s head in its normal posture. The angular values involved in these conversions were obtained using rhe following relations : tg io* = tg w COSrit cos (2” = cos 0 cos ;’ + sen * sen w sen ; tg 0 = tg vusen II, F=Q..-;. By this procedure we come to the conclusion that the ONH projection is located 26.5’ from the midline and 4.3’ above the horizontal plane. . . Similar calculations indicate that. with the animal tn tts normal pos-

A schematic

Fig. 8. Representation of the reference planes of the blind axis in respect

eye for the opossum

and angles involved to the head. For

the optic axis makes an angle of 24.3’ with the midline coinciding with the horizonal plane. Thus. considering the plarre offixatior~ as that which includes both optic axes, we can afirm that when this animal is in its normal stance this plane lies at the horizon. ture.

Cyclopic

t.hal

field

The cyclopic optical visual field. a concept introduced by Helmholtz (1924). is defined as the spatial extent covered by the combination of the uniocular fields. At the level of the horizontal plane the uniocular field in the opossum covers 174’, with its center lying 24.3’ from the midline. Thus at this level the uniocular field extends 62.7’ past the midline, while its temporal extreme lies 111.3’ away from the midline. The binocular retinal cyclopic field is the region of the space accessible to both eyes; in this animal it extends over 125’. The total cyclopic field in this animal covers 222.6’. A three-dimensional representation of the cyclopic retinal visual field is illustrated in Fig. 9. DISCUSSION The validity of a schematic eye depends on how closely the adopted values reflect those of the intact eye. In the present study it was not possible to ascertain whether significant changes in the shape or in the dimension of the eye occurred as a result of excision. Measurements of the eyeball adopted for the

in the determination explanation see text.

273

of the position

schematic eye of the cat (Vakkur and Bishop, 1963) and rabbit (Hughes. 1972) were carried out in excised eyes inflated to a pressure of 30 cm of water so as to restore normal intraocular pressure. In the present study this procedure was not found necessary, since the opossum’s eye remained turgid for over an hour after excision. This increased mechanical stability is possibly the result of its small diameter as well as of the large volume occupied by the rigid crystalline lens. Concerning refractive indices, the values adopted for the cornea, aqueous and vitreous humours are similar to those described for other animals. However, the values adopted for the crystalline lens, obtained by vertex power measurements, is higher than that previously reported for mammals. In the study of the schematic eye of the rat Block (1969) obtained an overall index of 1.61 based on measurements of vertex power of lenses of known dimensions, in air. Hughes (1972), measuring the vertex power of rabbit’s lenses in air and in saline-fluorescein, obtained a total index of 1.6, while Vakkur and Bishop (1963) reported a value of 1.5544 for the cat crystalline lens as calculated from vertex power determinations carried out by means of the saline-fluorescein method. A revision of the rat’s schematic eye was presented by Massof and Chang (1972), criticizing the results presented by Block (1969), on the grounds of the high refractive index of the lens adopted by this author. The refractive index adopted for the rat’s lens by Massof and Chang (n = 1.433) was based on the average of the values for the lens cortex and nucleus

274

E.

OSLVM_DO-CRW

J. N.

HOK~

and A.

P. B. Sous-

Fig. 9. A three-dimensional representation of the retinal cyclopic field of tbe opossum in its normal posture. Vertical and horizontal meridians are indicated by a heavier line. The limits of the uniocuIar retinal fields are indicated by broken tines. The dark circles represent the blind spots.

obtained by Philipson (1969) by means of refractometry. The high total effective index of the opossum’s lens is possibly due to its large spherical central nucleus with a high refractive index. Measurements of the lens cortex by refractometry gives a mean value of it = 1.411, while the outer portion of the nucleus presents a higher refractive index (n = 1.492). It was not possible to measure the refractive index of the nucleus’ core using both Abbe and Fulfrich type refractometers; this extremely rigid region loses transparency when sectioned or pressed upon the measuring prism surface. An additional argument which gives support to the value adopted for the refractive index of the lens in the calculations of the schematic eye of the opossum is the close agreement observed between the experimental and calculated values of posterior vertex power and back focus distance, using data obtained from measurements of the aerial image of a distant object observed under a microscope. The aerial image determinations in a sample of four lenses gives an average index n, = 1.676 identical to the average value obtained with the saline-fluorescein method.

The schematic eye described in this paper, based on measurements of excised eyes, is myopic, a predictable result if the mechanism of accommodation in this species operated according to Helmholtz’s reiaxation theory. The lens of the opossum is very rigid and nearly spherical in shape. and thus it would be difficult to explain the alterations in power required for accommodation as arising from changes in the curvature of its refractive surfaces. In their study of the cat’s eye Vakkur and Bishop (1963) brought forth evidence that accommodation is possibly accomplished by a forward displacement of the lens. If accommodation in the opossum were accomplished by a similar mechanism our results would indicate either that the animal is truly myopic or that a systematic error was introduced in the determination of the values adopted for the calculations. We will now consider the possible sources of error: 1. The determination of the refractive indices of the cornea, aqueous and vitreous humours is unlikely to introduce significant error. 2. The total refractive index of the lens was calculated based on measurements of posterior vertex distances. As these measurements were carried out on

RABBIT

G0A-r

UNIOCULAR CRESCENT-162. BINOCULAR FIELD 30. TOTAL FIELD 354. Hughes, lS7t

UNIOCULAR CRESCENT- 130* BINOCULAR FIELD 604 TOTAL FIELD 320* Hughes 8; Whitteridge. I973

CAT

OPOSSmi

UNIOCULA~ CRESCENT - 44’ 8lNOCULAA FIELD 98’ 1860 TOTAF f IELD Hughes, (976

UNtOCULAR CRESCENT - 49* BINOCULAR FtELD 125’ TOTAL FtELD 223”

Fig. 10. A comparison of the extent of the uniocular and binocular field in preys (A) and predators (B).

enlarged photographic prints, the values obtained for the back focus distances are accurate within 0.1 mm. A systematic error of this order of magnitude would resuft in a change of X3 in the total refractive power of the eye. Thus a systematic underestimation of the back focus distance of the lens couid justify the myopia obtained in the schematic eye. However, as the value adopted is an average of measurements estimation errors are minimized. 3, The refractive state is sensitive to the position of the principal planes of the lens. To account for the ammetropia of the schematic eye an error of 0.46mm would have to be made in the estimation of the position of the lens vertex, a value considerably larger than the estimation error for linear measurements. 4. Displacements of the receptor plane with respect

to the aptical system of the eye would cause substantial alterations in the refractive state of the eye. A forward displacement of ?O~rn would render the eye emmetropic. Displacements of this order of magnitude could be aftributed to slight alterations in the shape of the eyebafl caused by pressure exerted by surrounding tissues. Another possible source of error lies in the determination of the distance separating the posterior vertex of the eyebalf from the receptor layer. Underestimation of the shrinkage resulting from the histological procedures combined with the absence of blood supply to the coroidal tissue are additional factors that result in a backward displacement of the receptor layer. Another factor that may play a role in rhe determination of the refractive error of the eye is the light funneling effect that possibly occurs at the outer seg-

176

E. OSWALDO-CRGZ.1. N. Hokoc and A. P. 6. SOLS.+

ment of the receptors. as discussed by Rodieck (1973. pp. lli147). This effect in the opossum’s eye would amount to t.l1D, a value considerably larger than that calculated for the human eye, and thus it may play- a significant role in improving the depth of focus. There are conflicting reports in the literature concerning the refractive state of the eyes of experimental animals. As a rule the eyes of small-eyed nocturnal mammals are said to be hypermetropic (Wails. 1942). For instance. hypermetropia has been reported in the rat by Block (1969) and Massof and Chang (1972): however evidence based on electrophysiological recordings suggest myopia (Brown and Rojas. 1965: Montero, Brugge and Beitel, 1968). Using refractometry by rerinoscopy, optometry and neurophysioiogical refraction. Hughes (1977) has shown that jn the presence of a large pupil the rat’s eye presents a 6-10D ametropia. However, he has also shown that when the pupil is small the eye is nearly emmetrope. Glickstein and Millodot (1970) suggest that the paradoxical farsightedness observed in small-eyed animals by retinoscopy is due to reflections occurring at the vitreous surface of the retina. Based on Fig. I of their paper on retinoscopy we have calculated the hyperbolic regression in order to evaluate the expected refractive error for the opossum’s eye. The results indicate that the refractive error can be obtained by the following equation: y = 48.6.~-‘.~~ where .r is refractive error in diopters and .K is the corneo-retinal length (A, A,). in milimeters. An apparent hypermetropia of + 7.32D is obtained when solving this equation for the opossum’s eye {A, A j = 9.68 mm). By means of slit retinoscopy the refractive states of 13 opossums’ eyes were determined. and the average value obtained (+ 2.32D) coincides with the apparent hypermetropia which should be expected based on the size of the eye of this animal. Only through the use of objective refraction techniques such as used by Millodot and Rig8s (1970) and by Millodot and Blough (1971) will it be possible to clarify whether the average adult opossum is slightly myoptic or emmetropic. The high light gathering power of the opossum’s eye. as in other nocturnal animals. is a consequence of the large dimension of the cornea which permits the crystalline lens to be of large diameter with a correspondingly large maximal size of the pupil. The brightness of the retinal image of a luminous object, in the opossum. is comparable to that of the cat, being 6 times greater than that of the human eye. This difference is further accentuated by the presence of the tapetum. The tapetum may play a role other than lowering the visual threshold at the expenses of resolution. It may lead to a reduction of pupillary diameter for a given illumination level with a consequent reduction of optical aberrations present in an optical system of wide apperture such as the opossum’s eye. Following the procedures used in the studies of the cat‘s schematic eye (see Fig. 7 in Vakkur and Bishop, 1963) and of the rabbit’s schematic eye (see Fig. 3 in Hughes. 1972) we have found that the angular extension of rays entering the unobstructed eye of the

opossum does not differ significantly from the values reported by these authors in other species. The theoretical visual field determined by light rays that eventually reach the retina, corresponding to ray B in the studies of Vakkur and Bishop (1963) and Hughes (1972) was not presented here because the relation between the cornea-sderal junction and the anterior surface of the lens, in the opossum, differs considerablv from that found in cats or rabbits. In these studies ray B corresponds to a light ray that enters the eye at the level of the cornea-sclerai junction and is refracted towards the lens vertex. Due to the relation of these two structures in the opossum a similarly directed light ray would impinge on the lens surface at an angle greater that the critical angle for aqueous humour-fens cortex surface. thus being totally reflected at this point. Goniometric measurements in the cat’s eye (Hughes, 1976) showed that light rays which impinge on the cornea1 surface making an angle of 92.1” with the optic axis reached the vitreous humour. This angle has a value comprised within the limits of rays A and B as determined by Vakkur and Bishop (1963). Our measurements in the opossum’s eye are also in accordance with the calculated values, the values obtained by the goniometric technique being of the same order of magnitude as that found for ray A. Thus, although the cornea of the opossum is almost hemispheric. the extent of its uniocular optical visual field does not differ significantly from the values obtained in man, cat and rabbit. supporting Walls’ statement that the uniocular field of mammals “is rarely much greater or much less than 170”” (Walls. 19-Q). Ophthalmoscopic observations in the opossum showed that. as reported in the cat (Hughes. 1976). the extent of the retina is the determining factor for the angular extent of the visual field, for the ciliary body could be clearly visualized far an additional extension of 7” beyond retinal borders. Therefore the retinal visual field is more restricted than the optical one as previously reported in the cat (Hughes, f976). Orientation of the optic axes determines the extension of the total visual field. In foveate animals or in other species which possess a morphologically differentiated retinal region the determination of the extent of the visual field is achieved by assessing the angle formed between the optical and visual axes and by assuming that when the eyes are in the primary position the animal is gazing at an infinitely distant object in the horizon. In the absence of morphologicailp differentiated fundal regions such as the fovea. area centralis or visual streak the optic nerve head is the landmark usually taken as reference when establishing the spatial relationships between the retina and the external world. In non-foveate animals the position of the horizontal meridian or fLvation plane has been estimated by some investigators considerin8 that the upper and lower hemi-fields are equally represented in the rettna. Following this rationale. Kaas. Hall and Diamond (1970) found that the optic nerve head projection in the hedgehog lies I’ above the HM. Similar considerations by Lane. Allman and Kaas (1971) in the grey squirrel and in the tree shrew indicate that in these species the ONH lies 16’ and 5’ below the HM. respectively. However. these determinations did not take into consideration

A schematic eye for the opossum

the position of the blind axis in space when the animal is in its normal posture. Adams and Forrester (1968) and Siminoff, Schwassmann and Kruger (1966) in the rat, Tiao and Blakemore (1976) in the hamster, and DuPont and DeGroot (1976) in the frog, give >orne mdtcations as to the orientation of the blind axis in space; however, they do not give a precise definition of the plane of fixation with respect to the head when the eyes-are in the primary position. Only with data obtained from animals which possess well defined fundal landmarks such as those presented by Vakkur and Bishop (1963) for the cat, and by Hughes (1971) for the rabbit. is it possible to accurately describe the extent of the visual field. Food perimetry (Sprague and Meikle, 1965) is a method of great value for the determination of the effective visual field but its practical application is rendered difficult by the presence of small eye movements. In the absence of a macroscopically observed funda1 regional specialization in the opossum’s retina the position of the blind axis was indirectly determined by correlating the posture of the head under experimental and normal conditions. Following this procedure the HM was found to tie 4” below the blind axis. Therefore the HM was found to divide the retina into two equal halves. This finding gives support to the simplified procedure adopted by other authors (Kaas et al., 1970; Lane et al., 1971). Our findings indicate that the opossum is endowed with a visual field similar to that found in animals which display an active predatory behavior. The total extent of its visual field (222.6”) and the wide binocular coverage (125”) are comparable to those reported for the cat (Hughes, 1976). a typical representative of a highly successful group of prey catchers. The type of visual field organization found in the opossum lends support to Walls’ (1942) statement that the forward displacement of the visual axes is not a gradual process associated with a transition from “lower” to “higher” forms along the evolutionary scale. In reality this alteration reflects the role played by the species in its ecological niche; hunters, whether diurnal or nocturnal, possibly use binocular disparity clues to achieve a better localization of their prey, and to more efficiently direct the attack. In nocturnal hunters, the reduction in threshold associated with binocular vision may also be of importance (Pirenne, 1943). Different tasks are imposed upon the visual system of species that are preyed upon. Early detection of the natural enemies leads to freeze or flight manoeuvres. and thus a wide coverage of the surrounding space is of paramount importance. Examples of the organization of the visual field in both preys and predators are shown in Fig. 10. The gain in binocular vision at the expense of total visual field is the main distinguishing feature between these two groups, for the extent of the uniocular field in mammals remains approximately constant. Acknowledgemenrr-We are grateful to Professor P. 0. Bishop for supplying additional information concerning the cat’s schematic eye. We extend our gratitude to Professors Gordon Heath (School of Optometry, Indiana University) and Francois Lacoste (Instituto de Fisica UFRJ) for helpful discussions on the calculations of the exit pupil.

277

We thank our colleague. Or C. E. Rocha-Miranda for giving access to his data on keratometry and retinoscopy of the opossum’s eye and also for his helpful suggestions on the manuscript. We extend our thanks to our head technician. Mr R. F. Bernardes. for his unfailing assistance. and to Miss Maria Luiza da Silva for secretarial help. This work was supported by research grants (TC-16.872) from Conselho National de Desenvolvimento Cientifico e Tecnologico (CNPq). Conselho de Ensino para Graduados da UFRJ (CEPGUFRJ). and by Financiadora de Estudos e Projetos-FINEP (FNDCT-375CT). REFERENCES Adams A. 0. and Forrester J. M. (1968) The projection of the rat’s visual field on the cerebral cortex. Q. J. rxp. Physiol. 53. 327-336. Bishop P. 0.. Kozak W. and Vakkur G. J. (1962) Some quantitative aspects of the cat’s eye: axis and plane of reference, visual field co-ordinates and optics. J. Physiol. 163, 466502. Block M. T. (1969) A note on the refraction and image formation of the rat’s eye. Vision Rrs. 9, 705-71 I. Braekevelt C. R. (1976) Fine structure of the retinal epithelium and tapetum lucidum of the opossum (Didelphis cirginiano). J. Morph. 150, 2 13-226. Brown J. E. and Rojas J. A. (1965) Rat retinal ganglion cells: receptive field organization and maintained activity. J. iveurophysiol. 28, 10731090. Charman W. N. and Tucker J. (1973) The optical system of the goldfish eye. Vision Res. 13. l-8. Duke Elder S. (1958) The Eye in Evolution, Vol. 1. chap. XV, plate XIII. Henry Kimpton. London. DuPont J. S. and DeGroot P. J. (1976) A schematic dioptric apparatus for the frog’s eye (Runa esculenrn). Vision Res. 16, 803810. Glickstein M. and Millodot M. (1970) Retinoscopy and eye size. Science 168, 605-606. Helmholtz H. von (1924) Helmholtz’s Trearise on Phgsiological Optics. Translated from the 3rd German Edition (edited by Southall J. P. C.). Vols I and II. Dover Publications Inc., New York. Reprint 1962. Hokoc J. N. and Oswaldo-Cruz E. (1978) A regional specialization in the opossum’s retina: quantitative analysis of the ganglion cell layer. J. camp. Neural. In press. Hughes A. (1971) Topographical relationships between the anatomy and physiology of the rabbit visual system. Dot. Ophth. 30, 33-159. Hughes A. (1972) Schematic eye for the rabbit. Vision Rex 12, 123-138. Hughes A. (1976) A supplement to the cat schematic eye. Vision Res. 16, 149-154. Hughes A. (1977) The refractive state of the rat eye. Vision Res. 17, 927-939. Kaas J. H., Hall W. C. and Diamond I. T. (1970) Cortical visual areas I and II in the hedgehog: relation between evoked potential maps and architectonic subdivisions. J. Neurophysiol.

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